05.03.2008

Sharon Kanach'i tõlge ameerika inglise keelde ARTS/SCIENCES: ALLOYS The Thesis Defense of IANNIS XENAKIS ARTS/SCIENCES: ALLOYS The Thesis Defense of IANNIS XENAKIS Before: Olivier Messiaen, Michel Ragon Olivier Revault d’Allonnes, Michel Serres Bernard Teyssèdre Translated by Sharon Kanach AESTHETICS IN MUSIC No. 2 Pendragon Press New York, N.Y. Copyright 1985 Pendragon Press New York Originally Published by: Editions Casterman, s.a. 28. rue des Soeurs Noires Tournai, Belgium (1979) CONTENTS Author’s Preface Translator’s Preface by Sharon E. Kanach Notice List of Illustrations Preliminary Statement by Iannis Xenakis Dialogue with Olivier Revault d’Allonnes Dialogue with Olivier Messiaen Dialogue with Michel Ragon Dialogue with Michel Serres Dialogue with Bernard Teyssèdre Appendixes I Correspondences Between Certain Developments in Music and Mathematics II Sieve Theory III New Proposals in Microsound Structure IV A Catalogue of Musical Works by Iannis Xenakis V Bibliography Postface AUTHOR’S PREFACE In France, the "Doctorat d’Etat" may be awarded on the basis of a “file" consisting of previously published theoretical and creative works. This thesis file must then be defended before a jury whose members (not necessarily academic personalities) are suggested to the sponsoring university by the candidate. Once all the members have been agreed upon, a five-hour deliberation session is held between the candidate and the jury. At the end of this "defense," the jury decides whether the degree should be awarded, and if so, with what honors. The present volume is a translation of the defense of the material in my file which was recorded at the Sorbonne in 1976. I am very proud to have had the chance to debate the issues covered in this volume with this distinguished company. Many of these subjects have preoccupied me since my youth, and it was an honor to discuss them with the specialists on the jury, each of them being part of the French intellectual avant-garde in his domain. I admire the perseverance, courage, and intelligence of the young composer Sharon Kanach, first for having translated this book and, second, for finding Pendragon Press, an American publishing house that was willing to bring out a work which guaranteed no particular commercial success. Through the innocence of her youth and her love for these same subjects, Sharon fought through the problems of publication, mostly on her own. I would like to express my gratitude to Sharon and to Robert Kessler of Pendragon Press. Iannis Xenakis TRANSLATOR’S PREFACE The text of Arts/Sciences.Alloys is a transcription made from the tape recordings of Xenakis’ thesis defense for a "doctorat d’Etat" at the Sorbonne in the spring of 1976. In this translation, I have tried to render the written word as close to "speech" as possible while not betraying the grammatical logic behind the statements. French and English verbal patterns differ greatly. and I have tried to make them coincide in written expression with the intention of avoiding the impression of a translation per se. A note of thanks is due first of all to Iannis Xenakis himself for initially suggesting this translation to me. His encouragement. help. and meticulous attention throughout the years and especially during this project have been very valuable and are most appreciated. My gratitude goes to Cornelia Coyler of CEMAMu* for her efficient cooperation in putting essential materials at my disposal. Deep thanks to Robert Pépin for his patience and thoughtful eye. ear. and translation experience and friendship throughout the various phases of this undertaking. A special note of thanks must also go to Robert Kessler. who first recognized the importance of an English language edition of this book and without whom it would not now exist. Finally. I would like to dedicate this translation to my parents Elizabeth and Walter Kanach. Sharon E. Kanach NOTICE This is a transcription of IANNIS Xenakis’ thesis defense which took place on May 18, 1976 at the Sorbonne (Paris). Presiding over the jury was Bernard Teyssèdre. professor of aesthetics at the Umversity of Paris-Sorbonne. Jury members were: Olivier Messiaen, professor at the National Conservatory of Music: Michel Ragon, professor at the National School of Decorative Arts; Olivier Revault d’Allonnes, professor at the University of Paris-Sorbonne (thesis director and advisor); Michel Serres, professor at the University of Paris-Sorbonne. PRELIMINARY STATEMENT BY IANNIS XENAKIS Subtended Philosophy* The worlds of classical, contemporary, pop, folk traditional, avant-garde, etc., music seem to form unities unto themselves; sometimes closed, sometimes intersecting. Not only do they present extraordinary deviations, rich in new creations, but also fossilizations, ruins, and wastes, all in continuous formations and transformations, much like clouds - so distinct yet so ephemeral. This can be explained by the proposition that music is a sociocultural phenomenon; therefore, subordinate to a given moment in history. Yet we can distinguish the parts which are more invariable than others and which then form materials of hardness and consistency resulting from various epochs of civilization; materials which move in space, have been developed, put into use, and have followed the course of ideas, colliding one against the other, influencing and annihilating one another, mutually fecundating. But what is the essence of these materials? This essence is man’s intelligence, in some way solidified. Intelligence which searches, questions, infers, reveals, foresees - on all levels. Music and the arts in general seem to be a necessary solidification, materialization of this intelligence. Naturally, intelligence, although humanly universal, is diversified by the individual, by talent, which distinguishes one individual from others. Talent, then, is a kind of qualification, a grading of the vigor and richness of intelligence: for intelligence is, fundamentally, the result or expression of the billions of exchanges, reactions and energy transformations of the body and the brain cells. Using the model of astrophysics, we could say that intelligence is the form which minimal acts take in cellular condensations and movements as it seems to be with solar, planetary and galactic movements, and in galactic constellations, born of or reduced to cold interstellar dust. However, this image is inverted (at least on one level), for in condensation, this cold dust becomes hot. contrary to intelligence which is cold, "’a cold fire," resulting from the exchanges between the hot cells of the brain and body. Therefore, colors, sounds and dimensions are condensations in our sensory-brain system. A brutal and perfectly superficial exterior aspect of this system is perceived and comprehended on the conscious level. The periodic vibrations in the air and the electromagnetic field of light are inaccessible to the conscience but are magnificently well followed (within limits, of course) and converted by our senses and brain. One’s senses are the extension of the brain. Conversions, on the other hand, operate on several levels, from that of immediate perception to those of comparison, appreciation and judgment. How, why is all of this produced? It is a mystery, elaborated as it is among the animals, and this has been so for millions and millions of years. All the same, let’s take an example which appears to be relatively obvious, that of musical scales. There have been, at least in the Western world, stronger and stronger condensations: the perfect fourth and tetrachords, and perhaps even earlier, the perfect fifth (whose origins remain unknown): then. the octave, followed by the construction of "systems" by tetrachordal juxtapositions that had engendered Antiquity’s scales, from which the diatonic scale of white keys on the keyboard is one survivor. Next came the evenly tempered chromatic scale, and finally, continuity in the ensemble of "pitches." It follows from this example that music is a strong condenser the strongest, perhaps, of all the arts. This is why I am giving a comparative table* between certain conquests achieved by music and several mathematical realizations such as history teaches us. This table shows one of the paths music has taken since its origin (since Antiquity) and to which it has kept with remarkable fidelity through millennia, marking a significant acceleration during the twentieth century. This proves that the faculty of condensation-toward-abstraction is part of music’s profound nature (more than any other art’s) rather than simply being a function. Consequently, it seems that a new type of musician is necessary, an "artist-conceptor" of new abstract and free forms, tending toward complexities, and then toward generalizations on several levels of sound organization. For example, a form, a construction, an organization based on Markov chains or on a complex of interrelated probablitiy functions can be simultaneously conveyed on several levels of musical micro-, meso-, and macro-composition. We could even extend this concept to the visual domain, for example, in a spectacle involving laser rays and electronic flashes such as those of the Cluny Polytope.* From here on nothing prevents us from foreseeing a new relationship between the arts and sciences, especially between the arts and mathematics: where the arts would consciously "set" problems which mathematics would then be obliged to solve through the invention of new theories. The artist-conceptor will have to be knowledgeable and inventive in such varied domains as mathematics, logic, physics, chemistry, biology, genetics, paleontology (for the evolution of forms), the human sciences and history: in short, a sort of universality, but one based upon, guided by and oriented toward forms and architectures. Moreover, the time has come to establish a new science of "general morphology" which would treat these forms and architectures within these diverse disciplines in their invariant aspects and the laws of their transformations which have, in some cases, existed for millions of years. The backdrop for this new science should be the real condensations of intelligence: in other words, an abstract approach, free from anecdotes of our senses and habits. Let us now delve into the fundamental system on which art is based. Art has something in the nature of an inferential mechanism which constitutes the platforms on which all theories of the mathematical, physical and human sciences move about. Indeed, games of proportion - reducible to number games and metrics in architecture, literature, music, painting, theatre, dance, etc., games of continuity, of proximity, in or outside of time, topological essence—all occur on the terrain of inference, in the strict logical sense of the word. Situated next to this terrain and operating in reciprocal activity is the experimental mode which challenges or confirms theories created by the sciences, including mathematics. Mathematics, ever since non-Euclidian geometry and theorems such as Gödel’s, has proven itself experimental, but in a wider sense than is applicable to the other sciences. It is experimentation which makes or breaks theories, pitilessly and without any particular consideration for the theories themselves. Yet the arts are governed in a manner even richer and more complex by this experimental mode. Certainly there is not nor will there ever be an objective criterion for determining absolute truth or eternal validity even within one work of art, just as no scientific "truth" is ever definitive. But in addition to these two modes-inferential and experimental-art exists in a third mode, one of immediate revelation, which is neither inferential nor experimental. The revelation of beauty occurs immediately, directly, to someone ignorant of art as well as to the connoisseur. This is the strength of art and, so it seems, its superiority over the sciences. Art, while living the two dimensions of inference and experimentation, possesses this third and most mysterious dimension which permits art objects to escape any aesthetic science while still enjoying the caresses of inference and experimentation. But on the other hand, art cannot live by the revelation mode alone. Art history of all times and of all civilizations shows us that art has an imperious need of organization (including that of chance); therefore, a need for inference and its confirmation; hence, a need for its experimental truth. To shed some light on this trinity of modes in art, let’s imagine that in a distant future, the power of artistic action will increase as it never before has in history (which has been humanity’s path in the development and dissipation of the quantities of energy growth). Actually there is no reason why art cannot, following the example of science, rise from the immensity of the cosmos; nor why art cannot, as a cosmic landscaper, modify the demeanor of the galaxies. This may seem utopian, and in fact it is, but only temporarily when viewed in the context of the immensity of time. On the contrary, what is not utopian but possible today is to cast luminous spiderwebs of colored laser beams like a giant polytope over cities and countrysides: the use of clouds as reflector screens, the use of artificial satellites as reflecting mirrors so that these "webs" rise in space and surround the earth with their phantasmagorical, moving geometries: joining the earth and the moon by filaments of light. One could even willfully create artificial aurora boreales in the night skies whose movements, forms and colors would be controlled by electromagnetic fields aroused by lasers in the highest atmosphere. As for music, loudspeaker technology is still at the embryonic stage, too underdeveloped to send sound into space and have it received there, in thunder’s home. But hedgehopping sound displacements in cities and over the countryside are already possible thanks to national networks of air raid alarm system speakers. It would suffice to merely refine them.* If countries’ economies were not tortured by strategic and armament needs - in other words, on the day when the nation’s armies would diminish into simple, non-repressive police forcesthen, financially, art could fly over our planet and soar into the cosmos. Technologically speaking, these things are feasible today. In these planetary or cosmic artistic productions, it is apparent that the artist, and consequently art, must be simultaneously rational (inferential), technical (experimental) and talented (revelatory): three indispensable and coordinated modes which shun fatal failures, given the dimensions of these projects and the great risk of error. This greater complexity of the fundamental system of the three modes which govern art leads to the conclusion that art is richer and vaster and must necessarily initiate condensations and coagulations of intelligence; therefore, serve as a universal guide to the other sciences. COAGULATIONS For more than twenty years now, I have strived like a mosaic artisan, unconsciously at first, then in a more conscious way, to fill this philosophical space with an intelligence which becomes real by the colored pebbles which are my musical, architectural and visual works and my writings. These pebbles, at first very isolated, have found themselves brought together by bonds of relationships, of affinities, but also by opposition, gradually forming figures of local coherencies and then vaster fields summoning each other with questions and then the resulting answers. Mathematics plays an essential role here as a philosophical catalyst, as a molding tool for forming auditory or visual edifices, but also as a springboard toward self-liberation. Here I will outline only the fundamental questions and, in opposition to these, the answers given by the works I have created, I will not, in any case, go into detail nor explain the mazes of their elaboration. Furthermore, several of these questions are interrelated and create intersections belonging to the same philosophical domain. For example: causality - determinism- continuity, indeterminism (chance)-- existentiality—determinism, etc. This is also why a work (answer) can in itself, respond to a whole group of questions. It’s a bit like being in the presence of sound-as-questions, rich in harmonics and considering one or another harmonic as being the fundamental following the quest at a given moment. In addition, I will mention only a few works from the thesis file. * Questions -> Answers existentiality -> ST/l0-l,080262 in-time, outside-time -> Nomos gamma causality -> ST/10-1, 080262, Nomos gamma Tourette Convent (facades), repetition or not of modules. inference -> Nomos gamma, ST/10-1, 080262 connectedness -> Empreintes (aborescences), Metastasis (glissandi forn1 s) Philips Pavillon (shell, line forms) compacity -> Metastasis, Philips Pavilion, Nomos gamma [puudub] impure determinism -> Strategie, Syrmos, game theory Markov chains pure determinism -> Nomos gamma (groups) identity (similitude, equivalence) -> All works The visual theatrics of the Polytopes* * deal with questions and answers musically set and resolved, but here with lasers, electronic flashes and in space. What is remarkable to ascertain is that these questions can be found in all areas of musical or visual composition; in other words, from the general form (macrocomposition) down to computer-generated sound synthesis and numeric-analogical conversion (microcomposition), but also passing by all the intermediary stages along the way. "The paths from both the top and bottom make but one." I was saying that all the work I have done over the years is a sort of mosaic of hierarchical coherencies. At the hierarchy’s summit I’d place philosophy. Philosophy, but in what sense? In the sense of the philosophical impulse which pushes us toward truth, revelation, research, general quest. interrogation, and harsh systematic criticism, not only in specialized fields but in all possible domains. This leads us to an ensemble of knowledge which should be active, in the sense of "doing." Not passive knowledge but knowledge which is translated into creative acts. I repeat, in all possible domains. Following the methods which I will examine presently, one can divide this coherency roster, mosaic, this table, into three categories or three chapters. The first is the method which allows us to obtain this active knowledge through creativity-which (through theoretical demonstration) implies inference, meaning reason, logic, etc. Following these criteria, there are aspects of activity and knowledge which are partially inferential, entirely inferential and experimental, and others which remain unknown. I’d put the arts in the "partially inferential" region. The arts take part in inference. Consequently, we construct and tie things together in a reasoned manner and can demonstrate them up to a certain point. On the contrary, the human and natural sciences, physics, mathematics, and logic are experimental as well as entirely inferential. It is necessary to build a theory and to verify this theory by experimentation. In the artistic domain, we can partially build by inference, but experimentation is not immediate. There is the problem of aesthetics and there is no possible demonstration of the aesthetic value of these things. I will leave the door open to any methods which have not yet been discovered. As a corollary to this artistic discrimination, it can be said that the arts are freer since the arts take part in the inferential operation as well as in the experimental one. It is perhaps ambitious to say it, but the arts could possibly guide other sectors of human thinking. In other words, I would place the arts at the head of man’s activities in such a manner that they would seep through all of his daily life. Going down one rung in this hierarchy. I’d say that after this, there is a category of questions which can be asked, questions which have been dodged by history and which can be rediscovered and asked a new: meaning a sort of creatively philosophical fragmenting of directions. Within these categories, there is existentiality (ontology, reality), causality, contiguity or connectedness, compacity. temporal or spacial ubiquity, even inference, all taken as consequences from potentially new mental structures. There is also determinism and its extreme pole, indeterminism. I am reaching back, in one way or another, to certain very important categories of thought which have been more or less consciously and systematically stated since Aristotle but which have drifted by the wayside or been claimed by experimental psychology (Jean Piaget) and certain branches of modern mathematics. These categories of thought-questions invite or could invite families of solutions and this is what I have endeavored to achieve musically. I hope I am being clear. What I am trying to say is that man has attempted to answer this multitude of questions by giving temporary answers from certain families of solutions, especially with regard to determinism. Here I would like to open a parenthesis: causality. for example, is one form experienced in life which refers to this fundamental question of determinism (which itself can be considered a nuanced differential aspect of indeterminism). Something I neglected to state before is that it can even be ascertained that order and disorder are parts of indeterminism. Connectedness and continuity are other facets of the bi-pole of determinism-indeterminism. Picking up where I left off before, solutions and procedures capable of giving answers to categories of fundamental questions are necessarily defined in a very schematic manner by a few sub-chapters, a few paragraphs. Probabilistic thinking - with its extreme limit which I will call free or memory-less stochastics on the one hand, and Markov chains which agree to a certain degree of causality, a certain elementary determinism (which is upstream from this) on the other hand-is one example. But at the heart of probabilistic thinking and indeterminism, there is what can be called symmetry or periodicity, which is another way to define or to speak of these types of thinking. Symmetry or periodicity, meaning the cyclic return of events, procedures, etc., can coagulate through group structures at the bottom of the determinism scale. Between the two, there is what can be called the hybrid or mixed phase. One of the interesting forms in this phase is game theory. Lower, at the lowest threshold of the mosaic, in answer to these topics and ways of thinking (which have also been established by other sciences, including music) specific works can be found which are reflections on and tentative answers to these questions. I don’t want to enumerate them here for that would be too tedious. But I could say, for example, that the topic of free stochastics is treated in a piece such as "Achorripsis", which was later formulated by a machine program, a program which represents a free stochastic system. This program made it possible to write works such as ST/10, ST/48 for orchestra, but also to enter the realm of sonic microstructures and computer-generated sound synthesis. By the way, this same program has been in use for the past few years in the United States as well as in Europe (Sweden, France, etc.), in studios other than CEMAMu, * as well as by other composers. In the realm of Markovian stochastics, there are pieces such as Analogiques and Syrmos for strings. In game theory: Strategic, Linaia-Agon, etc. From symmetrical/periodical systems, there is Akrata, Nomos Alpha, Nomos Gamma, and Persephassa, works composed on group structures. I am mentioning only the principal works. In the report I submitted to the jury, and at the beginning of my statement, a few more details can be found which concern my visual works such as the Polytopes and my architectural works. By continuing in this manner down to the very bottom of the hierarchy, one finds the pressure-time space of sound. Analogous things could be said about the visual realm, meaning that from the questions asked on the microstructural level (that is to say, from the level of the next higher element), macrostructures can be seen as resolved or as being treated by procedures and thoughts equivalent on the primordial level. At this primordial level, we find pressure in function with time for the ear and in function with electromagnetic actions for the eye in the visible spectrum. We can summarize by saying that all which has been drawn from the macrostructures’ most general fundamental problems is duplicated on all of the elementary structural levels within medio-structures, meso-structures, all the way down the scale which intermingles with quantic action, as I call it, dealing with the two senses of vision an d hearing. I believe I have given you a very general outline of the binding thread throughout my work, without speaking of the work itself. BERNARD TEYSSÈDRE Thank you very much, Iannis Xenakis. It is certain that your statement was brief and could seem complex since it is so dense. I hope that the discussion which will now get under way will throw some light upon your presentation. It is quite unambiguous for those who already know your work well. But your presentation may seem a bit vague to others, precisely because too many subjects were broached simultaneously. I believe that Revault d’Allonnes, your thesis advisor, could intervene at this point. DIALOGUE WITH OLIVIER REVAULT D’ALLONNES OLIVIER REV AULT D’ALLONNES Indeed, because of some administrative peculiarity, I am the thesis advisor. In reality, IANNIS Xenakis’ thesis advisor is IANNIS Xenakis himself. He managed that well. I am also the chairman of the jury for this defense. Faced with such a considerable mass of research and works, this chairman feels pretty insignificant. What I believe I can be is a spectator among others, and a spectator fascinated by the whole of Xenakis’ work. Xenakis has chosen a title to present his fundamental theoretical works and, in support of these theoretical works, a certain number of documents which are the musical scores of some of the works he just referred to, plus architectural sketches, designs, schemas, abstracts, etc. This general titles defines not only this file, but also the whole of Xenakis’ artistic output: Arts/Sciences: Alloys. Xenakis introduces a few of these alloys, and has just told us, in a very dense manner, how we can gain insight into these. "Art," as understood by Xenakis, refers to the latin artifex, the creative inventor. This man has a certain attitude before the World, a certain vision of the world, and he feels the permanent and haunting obsession that there is always something to do. For nearly twenty years, I have never seen him other than as prey to a Sort of creative demon. For him, science is something which always accompanies this creative demon. Xenakis wants to do something, but not just anything. He always wants to compose a determined work, a work which, on a certain level (precisely on the aesthetic level) communicates itself: you go to a concert, you hear a piece by Xenakis: but the work, on another level. can he communicated in another way. by an analytical rational language which simultaneously analyzes and justifies this work. In books such as those he presents today: Musique.Architecture. and perhaps especially Formalized Music, * we see that works are analyzed, decorticated, and at the same time. they are justified, legitimized. Xenakis says why he wanted to do this and how he did it. but the "why" is at least as important as the "how." These "alloys" are indeed not without problems. for me at least. They are architectural and musical works, the polytopes, but also included is the theoretical work we have before our eves I would now like to invite those more competent than myself the carefully reflect on art and science and to ask Xenakis questions concerning the "alloys." The first question will be as follows: Xenakis proposes in his theoretical works to fight against the current separation between the arts and the sciences and to create a sort of free movement of thought: hence a mutually fecundating of scientific and artistic thought. To achieve this, Xenakis relies simultaneously on a vision of the past and on his current realizations. Little by little. we see a vision of the past reappear in each of his works and even in the presentation he has just given. The best periods of mutual fecundating between the arts and the sciences have been during Greek Antiquity, the Italian Renaissance, the classic age, etc.~ when artists and scholars ignored each other less than they do today and from whence an entirely legitimate nostalgia is born for this free movement between art and science. But today, the benefits which the arts and sciences could share seem to me to be quite unequally divided and possible. I’m under the impression that the sciences can bring infinitely more services, more illuminations, more fecundations to the arts, and particularly to music, than music can bring to scientific knowledge. For example, the application of stochastic calculations to music. including the sieve theory ** which Xenakis personally tailored to apply to the problem of pitch scales is, in essence, ;she says in the first part of Musiquc. Architecture., for the renewal of music and musicology. But from a purely mathematical point of view, I fear that these tools neither present any particular interest nor fecundity nor invention nor difficulty to sunnount, and, by consequence, there is no new realization to be made. Likewise, the use of computers has certainly posed problems, but entirely classical problems in tenns of programming and information theory. In short, pro blems which have been mastered perfectly enough. This is not at all apparent in the other direction. Today, it can be said (and a large part of Xenakis’ output has proven) that musical thinking has not yet sufficiently utilized all the mathematical resources it could. When Xenakis realized that for a musician, pitch scales constitute a well-ordered group, an abelian scale, (a trivial definition for a mathematician’s mind), this put the "bug in his ear," as they say. There are well-ordered groups; therefore, perhaps there are groups that are not orderly. Here’s an abelian scale, can’t there be a scale which is not? We understand very well how musical thought can thereby be fertilized by mathematics, but given the relatively elementary level of mathematics in these concepts, I would say that the interest is null for mathematics. If one can dream of an exchange between the arts and the sciences, it would consequently be necessary to declare that, in our day and age, the terms of exchange seem extremely unequal. Hence my question: How can we hope to interest the scholars and scientists and thereby perceive these new mental structures which Xenakis himself alludes to today? Art’s use of science benefits the former more than the latter. Is this lack of balance bad? And if yes, how can we overcome this? My second question is simply derived from the first. The position of free movement and alloys is but a proposition-meaning it doesn’t refer to any real situation today; it is a desired state. An alloy is a utopian thing, meaning that it is a creative invention. It is created, so to speak, by the fecundity of Xenakis’ work. But can it pretend to apply to the whole of society? Can it pretend to become if not the sole law, at least one of the elements in the relationship between art and science? Would the proposition of "alloys," assuming science to be on one side and art on the other, have something which resembles a meaning-unto-itself, a sort of truth-in-itself; or, with art on its own side and science on its own side, could they not be vehicles of something other than themselves? Would they stem from somewhere else, a somewhere which would be elsewhere than in the axiomatics to which we enjoy referring them? In other words, is there a purely technical union between the arts and sciences, or is there a social division after all which would be hiding behind this technical division (and if so which)? Here, I’m not particularly thinking of a class difference between intellectuals and laborers. Indeed, who would be who and who would not? Here we are faced with a division, a separation between functions. Science is turned toward so-called rational action, toward nature and man; it prides itself on being part of reality. Art is turned toward the creative invention of imaginary objects. Is Xenakis proposing something imminently realizable or something which presupposes transformations-notably social ones which are much more radical-by partially changing both science and art, in having them confront one another? In summary, the sciences have given men a certain control over things. Xenakis now proposes, in some way, to control this control so that this higher control could help man rather than use him. Therefore, is it conceivable that this reversal of terms which circulates throughout Xenakis’ entire oeuvre limits itself exclusively to the realm of the arts and sciences? The third question will come back to aesthetics. The opinion is, alas, very widespread that Xenakis’ music is composed by computers. This opinion is but one of the aspects of the well-known scientific and technocratic ideology in society. When we look more carefully we can see that this obviously has no meaning. In Formalized Music we can find an admirable formula: "In this domain we find that computers render certain services." In other words, it is possible that one may not benefit from these "services." This was the case with Metastasis in 1954, and I can still see Xenakis calculating "by hand" (as he said) with incredible patience, no, obstinacy, taking several months to do what a computer could· achieve in a few hours. Fine. We have here then months of hard work: If possible, we would use a machine which could work much faster and more efficiently. There are works from Xenakis’ more recent output which were also calculated "by hand," works which we could call "hand-crafted," without the use of computers. Perhaps Xenakis can tell us why? I’m thinking of such works as Nuits, for example, from 1967 and more recently, Evryali, from the summer of 1973. I’ve been trying to analyze these scores for over two years now. It is not true that these works are the least interesting (at least for my taste); I was going to say in terms of beauty, but let’s say in terms of aesthetic success. If I cannot successfully analyze Enyali, obviously I must first examine my own limitations. This does not embarass me since it’s a particularly difficult score. But nevertheless, must something else be blamed? Isn’t there an outburst of what we could temporarily call a xenakian style in this score which would be more than a soul-supplement? Xenakis speaks very little of style, though he arranged to comper computers to respect this notion which the profane can recognize only while listening. Xenakis barely touches upon the subject in his theoretical writings. Is this out of a sense of decency? Out of modesty? I don’t know. Sometimes, an allusion, a short sentence will emerge concerning the beauty of this or that device, of this or that result, on the absurdity or the baseness of what Xenakis somewhere calls "the lowest strata of musical intelligence." Iannis, you speak too little about this xenakian style. You can respond by saying that you leave that up to your historiographers. They thank you for your trust in them. They certainly thank you less for your silence! If you could help them just a little bit, they would be even more grateful. Would it be going beyond the limits of this thesis, Arts/ Sciences: Alloys to credit techniques with only a secondary role, a role which serves only in relation to intuitions or aesthetic intentions which, most certainly, tend toward alloys or even end up becoming alloys? The techniques, however, do not subjugate themselves to the alloys. In short, what presides over all of that. what "inspires" (as they used to say) the totality of these approaches? Perhaps here we are venturing beyond the limits of your thesis. Nevertheless, it would be a bit paradoxical to have Xenakis right here, obliged to answer in some way because of the particular situation (laughs), and still not ask him what’s going on or what is being protected behind this scientific fortress, behind this front of computers. How is it that Xenakis convinces himself and us about this wonderful power of knowledge, a power which I myself believe in (up to a certain point), while in the meantime; he writes his most brilliant works simply with a pencil and paper? If you please, Iannis, where in this realm have things changed so totally and profoundly since Bach or Mozart, for example? IANNIS XENAKIS The last question is a very important one, in my mind. The answer is that I have sometimes been accused of being calculating, of being a mathematician, of being "dry," and all these in opposition to being a musician. This accusation is now out of date. Today it seems that I am no longer subject to it. Even musicians consider me a musician! This is a parenthesis I would like to open. For the first time, I find myself in an institution as "respectable" as the Universite de Paris and even the Sorbonne. Up until now, I was always kind of "on the fringe," and little by little I’m putting this newly established position in order (since I now teach at Universite de Paris*) by defending this thesis. It’s true that almost all my writings refer to questions which can be demonstrated and expressed in a language which everyone understands, be it here, in Japan, in America, even by the Eskimos. On the other hand, the part which cannot be expressed, can be said only by art itself, by music itself or by the architecture or visual expressions themselves. and even then, I don’t know if there are many things one can say, aside from "I like that" or "I don’t like that" or "that’s beautiful" or "that’s ugly" or "that’s revolting" or "that’s fantastic," "interesting," etc. It’s true that we fall back into aesthetic or psychological problems, but what can be said about construction or sonorities, etc., without using a technical or analogical or proportional or architectural language? What can be said? There is no language which could encompass these questions aside from the questions themselves which deal with construction, structures, rules and laws. But I agree with you: there is something else in music, in any music, even in the "ugliest" music. But this "something" is neither distinguishable nor discernible; it is "unspeakable." It’s the traits’ which are not yet describable. It is the art-object which must express them. That is why it’s sort of an amputated aspect, no? OLIVIER REVAULT D’ALLONNES That’s clever ... IANNIS XENAKIS What do you mean, "clever"? OLIVIER REVAULT D’ALLONNES You tell me that you can’t answer, yet you yourself make comparisons between works of the past and a certain number of current trends. IANNIS XENAKIS I can do that! I can speak of structures. That’s what I just said. But I can neither question nor speak of something’s value when it is not immediately perceptible on a structural level. For example, you said that I calculate either with computers or "by hand," but amidst all that there is still a style which comes through, independent of these calculations or any "metacalculation." OLIVIER REVAULT D’ALLONNES Or "infracalculations," I don’t know ... IANNIS XENAKIS Or "infra." I would still say "meta," or "behind," which comes down to the same thing! I could even generalize here. I’ll bet that any choice presupposes an arbitrary choice. There is no man-made construction which is not arbitrary in some way. To accept the laws which govern something’s construction is already an arbitrary act. In mathematics we encounter this when modern as well as ancient mathematics arbitrarily sets axioms and then, only at a secondary stage, uses formalistic logic and thereby builds their entire structures. The group of axioms is set at the base or at the summit, in my mind, since the base is inversed. The point is on the ground and the base is in the sky since there is more room for it to grow there. That which is axiomatic infers an arbitrary choice. But is it completely arbitrary? Yes, but after first separating certain theoretical necessities added to the conditionings of actual and historical experience. OLIVIER REVAULT D’ALLONNES Nevertheless, there is a parallel which you yourself make. I believe it’s in the latest edition of Musique.Architecture, and also at the end of your thesis report*. A parallel is drawn between the history of mathematical thinking and the history of musical forms, plus practically a third element. a third parallel which is not, of course, at all parallel, and which is the history of musical taste. Just as the fugue is a musical structure of the fugal period, so are your works typical of the twentieth century. But of course there is Xenakis the individual, and it seems to me that this totality is not arbitrary. IANNNIS XENAKIS I’m afraid we are drifting a bit from the question you asked earlier since what you are talking about is a question of musicology and forms. or better yet, a science of forms and of historical revolutions. If the fugue was, in fact, fundamental at a given moment, it was certainly not so before its discovery, before it imposed itself! The fugue is by no means fundamental today. That’s for sure! Therefore, this is first and foremost a technical problem, since what is, after all, a fugue? It’s a group of rules and procedures with a view toward constructing a musical edifice. This group of rules was born. Consequently, it did not exist before that! And now it no longer exists in the broad sense, from the point of view of creative invention. This rather convincingly proves its at-least-partially arbitrary character. OLIVIER REVAULT D’ALLONNES The question was not about fugues but about your work, Iannis! IANNIS XENAKIS If I try to explain my ideas in books and articles or in lectures on this or that technique, it is because I can easily speak of these things. Or, when I teach, it’s to incite others to delve into these same questions. But I don’t say everything, even if I sense or perceive it because I don’t know how to say it. Therefore, eventually, I have the students listen and see the results. There you have a quick summary of my answer. Perhaps I didn’t answer your other question... OLIVIER REVAULT D’ALLONNES Yes, perhaps ... One is tempted to ask you: Why is there a certain historical gap between the arts and sciences and in what measure is there not more of a unilateral contribution directed from the sciences toward the arts rather than the opposite’? That’s one question: and the second one is: If this alloy-ing which you propose between the sciences and arts is something utopian (therefore creative). doesn’t that imply something other than a simple transformation in the realm of the arts and sciences? For instance. almost a transformation of civilization’? IANNIS XENAKIS That’s perfect, because I had noted more or less the same thing! It brings one back to Olivier Revault D’Allonnes’ first question, which points out a delay, .. a one way street in the wrong direction, .. why have the roads narrowed with time? I believe it’s a question of civilization. Antiquity had also witnessed this free movement between the arts and sciences. We see Polycletes trying to apply geometry to sculpture with his canon; this same free movement which similarly occurred in architecture, painting and music. Aristoxenus’ text came later. as a follow-up. I believe the fundamental point of the Renaissance was its rediscovery of man’s uniqueness. Man is something unique, singular. There are not many men, there is but one. This man encompasses all thinking and acting possibilities. and consequently, the interpretation between the sciences and arts. On the other hand, the arts too have contributed to scientific thought in a direct or indirect manner at certain crucial moments in history. This is what I have tried to show in the table which I added to the last chapter of Musique.Architecture. by drawing a parallel especially between musical and mathematical thinking. * What is indeed curious and immediately jumps off the page is that music is much closer to mathematics than any of the other arts. Why’) I’m not going to show that now. However, I can say that the eye is quicker, much more immediate and in direct contact with reality. than the ear, which is less agile and more recessed. demanding reflective thinking. Consequently. the ear must be more abstract and therefore create bases which also are more abstract. bringing them closer to mathematics. It is with this type of idea that I have tried to show the tendril between music theory (and hence. a part of music) and mathematical theory: how they coil around each other, although they do. at times. go about in parallel motion without coiling at all. Today. the artist’s domain is behind the times. I was already struck by the poverty of "combinatory" thought in music before leaving the Athens Poly technical School where I studied compositional procedures. This is also true for serial music which I later studied. Here, I would like to pay tribute to Olivier Messiaen. He was the only one whose thinking was completely open to these topics, Some of his work rested on the premise of "interventions." Furthermore, I believe that this came about thanks to the artistic side of his nature. But this is entirely another facet which does not belong to structural ones. Also, let’s take another example: Olivier Messiaen’s Modes of Limited Transposition. These were the beginning of my work on scales. Without generalizing, this beginning certainly allowed me to grasp some of the difficult principles of musicians’ mental structures: their ways of thinking and acting. Over fifteen years ago, I came upon these scale problems in musical composition. In the course of my work, I was led to resolve them with the help of almost-already-made mathematics. The result was my "Sieve theory."* It’s not the opposite; I have almost never done the opposite. Compared to what mathematics offers the artist today, this is really nothing; it is minimal. What must be done then? Well, in my opinion, a concrete transformation of the musician’s (the artist’s as well as the scientist’s) training. This training must not occur too late. It should start in grammar school, if not in nursery school. And it’s all a problem of education, of the educational system, of man’s training (from infancy to adolescence, and even later, up to his death); this is what is in question. Yet this separation between the literati (or artists) and the scientists occurs very early on, and it’s a question of up-bringing, from the baby bottle onward. This results in a delay since there is no communication at all. In any case, the consequent lack of free movement and contact makes itself deeply felt. Moreover, this is why I have agreed to teach, to give lectures and seminars. Also, now at CEMAMu, we are making an effort to utilize the most advanced technology known to information theory in pedagogic directions. By combining problems of musical composition and thinking with those of space and vision and finally with those of mathematics (which the child necessarily learns when five, six. or seven years old), a revolutionary approach to music can be attempted. I think the core of the problem lies here. It’s the question of man’s survival, in harmonious surroundings, of course admitting contradictions, but affording richer surroundings than he knows at this time. Therefore, this differentiation is a residue of recent history. Little by little, the artist has strayed and has made a sort of selection. He has examined only one of the aspects of art: precisely, the inexpressible aspect. BERNARD TEYSSÈDRE I believe that Michel Serres would like to intervene on certain points. MICHEL SERRES I would like to defend this thesis instead of Xenakis and for just one minute would like to answer Olivier Revault d’Allonnes. He poses the problem of exchanges between the sciences and arts. He would like to know if the exchange is not unbalanced; in other words, if you haven’t borrowed some mathematical techniques while mathematics, on the other hand, hasn’t taken anything from music. The reverse thesis would say that music is a step ahead, that Xenakis’ music is in advance. I don’t see the problem as being one of exchange (which would be a commercial point of view), nor from the point of view of scientific techniques. It’s one thing to say that one borrows techniques from a given aspect of science and another thing to say that in his music, Xenakis presents a general idea of scientific thinking. The scientific world has changed and no one has become aware of this, perhaps not even the scientists. What has changed is not that combinatory algebra has been replaced by group theory nor that Fourier transformations have been replaced by information theory. That is not important. What is important is that something called a "paradigm" has been completely transformed. A new world, a new scientific world has emerged in the second half of the twentieth century. The first to have stated this was not a philosopher, not a scientist, not an epistomologist, but Xenakis. It’s Xenakis who first showed what a symbol detached from its background actually is; it’s Xenakis who was the first to use not this or that mathematical technique, but only the most important and significant among them. To say that there is a delay has no meaning unless the problem is posed on local exchanges. If it is the global vision which is thrown into question, it can be found with Xenakis. All the traditional discourses hide this general vision of science and this paradigm from us. No, Xenakis, you are one step ahead and thank you for being there. (laughs and "bravos") OLIVIER REVAULT D’ALLONNES Michel Serres has just shown how the minds of numerous scholars can be opened by approaches such as Xenakis’. I never doubted that. My initial question was what could music (for example) bring not only to scholar-scientists, but to science itself. It’s here that I see a certain gap and not a "delay"; moreover, we could define such a delay on the basis of which ideal calendar? Finally we are left with the problem of the social conditions of the "alloy" in question. IANNIS XENAKIS Fine, thank you very much; that answers the first question (laughs). I couldn’t have said it better myself The second question concerns this "social transformation." Naturally, it’s a question... but I don’t know which social transformation you mean in this case. This particular problem has remained absent from all the social transformations which are produced in the entire world. No one has answered this problem and I think I will come back to what I said earlier: the desired social transformation would be the one which would tackle the coexistence and interpenetration of these aspects of human life from the earliest education onward. OLIVIER REVAULT D’ALLONNES Speaking of pedagogy, it seems clear to me that neither innocently nor by chance, pedagogy, such as it is practiced in our society, creates literati on the one hand, and on the other hand, scientists. as you were saying. IANNIS XENAKIS Yes, it is certain that if one tras only scientists, it’s probably due primarily to the time factor involved in specialization. But I believe that we can go beyond this stage. I myself have worked in at least two professions simultaneously. and I think that it’s entirely possible to do even three and not only superficially, but by pushing these professions toward research. It’s also a question of submission ... I won’t say of class struggle because it’s much more nuanced and complex than that But it goes without saying that it comes down to the question of a ramification of man’s organization which produces spiritual and intellectual invalids. That’s for sure. In my opinion these illnesses can be cured. How can we attain this radical pedagogical and also socio-environmental change? This is a reform which politics should be undertaking instead of merely asking questions about salaries, technical stuff, improvements, social progress. The fulfillment of man’s totality lies especially in this. I think that art (as well as science) has its role to play in putting everything together. What Michel Serres said is true: at the basis of art (and equally of science), there is this whole vision which can be called the vision of the twentieth century, which is a totality and which is hope, and finally which should be the hope of humanity. BERNARD TEYSSÈDRE Well, perhaps now we should give Olivier Messiaen the floor, since we have covered the first cycle of questions and answers. DIALOGUE WITH OLIVIER MESSIAEN OLIVIER MESSIAEN A hero cannot be criticized! Therefore, I will ask only a few questions. But, dear friend, I wouldn’t want these questions to seem to be indiscreet to you. If they displease you, say so. These are not really questions, but more like requests for elucidations to enable you to clarify your thoughts. Instead of making a brilliant statement like my colleagues, I will simply ask you my questions one after the other. This will be easier for you, for me, for everyone. First question: somewhere in your thesis and also at several places in your book Musique.Architecture, you seem to lead history, and especially the beginnings of music, back to the birth of scales and modes, and scale-constructs. Before these scales (and you yourself recognize this) only tetrachords were utilized. But, don’t you think there was first of all the "cry" at the very beginning of humanity? Shouts of joy and shrieks of pain: this is exclamatory language (spoken as well as musical). Then, the perception and imitation of other sounds, of the wind, of water, bird songs, etc.: this is imitative language (which is mostly music yet it can also be found in primitive onomatopeias). Syntactical spoken languages came much later as did organized musical phrases, and with these, preliminary, "outside-time" (as you call it) scales, modes, and scale-constructs. Why have you stopped at this scale material, to the exclusion of all the rest? IANNIS XENAKIS No, not at all. Would you like me to speak of this right away? It is true that I did not go any further, perhaps out of ignorance. I don’t know what went on on the mind of the paleontological man, a million or two million or even thirty million years ago, as We have just discovered. We have no way of knowing the form of his thinking. If I look upon past centuries from this present century, it is because I belong to this century and consequently can only speak of things which are comprehensible to me. I admit that it’s doubtlessly a drawback not to be able to deal in greater depth with the questions you have raised. Furthermore, what does it mean "to imitate"; what does it mean "to exclaim," which came before syntax, before all rules, before constructions. no matter how small they may be? This is already an indication of a recognition of form, therefore of a structural vision of the environment, admitting that man was sort of an object-unto-himself. Nature and his environment were something outside of him and what he perceived through his senses was consequently imitated. Here also I think it probably can be said that his being capable of imitating the sound of the wind, hail or thunder, etc., was a way of constructing, a primitive way perhaps, but nevertheless already very complex. Science today (and when I say science, I mean scientific thinking), has merely glimpsed over certain mental structures of man for only a very little time. Others will come, but it’s difficult to speak of those; I can only speak of things which are already well formulated and visible. This is why I started with tetrachords, which are already at a rather advanced stage of construction. I must also add that tetrachords are part of a cultural, scientific or organizational approach, meaning a material. All the same, in other civilizations such as those of Japan or China or Africa, all very ancient, even more ancient than Greek civilization (we don’t know too much about the Egyptian), there are other approaches where the tetrachord doesn’t play a role. For example: in No music, there is the interval of a fourth. We could say that the fourth is a sort of universal reality, but the interior construction of the fourth is something perhaps specific to the third or fourth century before the Christian era in the Greek world. Since tetrachords were at the base of the diatonic system, and hence of all music up until our present epoch, they can be viewed as the historical and musicological guiding line which enables us to extrapolate further. This is not so true for earlier periods (which I call pre-logical, even though they are not at all pre-logical in the musical realm). And what you tell us is fundamental because even if we want to dig more deeply into these questions of structures today, it would be necessary to come back to, or, more precisely, distance ourselves from these same structures, from these musical concepts, which, besides, would now tend toward extra-musical reasoning. Now, let’s look at these things with a completely new eye or ear, with new tools. This is the recognition of forms. If we received (and in fact, we do receive) signals from intrastellar, galactic space, well, it would be necessary to know how to distinguish these from noise (as Michel Serres said earlier), to see if they are structured, if they are coherent, and if this coherency is meaningful or not. By meaningful, I mean to say if it comes from natural sources (which is to say, from nature itself) or if it comes from other beings who would resemble man. It would be necessary to go back, well before all structures, before all forms of thought which we have received from civilization and schooling, and to get back to pre-rational, pre-logical, pre-structural, pre-syntactical situations. I don’t know if I have answered your question. OLIVIER MESSIAEN That’s a very beautiful response. But you have also said that the past was in the future and the future in the past. This is why I allowed myself to touch upon some regions where our knowledge becomes feeble. Second question, absolutely personal: You know as well as I do that a certain number of objects gives a certain number of permutations, and the more the number of objects increases, the more the number of permutations increases and with a speed and in quantities which can seem disproportioned. So, three objects give six permutations, six objects give seven hundred and twenty, and twelve objects give (if I’m not mistaken) four hundred ninety seven million, one thousand six hundred permutations. Suppose these objects correspond to durations: I would have to write out these durations in order to know what gesture or what movement they could create in time. There has been a lot of talk about retrograde movement these days: this is but one movement. one single movement among thousands of others. and its permutation follows the original trajectory. And all the other permutations? I can’t write out the millions and millions of permutations ... and yet I must write them out in order to know them and to love them (I insist on the verb to love!). In your case, a machine will give you the millions of permutations within a few minutes: it’s a cold and unexplicit list. How can and do you choose directly from within this immense world of possibilities without intimate knowledge or love? IANNIS XENAKIS I believe there are two questions grouped together in your last question. The first is the question of love; fine. The second is the possible choice among a large quantity of possibilities ... OLIVIER MESSIAEN And I believe you are going to answer M. d’Allonnes’ first question ... IANNIS XENAKIS Perhaps. I don’t know. The question then of having to love something in order to use it naturally implies an initial taming. To tame or "win over" means live with, and live with means to love and also to not love; for loving leads to its corollary. OLIVIER MESSIAEN I’ve expressed myself poorly. What I wanted to say was "to know!" To know with a real and emotional knowledge, out of love or hate ... IANNIS XENAKIS Yes, that’s the emotional side, the epiphenomenon of knowledge,; the pain, or on the contrary, the joy, or the two together which one can experience when loving a beautiful woman, for example. But possessing something out of love or hate is perhaps one form and consequently, the only possible form, of knowledge. When I look at the starry sky, I love it in a certain way because I know it in a certain way; but if I must know the successive stages of astrophysics, well, that may happen without love. Love would here be surpassed by a kind of revelation which is beyond this epiphenomenon called love. Consequently, I can handle the concepts of things themselves without being in direct possession of them, under the condition that I may conceive of them and feel them from within in some way. This is the beginning of an answer to your question, which I find to be fundamental. All this means is that even if I am incapable of dominating a certain phenomenon, I am capable of obtaining a truth which is inherent to the conceived or observed phenomenon, thanks to a kind of immediate revelation. Henceforth, I can accept and use this, in and as itself. When I tape record a sound which I find interesting, I don’t know exactly what is in this sound. I perceive things which interest me and I use them. Therefore, I cannot love the things within this sound which are so refined that I cannot totally perceive them. I am not consciously nor unconsciously capable of naming them, but I accept the whole, in itself, since I am attracted by that. OLIVIER MESSIAEN You are attracted, therefore there is a revelation! IANNIS XENAKIS That’s right, yes. OLIVIER MESSIAEN A revelation is like falling in love, like a thunderbolt. It’s the Romantics’ inspiration. IANNIS XENAKIS Yes, I don’t deny that at all. On the contrary. OLIVIER REVAULT D’ALLONNES I didn’t know you were a romantic, Iannis! (Laughs) IANNIS XENAKIS I said earlier, (or maybe I didn’t) that in the artistic realm there is revelation. In philosophy, in knowledge, it’s the same thing. Yes, revelation is absolutely indispensable. It’s one of man’s crutches. He has two crutches: revelation and inference. And in the artistic realm, both are valid. In the scientific domain, there is one which takes precedence over the other, and that is inference. To get to the second part of your question, that is, how does one choose from a great wealth of possibilities? Well, there are many ways of going about it. I can imagine - I don’t, need a machine for that - I can imagine and intellectually make a choice. There are several ways of making this choice. It’s true that when there are a few sounds, or more precisely, a few pitches to control, it is easy to proceed in an arbitrary or intuitive manner, directly. But, when it’s a question of a great quantity of sounds, well, there it would be handy to borrow from other domains. When I look at a small number of individuals, I see them as individuals; I see their relationships, their characteristics, and their relations to space and time, their own physiognomies, etc. But if there is a crowd, I can no longer distinguish the individuals, because they are too numerous. On the contrary, what I can see are the aspects, the characteristics of the crowd. When I need a great number of possibilities, I must manage to use characteristics of large numbers: which are, for example, density traits, traits of order or disorder, spacial distribution, sound-space distribution (such as pitch, time, order, disorder, etc. dimensions), and there we find potential tools to make certain choices. I am not saying that this applies to all choices, but we can thus eliminate a fair number from this apparent impossibility of choice within such a vast number of elements. I am going under the principle that man is incapable of saying "yes, I mean this object which is there," when the density is too great. A certain hesitation while choosing is permissible at such times because other characteristics are then important. It’s the same phenomenon which was produced when probabilistic calculations were introduced into the kinetic theory of gases. In any case, it was a little different in that it was a problem of calculation and not a psychological problem. We arrived at the kinetic theory of gases, that is to say, concepts which enabled many different sciences, and not only thermodynamics, to make great leaps forward. I believe that in the artistic, sensory and also sensual realms, this is what’s happening. Have I answered your question? Am I making any sense? OLIVIER MESSIAEN Yes, yes. Third question (this one is absolutely indiscreet and if you don’t want to answer, you may do as you see fit!). In Musique.Architecture., you quote a magnificent text of Parmenides which is generally applied to the universe and which contains the notion, among others, of "Being," or the quality of that which is.* In summarizing this text to the optimum, these few words can be isolated: "it is," "without birth," "indestructible," "imperturbable," "without end," "being simultaneously one, continuous." Having studied theology, I can apply this only to God, since only divine attributes are expressed. Yet you explain this text in terms of energy and energy conservation. I’m well aware that one of the new theories explaining the beginning of the universe is the explosion theory, which affirms that the universe started by a fantastic combustion. This presupposes an energetic force which itself could be considered a divine attribute. But I think your explanation of Parmenides is altogether different. Can you tell us why you have chosen energy? IANNIS XENAKIS Parmenides’ "Being" is one of the first texts where he tries to encompass what is "real." In order to accomplish this, he is obliged to detach himself from it, or make a sort of abstract definition of it, even if it is in contradiction with daily experience. This is what enabled Aristotle to say that Parmenides was crazy. It’s true that what Parmenides says about "Being" corresponds to what could be said (as you yourself have indeed said) about a unique god. But on the other hand, if we don’t think of theology or of any religion, but stay in the realm which is, I believe, simultaneously fundamental and much more universal (that of Parmenides), the text in no way indicates any reference to any god. He simply says that it’s "the notion of Being." He speaks only of being, of being as existence, not an active being. This is why he doesn’t put the notion of being in the infinitive. As contradictory as Parmenides’ direction may seem in relation to reality, I think it is one of the revelatory sparks among the conflicts of human thinking, all while trying to envelop man’s problems throughout the ages. Now, there is but one spectral answer to Parmenides’ notion of "Being" and that is this correlation I made between it and energy because I found this to be the closest in content (in the scientific domain) to what he describes. Because energy is, in fact something which fills the world. The principle of energy conservation is, of course, just one principle, but one which holds fast to this definition of "Being." Therefore, I have tried to give an answer in nature’s realm, meaning science and physics. By no means is this an exclusive answer; it’s merely a sort of comparison that I make. I don’t say that "Being" is this, but it does strangely call up the definition or, more precisely, the conception of energy which fills the world. Energy has no known beginning nor end since, due to the principle of energy conservation, there could be no end nor beginning. This, of course, is a bit in contradiction with the theory concerning the explosion of the original atom, at the outset of our extremely condensed universe. But I am allowed to think of this as a temporary theory, as are all theories. This comparison of Parmenides’ "Being" with energy is only a kind of analogy. In fact, God’s attributes are identical with those of "Being" since, subadjacently, man’s same logic can be found. OLIVIER MESSIAEN Now, the fourth question ... IANNIS XENAKIS If you please, to finish with Parmenides, I would like to mention one other fundamental thing which can be found in one of his fragments: It’s the question of the equivalence between a being and thinking, which is also one of the guiding lines in man’s thought throughout the ages. In one verse which has remained famous, and which Plato reproduced in his Republic, Parmenides said, "For it is the same to be and to think." Yet, the structure of the sentence is symmetrical in relation to the verb "is." To be, meaning "Being" and thought are the same thing. This is where I see the symmetry. Much later on, there is dissymmetry when Descartes states "I think, therefore I am." It’s curious to note when comparing these two sentences (which, I do believe, is necessary) that it demonstrates precisely the same preoccupation throughout the ages. I don’t know whether Descartes knew ... BERNARD TEYSSÈDRE It’s not at all the same. IANNIS XENAKIS No, "I think, therefore I am" is asymmetrical and if we look to the solipsists, to Berkeley, for example, there we have another inversion which is reminiscent of Descartes’, but which leads to another direction. This means that objective reality, or "Being," cannot at all "be" except as thought. This is to say that there is an identification between "Being" and thought, outside of any reality. If Descartes is a realist, Berkeley suddenly becomes abstract with his solipsism, and everything comes back to "thought." Since then, of course, there has been nineteenth century philosophy with marxist reasoning which admitted an objectivity that is independent from man and there has also been science which is ambiguous because of the memorable failures of its succesive theories of classical mechanics, etc. And we haven’t seen the end of it! This is why scientists say today, "Everything happens as if ... " OLIVIER MESSIAEN Fourth and last question: from page eight on of the French translation of the last chapter of your book Formalized Music which you have included among the documents submitted as your thesis file, you give several methods of microcomposition based on probability distribution.* Under Method 4, I found the following sentence: "The random variable moves between two reflecting elastic barriers." It’s very poetic and thanks to it, I can wallow in an abyss of daydreaming ... Later, you give the calculated explanation, which I did not understand. Could you give us another explanation of this process with a concrete musical example, perhaps from one of your works? IANNIS XENAKIS Method 4 refers to the basic hypothesis which can be found in the previous pages, starting on page 242**, "New Proposal in Microcomposition Based on Probability Distributions." This refers to pressure-time space, the pressure which your eardrum receives from atmospheric air in the course of time. So if we consider that this pressure takes on greater or lesser values, expressable in numbers, we can make pressure correspond to notes placed on a pitch axis and then we could write this on a music staff. We will obtain a passageway, a variety of pitches in function of time, forming a continuous melodic curve. In the case of pressure-time periodic space (where a square, triangular, or sine wave can be formed) the sound wave repeats itself identically and systematically. But if the variation is not periodic, it will adopt curves possessing just about any sinuosity. We could imagine that this curve is drawn by a floating point moving on a plane, without ever retracing its steps, neither in pitch-time space nor in pressure-time space, which comes down to the same thing from the point of view of its path’s definition. These paths will obviously depend on the laws which will set the moving point in motion. Periodic functions are very strict laws which correspond to melodies or equally to boring sounds. Probability theories and their mathematical combinations can, on the contrary, produce very free paths which never repeat themselves and which correspond to much richer melodies and sounds. The only thing is, these probabilistic treks can take on any value. Consequently, they can make the moving point surpass the weakest limits of the ear. In other words, in the case of pressure-time space, there could be pressures equal to those of the atomic bomb! Therefore it is necessary to limit untimely growth, these colossal probabilistic energies! It’s exactly the same case with a bullet which is channelled by a gun barrel while it ricochets off the barrel’s inner walls. OLIVIER MESSIAEN It’s what you call barriers ... IANNIS XENAKIS They are elastic barriers ... OLIVIER MESSIAEN They reflect ... IANNIS XENAKIS Because they reflect inwardly, following the law of elastic planes’ reflection, without loss, without absorbing energy. In other words, the pathway created by a probabilitistic or stochastic process is reflected as if it were off a mirror when it reaches the chosen barriers. It is, if you please, exactly like intervallic inversions. In melodic inversion, the intervals are reflected in a horizontal mirror placed in retrograde on the time axis, It’s a reflection in a vertical mirror. These are the very same and simple principles which can be found all over, even in music. At present, we can imagine nonreflecting surfaces with fields of gravitation; finally, all kinds of forces (in the abstract sense of the term, of course.) OLIVIER MESSIAEN This is absolutely wonderful ... So, as far as I’m concerned, I have finished. But earlier, when Olivier Revault d’Allonnes spoke, I didn’t intervene. He was making such a brilliant speech - I didn’t dare interrupt! Perhaps he would now like to bring up some of his purely musical questions, seeing that I have the good fortune to have the floor? OLIVIER REVAULT D’ALLONNES Personally, I failed. He, Xenakis, didn’t speak! OLIVIER MESSIAEN It’s not out of malice, but out of curiousity, instinctive appeal, and also out of admiration ... OLIVIER REVAULT D’ALLONNES I wanted Xenakis to speak of his compositional style, and he gave simultaneously a most satisfying yet very hermetic answer. He told me, "Listen, I have nothing to add. Listen, and if you don’t understand, listen again. And then, like it, if you like it. OLIVIER MESSIAEN There’s a certain modesty in that which surprises me personally because I’m not in the same profession as he is, I teach composition class at the Conservatoire* where, for the past forty years, I’ve spent my time decortiting musical works, trying to figure out what happens in them ... These things of which you don’t dare speak, which scare you, I deal with all day long ... IANNIS XENAKIS It’s true, I remember very well. I was in your musical analysis class, and what interested me the most was precisely the lectures you held on the subject of technique... (laughs) because all the rest amounted to, "As we were saying, that’s beautiful, isn’t it?" OLIVIER MESSIAEN I didn’t really say it very much. I kept quiet! IANNIS XENAKIS This is true; it was rare, but you did say this sometimes. But that’s all you said about the problem of style. Or perhaps style no longer is a question of technique, so then it must be something else. For me, style refers to technique as well as to music’s "perfumes" (which may just be more interesting), and on several levels besides. OLIVIER MESSIAEN Yes, but aside from all structures, it seems to me that each individual and every particular musician (since we’re speaking of music) possesses what we call in philosophy "his accidents," his "tics," his personal habits. A second or third Xenakis who would try to write Xenakis’ music in your place, using the same structures, would certainly not obtain the same results. There is, then, a question of personal style. IANNIS XENAKIS Yes, I’ll admit that ... OLIVIER MESSIAEN One immediately recognizes Xenakis’ music. Not only because of the glissandi or permutations; one can recognize it because of a certain sonority, a certain way of orchestrating, a certain way of distributing the sounds which differs from all others. IANNIS XENAKIS Perhaps the answer to Olivier Revault d’ Allonnes’ question is the following: In life, there are two ways of proceeding: one is to do things and the other is to analyze them. But the best analysis, for me, is to do things; in other words, I refuse analysis -psychoanalysis, if you prefer - as a method of introspection. If one gets involved in these domains, one doesn’t know what is going to be discovered, and one risks falling into holes, dreadful traps. Therefore it’s a tactic, and that’s why I insist on saying that it’s the "thing," music itself, which is not hermetic as opposed to an analytical discourse which is hermetic. OLIVIER MESSIAEN And nevertheless, I question the sphinx every day, since I have an analysis class, and I’m not at all unhappy. That doesn’t prevent me from making music! IANNIS XENAKIS Outside of technical questions, don’t you give other answers? OLIVIER MESSIAEN I handle only technical questions. IANNIS XENAKIS So ... OLIVIER MESSIAEN Outside of purely musical fact, of course, I would not allow myself to reconcile intentions because I would certainly be incapable of doing so. Or if I do it, it’s only very occasionally. IANNIS XENAKIS But what do you mean when you say musical technique? Isn’t it, in fact, a question of proportions, durations, combinations? OLIVIER MESSIAEN I do often speak of durations, harmonies, modes, colors. I know that you don’t believe in this ... IANNIS XENAKIS In my opinion, it’s already outside the realm of technique. OLIVIER MESSIAEN Orchestration is also a question of technique in my opinion. IANNIS XENAKIS Which means one can speak of these things. OLIVIER MESSAEN It is technical: perfectly, purely and completely musical. It’s on this point, it seems to me, that Olivier Revault d’Allonnes tried to question you. OLIVIER REV AULT D’ALLONNES ... As well as what is next to and underlying technique. I don’t believe I’m revealing any secret in saying that one day I saw Xenakis at his work table. He was working on a piece. Reviewing it, he was stopped by a detail. He said: "Oh no, that’s going to be horrible," and he changed it. So that then is technique? (laughs) I believe that happens to all composers. MICHEL SERRES In a word, we’re getting back to the question of choice. IANNIS XENAKIS Yes, of arbitrary, intuitive, etc., choice. MICHEL SERRES ... That which can be called inspiration, if you wish, but which remains a choice. OLIVIER REVAULT D’ALLONNES So there we avoid diving into the muddy regions of subjectivity? IANNIS XENAKIS Isn’t the best way to dive into it precisely by making music? OLIVIER REVAULT D’ALLONNES To choose among a vast number of possibilities seemed to be a difficult problem for Olivier Messiaen. Actually, any sensory organ, the ear, the eye, even touch, functions in exactly the same manner, receiving an enormous quantity of information in such a way that you must contrast the constitutive elements (which thereby establishes the technical problem of choice making); to choose among the millions of possibilities in front of you, on the one hand, and on the other, the subjective problem of saying (as they say "off the cuff") "that’s dreadful." It’s exactly the same thing. The "cuff," or the ear or the eye, functions in exactly the same manner as a computer, meaning it receives fifty million bits of information that it sorts out and faithfully transmits. Consequently, there is no opposition between what you call power, inspiration, event, "sensorality" and on the other hand, this problem which you find so difficult; that is to say, making a choice among a vast number of elements. That’s how it works, in living flesh. IANNIS XENAKIS In set theory, there is even Zermelo’s famous axiom regarding choice, which postulates that we can choose an element in a given set either in an arbitrary manner or with the help of "revelation." This is mathematical and the mathematics used here are wholly aesthetic, I dare say. Here is the problem, and calculating machines are the filters. OLIVIER MESSIAEN Simulators. IANNIS XENAKIS Choice simulators, housing the rules which enable choice making. Man, with his ear and senses, makes much more complex choices than a computer can today. In other words, choice simulation is still very rudimentary compared to man’s capabilities. OLIVIER REVAULT D’ALLONNES Yes, we still don’t know how to command the computer. Sensory terminals do it without knowing how they do it. OLIVIER MESSIAEN I’ll give you a concrete example. When I note bird songs, I do it with paper and pencil. Sometimes my wife accompanies me and tape records these same songs which I’m copying down. Yet, when we sit home and listen to what the recorder has captured, I can’t help but notice how unmerciful the machine has been. It recorded everything, including horrible noises which have no relation to what I went to find. I hadn’t heard these noises: I heard only the bird. Why didn’t I hear these other noises? That’s it, there’s a "Why?" Because my ears, of course, acted as filters. IANNIS XENAKIS This is what can be called intelligent or directional hearing. It corresponds to one of the choice criteria you unknowingly imposed upon yourself because you wanted to hear only bird songs amidst all the forest sounds. OLIVIER MESSIAEN My attention was directed to the birds, and I heard them, but I heard them at the exclusion of disagreeable sounds such as passing cars or planes ... IANNIS XENAKIS At the exclusion of other sounds. Moreover, in information theory, anything which is not the desired or a selected signal is dismissed as being noise. OLIVIER MESSIAEN We hear what we want to hear. MICHEL SERRES We hear signals. IANNIS XENAKIS Yes. And the difficulty in appreciating any work is in choosing precisely what is important. That’s why when you hear a piece of Bach which has already been played a hundred, a thousand times, it can seem altogether different than what you’re used to hearing, depending on the choices you make at that given moment. It’s not only a given work-in-itself which is interesting, but also the individual and personal choice of the listener. That’s why Newton, suddenly getting hit on the nose by the falling apple, said, "I’ve found it!" OLIVIER REVAULT D’ALLONNES All of this tells us more or less how you Iannis, conceive of choice, but not how you decide what is "dreadful" or the contrary. And who can we ask if not you, the composers? OLIVIER MESSIAEN Bach fugues were mentioned earlier, when we spoke of structures. Yet there is nothing more structural and (excuse me) more boring than an academic fugue. Bach wrote thousands of fugues; they’re all over, in all of his works, in his cantatas, Passions, his mass, organ works, and in his keyboard works. These fugues are never structured like academic fugues, and they are different from all other fugues written during the same period, because they possess a certain melodic joy and harmonic control which belong only to "Papa" Bach. IANNIS XENAKIS Yes, I believe the problem is there. OLIVIER MESSIAEN I’ll take it even further. In Bach one finds a little of what you have. Sometimes, there are superimposed intentions! For example, in certain chorals there is the choral line which Bach didn’t alter because it was a sacred text. He left it as such. It was willed, intentional. In the lowest bass part, there is an ostinato which is also intentional. In the inner voices, there is chromaticism: this too is intentional and he doesn’t let up. The three superimposed intentions account for the extraordinary encounters, modern chords and counterpoints, which could almost be signed by Debussy. There is, perhaps, one way of understanding how structure can give birth to something new and personal. IANNIS XENAKIS In a more contemporary light, a fugue structure is not totalitary, meaning it reveals free and less-clearly defined parts, and schema which are more or less followed. But with these schema, there are "data entries," (as these are called in information theory today) which allow you to obtain different results from these same schema. Large quantities of intelligence (in the broadest sense) and contradictory intentions can be included in these data entries, which are free in themselves. But these schema can be translated by a kind of system or automaton since they function autonomously, and the fugue’s significant lead over all the scientific thinking of its time occurred precisely because the fugue proposed systems which science then ignored. Only for a short time has science been systematically preoccupied with its own systematic methods; in other words, stochastic or determinist clockworks. MICHEL SERRES No. In the seventeenth century, a little before Bach wrote fugues or before schools required fugal writing, all scientific thought occurred automatically. Finally, it’s a demonstration of contemporaneity between the sciences and arts. IANNIS XENAKIS Yes, you’re right. Descartes treats this extensively. MICHEL SERRES That’s right, Descartes ... Olivier de Serres. IANNIS XENAKIS But the abstract automaton was proposed only by musicians. MICHEL SERRES Ah, right, yes ... that’s possible ... music boxes were the rage. IANNIS XENAKIS Musicians materialized the products proposed by the abstract automaton by playing them. MICHEL SERRES Yes, it’s true, they were ahead of science, as usual. BERNARD TEYSSÈDRE But to get back to our topic ... curiously, what is interesting in fugues is not the abstract automaton, in my opinion, but the specifically freer parts where Bach was able to introduce his personal genius. IANNIS XENAKIS Yes, but neither can we ignore the fact that here, in relation to other musical forms, we have an extremely compact form with a subadjacent structure onto which we can add other "forms." Naturally, the results would not have been the same if there had not been these subajacent structures, this schema. BERNARD TEYSSÈDRE Good enough. Seeing that the debate with Olivier Messiaen has dealt essentially with music, I believe the discussion with Michel Ragon will deal more particularly with architectural problems. DIALOGUE WITH MICHEL RAGON MICHEL RAGON In the course of this debate Xenakis’ book Musique.Architecture. has been frequently quoted. It’s one of the two books compiling all of Xenakis’ texts, the other being Formalized Music. If this book is entitled Musique.Architecture., it is precisely because two creative products are closely linked in Xenakis’ work: music and architecture. If these two subjects were separated by Xenakis for a certain period, they are now absolutely reunited. They were separated at a time when we didn’t really know Xenakis; that is to say, during the period when Xenakis was a "pure" (so to speak) architect, as Le Corbusier’s collaborator. Xenakis worked for Le Corbusier for twelve years, I believe. You know that when one works for an architect, for a boss, all that one does, all that one produces under this boss, is obviously attributed to the boss. This is why I would like to draw attention to the two projects signed by Le Corbusier but which Xenakis worked on particularly. I mean the façade of the Tourette Convent in 1954, and it is easy enough to see that Xenakis worked on it since the architecture is conceived somewhat like a score. Then there is the Philips Pavilion in 1956, which one could call a "musical recepticle." These two works, conceived with Xenakis’ participation in Le Corbusier’s studio, have since been verified by Le Corbusier himself as being Xenakis’ work. There are two texts by Le Corbusier at our disposal, quoted in Musique.Archtecture, * which indicate Xenakis’ considerable contribution to these works. I mention this in passing because certain architects deny Xenakis the right to appropriate works signed by Le Corbusier. Being less royalist than his students or disciples, Le Corbusier has, in effect verified the works in question as being Xenakis’. ' And then there are the Polytopes! Olivier Revault d’ Allonnes has written a very copious book on the Polytopes which speaks of them better that I could even mention. In these transparent architectures of steel strings (which serve as a support to luminous points where light itself is architecture), light "architectures" space in ephemeral designs. This is also an important part of Xenakis’ architectural work, and in this case, an architect’s work intimately combined with that of a musician. There is also Xenakis’ recurring utopia of a total spectacle. Without a doubt it’s a total spectacle such as one could witness on that fabulous night at Persopolis* with the two hundred and fifty torch carriers which are so often alluded to. But also, it could encompass Xenakis’ more recent ideas of casting out shining spiderweb-like canvases over cities and countrysides, to link the earth and the moon by luminous filaments, to create artificial aurora boreales... all things of which he speaks, and about which you, Iannis Xenakis, tell us in your resume accompanying your thesis file. Finally, there is another aspect of your work which I believe is better known and that’s why I would like to look into it. I’m referring to you; prospective architectural project, or your utopian architecture. Let’s go back to your chapter entitled "La Ville Cosmique" in Musique.Architecture.* I would like to ask you a few questions on this topic, since that is the rule of the game. I will quote some passages from your text, "The Cosmic City. " You begin by asking yourself if it isn’t necessary to opt for an architectural decentralization and a decentralization of cities or if, on the other hand, centralization should not be accepted. And you categorically favor the option of a centralization which no one could consider abusive. In other words, you object to the theory of linear cities (Le Corbusier is one of this theory’s authors), Which you accuse of being naïve. You propose to construct vertical, narrow cities which would reach up to three thousand indeed even five thousand meters in altitude; therefore, cities not very vast, but entirely in metal: some kind of giant skyscrapers but ones containing a city’s complete morphology. You find that concentration is a vital necessity for humanity, as you say, and that it’s necessary to completely change present urbanist and architectural ideas and replace them by others. This will therefore be my first question, even though this text is quite old. It dates from 1964. It’s possible that you have evolved since then. Today’s session is a chance to chat a little with you and ask you questions. I’m finally allowed to ask some questions I’ve wanted to ask you for a long time now. Do you still believe in this rather elaborate idea of centralization now, twelve years later? Do you think that it’s necessary at a time when electronic energy dispersion, or natural energies such as solar or eolian energy can admit a decentralization which precisely has nothing in common with past decentralizations? In other words, where culture itself can easily be decentralized by electronic means? Do you believe that such an elaborate centralization is still necessary? Or has this idea become dated since you thought of it in 1964? IANNIS XENAKIS I believe that centralization (which I prefer to call a "densification") of human dwellings and relations is, first of all, a historical necessity which we can find in all examples of urban construction and human dwellings as well as in human relations, in culture, all over. What makes it even more necessary today is the pellicular invasion of planetary space by dispersed cities which destroys the environment. Actually, there are two tendencies: one of densification-toward-compaction (a greater densification); and the other is a centrifugal tendency which prefers to reintroduce rural habits in the middle of green nature, where possible. If this is not possible, then they must be created by artificial means. Each of these two tendencies is as natural as the other, but the compaction tendency becomes a necessity during industrial eras because of an inherently more explosive densification of human population. The second tendency is natural, because it corresponds to past nostalgias and also because our present cities are far from offering the natural environment which the human body and spirit demand. Actually, these two tendencies struggle against one another. In fact, the saturation (or compaction) tendency is winning out because of economic as well as all sorts of other reasons. I still agree with what I proposed in 1964. I’m persuaded that it’s a solution, perhaps a temporary one, but one which is more interesting and less criminal than dispersion over the global surface. Such a great densification does not mean that I refuse man’s solitude, his right to isolate himself as an individual in this enormous beehive which is today’s city. I say only that instead of spreading out over a surface, which creates problems of contact for human activities, we must organize cities in a vertical manner. This is not at all a new idea, since it already existed on a smaller scale in the argument which started in the twenties, when there was a question of having to choose between "garden cities" (as they were then called) and "vertical cities." Le Corbusier was one of the defenders of these vertical cities. But these vertical cities then corresponded only to the pure and simple dwelling, and not to an entire city. They didn’t encompass all of a city’s activities whereas I think that we must extend this principle to all of a city’s activities for technical reasons, for reasons linked to human relations, and also in order to explore in greater depth what is left for us on this earth, and finally because such a system would allow us to install cities in truly uninhabitable climates, either very hot or cold climates and in overpopulated or deserted areas. I believe I’ve answered your first question. MICHEL RAGON This text was written twelve years ago. It is contemporary with other texts, other neighboring theories, for example, the "spatial city" of Yona Friedman, of Nicolas Schoffer’s "cybernetic city," or even Paul Matmond’s inhabited pyramids. How do you situate yourself in relation to these prospective architectural theories which were born at the same time as your theory? IANNIS XENAKIS I find them shy in comparison to mine! In reality, they are merely extrapolations on a relatively weak scale of what should be a very great concentration and, generally speaking, they refer only to individual dwellings and not to a city as a global phenomenon. MICHEL RAGON No one before our time had even envisioned a three or four or five-kilometer-high construction. The most utopian in this progression toward a vertical city, until you, was Frank Lloyd Wright and his project for a 1 660-meter-high tower. IANNIS XENAKIS Yes, but this l660-meter tower was an office building which had two faults: one, it wasn’t high enough; and then, it was subordinate to its surface structure (which was constructed of "porticos") which, in the end, transformed this thing into a sort of l660-meter-high obelisk. MICHEL RAGON This is true, it was a sort of obelisk, while you have invented some extremely interesting forms in your project. IANNIS XENAKIS That is to say it all happened out of a kind of revelation I had while designing the Philips pavilion, which is formed by S-curve surfaces; Because of some experiments which were done in a laboratory near Eindhoven in Holland, I realized that the S-curve was excessively resistant and its form could not be destroyed. These experiments were done because calculations based on the materials’ resistance as well as on the theory of elasticity did not at all allow foreseeing it through to the end, and there were some large margins of uncertainty which remained. The experiments demonstrated the extreme rigidity inherent to the geometry of these surfaces. They were "PH" (or hyperbolic parabolics). It is essential that the S-curve be well chosen, meaning an S-curve which is sufficiently isolated from the layout. I then thought that it was absolutely necessary to use this geometric property as the surface structure and, from there, create a city, not in an obelisk form or a skyscraper, such as we see here in Paris or in the United States, but one in a continuous S-curve form. These are pellicles in space with a width of one hundred or one hundred and fifty meters, perforated, of course, and transparent, which would insure ventilation and visibility, light, etc. And there are already cities at an altitude of two thousand meters in Mexico and Bogota. Therefore, it’s a completely habitable altitude. Of course, it is different at five thousand meters, since the rarification of air becomes critical. No one really knows what happens. But with present technology, it is possible to obtain sufficient pressurization as well as temperature control and air renewal, such as in airplanes. After all, a city such as this one would simply be like stretching a garment. Man has not known clothing for a very long time. He has worn clothes for only about ten thousand years, no more. Before, he was nude. He later put on individualized, personalized garments. He works from morning to night in places such as we are right now, for example, which have no air and from where he cannot see the light of day. Most people work like that in offices and factories. This environment can be very nasty to man’s health, and I think with present technology and the technology of the immediate future, these problems will be resolved in such a manner that everyone will be dressed for the city itself, allowing for a greater physical, conceptual, mental and spiritual freedom for man. This merely implies an extrapolation of today’s technical possibilities, exploited on a larger scale. A city such as I propose is not conceivable under a restrained capitalistic system. It could be realized, though, by multinational companies or by centralized states (such as France, for example) which could build them but while avoiding a municipality system. Only a country with several tens of millions of inhabitants or even a sort of international corporation which could construct units of this type could consider such a program, which would be valid for either deserted or extremely cold regions such as Siberia, Alaska, or Northern Canada. MICHEL RAGON Aren’t there any energy constraints which make the idea of heating such a volume seem difficult? IANNIS XENAKIS It’s linked, of course, to energy problems. But we now have products and insulation systems which could reduce much of the thermal and caloric waste. I really don’t think that the technical obstacles are real obstacles. The greatest obstacles fall under two categories. First of all, there’s the question of organization, since a city is an organization ... MICHEL RAGON I was getting to that. I was going to say, precisely, that you must envision electronic management and decision-making groups in order to organize such a vertical city. In Nicolas Schoffer’s "cybernetic city," though, we also find this belief in cybernetics and electronic management and decision-making groups. Don’t you practice a belief which, to me, seems to be a dangerous one with regard to the political virtues of science? This occasionally comes across in your writings, by the way. IANNIS XENAKIS I don’t know what Nicolas Schoffer said exactly. I believe he’s rather mystical about cybernetics... MICHEL RAGON Yes, he goes further than you: it really does become a kind of mysticism, in fact. IANNIS XENAKIS We must recognize that, for the time being, data or management systems are rather rudimentary and vulgar. Only a few tasks could presently be undertaken and controlled by automatic management. But there are some which do work. For example, city traffic lights are becoming more and more automated, due to reactions and counterreactions from street to street, from neighborhood to neighborhood; that’s a fact. MICHEL RAGON But this automation is almost always repressive. IANNIS XENAKIS We are faced with two problems: the problem of organization, and then, a deeper problem in that it’s a problem of social structure. When I say organization, it’s obvious that a city like this, which must comprise millions of individuals and at a five thousand meter altitude, cannot be entirely conceived in advance because one risks creating a dead city. This was the case with Detroit, with Le Havre, Brasilia, and even Chandigarh. They do not work because they were conceived in the laboratory - I mean, in architects’ studios-following certain rules stemming from drawing board traditions, or even occasionally, from revolutionary ideas. They cannot take into consideration the whole complexity of a city because of the simple fact that they have stemmed from one single brain. On the contrary, it is possible to give the framework (meaning the container) and not define or determine the contents. This would allow a freedom sufficiently great so that the contents could develop progressively. It must be understood that this sort of city could not be put up in five or even ten years, but could take up to twenty or thirty years to construct. Therefore, it’s not the city itself which would be designed in advance, in twenty or thirty years, but the "container"; in other words, the fundamental structure which must be built up to this altitude. On the other hand, it would be necessary to allow for improvements, if not developments, if not contradictions, which would progressively occur during the construction of this city. Consequently, it’s absolutely necessary to conceive of a kind of mobile architecture. A hint of that idea can be found in Japanese architecture, which allows for the transformation of rooms or houses following diversified functions. MICHEL RAGON Internal nomadism is possible thanks to the permutations of the architecture’s mobility, as you accurately point out. IANNIS XENAKIS I haven’t spoken of internal nomadism yet; I simply spoke of nomadism, let’s say of the city’s physical aspect. This is to say that we can assign this or that function to an area or region of the city, let’s say a factory, and then change these functions into dwellings or a park, etc. after a while. It’s a question of the internal structure mobility within the physical city. As for the second and more difficult obstacle, human dwellings and functions within this container: it’s absolutely necessary to leave freedom or to propose a sufficiently free schema which would insure an autonomous development in this domain so that the contradictions can be displaced, can change form. (I don’t say that they will be cancelled or absorbed; this can’t happen. It’s a utopia which dates back to the nineteenth century, if not earlier.) MICHEL RAGON You also write, "Since this city, your city will be fashioned following universal technique, it will be equally apt to house populations from the great north or south, from the tropics, and from the deserts." In other words, it seems to me that a dangerous technocratic belief in a universal or typical man appears in this text. It’s a very widespread idea. It can be found in Le Corbusier, as well as Gropius. And since there is a universal, "typical" man, architects deduce that a typical and universal architecture can be constructed for this man: a belief we’ve strayed away from a bit these days. IANNIS XENAKIS Yes, it’s just that technology imposes a certain universality, but I wonder if we have really strayed away from this idea or whether only in spirit. If you consider to what extent technological means have spread ... all the way to the heart of the most primitive societies, with electricity, with different sorts of energy and energy transformations but also with institutions which means that now, there are schools, universities, and textbooks everywhere you look. The scientific textbooks and laboratories are the same, the clothing is the same, even if they are different on the historical level. It is rare now to find people dressed in their national costume, a fact which is due to a general universalization, caused by all sorts of reasons. On the other hand, I am not a technocrat, far from it. On the contrary, I don’t mean to say, though, that present technology should not be used and exploited. There are at least two aspects to every proposition: the black and the white. It’s the same for atomic energy. It’s an incredible miracle that man has been able to see and enter into the microcosmos of matter and subsequently take advantage of what he finds there. It’s also absolutely normal to now find deviations since this is part of man’s nature, it’s one of man’s inherent contradictions, and it’s also a question of individual and social struggle. MICHEL RAGON Finally, one last question: how do you situate yourself as an architect, since you are still an architect, seeing that you have invented an architecture for the esplanade at the George Pompidou Center* in Paris (which is destined to be very closely associated with music) which will, without a doubt, be a Polytope and in which there will be music? You have also recently constructed a private home for the musician François-Bernard Mâche. How do you situate yourself in relation to your former employer, Le Corbusier, who is highly objected to these days by many of your colleagues and by many architectural theoreticians? IANNIS XENAKIS First, in relation to architecture ... When I decided to do only music, I was very distressed because architecture was very important to me. I did it because I had to make a choice. Either go into research or become a businessman. In the sixties, I went to architects’ studios and said, "Here I am! Let me introduce myself as an architect who would like to collaborate, but I don’t want to be someone’s slave; I want to do research." That was impossible. You know very well that this is true the majority of the time and that there are very few opportunities to do architectural research. I therefore confined myself to music where, despite all the difficulties, I could devote myself to artistic research. All this said and done, I’m always ready to do architecture whenever I can. For example, for this "thingamajig" at Beaubourg, I designed a portable structure which will be installed for several months and will house the means to put on a spectacle with lasers and electronic flashes, like at Cluny*, only more elaborate. And the structure is a cloth structure~* which therefore implies some fundamental architectural solutions. On the other hand, in relation to Le Corbusier, I don’t know if there are many other architects who have achieved what I consider to be artistic expression. Independent of an architect’s or urbanist’s subjacent ideas, this is something very complex which comes from different sources and directions. The cellular apartment included the Marseille project can be contested, of course, and is but one possible solution. It cannot be said that it’s the only solution. Besides, Le Corbusier proved this himself since he designed all types of houses. On the contrary, his artistic and architectural qualities, which are demonstrated in practically all of his works, cannot be contested. Ideas move on, but artistic fact remains. It’s one of history’s lessons, as Marx himself noted with regard to antique art. Approximately, he said or asked how is it that, at the rim of civilization and western culture in spite of slave societies, etc., works were created which still affect us today? It’s a miracle inherent to artistic fact and corresponds to the discussion earlier, to the question which Olivier Messaien and Revault d’ Allonnes asked. Therefore, Le Corbusier can be criticized on a lot of points; I even do it myself, but I believe he was one of the greatest architects of our time. There are not thirty-six of them today, perhaps there isn’t even one. MICHEL RAGON I have no more questions, and since I quibbled with you a little about technocracy, I would not like to omit pointing out that, in all of your texts, there is an eulogy to art. Such praise of art is so uncommon and remarkable today, when we hear mostly about the death of art. Also, your definition of the artist-conceptor seems to me to be of major importance. In all of your texts, one acknowledges your intelligence and also what you call that "cold fire," not about you yourself, but in relation to the manner by which you could be accused of working. I’ve always seen you a bit like a "cold fire." This has always fascinated me, both in your music and your architecture. Because of the very fervent admiration I have for you, I consider it a great honor to be here today, not to judge you, but to welcome you. DIALOGUE WITH MICHEL SERRES BERNARD TEYSSÈDRE Now I’d like to give the floor to Michel Serres. MICHEL SERRES I don’t think that space is the image of society only in architecture. For example, today, there is an admirer behind this table and an inventor in front of it; it’s not my fault if this is the University’s image. The University is partial to theses and not to works, creative outputs. Since for once we have a creative output rather than a thesis before us, it is with much admiration that I would like to praise this phenomenon which is so rare within the general waste of intelligence which occurs in institutions. Hence, it is an admirer who will be asking the questions. Later, we will come back to the relationships between mathematics and music. On page 14* of the thesis presentation you proposed the global idea of a general morphology when speaking of the artist-conceptor. What is this general morphology? IANNIS XENAKIS Well, in every domain of human activity, form exists as a sort of froth. I have noticed some figures, some forms, which belong to either the domain of abstract speculation (such as mathematics, logic), or to more concrete speculation (such as physics, treating either atomic or subatomic phenomena), or to geometrical expressions of genetics (such as chemical molecular reactions). Yet these figures, these forms which belong to so many dissimilar domains also have fascinating similarities and diversifications and can enlighten other domains such as artistic activities. MICHEL SERRES When did you write that? Recently? IANNIS XENAKIS Oh! I don’t know, a few years ago. MICHEL SERRES Two questions or subquestions. At the end of the paragraph near the end of the article where you introduce this general morphology, you use the example of the formal evolution of vertebrates. IANNIS XENAKIS Vertebrates, yes, that’s one example. MICHEL SERRES It is a very good example. Someone before Xenakis also had this idea of a general morphology, but in biology. Geoffroy SaintHilaire had the idea of a general layout which could be projected onto the whole of vertebrates and then, more generally, onto the whole of the animal kingdom. But, at present, there is someone else who is dealing with this idea of general morphology in such a way that your idea of morphogenesis coincides with an aspect of science already at work; I mean Reví Thorn. As usual, the musician took the lead. IANNIS XENAKIS All the better! It would also be necessary for Thorn to be fluent in the artistic domain and not only in physics. But I believe that this same idea has a much earlier antecedent, under another form. MICHEL SERRES I believe Geoffroy was the first, wasn’t he? IANNIS XENAKIS I don’t know. I believe this idea can be traced back to antiquity; for example, when the idea of proportion was first applied to architecture on man-made forms. This is a case of local morphology. MICHEL SERRES This local morphology is not the same thing as Xenakis’ idea of general morphology. IANNIS XENAKIS But I think it’s indispensable to create a kind of convergence of all possible forms, from all sides which would presuppose a knowledge of these different sciences. MICHEL SERRES Was there a mathematical framework at the base of your project for this kind of morphology? IANNIS XENAKIS Oh no! Nor at all ... MICHEL SERRES Topology? IANNIS XENAKIS Topology? Topology, from what point of view? Because if topology is the most fundamental science in the mathematical realm ... MICHEL SERRES Certainly, with regard to forms. IANNIS XENAKIS With regard to forms, but not only forms; also, to the philosophical thinking behind mathematics, don’t you think? It’s a problem of continuity, discontinuity, contacts and connectedness. MICHEL SERRES Borders. IANNIS XENAKIS Yes, borders, and consequently, forms. Topology is probably the subadjacent tool, though I think it’s still rather crude at this time. It’s too imperfect to tackle problems as complex as cloud formations or population forms. MICHEL SERRES But the idea of general morphology began precisely when dealing with problems such as cloud formations. As for your first appendix on the list of coincidences between musical and mathematical developments,* I agree with you and I would like only to add to it. When you say that before our era there was something like a comparative analysis between string lengths and pitches, I suppose your were referring to Pythagoras and the Pythagorean school. Today, the conviction that there was no analogy between the first musical intervals and mathematical invention is more and more frequent. It is now thought that it’s more a question of cause and effect, meaning that thanks to music, the idea of a group of natural numbers, as well as fractions and relationships, was developed. If this was the case, music would have been the matrix of mathematical invention. IANNIS XENAKIS Yes, this is an archeological problem. MICHEL SERRES Once again, musical thinking is in the forefront. What do you mean when you say that the fugue is an automaton, that "the fugue is an abstract automaton conceived two centuries before automated science?" I don’t believe this is true. I think they coincided, if science didn’t appear first. IANNIS XENAKIS Oh no, not automated science. Automated science was born in the 20th century. MICHEL SERRES Not automated science, but the construction of automatons. IANNIS XENAKIS That makes a difference, because the use of automatons dates from Alexandrian times. MICHEL SERRES In A Thousand and One Nights, for example, there are automatic fountains, water machines. IANNIS XENAKIS Yes, but A Thousand and One Nights dates from the 12th century, but the use of automatons occurs much earlier than that. The Alexandrian period already knew Heron and the first steam machine. MICHEL SERRES Yes, even Archytus’ dove. IANNIS XENAKIS All of these are concrete inventions. It was music, I believe, which introduced its abstraction. MICHEL SERRES So then, why is the fugue an automaton? IANNIS XENAKIS I think that it corresponds more or less to the definition of a scientific automaton which came about in the twenties thanks to Wiener and cybernetics. It can be summarized in the following manner: An automaton is a network of causes and effects, meaning a temporal chain of events, eventually coupled or multicoupled with certain liberties. An automaton can be closed. It suffices to plug in energy and it works cyclically. It can be relatively open, complete with data entries and external actions, thanks to the help of buttons, for example. Every time new data entries are given, an automaton can produce different results, despite the internal rigor which defines it. MICHEL SERRES Its syntaxes are repetitive but not its performances. IANNIS XENAKIS Yes, its syntaxes are repetitive. Why? Because there is an internal structural rigor. MICHEL SERRES Is the fugue’s syntax always stable? IANNIS XENAKIS The fugue does not constitute such an absolute automaton; it is a relative automaton, especially when compared to the automatons studied by science, which are relatively rigorous in relation to musical ones. When I say musical automaton, I consider that a minuet is also an automaton. The value specific to musical invention is that it was the first to give, to create an abstract automaton meaning that it produced nothing at all except music. MICHEL SERRES Is time in this music reversible or not? IANNIS XENAKIS Well, there, the problem is one of time in general, whereas here, there’s a sort of confusion in the minds of most men, including musicians. The fact that things can be repeated, experiences or phenomena renewed, offers them a kind of security with regard to time, which, in fact, never repeats itself. MICHEL SERRES Sometimes we encounter reversible time. IANNIS XENAKIS Which time is reversible? MICHEL SERRES Planetary movement. IANNIS XENAKIS Time is not reversible; it’s time’s movement which is reversible. Time itself (to my knowledge, it’s a kind of postulate) or the temporal flow never goes backwards. MICHEL SERRES In any case, this is a very recent discovery. IANNIS XENAKIS That time never goes backwards? MICHEL SERRES Absolutely. IANNIS XENAKIS But it’s so natural to think that it doesn’t go backwards. Heraclitus said the same thing, by the way. There could eventually be a reversibility of time if the universe’s movement were pendular meaning that it would contract and dilate. For example, when I talk about time intervals, they are commutative. This is to say that I can take time intervals now or later and commutate them with other time intervals. But the individual instants which make up these time intervals are not reversible, they are absolute, meaning that they belong to time, which means that there is something which escapes us entirely since time runs on. This corresponds to the research Piaget did while experimentally observing the phases of childrens’ apprenticeship in time. MICHEL SERRES What I have in mind is Xenakis and not Piaget. IANNIS XENAKIS Ah! MICHEL SERRES Yes, when you come along with compositions based on stochastics, that touches upon the problem of time. IANNIS XENAKIS Yes. MICHEL SERRES When composing, what relations do you draw between order and disorder? IANNIS XENAKIS Order and disorder? MICHEL SERRES I know what disorder is because I know how you handle that. But what is order, what is your syntax? IANNIS XENAKIS Well, there are several facets. For example, I can say there’s order when there’s symmetry. MICHEL SERRES That’s it; already, with symmetry, we’ve won. IANNIS XENAKIS Yes, there you’ve won, of course. But it’s not a question of winning; it’s a question of vocabulary. MICHEL SERRES No. No, I’ve won, so that means we’re going to come back to the question of time. If there is symmetry there can be reversibility... IANNIS XENAKIS No, because there can be order in non-temporal things. That’s why it’s absolutely indispensable to distinguish between what is in and what is outside of time. For example, I’ll take a group of keys on a piano (an elementary case). I then have intervals which repeat themselves, but they are never repeated in time; they’re there, fixed. The piano keys are on a piano which doesn’t move. MICHEL SERRES Therefore these keys are outside of time? IANNIS XENAKIS Yes, outside of time. MICHEL SERRES The syntax is outside time? IANNIS XENAKIS Yes. MICHEL SERRES I suspected that! IANNIS XENAKIS There, I have symmetries because I have relationships; therefore, I have repetitions. MICHEL SERRES Yes. Then order is outside of time? IANNIS XENAKIS There are some orders which can be outside of time. Now, if I apply this idea to time, I can still obtain these orders, but not in real time, meaning in the temporal flow, because this flow is never reversible. I can obtain them in a fictitious time which is based on memory. MICHEL SERRES Is the piano a recollection? IANNIS XENAKIS Yes, it is a concrete recollection. MICHEL SERRES A concrete recollection. The question then would be the following: Can you obtain an irreversible flow? IANNIS XENAKIS Of course I can, since I’m not a gas, and at the same time I’m possessed by Maxwell’s demon.* MICHEL SERRES Maxwell’s demon puts things in order. IANNIS XENAKIS Maxwell’s demon can reverse things. MICHEL SERRES Now we’re getting there. So, there are reversible structures in music. IANNIS XENAKIS They are reversible outside time.   MICHEL SERRES Would Maxwell’s demon go on outside of time? IANNIS XENAKIS I chose Maxwell’s demon, but this demon doesn’t change the order of the temporal flow itself. You must understand what happens. For example, when a flow of light is said to give lasers, laser light (after having gone through certain conditions and therefore having become organized and orderly), well, it’s as if Maxwell’s demon intervened within. Because otherwise, we would have had just any disorderly light. But this applies exclusively to notions or beings which, by definition, could be reversible. Time itself is not reversible; I insist upon that. MICHEL SERRES Xenakis, if anyone, has proven that. The drift from order or structure to disorder is one of your compositional secrets. Do you agree? IANNIS XENAKIS Yes. MICHEL SERRES The first proposed theorem in physics was about vibrating strings. Isn’t a vibrating string a reversible phenomenon? IANNIS XENAKIS Outside time positions are reversible. MICHEL SERRES What do you call outside-time positions? I don’t understand. IANNIS XENAKIS Spatial intervals, for example, string positions. They are reversible because they belong to space, which is not temporal. MICHEL SERRES Therefore it’s a clock! IANNIS XENAKIS Therefore it’s a clock. MICHEL SERRES In fact, a clock, like a vibrating string, counts time. A vibrating string can be a time index. It’s measurement. IANNIS XENAKIS It’s a time index which is based not on time, but on the reversibility of positions. This is the fundamental idea. As Heraclitus said, no one can live the same instant twice. Someone tried to prove the reversibility of time about 15 years ago using the idea of parity in microphysics (no one has demonstrated this yet) but we don’t have the experimental data ... MICHEL SERRES The kinds of music in question are an attempt to fight against temporal irreversibility? IANNIS XENAKIS If you wish. MICHEL SERRES We’re going to be able to generalize on this topic little by little and move on from technique to composition. Is there a relationship between glissandi and the aforesaid irreversibility? This seems to me to be a very important point. You’ll see why later. IANNIS XENAKIS I don’t know whether the glissando is in direct relation to this or not. MICHEL SERRES You do agree that the glissando is an important element in your composition? IANNIS XENAKIS Yes. MICHEL SERRES Why did you chose the glissando? IANNIS XENAKIS Perhaps it’s an influence from Euclidian geometry. Perhaps because the glissando is precisely a modification of something in time, but imperceptible, meaning that it is continuous but can’t be grasped because man is a discontinuous being. Not only is he discontinuous in his perceptions and judgments, but in everything. Continuity is something which constantly escapes him. It’s a Zenonian problematic or simply a change in itself and it’s a sort of perpetual fight to try to imagine continuous movement in our perceptions and judgments. This is what happened especially in mathematics by the way. The maths first started with the discontinuous only to end up with continuity much later. MICHEL SERRES There are two elements in your work which make me think of irreversibility. The first is the drifting from order to disorder by way of probability functions, and the second is the consistently used glissando element. IANNIS XENAKIS Yes. MICHEL SERRES Then, Xenakis’ music no longer corresponds to the definition of a fight against irreversibility which was stated earlier since you accept irreversibility in these two fundamental techniques. Isn’t your music different than all others specifically in that it has admitted, once and for all, the irreversibility of time? As opposed to any other music. IANNIS XENAKIS I’ll have to get back to that because I don’t believe in the reversibility of time, of real, immediate time, the temporal flow. I think that it’s impossible to make time go backwards. MICHEL SERRES Yes, so it is. IANNIS XENAKIS Therefore, time is irreversible. Judgments which are made in the time flow are, if you please, reversible. As an example, let’s take the most elementary thing there is: durations. A duration is something that can be moved about within time, it is therefore reversible, commutative. A duration always occurs in the same direction as time, of course (it can go against the temporal flow). This is to say that if I want to write, design, or, especially, visually represent time, I would have to put it on an axis, as physicists do, as musicians do (first musicians, and later, physicists). It must be pointed out that musicians with the musical staff were the first to invent a Cartesian representation of this principle. Fine. The temporal flow would be represented by a straight line which, by definition, would be a continuity. I’ll put points on this line: these are instants. The difference between any two points is a concept which stems from comparisons and mysterious judgments I make about the reality of the temporal flow, which I accept a priori. The distance between the two points is what is then identified as a duration. I displace this duration anywhere; therefore, it is reversible. But the temporal flow itself is irreversible. And if I draw an axis on a spatial plane and place pitches on it, on an axis perpendicular to an horizontal time axis, then, to go from a low point to a higher point to the right of it, I can only move in one way: from bottom to top, and from left to right. That’s irreversibility. MICHEL SERRES We have reached the notion of irreversibility which characterizes your music by two technical methods: on the one hand, by the drifting from order to disorder and, on the other hand, by the use of glissandi. What also strikes me, generally speaking, in both your music and your architecture and which is another invariant of your vision of the world, is ruled surfaces, meaning PH, hyperboloides, etc. Why such persistence on ruled surfaces? IANNIS XENAKIS For many reasons, I believe. MICHEL SERRES Be very careful about answering because this is exactly the contrary to what was said earlier. Earlier, there was the drifting toward chance, whereas if we start from this insistence on ruled surfaces, there is a renewal of repetitive structures. IANNIS XENAKIS Yes, this is another kind of preoccupation. It’s a problem of continuity and discontinuity stemming from linear elements. A line is perhaps the most basic element of continuity, of an expression of continuity. MICHEL SERRES Isn’t it merely the result of a framing technique? Because it’s easier to frame off ruled surfaces. IANNIS XENAKIS No, it’s impossible to frame them off since they are S-curves; it would be necessary to ... MICHEL SERRES Yes, it’s possible. Since the surfaces are ruled, you necessarily have frameworks made up of ever-straight planes on a PH or a hyperboloide. IANNIS XENAKIS Yes, but since it’s with S-curves, space is distorted, and the ordinary framework made up of flat planes would adopt S-curves only very imperfectly. If it were necessary to construct a "warped" framework, as for boats for example, it would cost much too much. MICHEL SERRES Let’s get back to ruled surfaces and the situation which they’ve allowed us ... a ruled surface can be developed from straight lines. IANNIS XENAKIS Yes, there’s something absolutely fascinating about a straight line. A ray of sunlight is fascinating in itself. Rays of sunlight can be seen when looked at through clouds. The rays of sun which converge near the ground are, in reality, parallels. A laser’s beam line is something absolute, the line of a mason’s edge is also absolute. The straight line, therefore, exists in nature. But as an intellectual entity, it’s most fascinating from the point of view of speed, direction, and also continuity. From the point of view of continuity, it’s impossible to imagine anything simpler than a straight line. Because once you have a curve, for example, you can imagine the forces which produced it, and there are all sorts of torsions and rich curves, while a straight line is one, without forces, identically repeating itself. Excuse me, I haven’t finished yet with ruled surfaces. Ruled surfaces are developed from straight lines in three dimensions (the glissando being a two-dimensional line ). The straight line enables us to imagine very complex forms with very simple and controllable elements. MICHEL SERRES Minimum of techniques, maximum of realizations ... IANNIS XENAKIS Of results. MICHEL SERRES Yes, all right ... The final question will be the following (I’ll stop here): in the beginning of your book (Formalized Music), you have yet another bone to pick with data processors, but it’s nevertheless necessary to distinguish between data processing and information theory. IANNIS XENAKIS The good guys and the bad guys! MICHEL SERRES Finally, when we speak of disorder, it has to do with thermodynamic disorder, but it also has to do with background noise. Consequently, they are the same thing. Here’s the last question: there are two things concerning Xenakis that I can’t put together. First, there is a sort of fascination for ruled invariants (in other words, ruled surfaces) and then, for syntactical invariants, and following suit, invariance in general; in sum, repetitive syntax. Second, there is a fascination which indicates your thermodynamic preoccupations, for background noise, etc., and the glissandi which are elements of this; in other words, the inverse preoccupation, the preoccupation to "gliss" or slide irreversibly toward disorder, toward background noise. How do you account for this unvarying fascination for syntax and this fascination for this drifting toward disorder? Can music be defined as such? IANNIS XENAKIS No, because disorder is a negation of order (which here means repetition). Disorder, then (in the periodic sense) is reversible, of course. (Something periodic is reversible, but by its own definition). What I mean by this is that what is not temporal by essence is reversible. Beings can position themselves in any order in this domain which is, by definition, outside time. It’s this constant preoccupation with these two poles, with order or disorder, personified by periodicity (he who says periodicity, also says invariant); it’s the whole scale of possible levels which, in my opinion, constitutes a sort of mental category. This is what can be found throughout all of history and philosophy as well as science, and which is one of the subjacent preoccupations in my music. MICHEL SERRES One last corollary question: Starting from noise, can there be order? IANNIS XENAKIS Yes. And then what’s interesting is that we can simulate noises, which is, physically speaking, a pressure variation that never renews itself identically. It can be fabricated either with cathodic tubes or by calculating machines. Yet the listener goes one step beyond. He doesn’t stay at the lower level of the specimen’s microscopically individual event, and he perceives noise as a macroscopically individual whole; in other words, as something possessing a regularity, an order! MICHEL SERRES So, the answer can now be given; it is perfectly general. You know that all the questions which have just been asked revolve around the problem: Can order be established from noise? Well, your music was the first to discover this. IANNIS XENAKIS Thank you so very much. DIALOGUE WITH BERNARD TEYSSÈDRE BERNARD TEYSSÈDRE Well, since the moment has come to conclude this defense and since habit (or protocol) leaves the last words to the jury’s president, please allow me, dear Iannis Xenakis, to express my joy and excitement at seeing you present this thesis. First of all, for personal reasons. I’ll never forget your surprise and even skepticism when I suggested to you a few years ago that you should apply to the U.E.R* for an associate professorship at the Plastic Arts and the Science of Art School, where I was then director. Within this new framework you progressively built up a pedagogical idea which has become your graduate and postgraduate seminars: "Formalization and Programming in the Visual Arts and Music." Neither will I forget your surprise when, in agreement with our mutual friend Olivier Revault d’Allonnes, I suggested that you present a dissertation for a doctorat d’Etat,t bringing together the scores and texts we are discussing today. Here, the personal reasons arouse the same questions of principle which Michel Serres brought up earlier. Like him, I’m pleased that high quality researchers can be granted the state doctorate, regardless of the fact that their career and training have nothing "Sorbonne-ish" about them. For a while now, this practice has been accepted in foreign universities, especially in America; nevertheless, in France this is brand new. I remember the incredulity I encountered, even in 1969-70, when defending the mere idea that a musician or sculptor could have his place next to a learned history or philosophy professor at the Sorbonne. The university is not made for artists, they objected. And why not? Since then, it seems to me that they’ve gone straight for it. There are no longer only programs in musicology, filmography, and art history, but also now, music, cinema, and plastic art programs are in effect where theory and practice are combined. Artistic application is no longer practiced for the sole benefit of reflective theorization, as it has been even up until the recent past. This type of discourse is often relegated to history’s hegemony. But, in less than five years, university programs, complete with artistic subjects, have been put into use, from the first cycle to the various diplomas, to masters’ degrees, from IPES to the CAPES and to the "agrégation." * Personalities such as Michel Butor, Maurice Lemaitre, Georges Charbonnier, and Frank Popper today have their state doctorates. A fresco painter such as Jose Balmes or a theatre man such as Jacques Clancy teach their art as associate conference masters, and this present defense registers its fullest meaning from this perspective. Your dissertation, dear Xenakis, is a real dissertation, in the most sanctified meaning of the word-almost in its medieval sense. It is so in that first, it avoids the snag of other defenses or " file -dissertations": it is by no means a haphazard collection of incongruous works. On the contrary, it distinguishes itself by a profound unity since the presented texts, along with their accompanying scores, converge around the same fundamental theme and this theme has been the basis of much of today’s debate: the alloys (and not a "marriage") between the arts and sciences. Would this not more likely refer to one certain conception of art? And one certain conception of science? I admit that this is what I believe. But it’s specifically because of this that your dissertation is really a dissertation, in a second way: it is not an erudite research report on some little point (as is often the case), but an original theory, and consequently arguable and even contestable - once again as during the Middle Ages when the "doctors" confronted each other around Duns Scotus or William of Occam. I would like to examine this one point, however briefly, so as not to delay the conclusion of this already rather long session. Using only one of the written works in your file, I would like to bring into light the other side of the latent hypotheses which subtend your dissertation. These form the coherence and define the philosophical option of your work: an entirely personal option, validated by this same coherence. Perhaps I’m mistaken, Xenakis, but it seems to me that yours is one option among others which could be different, if not contradictory, though neither more nor less valid than others. I’m going to raise a few objections to that which underlies (or what seems to me to underlie) the perhaps unperceived or unacknowledged group of underlying hypotheses which are the basis of your dissertation. I specify ahead of time that I will not handle all the objections (at least in their extreme form). Nevertheless, it seems to me that one of the rules of the game is to play the "devil’s advocate," so as to instigate your reactions, and your counterattack with the hope that you will be able to clarify your own point of view. And then to proceed to the extremities to better appreciate how and how much your point of view is your own. This will help me to dissipate the uneasiness I am weak enough to feel when confronted by any aesthetic theory which claims to be universally valid and will also help me to eliminate the hints of "cultural imperialism". I’d be likely to suspect from it. I’ll say this on the subject: I found a major advantage in your work Formalized Music which would be comparable to axiomatics in Hilber’s or Paeno’s meaning, and that is to found music on the basis of certain generalities through the annexing of the restrictive constraints which would determine them so that specific types of music (not all) could be deduced as partial ensembles. These constraints (which are, in other words, keys, modes, series, etc.) would determine the sonic universe which would then distinguish the fields of musical possibilities within. I did say universe and not "pluriverse." And I want to say that Formalized Music (though perhaps Xenakis’ thinking has evolved since) seems to me to reason as if there were hope of an all-encompasing theory, covering the group of thinkable realms without a gap, as if Gödel’s theorem could be surpassed and be more than merely shaped by procedural stratagems. I sense that Xenakis has opted in favor of a "system of the universe," and because of this, his thesis seems to be even more fundamental since it is really a thesis, agreeing with the conditions which have generated a large number of musical works. Nevertheless, your thesis allows for other theses to subsist alongside yours which would be capable of serving as the basis for other musical works. Leaving this general level, I’ll get to more specific questions and attempt to show that Xenakis’ theory entails at least two postulates and several options, some being methodological while others are clearly subjective. The first postulate will be this: in Formalized Music, history and culture seem to be relegated to the background, leaving priority to research on logico-mathematical invariants. Perhaps Xenakis’ musical theory would find certain conceptual equivalents in this regard to serial, or systematic or programmed painting. (For example, an inventory or "trick list" of Vasarely’s optical effects.) However, I wonder if the hypothesis of stochastic distribution can really be defended when it entails absolute probabilistic equivalences at their starting points and in the course of their trajectories. On the contrary, the anatomy and embryology of higher vertebrates could show that the code of genetic determinations isn’t all that "enriched" during the course of their evolution ("enriched" in the sense of "enriching" an information bank.) They could also show that the nervous system’s development (especially the cortical centers) unveils itself mostly by a proliferation of neurons and by the relative instability of their synoptic connections. In other words, the most archaic mammals known to man (or the inventing of pre-established regulations) wouldn’t be increased at all. It would even be significantly decreased if it’s referred back to the multiplicity of networks, of possible connections. A sort of "aleatoric trailblazing" results, a guided aleatory: not because there is a lack of determinants, but because this inventory is governed by determinants other than genetic ones; in other words, because the role of apprenticeship tends to progressively deter pure and simple maturation. This apprenticeship is, moreover, conditioned by a context which could be qualified as being historical (in the most general sense of the word), starting from the intrauterine stage and leading up to family life and scholastic situations, up to the sociocultural environment. You wonder what I’m getting at? This: the inference between pre-established elements, including formalizable invariants (those which Xenakis formalizes) on the one hand" and, on the other hand, a bundle of cultural and historical accidents which an individual man could not dismiss. It seems to me that this must be taken into account. In relation to the genetic inventory, or "chance" series, in the most banal sense (that of Counot), this inference constituted an intersection of independent causal chains. And what makes this chance series a continuous guided chain instead of an erratic dispersion is that it is permanently stowed away in a relatively constant sociocultural con text. I wonder whether it is possible under these conditions to maintain (as Xenakis does many times in his book) the fiction about amnesia? Is it advantageous to consider man as being "amnesiac," to pinpoint him the instant his perceptions occur, by abstracting his individual past? Or, on the contrary, is it not necessary to admit that a purely stochastic distribution is nearly excluded from the musical realm since there would be no probability equivalences either at the starting points or in the trajectories? In other words, is it possible to isolate the logico-mathematical invariants, as if a musical experience did not integrate determinants of different orders such as sociocultural or historical ones? Is my question clear, Xenakis? IANNIS XENAKIS Perhaps, I don’t know. [puudub] BERNARD TEYSSÈDRE What I mean to say is that the sociocultural conditioning wouldn’t be only an extension of something which itself would be added on to the probabilities that are considered as being initially equiprobable, but on the contrary, the networks themselves of relationships would constitute it. And all this in such a manner that we could never start from a sort of absolute "no man’s land," from a "clean sweep," but on the contrary, from a highly stratified terrain. IANNIS XENAKIS Yes, but this "highly stratified" is not at all proven. It is precisely one of the fundamental subjects of research in all domains. In biology or genetics, for example, very little is known about the heredity of more or less elaborated and complex mental structures. It’s a hereditary fact which establishes that we are not plants or minerals. We are men who, moreover, resemble one another, with eyes, with organs. But the one place where we have no idea what’s going on is there, in our brain’s constitution, since we don’t know heredity’s role in what we could call "categories." We don’t know how the principle of causality was born or why it was born. Moreover, this principle is equivalent to referential reasoning. Furthermore, the meaning we give to time, to the temporal flow depends not only on experience but also on our brain’s concrete constructions. We don’t know when these constructions occur: is it after birth, or well before that, meaning thousands or millions of years ago. No one can decide. On the contrary, what we can eventually say is that there is indeed a nondetermined part within our mental structure. Why can we say that? Well, because there are so many cultures, so many approaches to reality, so many reactions before an objective universe (if such a thing exists!) This plurality enables greater freedom on the higher planes. Therefore, in this case, can’t we change things which, at the moment, seem immutable and universal? Let’s imagine the flow of time as we conceive it, including its orderly structure which is subjacent to our knowledge and which is part of our daily life, be we atomic physicists or musicians. Is this concept of the time-flow absolute or could it be? In order to define these types of things and also to eliminate all the dust of education or sociocultural tradition, it’s necessary to assume, to make perhaps rather extreme hypotheses from time to time, such as amnesia, for example. It’s simply a work tool. BERNARD TEYSSÈDRE I was very surprised, Xenakis, when you referred to Greek music as being the nutritive humus from which our Western tradition has developed. I wonder if it isn’t also the humus on and from which Xenakis’ theory of a universal music has been founded. And I dare say, what Olivier Messiaen said about the possibilities of radically different structures from these does not contradict me. I’ll remind you of my argument: given that genetic coding is extremely insufficient in relation to the multiplicity of synaptic connections between neurons, the trajectories are blazed in the course of their individual development, with these developments themselves being conditioned in large part by the sociocultural context. Why did a chord based on thirds, which was considered "dissonant" in the Middle Ages, become "consonant" in Bach’s or Rameau’s time, to the point that a major or minor third defined a "perfect chord" as being major or minor? My conclusion is that the postulate of initial equivalency between what is probable isn’t, in fact, admissible, and to relegate the acculturalization or history of music to a secondary role merely to link it to logico-mathematical invariants, could be a very dangerous hypothesis. I’m not at all sure that we can just eliminate musical culture, not even with regards to sonic perception. IANNIS XENAKIS Well, if we climb up a ladder and look at history from a certain height, we’ll see that a lot of things have happened. In order to see more clearly, it would be necessary to eliminate precisely these socio-cultural acquisitions. Once this is done, we could eventually find things which are independent from those, which are acquired or permanent, meaning time as well as space invariants. And that’s why we suddenly find a "personality" which seems to be universal in the case of scales, which changes only a bit throughout the world. This "personality" is the interval of a fourth. As if it were by chance, Aristoxenus starts his musical theory with this; he speaks of the perfect fourth. Nevertheless, he does not mathematically define this interval, because he does not reason as a Pythagorean, even though he knows mathematics and Pythagorism. But he does consider the perfect fourth as being the basic interval, and he begins his treatise with it. Moreover, we encounter the perfect fourth in all cultures throughout the world. On a higher level, it corresponds to a sort of musical invariant. But in order to understand, it’s necessary to make a clean sweep of all the epiphenomena, of all the specific colors of this or that musical culture, when we say that it’s a sad, minor tonality or that it’s in major. Obviously, this example is rather trivial. It’s exactly the same on another level: when we say that music is melodic, must be melodic, must be polyphonic, and we can no longer conceive of any other music outside of this context. This also is a prejudice which comes to us from our socio-cultural conceptions. What must we do in order to get rid of all of that, in order to establish fundamental thinking? The mathematicians and logicians of the nineteenth century showed us one way when they got rid of verbal mathematics and replaced it with symbolic mathematics. And it is in this manner that I have tried to see more clearly. BERNARD TEYSSÈDRE That’s what I said at the beginning; and that certainly is one sort of axiomatic open to us. Excuse me, I’m obliged to move on quickly because we don’t have much time left and I still have a lot of questions to ask you. I’d like to leave this subject and go on to another point, another of your postulates, in my opinion: the one which could be called the principle of "composed dispersion." When reading Formalized Music we could think that you allow for a precedence (at least a methodological one) of elements let’s say of sounds or particles or clouds of particles or logical classes, or even organigramic cases, etc. And I wonder in what measure (and this is a question I’m asking you) is this precedence compatible with the most simple of data perceptions, meaning those on which Gestalt theory was based nearly a century ago. In your book, this is generally translated as follows: once a certain number of sound constituents have been isolated and considered as basic elements, these fundamental elements are then placed in relation to the experience of listening to music (following a model which would apply Fechner’s law, using the sensation variant as the logarithm of sensory excitation). How is this compatible with Von Ehrenfels’ already-dated reflections on the very banal transposition experiment? It’s possible that with a musical phrase which is first heard in C major and then, I don’t know, in F# minor, there would be no elements of physics shared between the two groups. Nevertheless, both are perceived as being the "same musical phrase," merely transposed in two different keys. How can it be explained that they are heard as being at least analogous if not identical? Instead of using elements (particles or clouds of particles or logical classes, etc.) as starting points, couldn’t we imagine the relationships themselves as coming first and not the two extremities of these relationships? Isn’t this what would suggest the use of glissandi in your own music? Your use of the glissando would’ almost be in contradiction to what your theory expounds: you would no longer use elements as starting points, but rather their relationships, their intervals, and in relation to one of these intervals, we could say that the sound particles would play merely a secondary role as "trail-markers" between the two extreme points of a glissando, while the glissando itself would be the only perceived reality? IANNIS XENAKIS Yes, that’s a very good question, because it’s true that in the musical domain the words "composition" and "composer" mean to put things together; therefore pre-existing things which are already defined in a certain manner. BERNARD TEYSSÈDRE That presupposes a priority for analysis over synthesis. In any case, the way in which the "elements" are first introduced seems contradictory to the more structural aspect of the method of presentation itself. IANNIS XENAKIS It doesn’t necessarily presuppose that, but it presupposes something else. It presupposes a concrete universe where the composer comes and imposes relationships, structures, constructions and architectures. But this is true only to a certain point, because there is a whole area of music as well as of perception which is absolutely unknown. A large part of Formalized Music is, in fact, based on this organization of given sound objects, but another part (the last chapter) starts from a sort of global perception. If I say global perception, I mean where there are no molecules (objects which the composer puts together to create more or less evolved organisms) but a magma of possible punctual states (discontinuous pressure values), within which he is capable of coming up with forms following criteria he himself must invent. The last chapter marks another starting point, entirely in opposition to what you just said. If I’ve been eager to speak here about discontinuous things, it’s because when we speak of pressure samples, we’re speaking of discontinuous things. Finally, when we speak of music history, either past or present, this is equally the easiest, most direct, and richest approach possible. We are more familiar, more at ease with discontinuous rather than continuous things when dealing with perceptions as well as judgments, but this in no way excludes undefined or undefinable things. BERNARD TEYSSÈDRE I was in no way refering to what is undefined. I said that a melody could be transposed in such a manner that no two of its physical elements remain the same; but nevertheless, it can be recognized as the "same melody." The point of view which comes from the consideration of sonic form as a meaningful totality is entirely different from the point of view which starts with sound particles, or clouds of particles before establishing a relationship between these clouds. To say that the contrary is true would imply confounding perception with sensory stimuli. IANNIS XENAKIS Fine, I don’t see ... BERNARD TEYSSÈDRE Not one of the sensory stimuli would remain the same, and yet they would be perceived in the same manner? IANNIS XENAKIS Yes, but be careful. There you are speaking about different levels of perception. When you say the notes aren’t the same, all right. There are not only notes though in a melody; there are relationships between the notes-intervals, etc. BERNARD TEYSSÈDRE That’s precisely what I said: that from a sort of "molecular" point of view, we can oppose a "relational" point of view, according to which these infamous molecules would merely be the extreme points of the relationships. IANNIS XENAKIS Naturally! In this book, Formalized Music, I’m dealing with relationships between levels (both in the plural), especially with the higher levels, over and above the elements! BERNARD TEYSSÈDRE So be it. Let’s move on to another question. It has a little bit to do with what was said earlier about the notion of style. I wonder if in your theoretical and compositional works, priority isn’t given to the notion of saturation: in other words, a kind of option or subjective taste for dense, full, and not rarefied sonic spaces. It is striking to read on p. 56 of Formalized Music: "The ergodic principle states that the capricious effect of an operation that depends on chance is regularized more and more as the operation is repeated." However, it’s just possible that the choice itself of the ergodic principle is of a stylistic nature. It’s possible that it is a subjective option, or one of personal taste, which motivates Xenakis to choose saturated rather than rarefied sonic spaces, to choose large numbers over rare individuals, as Leibnitz would say, those whose definition would imply infinite analysis. It is without a doubt that the will to control prevails over the saturation of sonic spaces out of an economical principle (but this economic principle is also a claim for power). We could very well imagine the inverse option which would distinguish a preference for rare individuals from uncontrollable chance. In summary, John Cage’s or Marietan’s choice are the polar opposite to Xenakis’ choices. IANNIS XENAKIS I think you are confusing many things. Excuse me for telling you that. To get back to ergodism: the definition given there is a mathematical one; I was not the one to say it. BERNARD TEYSSÈDRE I know that well enough. IANNIS XENAKIS I found it in a book by a very important French mathematician who wrote about Markov chains in the forties, Maurice Frechet. He gives this definition of ergodic processes, of ergodicity. But this is absolutely restricted to this one aspect of my work. On the other hand, when we speak of chance,’ we must be extremely careful. BERNARD TEYSSÈDRE More than the simple fact of using probabilistic calculations as a principle, a repeated choice in favor of large numbers seems to me to imply a preference for control over plentitudes rather than over rare events, which, in themselves, would not be controllable. IANNIS XENAKIS But I did a whole study around rare events and rarification in Achorripis* and other compositions. It’s a question of density, and density is a notion which I treat at length and in depth in Formalized Music. BERNARD TEYSSÈDRE Doesn’t your music favor fortissimo and pianissimo for example rather than any impalpable nuances; vast sonic masses rather than voids or silence; an intense emotional charge rather than meditative destitution? IANNIS XENAKIS It’s true that I haven’t written a lot of rarefied music. BERNARD TEYSSÈDRE No, not a lot of rarefied music. Nor music which would try to capture individual events, in the way that Olivier Messiaen has used bird song or in the way that John Cage used the fortuitous encounter of seven radios, each broadcasting a different program. In these types of music, there is room for rare encounters instead of finding a relentless search, as there seems to me to be in this book Formalized Music, for highly probable encounters (even if you were to deviate from this later). IANNIS XENAKIS It’s much more complex than that. First of all, "highly probable" has no meaning except in relation to probability distributions which would be known a priori, and concerning certain groups of well-defined events. The notion of fortuity or the unpredictable is fundamental to probability. What is highly probable does not contradict what is highly fortuituous and becomes predictable and is no longer fortuituous not only stochastically, but eventually statistically too. Consequently, whenever an event occurs within a given group, everything happens as if we were in front of a phenomenon created by chance. It occurs unexpectedly and is therefore "rare" in the strictest meaning of periodicity. On the other hand, we can turn on several radios at once, but as soon as they are turned on, we find ourselves in front of a "fait accompli" and therefore a determinacy void of chance. In this case, everything happens as if we were in front of a globally predictable phenomenon even though it is locally fortuituous. This then would constitute the definition of what is highly probable. In some way, the two approaches are equivalent. The appreciable difference is that, in my case, I tried to create not only chains of events but also the events themselves in a manner which would be much more faithful and homogeneous to the basic idea of unpredictability and fortuity. On the other hand, the notion of rarity is relative to an ensemble of possible states and their recurrences. Many or few recurrences of a given event, are decoded in time by the notion of density (of rarity). Moreover, the second chapter of Formalized Music begins with rare events and their treatment. BERNARD TEYSSÈDRE You deal with them in order to dismiss them ... IANNIS XENAKIS No, not at all ... BERNARD TEYSSÈDRE ... or to relegate them to a secondary order of importance ... IANNIS XENAKIS No, because from the technical point of view, I begin with Poisson’s formula which specifically deals with rare events and which I also integrate into my compositions. All this said and done, rare events are rare only in relation to the temporal scale. And there are times when rare events can be considered dense and frequent. In fact, if the chosen temporal unit is small enough, the events within a given music work can seem aggregated in a rarified manner. On the other hand, if the chosen temporal unit is sufficiently large, the same events will seem denser or closer together although they are distributed in the same manner and will create the same fortuitous encounters. Qualitatively speaking therefore, it is the same phenomenon. It’s like when you place a Geiger counter close to a radioactive source, or when you move it away: the probability distribution is the same, independent of the distance (the temporal unit). It’s the same phenomenon. It’s the same law. BERNARD TEYSSÈDRE Yes, but will you pardon me if I try to get back to what Michel Serres said earlier when he posed the problem, but I must repeat that we could also conceive of a different type of musician who would not propose to create order from noise but, on the contrary, would strive to isolate the rare, individual events as such; for example, John Cage or Marietan. Not to encourage anyone, rare event to rise out of disorder, but on the contrary, to accept it as an individual event for which an exhaustive analysis would be impossible because infinite. IANNIS XENAKIS That’s what I’m trying to say. BERNARD TEYSSÈDRE But how is it that this Xenakis here, and not another, was able to manage this? Once again, we find ourselves back to the problem of personal style which we already mentioned ... IANNIS XENAKIS Consider rare events within an ensemble of other events, and apply a temporal relationship in order to obtain rarification. Certainly you’ll find the rare events isolated. But if you conceive of the ensemble of events globally, the rare events will appear on a background within a much more complex environment. Logically, it would be a question of surrounding a sonic event with rests to the left, to the right; but this is not fundamental. It’s a question of scale which corresponds to the degree of attention you pay to this event, therefore, to the degree of prominence you choose to give it and which is a decision based on aesthetic order. But neither in the universe nor in time is there anything unique, "either in nature" or in human thinking. This means that, on the contrary, an event’s periodicity (in the broadest sense) and its recurrence unto itself or within its environment is absolutely natural and even unthinkable otherwise. BERNARD TEYSSÈDRE Surely, yet a certain restriction of the global field has intervened in your initial choice of elements, which means that the chosen matrix no longer contains even the totality of possibilities but only because it is initially agreed upon that there will be, for example, an orchestra. These preliminary choices no longer let us incorporate some listener’s cough or a flying buzzing around the hall into the realm of possible sounds and thereby integrating the fly or the cough as part of the music, as John Cage would. This brings up another musical principle, different than yours. IANNIS XENAKIS Fine, and I’ll tell you why. Very simply because we all have fortuitous sounds in our daily life. They are completely banal and boring. I’m not interested in reproducing banalities. BERNARD TEYSSÈDRE I completely agree with you; what I want to point out is that, in your case, it’s a question of aesthetic choice. OLIVIER REVAULT D’ALLONNES I believe, nevertheless, that in Formalized Music, on page 114, there is an element of a potential answer which tends to agree with what TEYSSÈDRE said. It has to do with musical strategy and Duel.* On page 113-14 you list the six events which can occur; a cloud of particles, sustained strings, percussions, etc., and silence is the sixth and last event. I’ll draw no conclusions for the time being. Then, on pages 114 (in the Table of Evaluations) and p. 115 (in Matrix M2) you mention only five events, the first five, which are the sonic events. Silence has disappeared and doesn’t reappear again until the bottom of the page (Matrix M2, p. 115). Why then have you silently (if I may say) passed over this silence only to reinject it in the second table (M2)? You say, "The introduction of the move of silence (VI) modifies (M1), and matrix (M2) results." (p. 115). And now, I’m referring to the bottom of page 114 in Formalized Music where the different events can be evaluated as "good", “good+," etc. and where silence receives a "passing grade" or “no grade" whatsoever. In summary, you don’t like silence. IANNIS XENAKIS Silence is banal. BERNARD TEYSSÈDRE I don’t want to go beyond the scope of this debate. It’s clear that M. Revault d’ Allonnes does not contest the fecundity of the perspectives opened by IANNIS Xenakis. And certainly, neither do!. For my part, what I do fear a bit is that these fertile perspectives could appear imperialistic when seen from the outside. I want to say that a very personal musical theory subtending a very personal musical research could only know how to break down other different, not to mention opposing musical theories. In the same way, computer programming of serial paintings does not render the most accidental painting obsolete, neither a Michaux "informal" print or a Pollack "action painting." Painting-painting, in the sense of support/surface did not relegate non-painting (in the Dadaist meaning) to the margin. I’d almost say that if metaphysics is an experiment around one idea, as Heidegger claims, then this cluster of doctrines which we have just been discussing constitutes more of a musical metaphysics than a musical science. From this side of his scientism, Iannis Xenakis takes a certain aim at science. The presented corpus can be as scientific as we please, but the subjacent goal of this corpus is not from the same category as the corpus itself, and it’s perhaps here that the personal coefficient this subjective question of style which we have debated, intervenes. It seems to me that choice criteria come into play: choices which subtend this thesis and which, henceforth, this same thesis holds as a certain number of percipients at its secret foundation. I would certainly consider Xenakis’ theoretical writings in the same manner as Alberti’s treatise, as a sort of "legitimate construction", "legitimate" provided that it does not become normative and that it accepts other methods of construction to subsist along side and against it, and that these will be considered just as legitimate. Of course, before being able to say that, it would have been necessary to develop other themes. I didn’t because of lack of time. Briefly, however, I would have liked to discuss problems concerning the relationship between in-time and outside-time. This seems to me to throw a certain philosophy of time into question, a conception which would oscillate between the Aristotelian idea of time as movement’s number on the one hand, and on the other, the notion (different, without a doubt), of time as an event’s fourth dimension. In no way would this involve unveiling, once again, the old Bergsonian paradox: time versus duration. What is in question is time which unravels in a linear, orderly manner; time which belongs to the same system of thought as Leibniz’ Monad (unravelling from a mathematical function), or to Hegel’s concept of the sphere which is always-already-there from within-itself, unravelling itself for itself in a methodical cycle. This concept of time is that of the western world, that of Mother Greece, where time drew first from one then from the other of its two sides: logic and rhetoric. According to such a conception, music is thinkable, is thought of as "discourse." To transpose a phrase of Barbaud, who affirmed his being on the look-out for "non-Beethovian music," I would say that, in agreement first with Greek and then with western tradition, Xenakis proposes an axiom of generalized Beethovian music. Is this the only possible music? I evoked Barbaud, but couldn’t we also evoke the Japanese Gagaku, the all-already-together, the irradiation of the same-around-the-same, all instead of the logico-rhetorical chain which is western musical "discourse," this passage from the same to the same’s other? And, going back to my original point, once we see that we could hold our own within the western "discourse," how can we reconcile these two extremes points of its pendular oscillation: sometimes time as an "event’s fourth dimension," and sometimes time as "movement’s number"? In this second case, movement would come first, and far from being one of the coordinates in series of events, would time merely enumerate the series? IANNIS XENAKIS I believe we spoke of that earlier; it’s metrics. There is the temporal flow, which is an immediate given, and then there is metrics, which is a construction man makes upon time. And we can’t avoid this. Whether you are a musician or a physicist, you have to cross the same bridge. I’ll answer you on another point: in no way do I exclude other musical approaches and I really wish you wouldn’t accuse me of being an imperialist for what I have done. BERNARD TEYSSÈDRES No, no. Xenakis is not at all an imperialist. It is even possible that behind his highly scientific approach. Xenakis remains a profound humanist while he works at his music: he allows a personal style to shine through, the artist’s "Me." His choices are well made, and his music is excellent. These choices though, are based on what, (aside from science) if not idiosyncratic choices made by a powerful personality, rich in initiatives? A sub-Xenakis who would apply Xenakis’ science, without having Xenakis’ personality, could never musically produce more than sub-Xenakis. Don’t these choices, so well-made, allow an irrational or unfounded part to subsist? To take an example which clearly illustrates the distance between two personalities, both with great breadth: when Barbaud resorts to the computer, it’s the program itself which is the musical work. We can hear a quantity of sonic versions stemming from the same program, without anyone of these versions being preferable to another since the work exists on the other side of its audible variants. On the other hand, it seems to me that Xenakis’ ear would not judge all of the versions as being equal; he would find a certain number of "preferable" versions, and scores would then preserve those whose sonic effect would have been "preferred." Isn’t this (with the exception of the Polytopes) often the case? IANNIS XENAKIS But this is my right, my privilege. It’s my task to prefer one thing over another. BERNARD TEYSSÈDRE Undoubtedly, since this is how your personality is determined. However, your maxim is not at all obvious; even at the risk of repeating myself, Barbaud doesn’t have preferences. He composes his program and any result is equal to all the others. Xenakis-and it’s his right-has his preferences. IANNIS XENAKIS But that’s natural. It’s absolutely normal. BERNARD TEYSSÈDRE Yours will be the last word. The jury will now retire in order to deliberate. (After a brief deliberation, the jury came back and its Chairman announced that the title of Doctor of Letters and Human Sciences had been awarded with "Very Honorable" mention to Iannis Xenakis.) POSTFACE Mathematics, in Xenakis’ music, plays an essential role as a philosophical catalyst, as a tool for the formal direction of sound or visual structures. Xenakis has also used computers in the composition of some if his scores. This musician who is also an architect, this man of science who is also a philosopher, has chosen the topic of "alloys" between the arts and sciences for his doctoral dissertation. Here we are publishing his defense of his dissertation complete with the jury’s questions and interventions. It is not surprising that Olivier Messiaen has treated aspects of musical composition; Michel Ragon, aspects of architecture; and Michel Serres, aspects of mathematics and science. Summoned to explain himself and his music, Xenakis demonstrates that his culture is both philosophical and scientific, which is, as we all know, exceptional. Thus, we will become better acquainted with the man, about whom Antoine Golea has written "Xenakis is perhaps the most engaging, the most poignant and also, the most provocative figure of twentieth century music." Let us also quote Claude Levi-Strauss who, when questioned on Xenakis by the Quinzaine Litteraire, responded, "I am very sensitive to his writings; I find them scholarly, intelligent, and subtle."

Kallastu tõlge eesti keelde KUNSTID / TEADUSED: SULAM Iannis Xenakise väitekirja kaitsmine Scripta Musicalia KUNSTID / TEADUSED: SULAM Iannis Xenakise väitekirja kaitsmine Komisjoni liikmed: Olivier Messiaen Michel Ragon Olivier Revault d’ Allonnes Michel Serres Bernard Teyssèdre Scripta Musicalia Tõlgitud väljaannetest ARTS/SCIENCES.ALLIAGES par Iannis XENAKIS avec la collaboration d’Olivier Messiaen, Michel Ragon, Olivier Revault d’Allonnes, Michel Serres, Bernard Teyssèdre Collection «Synthèses contemporaines», dirigée par Michel Ragon © Casterman 1979 ISBN 2-203-23170-X Imprimé en Belgique par Casterman, s.a., Tournai, août 1979. N° Impr. 4126. N° Édit. 6112. Dépôt légal 4" trimestre 1979; D. 197910053/105. ARTS/SCIENCES :ALLOYS The Thesis Defense of Iannis Xenakis Before Olivier Messiaen, Michel Ragon, Olivier Revault d’ Allonnes, Michel Serres and Bernard Teyssèdre Translated by Sharon Kanach AESTHETICS IN MUSIC No.2 Pendragon Press New York, N.Y. © 1985 Pendragon Press New York ISBN 0-918728-22-3 Tõlge eesti keelde Tõlkija Andrus Kallastu Vastutav toimetaja Maris Valk-Falk Konsultandid Mati Abel, ... Scripta Musicalia. Tallinn Tõlke valmimist on toetanud Eesti Kultuurkapital SISUKORD Autori eessõna Tõlkija Sharon E. Kanachi eessõna Märkus Illustratsioonide nimekiri Iannis Xenakise sissejuhatav sõnavõtt Dialoog Olivier Revault d’ d’Allonnesiga Dialoog Olivier Messiaeniga Dialoog Michel Ragoniga Dialoog Michel Serresiga Dialoog Bernard Teyssèdrega Lisad I Muusika ja matemaatika arengu seoseid II Sõelateooria III Uued ettepanekud heli mikrostruktuuris IV Iannis Xenakise teoste nimekiri V Bibliograafia Järelsõna Autori eessõna ingliskeelsele väljaandele Prantsusmaal on võimalik omandada riiklik doktorikraad "toimiku" põhjal, mis koosneb eelnevalt avaldatud teoreetilistest töödest ja loomingust. Väitekiri kaitstakse komisjoni ees, mille mitte tingimata akadeemilistest isikutest liikmed määrab doktoritööd juhendanud ülikool. Kui kõik komisjoni liikmed on nõus, toimub kandidaadi ja komisjoni viietunnine väitlus. Kaitsmise lõpuks otsustab komisjon, kas omistada kraad ning kui, siis milline. See raamat on tõlge minu toimiku materjalide kaitsmisest, mis toimus Sorbonne’is 1976. aastal. Olen väga uhke võimaluse üle väidelda selle väljaande kaante vahel olevates küsimustes nii väljapaistvas seltskonnas. Mõned neist küsimustest on mind köitnud noorusest peale ning mulle teeb au väidelda komisjoniliikmetega, kellest igaüks omal alal kuulub prantsuse vaimsesse avangardi. Imetlen noore helilooja Sharon Kanachi sitkust, julgust ja teadmisi selle raamatu tõlkimisel ning ameerika kirjastuse Pendragon Pressi leidmisel, millel jätkus tahtmist avaldada tööd, mis ei tõotanud ärilist edu. Oma noorusliku süütuse ja armastusega samade teemade vastu võitles Sharon väljaandmisprobleemidega suuremas osas omal jõul. Tahan väljendada oma tänu Sharonile ja Robert Kesslerile Pendragon Pressist. Iannis Xenakis Tõlkija eessõna ingliskeelsele väljaandele Tekst "Kunstid/Teadused.Sulam" on Iannis Xenakise kunstiteaduste doktori (doctorat d’Etat) kraadi taotlemiseks Sorbonne’is 1976. aasta kevadel toimunud kaitsmise lindistuse stenogramm. Tõlkides olen püüdnud kirjapandut edasi anda nii kõnelähedaselt kui võimalik, tagades samas loogilise lauseehituse. Prantsuse ja inglise väljendid on üpris erinevad. Püüdsin neid säilitada ka kirjalikus väljenduses suupärastena ja mitte tõlkida tõlkena per se. Kõigepealt kuulub minu tänu Iannis Xenakisele endale, kes soovitas mulle see tekst tõlkida. Temapoolne julgustamine, abi ja üksikasjalik tähelepanu eriti projekti ajal oli väärtuslik ja väga hinnaline. Tänan Cornelia Coylerit CEMAMu’st abi eest mulle oluliste materjalide kättesaadavaks tegemisel. Sügav tänu Robert Pépinile ta kannatlikkuse, terava silma ja kõrva ning tõlkimiskogemuse eest, samuti sõpruse eest, mida ta osutas eri aegadel kogu selle ettevõtmise jooksul. Eriti tänan Robert Kesslerit, kes esimesena mõistis ingliskeelse väljaande vajalikkust, mida praegu ilma temata ei oleks. Lõpuks tahaksin pühendada selle tõlke oma vanematele Elisabeth ja Walter Kanachile. Sharon E. Kanach Märkus See tekst on helisalvestise ümberkirjutus Iannis Xenakise väitekirja kaitsmisest, mis toimus 18. mail 1976 Sorbonne’is, Pariisis. Komisjoni esimeheks oli Bernard Teyssèdre, Pariisi Sorbonne’i Ülikooli esteetikaprofessor ning liikmeteks Olivier Messiaen, Rahvusliku Konservatooriumi kompositisiooniprofessor, Michel Ragon, Rahvusliku Dekoratiivkunstide Kooli professor, Olivier Revault d’Allonnes, Pariisi Sorbonne’i Ülikooli professor (väitekirja juhendaja) ja Michel Serres, Pariisi Sorbonne’i Ülikooli professor. Iannis Xenakise sissejuhatav sõnavõtt Filosoofiline taust Klassikalise, nüüdis-, pop-, rahva, pärimus- ja avangardistliku muusika maailmad näivad olevat kujunenud mõnikord kinniste, mõnikord lõikuvate iseseisvate tervikutena. Neis leidub nii uskumatut mitmekesisust ja rikkalikku uudisloomingut kui ka kivinemist, lagunemist ja hävinemist, kõike seda lakkamatus kujunemises ja muundumises nagu pilved, nii erinevad ja üürikesed. See on seletatav väitega, et muusika on sotsiaalkultuuriline nähtus, mis sõltub ajaloohetkest. Me võime eristada tsivilisatsiooni erinevatest ajajärkudest pärinevaid osiseid, mis on muutumatumad kui teised ning mis määravad ainete tugevuse ja koostise. Samuti võime me eristada aineid, mis ideede vaheldumisest sõltuvalt liiguvad ruumis, arenevad, mida kasutatakse, mis kisuvad endaga kaasa, mis üksteisega kokku põrgates mõjutavad ja hävitavad või vastastikku viljastavad. Aga millest on need algained tehtud? Need algained on seotud inimese järjest usaldusväärsema mõtlemisega. Mõtlemisega, mis kõigil tasanditel otsib, küsib, järeldab, selgitab, vaatab ettepoole. Muusika ja kunstid üldiselt näivad vajavat selle mõtlemise kristalliseerumist, materialiseerumist. Kuigi inimlikult universaalne, on mõtlemine loomulikult erinev individuaalsuse, ande poolest, mis eristab üht indiviidi teisest. Niisiis on anne teatud määrang, mõtlemise jõu ja rikkuse astmestik. Mõtlemine põhineb keha- ning ajurakkude miljardite seoste, reaktsioonide ja energiatransformatsioonide tulemustele või väljendustele. Astrofüüsika mudelit kasutades võime öelda, et mõtlemine on talitusviis, mis hõlmab minimaalses mõõtkavas selliseid rakkude kondensatsioone ja liikumisi nagu võib näha tähtede, planeetide, galaktikate ning galaktiliste massiivide puhul, mis kasvavad või kahanevad külmaks tähtedevaheliseks tolmuks. Vähemalt ühel tasandil on see pilt siiski vastupidine: kondensatsiooni korral, kui see külm tolm muutub kuumaks, vastupidiselt mõtlemisele, mis on aju ja keha kuumade rakkude seoste külm tulemus, "külm tuli". Niisiis värvid, helid, pinnamood on kondensatsioonideks meie sensoorses närvisüsteemis. Selle süsteemi [käega katsutav ja silmaga nähtav] aspekt on tajutav ja mõistetav teadvuse tasandil. Perioodilised õhuvõnkumised ja valguse elektromagnetväli on ligipääsmatud tunnetusele, kuid võrratult hästi (teatavates piirides loomulikult) jälgitavad ning töödeldavad meie meelte ja aju poolt eeldusel, et meeled on aju jätkuks. Teisalt toimuvad ülekanded paljudel tasanditel, alates vahetust tajust kuni võrdlemise, tunnetamise ja otsustustamiseni. Kuidas, miks see kõik nii töötab? See on mõistatus, välja kujunenud juba loomadel ning olnud olemas miljoneid ja miljoneid aastaid. Samas võtkem näide, mis paistab suhteliselt iseenesestmõistetavana, muusika heliread. Need on olnud vähemalt läänemaailmas üks tugevamast tugevamaid kondensatsioone: puhas kvart ja selle tetrakordid ning veelgi varem puhas kvint, mille päritolu jääbki saladuseks. Seejärel oktaav, kui järgime "süsteemide" konstrueerimisel tetrakordide ühendamist, millele tuginesid antiigi heliread — klaveri klaviatuuri valgete klahvide diatooniline helirida on üks selle tulemusi. Edasi võrdtempereeritud kromaatiline helirida ning lõpuks "heliklasside" koosluste read. Nagu näha, on muusika tugevaks kondenseerijaks, võib-olla tugevaimaks kõigist kunstidest. Seetõttu olen koostanud võrdleva tabeli muusika ja matemaatika mõnedest ajaloolistest saavutustest. See tabel näitab ühte teedest, mida muusika on käinud alates oma antiiksetest alglätetest ning seda, kuidas läbi aastatuhandete on säilinud selge side, saavutades olulise tihenemise kahekümnendal sajandil ja tõestades, et võime abstraheerimise kaudu kondenseerida (rohkem kui mõne muu kunsti puhul), kui osa muusika sügavamast loomusest, ei põhine lihtsale valemile. Järelikult näib, on vaja uut muusikutüüpi, uute abstraktsete ja vabade vormide "kunstnik-algataja", kes pürib komplekssuse ja üldistamise suunas kõlalise organisatsiooni paljudel tasanditel. Näiteks Markovi ahelatele või vastastikustes seostes olevate tõenäosusfunktsioonide kompleksidele põhinev vorm, konstruktsioon või organisatsiooni võib üheaegselt siirdada muusika mikro-, meso-, ja makrokompositsiooni mitmetele tasanditele. Seda ideed võib avardada visuaalsetele valdkondadele, näiteks etendustele, milles kasutatakse lasereid ja elektroonilisi välklampe nagu Cluny polütoobis. Nüüd ei takista miski meid ette aimamast kunstide ja teaduste, eriti kunstide ja matemaatika uusi seoseid: kunstid "püstitaksid" teadlikult probleeme, mida matemaatikal tuleks uue teoorialoome abil lahendada. Kunstnik-algataja peaks olema haritud ja loov erinevates valdkondades nagu matemaatikas, loogikas, füüsikas, keemias, bioloogias, geneetikas, paleontoloogias (vormide evolutsiooni tundmiseks), humanitaarteadustes ja ajaloos. Teatud universaal, kes tugineks vormidele, juhinduks vormidest ning püriks vormide ja arhitektuuride suunas. Veelgi enam, on tulnud aeg luua uus teadus "üldisest morfoloogiast", mis käsitleks vorme ja arhitektuure erinevate distsipliinide raames muutumatutest aspektidest ja teisenduste seadustest, mis on mõningatel puhkudel eksisteerinud miljoneid aastaid. Selle uue teaduse taust peaks olema tõeline mõistuse kondensatsioon: abstraktne lähenemine, vaba meelte ja harjumuste eelarvamustest. Näiteks dinosauruste selgroolülide vormide evolutsioon on üks paleontoloogilistest dokumentidest, mis tõestab vormideteaduse vajalikkust. Vaadelgem nüüd baassüsteemi, millele kunst tugineb. Kunst opereerib järeldusmehhanismidega tasandeil, millel liiguvad ka matemaatika, füüsika ja humanitaarteaduste teooriad. Tõepoolest, arvude mängule ja arhitektuuri meetrikale taandatav proportsioonide mäng kirjanduses, muusikas, maalikunstis, teatris, tantsus; jätkuvuse, lähendamise, ajalisuse või ajavälisuse, topoloogilise essentsi mängud – kõik need esinevad tuletamise maastikul selle sõna ranges loogilises tähenduses. Sellel maastikul ja vastastikuses suhtes lükkab ümber või kinnitab eksperimentaalne meetod teaduslikke, sealhulgas matemaatilisi teooriaid. Ka matemaatikas, alates mitte-eukleidilisest geomeetriast ja teoreemidest nagu näiteks Gödeli teoreem, tõestatakse katseliselt, kuid laiemas tähenduses kui teistes teadustes. Eksperimenteerimine loob või murrab teooriaid halastamatult. Ka kunstidega võiks eksperimentaalselt tegelda palju põnevamalt ja komplekssemalt. Kindlasti ei ole ega saa kunagi olema objektiivset kriteeriumi kunstiteose absoluutse tõesuse või igavese kehtivuse määramiseks, nagu ka teaduslik "tõde" ei ole eales lõplik. Ning lisaks kahele, inferentsiaalsele ja eksperimentaalsele, eksisteerib kunst ka kolmandal kujul: vahetu ilmutuse, revelatsioonina, mis ei ole ei inferentsiaalne ega eksperimentaalne. Ilu ilmutus ilmneb vahetult, otse, nii võhikule kui ka asjatundjale. See on kunsti tugevus ning arvatavasti tema üleolek teadustest. Kunstil, mis eksisteerib ühtaegu tuletamise ja katsetamise kahes dimensioonis, on lisaks kolmas ja müstiline dimensioon, mis võimaldab kunstiobjektidel eirata teaduslikku esteetikat, nautides samas tuletamise ja katsetamise hüvesid. Teisalt ei saa kunst eksisteerida ainult ilmutusena. Kõikide ajastute ja tsivilisatsioonide kunstiajalugu näitab, et lisaks juhusele vajab kunst tungivalt organiseerimist, tuletamist ja järeldamist, oma eksperimentaalset tõde. Heites mõningat valgust kunsti olemuse sellisele kolmainsusele, kujutagem ette, et kauges tulevikus kasvavad kunstniku tegutsemisvõimalused, nagu see iial ajaloos pole olnud (seda teed käib inimkond kasvava energiatootmise ja -tarbimise puhul). Tõepoolest puudub põhjus, miks kunst ei võiks teaduse eeskujul tõusta kosmose lõpmatusse ning miks kunst ei võiks kosmilise maastikuarhitektina muuta galaktikate käitumist. See võib paista ja tegelikult ka on utoopilisena, kuid vaid ajutine utoopia aja mõõtmatuse kontekstis. Mis aga ei ole utoopiline, vaid tänapäeval võimalik, on moodustada värviliste laserkiirte helendav ämblikuvõrk nagu hiiglaslik polütoop üle linnade ja maade, kasutades pilvi reflektoriekraanidena ning tehissatelliite reflekteerivate peeglitena, nii et need "võrgud" tõusevad kosmosesse ja ümbritsevad Maad oma fantasmagoorilise, liikuva geomeetriaga, liites Maa ja Kuu valguse hõõgniitidega. Sama kindlalt võiks öötaevasse luua kunstlikke virmalisi, mille liikumisi, vorme ja värve kujundaks kõrgeimates atmosfäärikihtides laserite poolt esile kutsutud elektromagnetväljad. Mis puutub muusikasse, on võimendustehnoloogia veel embrüonaalsel tasemel, liiga vähe arenenud, et saata helisid kosmosesse ja neid seal, äikese kodus, vastu võtta. Aga helide edastamine üle linnade ja maade on juba võimalik tänu rahvuslikele õhurünnakualarmisüsteemikõlarite võrkudele. Piisaks lihtsalt nende kasutamisest. Kui riikide majandusi ei piinaks strateegilised ja militaarsed vajadused - teiste sõnadega päeval, mil armeed kahaneks lihtsateks mitterepressivseteks politseijõududeks, võiks majanduslikult kunst lennata üle meie planeedi ja tõusta kosmosesse. Tehnoloogiliselt on see teostatav täna. Ilmselt peaks planetaarses või kosmilises kunstiloomingus kunstnik, järelikult kunst, olema ühtaegu ratsionaalne (järeldav, inferentsiaalne), tehniline (eksperimentaalne) ja loov (ilmutuslik): kolm asendamatut ja kooskõlas meetodit, mis välistaks saatuslikud ebaõnnestumised, kui võtame arvesse nende projektide mõõtmeid ja suurt veariski. Kunsti valitsev kolmele meetodile põhineva süsteemi suurem keerukus viib järeldusele, et rikkaima ja mahukaimana peaks kunst vääramatult algatama mõtlemise kondensatsioone ja konkretiseerumist, olles seega universaalseks teejuhiks teistele teadustele. Tulemused Nüüdseks enam kui kakskümmend aastat olen ma töötanud nagu mosaiigikunsti käsitööline, täites alguses ebateadlikult, seejärel järjest teadlikumalt seda filosoofilist ruumi mõtlemisega, mis konkretiseerus käegakatsutavateks värvilisteks kildudeks, minu muusikateosteks, arhitektuurseteks ja visuaalseteks töödeks ning tekstideks. Need alguses isoleeritud killud seostusid üksteisega tänu suhetevõrgustikele, sugulusele, aga ka vastuoludele, tekitades järk-järgult lokaalseid koherentseid kujundeid ning seejärel järjest laiemaid välju, kuuludes alguses kokku küsimuste ning hiljem vastuste abil. Matemaatikal kui auditiivse või visuaalne ehitise modelleerija töövahendil oli seejuures põhiroll nii filosoofilise katalüsaatori kui ka autoliberatsiooni hoolauana. Praegu visandan ma ainult põhiküsimuste piirjooni ja neile minu loomingus olevaid vastuseid. Igal juhul ei soovi ma sattuda nende väljatöötamise üksikasjade rägastikku. Pealegi on mitmed küsimused omavahel seotud, luues kokkupuutepunkte nende ühisosaks oleva filosoofilise valdkonnaga. Näiteks: kausaalsus – determinism – pidevus, indeterminism (juhus)– eksistentsiaalsus – determinism jne. Seetõttu võib üks teos (vastus) liituda terve rühma küsimustega. See on otsekui viibimine keset harmooniliste helide poolest rikkaid kõlasid-kui-küsimusi, mille üht või teist harmoonilist heli arvestatakse vastavalt olukorrale põhihelina. Järgnevalt nimetaksin ma mõningaid teoseid väitekirja toimikust. Küsimus -> Vastus eksistentsiaalsus -> ST/lO-l,080262 ajas, väljaspool aega -> Nomos gamma kausaalsus -> ST/10-1, 080262, Nomos gamma, Tourette’i nunnakloostri fassaadid, moodulite korduvus või kordumatus järelduslikkus -> Nomos gamma, ST/10-1, 080262 seotus -> Empreintes (puustruktuurid), Metastaseis (glissandovormid) Philipsi paviljon (kõverpinnad, joonpinnad) kompaktsus -> Metastaseis, Philipsi paviljon, Nomos gamma puhas indeterminism -> ST/IO-l, 080262, vaba stohhastiline süsteem ebapuhas determinism -> Strategie (mänguteooria), Syrmos (Markovi ahelad) puhas determinism -> Nomos gamma (rühmad) identsus [samasus, võrdsus] (samaväärsus, ekvivalentsus) -> kõik teosed Polütoopide visuaalsed etendused tegelevad küsimuste ja vastustega, mis tulenevad muusikalistest probleemidest ja lahendustest, kasutades lasereid, elektroonilisi välklampe ning ruume [ruumilisust, tlk]. Oluline on tõdeda, et neid küsimusi võib esitada kõigis muusikalise või visuaalse kompositsiooni valdkondades, teisisõnu alates üldvormist (makrokompositsioonist) arvutipõhise helisünteesi ja digitaal-analoog konversioonini (mikrokompositsioonini), läbides samas oma teel kõik vaheastmed. "Teekond üles ja alla on üks". Nagu öeldud, valmis kogu töö aastate jooksul hierarhilise seoste mosaiigina. Hierarhia tipus on koht filosoofial. Filosoofial, aga millises tähenduses? Filosoofilise impulsi tähenduses, mis suunab meid tõe, ilmutuse, uurimise, otsingu, küsimuse alla paneku ja karmi süstemaatilise kriitika poole mitte ainult kitsal erialal, vaid kõigis võimalikes valdkondades. See juhib meid teadmiste koosluseni, mis peaks olema aktiivne "tegemise" tähenduses. Mitte passiivne teadmine, vaid teadmine, mis väljendub loovas tegevuses. Kordan, kõigis võimalikes valdkondades. Meetodeid, mida ma selles seoste loetelus, mosaiigis või tabelis vaatlen, võib jagada kolme kategooriasse või ossa. Kõigepealt meetod, mis võimaldab meil omandada loovuse abil aktiivseid teadmisi ning eeldab teoreetilise demonstratsiooni huvides tuletamist, teisisõnu mõistust, loogikat jne. Järgmisena tegevuse ja teadmise aspekti kriteeriumid, mis on osaliselt järelduslikud ning lõpuks täielikult järelduslikud ja eksperimentaalsed ning muud, mis on veel tundmatud. Olen paigutanud kunstid osaliselt järelduslikku piirkonda. Kunstid võtavad tuletamisest osa. Järelikult me konstrueerime ja ühendame asju põhjendatult ning võime neid teatud maani demonstreerida. Samas nii humanitaar- kui ka loodusteadused füüsika, matemaatika ja loogika on järelduslikud ning ühtlasi ka eksperimentaalsed. Loodud teooriat on vaja tõestada katseliselt. Kunstis võime me luua osaliselt tuletades, kuid eksperimenteerimine ei ole vahetu. See on esteetika probleem ning asjade esteetilise väärtuse demonstratsioon on võimatu. Soovin avada ukse sellistele meetoditele, mis on inimmõtlemisele veel tundmatud. Kunsti sellise diskrimineerimise kohta võib öelda, et kunstid on vabad alles siis, kui nad võtavad osa nii järelduslikest operatsioonidest kui ka ekperimenteerimisest. Tundub auahnena, aga kunstid on võimalikeks teejuhtideks inimmõtlemise muudesse osadesse. Teisisõnu, asetaksin kunstid selliselt inimtegevuste etteotsa, et nad läbiksid inimese kogu igapäevast elu. Mingem selles hierarhias ühe redelipulga allapoole. Leian sealt küsimuste kategooria, mis on ajaloo käigus kõrvale jäänud, mis tuleks taasavastada ja uuesti küsida, teisisõnu filosoofiliste mõttesuundade loovat teatud moel fragmenteerimist. Nende kategooriate hulgas leidub eksistentsiaalsus (ontoloogia, reaalsus), kausaalsus, külgnevus või seotus, kompaktsus, ajaline või ruumiline kõikjaldasus [ubikviteet], kõik potentsiaalselt uute vaimsete struktuuride tuletised. Sinna hulka kuulub ka determinism ning selle vastand indeterminism. Olen üht või teist teed pidi jõudnud tagasi mõtlemise vaieldamatult väga oluliste kategooriateni, millel on olnud enam või vähem teadlik süstemaatiline staatus alates Aristotelesest, aga mis on kaldunud kõrvale või väidetakse eksisteerivat eksperimentaalpsühholoogia (Jean Piaget) ja kaasaegse matemaatika teatud harudes. Need mõtlemise kategooriad-küsimused kutsuvad või võivad kutsuda esile lahenduste perekondi, mida ma üritasin ma siduda muusikas. Ma loodan, et väljendusin selgelt. Leian, et inimesel ei ole õnnestunud vastata tohutule hulgale küsimustele, andes ajutisi vastuseid mõningatele eriliselt determinismi puudutavate lahenduste perekondadele. Näiteks kausaalsus on üks elu aktuaalsematest vormidest, viidates determinismi sellisele põhiküsimusele, mis on vaadeldav indeterminismi nüansseeritud diferentsiaalse aspektina. Ma ei maininud enne oma väites, on võimalik tõestada, et kord ja korratus on indeterminismi osad. Determinism-indeterminism bipooli teiseks tahuks on seostatus või pidevus. Jätkates sealt, kuhu ma enne jäin, lahendusi ja protseduure, mis võivad vastata neile fundamentaalsete küsimuste kategooriatele, on mõnes allpeatükis, mõnes lõigus paratamatult defineeritud väga skemaatiliselt. Üheks näiteks on tõenäosuslik mõtlemine ühelt poolt oma ekstreemse osaga, mida ma kutsun vabaks ehk mälutuks stohhastikaks ja teiselt poolt elementaarne determinism, Markovi ahelad, mis võimaldavad teatud kausaalsust. Aga tõenäosusliku mõtlemise ja indeterminismi keskmes on see, mida võib nimetada sümmeetriaks või perioodilisuseks, mis on teine võimalus defineerida või rääkida neist mõtlemise tüüpidest. Sümmeetria või perioodilisus sündmuste või protseduuride tsüklilise kordumise tähenduses võib determinismi skaala allosas moodustada rühmastruktuure. Nende kahe vahel on see, mida võiks nimetada hübriid- või segafaasiks, mille üks huvitavamaid vorme on mänguteooria. Allpool, mosaiigi kõige madalamatel astmetel, vastavalt neile teemadele, nende mõtlemise vormidele, mida esindavad ka teised teadused, kuhu ma liigitan ka muusika, võib leida teatud töid, mis on reflektsioonideks ja katseteks neile küsimustele vastata. Ma ei soovi neid siin loetleda, see läheks tüütuks. Kuid näiteks vaba stohhastikat on kasutatud teoses "Achorripsis", millest kujunes hiljem vaba stohhastilist süsteemi esindav arvutiprogramm. See programm võimaldas omakorda kirjutada orkestriteosed "ST/10", "ST/48", ning tungida ka heli mikrostruktuuri ja arvuti genereeritud helide sünteesi valdkonda. Seda programmi kasutati muuseas mõned aastad nii Ühendriikides kui ka Euroopas (Rootsis, Prantsusmaal jne.) lisaks CEMAMu-le teistes stuudiotes ja teiste heliloojate poolt. Markovi stohhastika valdkonda kuuluvad sellised lood nagu "Analogiques" ja "Syrmos" keelpillidele. Mänguteooria valda: "Strateegia", "Linaia-Agon" jne. Sümmeetrilis-perioodiliste süsteemide hulka rühmastruktuuride alusel komponeeritud tööd "Akrata", "Nomos Alfa", "Nomos Gamma" ja "Persephassa". Olen maininud ainult peamisi teoseid. Raportis, mille ma esitasin komisjonile ja minu sõnavõtu alguses võib leida rohkem detaile, mis käsitlevad minu visuaalset tööd nagu polütoope ja minu töid arhitektina. Jätkates sel viisil allapoole kuni hierarhia põhjani, leiame me helirõhk-aeg-ruumi. Analoogseid asju võib öelda visuaalses valdkonnas, esitades küsimusi mikrostruktuuri tasandil, teisisõnu makrostruktuuride kõrgeima elemendi tasandil võib näha, otsustada või töödelda ekvivalentsete protseduuride ja idedde abil nagu kõige algsemal tasandil, milleks on rõhk funktsioonis ajaga nii kõrva, kui ka silma nähtava spektri elektromagneetilise aktiivsuse puhul. Kokkuvõttes kõik, mida võib öelda makrostruktuuride üldiste põhiprobleemide kohta, leidub ka vahepealsetel struktuuritasanditel, meedio- ning mesostruktuurides, kogu skaala allapoole, kus see seguneb nägemise ja kuulmise kvantitatiivse aktiivsusega. Arvan, et andsin väga põgusa ülevaate oma töö põhijoontest, kõnelemata ometi tööst endast. BERNARD TEYSSÈDRE Tänan väga, Iannis Xenakis. On selge, et teie sõnavõtt oli lühike ja tundus oma tiheduse tõttu keerulisena. Loodan, et arutelu, mis nüüd algab, heidab mõningat valgust teie ettekandele. Usun, et see oli üsna arusaadav neile, kes juba tunnevad teie loomingut hästi. Teie ettekanne võis aga paista veidi ebaselge ülejäänutele, kuna ühekorraga oli käsitletud liiga mitmeid teemasid. Usun, et Revault d’Allonnes, teie väitekirja juhendaja, sekkub nüüd. Dialoog Olivier Revault D’Allonnes’iga OLIVIER REVAULT D’ALLONNES Tõepoolest, teatud administratiivsete veidruste tõttu olen ma väitekirja juhendaja. Tegelikult on Iannis Xenakise väitekirja juhendajaks Iannis Xenakis ise. Ning ta juhendas end väga hästi. Leian ennast ka kaitsmiskomisjoni referendina. Silmitsi sellise suure hulga uurimuste ja teostega tunneb see referent ennast küllaltki väheolulisena. Loodan olla vaatleja teiste seas ning lummatud vaatleja kogu Xenakise loomingust. Xenakis on andnud oma fundamentaalteoreetilistele töödele ning lisaks teoreetilistele töödele tervele hulgale dokumentidele, äsja tutvustatud heliteoste partituuridele, arhitektuurivisanditele, kavanditele, plaanidele ja kokkuvõtetele pealkirja. Üldpealkiri ei määratle mitte ainult seda toimikut, vaid tervet Xenakise loomingut: Kunstide ja teaduste sulam. Xenakis esitles äsja mõnda neist sulameist ja rääkis meile kokkuvõtvalt, mil viisil on neis küsimus sulamist. Xenakise puhul viitab sõna "kunst" ladinakeelsele sõnale ‘artifex’, looja. Sellisel inimesel on maailma suhtes teatud hoiak, teatud maailmapilt, jätkuv kinnisidee, et maailmas on kogu aeg midagi teha. Peaaegu kakskümmend aastat ei ole ma näinud teda iial teistsuguse kui otsekui loova deemoni saagina. Tema jaoks on teadus miski, mida alati saadab see loov deemon. Xenakis tahab teha midagi, aga mitte kunagi mida tahes. Ta tahab alati luua kindla teose, teose, mis puhtalt esteetilisel tasandil esindaks iseennast: Minge kontserdile, kuulake Xenakist. Kuid teosega võib muul tasandil suhelda ka teistmoodi, analüütilis-ratsionaalses keeles, mis seda ühtaegu analüüsib ja põhjendab. Raamatutes, mida ta täna tutvustab: "Muusika.Arhitektuur" ning eriti ehk "Formaliseeritud muusika" näeme me, et teoseid on analüüsitud, lahatud, neid samal ajal põhjendades, seadustades. Xenakis ütleb, miks ta seda teeb ja kuidas ta seda teeb, aga "miks" on vähemalt sama oluline kui "kuidas." Sellised "sulamid" ei ole ometi probleemitud, vähemalt minu jaoks. Sisaldades arhitektuuri ja muusikat, polütoope, aga ka teoreetilisi töid, mis on meie silmade ees, sooviks ma nüüd kutsuda pädevamaid kui ma ise ettevaatlikult käsitlema kunsti ja teadust ning küsima Xenakiselt "sulamite" kohta küsimusi. Esimene küsimus oleks järgmine: Xenakis pakub oma teoreetilises töös välja võidelda nüüdisaja kunstide ja teaduse lahutatuse vastu ning luua teatud mõtte vaba liikumise liik, viljastades sellega vastastikku teaduslikku ja kunstilist mõtet. Selle saavutamiseks toetub Xenakis ühtaegu minevikunägemusele ja selle nüüdisaegsele teostusele. Vähehaaval näeme me minevikunägemuse ilmumist uuesti igas tema töös ja äsja peetud ettekandes. Kunstide ja teaduse vastastikuse viljastamise parimad perioodid olid Antiik-Kreeka, Itaalia renessanss, klassikaline ajastu, mil kunstnik ja õpetlane ignoreerisid teineteist vähem kui tänapäeval ning seetõttu on sündinud selline läbini õigustatud kunstide ja teaduse vahelise vaba läbikäimise nostalgia. Kuid tänapäeval kasu, mida kunstid ja teadus võiksid ühisosast saada, näib mulle jaotuvat üsna ebavõrdselt ja olevat ebavõrdselt võimalik. Arvan, et teadus võib tuua lõpmatult rohkem kasu, rohkem valgustatust, rohkem viljastamist kunstidele ja eriti muusikale, kui muusika võiks tuua teaduslikule mõtlemisele. Näiteks stohhastilise arvutuse rakendamine muusika puhul, kaasa arvatud sõelateooria, mida Xenakis on kohaldanud eriti helikõrgusridade problemaatikas, on muusika ja muusikateaduse sisuliseks uuendajaks, nagu ta ütleb raamatu Muusika.Arhitektuur esimeses osas. Aga ma kardan, puhtalt matemaatilisest seisukohast ei paku need töövahendid mingit erilist huvi ega viljastamist ega avastuslikkust ega probleemide lahendusi, kuna neis ei toimu uusi realisatsioone. Ka arvuti kasutamine on kindlasti püstitanud probleeme, kuid läbini klassikalisi probleeme programmeerimisele ja informatsiooniteooriale. Lühidalt probleeme, mis on juba piisavalt läbi töötatud. See ei ole põrmugi nii vastupidi. Tänapäeval võib öelda (ja seda tõestab suur osa Xenakise loomingust), et muusikaline mõtlemine ei kasuta veel piisavalt kõiki matemaatika vahendeid. Kui Xenakis taipab muusikuna, et helikõrguste rida moodustab korrastatud rühma, Abeli rühma, (triviaalne definitsioon matemaatikule), paneb see talle "kilgi kõrva", nagu ta ütleb. On olemas korrastatud rühm, seetõttu on ehk olemas ka mittekorrastatud rühm. Kui on olemas Abeli rühm, miks ei võiks olla olemas helirida, mis ei kuulu Abeli rühma? Saame väga hästi aru, kuidas matemaatika muusikalist mõtet viljastab, aga teades nende mõistete suhteliselt elementaarset taset matemaatikas, võin ma öelda, et matemaatikas on huvi nende vastu null. Unistades kunstide ja teaduse suhtest, tuleb tõdeda, et meie ajal näivad suhte tingimused eriliselt ebavõrdsetena. Sellest minu küsimus: Kuidas võime me loota õpetlaste ja teadlaste huvile ning sealjuures tajuda need uusi vaimseid struktuure, millele Xenakis ise täna vihjab? Kunst, kasutades teadust, saab rohkem kasu kui teadus. On see tasakaalu puudumine halb? Ning kui jah, kuidas me võime seda ületada? Minu teine küsimus on lihtne tuletis esimesest. Vaba läbikäimise ja sulami seisukoht on väiteks tähenduses, mis ei viita tänasele tegelikule olukorrale, see on tõotatud maa. Utoopia sulamist, mis kujutab endast ise loovat leiutist. See on loodud Xenakise viljaka töö tulemusena. Aga kas seda võiks ette kujutada kehtivana terves ühiskonnas? Saaks seda ette kujutada muutuvat kui mitte ainsaks seaduseks, siis vähemalt üheks elemendiks kunsti ja teaduse suhetes? Kas väide "sulamist", eeldades ühest küljest teadust ja teisest kunsti, on miski, mis sarnaneb mõistele, teatud tõele iseeneses või võiks see kunsti oma külje ja teaduse oma küljega olla vahendiks millelegi muule kui iseendale? Kas see võiks pärineda kusagilt mujalt, kusagilt, mis paikneks mujal kui aksiomaatikas, mille pärast me selle nimetamisest rõõmu tunneme? Teisisõnu, kas see on puhtalt kunstide ja teaduse tehniline liit või on selles sotsiaalne jaotus, mis lõppude lõpuks peitub selle tehnilise jaotuse taga (ja kui, siis missugune)? Siinjuures ei mõelnud ma klassierinevusi intellektuaali ja töölise vahel. Tõepoolest, kes oleks kes ja kes mitte? Seisame silmitsi jaotuse, funktsioonidevahelise lahususega. Teadus kaldub niinimetatud ratsionaalse tegevuse, looduse ja inimese poole, uhkustades olevat ise osa reaalsusest. Kunst aga kaldub kujuteldava objekti loomisele. Kas Xenakis pakub mingit tulevikulahendust või midagi, mis eeldab muutusi - nimelt sotsiaalseid, mis on palju radikaalsemad võrreldes teaduse ja kunsti vastastikusest suhtest tingitud osalise muutumisega? Kokkuvõtteks, teadus annab inimesele asjade üle teatud kontrolli. Xenakis pakub nüüd samal viisil välja kontrolli selle kontrolli üle, nii et kõrgem juhtimine võiks aidata inimest seda paremini kasutada. On see mõeldav, et terminite inversioon, mis läbib kogu Xenakise loomingut, piirdub ainult kunstide ja teadusega? Kolmas küsimus naaseb esteetika juurde. Paraku eksisteerib väga levinud arvamus, et Xenakise muusika on komponeeritud arvuti abil. See arvamus on aga üks ühiskonnas tuntud teadusliku ja tehnokraatliku ideoloogia aspekte. Kui vaatame tähelepanelikumalt, võime veenduda, et ilmselt ei oma see tähendust. Formaliseeritud muusikas võime me leida imetlusväärse määratluse: "Selles valdkonnas me leiame, et arvutid annavad teatavat kasu." Teisisõnu, on võimalik, et sellest "kasust" pole kasu. Nii toimus Metastastaseis’ega aastal 1954 ja ma võin ikka veel näha niiöelda "käsitsi" arvutavat Xenakist uskumatu kannatlikkuse, ei, jonniga, tegemas mitu kuud seda, mida arvuti võib teostada mõne tunniga. Tore. Kuu aega rasket tööd: kui on võimalik kasutada masinat, mis võib töötada palju kiiremini ja tõhusamalt. Ning Xenakise uuemad teosed, mis on samuti arvutatud "käsitsi", tööd, mida me võime kutsuda "käsitöönduslikeks", teostatud arvutit kasutamata. Ehk võiks Xenakis meile jutustada, miks? Ma mõtlen näiteks sellist teost nagu Nuits aastast 1967 ja uuemat, Evryali, suvest 1973. Olen proovinud analüüsida neid partituure nüüdseks üle kahe aasta. Ei ole tõsi, et need teosed oleks muutunud vähem huvitavaks, vähemalt minu maitse jaoks, olen jõudnud ilu reeglite sõnastamiseni, aga seda esteetilise tulemuse terminites. Kui ma ei suuda tulemuslikult analüüsida Evryalit, pean ma ilmselt esmalt uurima minu enda piire. See ei oleks raske, kuna tegu on eriti keerulise partituuriga. Aga siiski, kas ei ole süüdi miski muu? Kas ei ole olemas midagi sellist, mida me võiksime kutsuda näiteks selle partituuri xenakislikuks stiiliks, mis oleks enamat, kui asja olemuse täiend? Xenakis räägib väga vähe stiilist, kuigi ta kohustab arvuteid lugu pidama sellest, mida võhik suudab tajuda vaid kuulates. Xenakis puudutas vaevu seda teemat oma teoreetilistes kirjutistes. Kas sündsustundest? Tagasihoidlikkusest? Ei tea. Mõnikord esineb allusioonina selle või teise võtte, selle või teise resultaadi ilu kohta lühike lause, kas absurdi- või alaväärsustundest, mida Xenakis kutsus kusagil "muusikalise mõtlemise madalamateks kihtideks." Sa räägid liiga vähe xenakislikust stiilist. Sa võid vastates öelda, et pärandad selle oma historiograafidele. Nad tänavad sind usalduse eest. Kindlasti aga tänavad nad sind vähem sinu vaikimise pärast! Kui sa võiksid neid pisutki abistada, oleksid nad tänulikumad. Oleks see minek üle selle väitekirja "Kunstid/Teadused:Sulam" piiride, hinnates tehnikat ainult sekundaarses rollis, ainult töövahendina seoses intuitsiooni või esteetilise sisuga, mis liigub sulami poole või lõpeb sulamina? Tehnika ei tohiks neid selles sulamis siiski enda alla matta. Lühidalt, mis selle juurde viib, või nagu ollakse harjunud ütlema, mis nende lähenemisteede täielikkuses "inspireerib"? Ehk riskime me sellega minna üle sinu väitekirja piiride. Siiski oleks veidi kummaline näha Xenakist isiklikult siin, kohustatuna oma erilise situatsiooni tõttu vastama (naerab) ja jätta temalt küsimata, kuidas on olla kaitstud selle teadusliku kindluse, selle arvutite rindejoone taga. Miks veenab Xenakis ennast ja meid teadmiste suurepärase jõu osas, mida ma isegi kuni teatud punktini usun, samal ajal kui vahepeal kirjutab ta oma ülimalt hiilgavaid teoseid lihtsalt paberi ja pliiatsiga? Kui lubate, Iannis, mis on selles vallas nii täielikult ja läbinisti muutunud võrreldes näiteks Bachi või Mozartiga? IANNIS XENAKIS Viimane küsimus on mulle väga oluline. Mõnikord on mind süüdistatud kalkuleerimises, matemaatikluses, "kuivuses" ja kõike seda vastandina muusikuks olemisele. See süüdistus on nüüdseks aegunud. Tänapäeval paistab, et enam ma seda ei ole. Isegi muusikud arvestavad mind muusikuna! Sooviksin seda vahemärkust selgitada. Esimest korda leian ma end nii "auväärses" asutuses nagu Pariisi Ülikoolis ja kohe Sorbonne’is. Kuni tänaseni olin ma alati teatud määral "väljatõugatu" ja vähehaaval olen ma kasutanud oma uut positsiooni (õpetan nüüd Pariisi Ülikoolis), et kaitsta seda väitekirja. On õige, et peaaegu kõik mu kirjutised viitavad küsimustele, mida võib tõestada ja väljendada keeles, millest saab aru igaüks, olgu siin, Jaapanis, Ameerikas või eskimote juures. On teine poolus, osa, mida ei saa väljendada, mida võib öelda ainult kunsti, muusika, arhitektuuri või visuaalse väljenduse endaga. Ja samuti, ma ei tea, on palju asju, mille kohta ma võin öelda, "see meeldib mulle" või "see ei meeldi mulle" või "see on ilus" või "see on inetu" või "see on eemaletõukav" või "see on fantastiline", "huvitav" jne. Õige, me jõuame tagasi esteetiliste või psühholoogiliste probleemide juurde, kuid mida võib rääkida konstruktsiooni või kõla kohta, kasutamata tehnilist või analoogilist või proportsionaalset või arhitektuurset keelt? Mida me võime öelda? Ei ole olemas keelt, mis võiks hõlmata neid küsimusi peale nende küsimuste endi, mis tegelevad konstruktsiooni, struktuuri, reeglite ja seadustega. Aga ma olen sinuga nõus: muusikas on midagi muud, igas muusikas, samuti "inetus" muusikas. Kuid see "miski" ei ole eristatav ega tajutav, see on "väljendamatu." See on omadus, mis ei ole veel kirjeldatav. Kunstiobjekt ise peab seda kirjeldama. See on nagu teatud liiki äralõigatud aspekt, kas pole? OLIVIER REVAULT D’ALLONNES Nutikas... IANNIS XENAKIS Kuidas, "nutikas"? OLIVIER REVAULT D’ALLONNES Sa rääkisid mulle, et sa ei oska vastata, ometi võrdled sa ise mineviku töid ja tervet hulka nüüdseid arengusuundi. IANNIS XENAKIS Ma võin seda teha ... ma võin rääkida struktuuridest, seda ma ütlesin äsja. Aga ma ei suuda ei küsida ega rääkida millegi väärtusest, kui see ei ole vahetult tajutav strukturaalsel tasandil. Näiteks sa ütled, et ma arvutan emb-kumb kas arvutiga või "käsitsi" ning selles on ikkagi stiil, mis neid arvutusi või seda "meta-arvutust" läbib. OLIVIER REVAULT D’ALLONES Või "infra-arvutust", ma  ei tea ... IANNIS XENAKIS Või "infra." Ma ütleks pigem "meta," või "taga," mis jõuab sama asjani! Üldistades võin ma kihla vedada, et iga valik eeldab juhuslikku valikut. Ei ole olemas inimese poolt ehitatud konstruktsiooni, mis ei oleks mingil viisil juhuslik. Konstruktsioone valitsevate seaduste tunnustamine on juba meelevaldne tegu. Me põrkame nii kaasaegses kui ka antiigi matemaatikas kokku meelevaldsete aksioomide hulkadega ja alles teisel astmel, kasutades formaalset loogikat, ehitame me üles nende tervikliku struktuuri. Aksioomide kogum on hulk püramiidi põhjas või pigem tipus, kuna põhi on pea peale pööratud. Tipp on maas ja põhi on taevas, kuna seal on rohkem kasvuruumi. Aksiomaatika on valik, valik, mis on juhuslik. Aga on see täielikult juhuslik? Jah, kuid alles pärast esimest eristuvat vaieldamatut teoreetilist paratamatust, liitudes praeguse ja ajaloolise kogemusega. OLIVIER REVAULT D’ALLONES See näitab, et on olemas paralleel sellega, mida sa ise teed. Ma arvan, see leidub "Muusika.Arhitektuuri" viimases väljaandes ja samuti sinu väitekirja järeldusosa lõpus. Paralleel matemaatilise mõtlemise ja muusikaliste vormide ajaloo vahel, pluss tegelikult veel kolmas element, kolmas paralleel, mis ei ole muidugi põrmugi paralleelne ning milleks on muusikalise maitse ajalugu. Just nagu fuuga on fuugaperioodi muusikaline struktuur, nii on sinu looming tüüpiline kahekümnes sajand. Aga loomulikult on olemas persoon Xenakis, ja mulle näib, et see juhuslikkus ei ole täielik. IANNIS XENAKIS Ma kardan, et me kaldusime veidike kõrvale küsimusest, mida sa küsisid varem, kui sa rääkisid muusikateadusest ja vormidest. Või veelgi parem, vormide teadusest ja ajaloolisest revolutsioonist. Kui fuuga oli teatud hetkel tõeliselt fundamentaalne, ei olnud see kindlasti mitte nii enne tema avastamist, enne, kui ta mõjutas iseennast! Fuuga ei ole mingilgi kombel fundamentaalne tänapäeval. See on kindel. Seepärast on esmalt ja ennekõike tehniline probleem, mis on lõppude lõpuks fuuga? Eelkõige on see rühm eeskirju ja protseduure koos visiooniga, mille eesmärgiks on konstrueerida muusikaline ehitis. See rühm eeskirju tekkis. Järelikult, neid ei eksisteerinud enne! Ja nüüd ei eksisteeri neid enam laias tähenduses, loominguna. See tõestab üpris veenvalt tema vähemalt osaliselt juhuslikku olemust. OLIVIER REVAULT D’ALLONNES Küsimus ei olnud fuugades, vaid sinu loomingus, Iannis! IANNIS XENAKIS Kui ma proovin seletada oma raamatus, artiklis või loengus üht või teist tehnikat, on see võimalik, kuna sellest võin ma rääkida lihtsalt. Või kui ma õpetan, tähendab see teiste sütitamist süvenema nendesse samadesse küsimustesse. Aga ma ei räägi kõike nii nagu ma seda tunnen või tajun, sest ma ei tea, kuidas seda öelda. Siis ma eksamineerin üliõpilasi ja näen tulemusi. See oleks sulle mu vastuse kiirkokkuvõte. Võib-olla ei vastanud ma sinu teisele küsimusele ... OLIVIER REVAULT D’ALLONNES Jah, ehk... Tekib kiusatus sinult küsida: miks eksisteerib teatud ajalooline tühik kunstide ja teaduse vahel ja millises mõõdus on ühepoolsem panus suunatud teaduse poolt kunstide poole, mitte vastupidi? See on esimene küsimus, teine küsimus on: kui see sulandumine, mille sa teaduse ja kunstide suhtes välja pakud, on midagi utoopilist, seetõttu loovat, kas me ei võiks eeldada midagi muud, kui lihttransformatsiooni kunstide ja teaduse valdkonna vahel? Näiteks, peaaegu tsivilisatsiooni transformatsiooni? IANNIS XENAKIS Suurepärane, olen rohkemal või vähemal määral tähele pannud sama! Pöördudes tagasi Olivier Revault D’Allonnes’ esimese küsimuse juurde, mis rääkis mahajäämusest ... ainsast ja mitte kõige paremast mõttest... miks on võimalused aja jooksul kahanenud? Ma usun, see on küsimus tsivilisatsioonist. Antiigis tekkis kunstide ja teaduse vaba läbikäimine. Polykleites proovis rakendada geomeetriat skulptuuris selle kaanonite raames, sama vaba läbikäimist, mis toimus sarnaselt nii arhitektuuris, maalikunstis kui ka muusikas. Aristoxenuse ja teiste tekstid tulid hiljem. Usun, et renessansi aluseks oli inimese unikaalsuse taasavastamine. Inimene on midagi unikaalset, ainulaadne. Ei ole palju inimesi, on vaid üks. Selline inimene hõlmab kõik mõtlemise ja tegevuse võimalused. Ja järelikult, teaduse ja kunstide seose tõlgenduse. Teiselt poolt, kunstid aitasid teatud otsustaval ajaloolisel hetkel teaduslikule mõttele otsesel või kaudsel viisil vägagi palju kaasa. Proovisin seda näidata tabelis, mille ma liitsin "Muusika.Arhitektuuri" viimasele peatükile, tõmmates paralleele eriti muusikalise ja matemaatilise mõtlemise vahele*. Tõepoolest kummaline ja silmatorkav on see, et muusika on matemaatikale palju lähemal kui teised kunstid. Miks? Ma ei hakka seda näitama nüüd. Siiski võin ma öelda, et silm on kiirem, palju vahetum ja otseselt tegeliku eluga kokku puutuvam kui kõrv, mis on vähem väle ja retsessiivsem, nõudes reflektiivset mõtlemist. Järelikult, kuulmine peab olema abstraktsem ja seetõttu looma aluse, mis on ka abstraktsem, lähendades seda matemaatikale. Seda tüüpi ideed proovisin ma näidata seose abil muusikateooria (seega osaliselt muusika) ning matemaatika teooriate vahel: kuidas nad keerduvad ümber teineteise, kuigi aeg-ajalt liikudes paralleelselt, ilma täielikult põimumata. Kunstivaldkond on tänapäeval ajast maha jäänud. Olin muusika "kombinatsioonide" nappusest löödud juba enne lahkumist Ateena Polütehnilisest Koolist, kus ma uurisin kompositsioonitehnikat. Sama kehtib ka seriaalse muusika kohta, mida ma uurisin hiljem. Soovin siinjuures anda au Olivier Messiaenile. Ta oli ainuke, kelle mõtlemine oli neile teemadele täielikult avatud. Mõned tema tööd tuginevad eeldusele "sekkumistest." Veel enam, usun, et see tuleneb tema loomuse kunstnikuomadustest. Aga see on täielikult teine tahk, mis ei kuulu strukturaalsete hulka. Samas, võtkem teine näide: Olivier Messiaeni piiratud transpositsioonidega laadid. Need olid aluseks minu tööle heliridadega. Nimelt see algus lubas mind mõndagi taibata muusikute vaimsete struktuuride keerulistest alustest: nende mõtlemisest ja tegevusest. Üle viisteistkümne aasta tagasi jõudsin ma heliridade probleemini muusikalises kompositsioonis. Töö käigus sattusin ma neid lahendama juba valmis matemaatika abil. Tulemuseks oli minu "Sõelateooria"*. See ei ole vaste, ma ei ole peaaegu iial loonud valmis vasteid. Võrreldes sellega, mida matemaatika pakub kunstnikule tänapäeval, on see tõepoolest tühine, see on minimaalne. Mida peaks tegema? Hästi, minu arvates, konkreetne muutus muusiku, kunstniku, nagu ka teadlase, koolituses. See koolitus ei peaks algama liiga hilja. See peaks algama algkoolis, kui mitte lasteaias. See on kõik hariduse, haridussüsteemi, inimese koolituse probleem: lapsepõlvest nooruseni ja hiljem kuni surmani, selles on küsimus. Lisaks ilmneb lõhe haritlaste või kunstnike ja teadlaste vahel väga varakult ning see on kasvatuse küsimus alates lutipudelist. See viib mahajäämuseni, kuna puudub igasugune kommunikatsioon. Igal juhul, vabast läbikäimisest ja kontakti puudumisest tulenev puudujääk annab rängalt tunda. Veelgi enam, seetõttu olen ma hakanud õpetama, andma loenguid ja läbi viima seminare. Nüüd teeme me ka CEMAMu’s jõupingutusi, kasutades informatsiooniteooriast tuntud tipptehnoloogiat pedagoogilistel eesmärkidel. Ühendamata muusikalise kompositsiooni probleeme ja mõtlemist ruumi ja nägemisega ja lõpuks neid koos matemaatikaga, mille laps on õppinud juba viie-, kuue- või seitsmeaastaselt, võib revolutsiooniline lähenemine muusikale olla juba kadunud. Leian, et probleemi tuum on siin. See on küsimus inimese ellujäämisest, harmoonilisest keskkonnast, mööndes muidugi vasturääkivusi, aga pakkudes rikkamat keskkonda, kui ta seni tundis. Järelikult, on see jaotus lähiajaloo jäänuk. Aja jooksul on kunstnik oma teatud valikutega eksinud. Ta on uurinud kunsti ainult ühte, väljendamatut aspekti. BERNARD TEYSSÈDRE Mulle näib, et Michel Serres soovib sõna. MICHEL SERRES Sooviksin selle väitekirja asemel kaitsta Xenakist ja vastata ühe minuti jooksul Olivier Revault d’Allonnes’ile. Ta püstitab probleemi teaduse ja kunstide suhtest. Ta peaks teadma, millal suhe ei ole tasakaalust väljas. Niisiis, kui ei laenata midagi matemaatilisest tehnikast või matemaatikast või teisest küljest ei võeta midagi muusikast. Tema väidet ümber pöörates võiks öelda, et muusika on samm edasi, sest Xenakise muusika on ees. Ma ei näe vahetuse probleemi ei ärilises ega ka teadusliku tehnika seisukohtast. On üks asi, kui keegi laenab tehnikaid mõnest teadusvaldkonnast ja sootuks teine on asi öelda seda tema muusika kohta. Xenakis esindab üldist ettekujutust teaduslikust mõtlemisest. Teadusmaailm on muutunud ja mitte keegi ei saanud sellest teadlikuks, isegi mitte teadlased. Muutunud ei ole see, et kombinatoorne algebra on asendunud rühmateooriaga või Fourier’ transformatsioonid informatsiooniteooriaga. See ei ole oluline. Oluline on, et miski, nimelt "paradigma" on täielikult muutunud. Kahekümnenda sajandi teisel poolel on esile kerkinud uus maailm, uus teaduslik maailm. Esmalt tõdegem, et see ei olnud filosoof, mitte teadlane, mitte epistomologist, vaid Xenakis. See on Xenakis, kes näitas esimesena, milline sümbol oma tähendust tegelikult irdunudnud on, see on Xenakis, kes kasutas esimesena mitte seda või teist matemaatilist tehnikat, vaid ainult olulisemaid ja tähtsamaid nende hulgas. Mahajäämus ei oma tähtsust, kui probleem on püstitatud lokaalseks vahetuseks. Kui aga kahtluse alla on seatud globaalne visioon, siis on selle taga Xenakis. Kogu traditsiooniline diskursus varjab meie eest teaduse ja paradigma sellist üldist nägemist. Ei, Xenakis, te olete samm ees ja tänan teid selle eest (naer ja braavohüüded). OLIVIER REVAULT D’ALLONNES Michel Serres näitas äsja, kuidas paljude õpetlaste vaimu võib vabastada Xenakise lähenemiste abil. Ma ei kahtlegi selles. Minu esimene küsimus oli, mis võiks näiteks muusika juurde tuua mitte ainult teadlasi, vaid teaduse enda. Siin näen ma teatud lünka ja mitte "mahajäämust": veelgi enam, kas me võiksime defineerida seda mahajäämust mingi ideaalse kalendri alusel? Lõpuks jääb "sulami" küsimuse sotsiaalsete eelduste probleem. IANNIS XENAKIS Hea küll, tänan väga, see on vastus esimesele küsimusele (naerab). Ma ei suutnuks sõnastada seda paremini. Teine küsimus puudutas "sotsiaalset transformatsiooni". Loomulikult, see on küsimus ... aga ma ei tea, millist sotsiaalset transformatsiooni sa antud juhul silmas pead. See üksikprobleem puudutab kõiki sotsiaalseid transformatsioone, mis tekivad kogu maailmas. Mitte keegi ei tea sellele probleemile vastust ja ma arvan tulevat tagasi selle juurde, mida ma ütlesin varem: ideaalne sotsiaalne transformatsioon püüaks lahendada inimeste kooseksisteerimise ja interpenetratsiooni elulisi aspekte haridusest alates. OLIVIER REVAULT D’ALLONNES ... mis puutub pedagoogikasse, tundub selge, mitte teadmatult ega juhuslikult, et pedagoogika, nagu seda meie ühiskonnas praktiseeritakse, toodab ühelt poolt, nagu sa ütlesid, haritlasi ja teiselt poolt teadlasi. IANNIS XENAKIS Jah, kindlasti, kui see koolitab ainult teadlasi, on see tõenäoliselt tingitud peamiselt spetsialiseerumiseks vajalikust ajast. Aga ma usun, et see on lahendatav. Olen ise pidanud samaaegselt vähemalt kahte ametit samaaegselt ma leian, et on täiesti võimalik teha sama kolmega ning mitte pealiskaudselt vaid uurivalt. See on ka küsimus allaheitlikkusest... ma ei taha rääkida klassivõitlusest, kuna see on palju nüansirikkam ja keerukam. Aga siin on endastmõistetavalt küsimus inimorganisatsiooni lõhestumisest, mis toodab vaimseid ja intellektuaalseid invaliide. Kindel see. Minu arvates neid haigusi on võimalik ravida. Kuidas saavutada radikaalset pedagoogilise ja ka sotsiaalse keskkonna vahetust? See oleks reform, mille poliitikud peaks ette võtma, selle asemel et esitada lihtsaid küsimusi palga, tehniliste vahendite, edukuse või ühiskondliku progressi kohta. Nimelt selles peitub rahulolu inimese terviklikkusest. Leian, et kunstil nagu ka teadusel on ühendajana oma roll. Michel Serres ütles õigesti: kunsti ja samuti teaduse aluseks on tervikvisioon, mida võib nimetada kahekümnenda sajandi visiooniks terviklikkusest ja lootusest, mis võiks olla inimkonna lootuseks. BERNARD TEYSSÈDRE Hästi, ehk me peaks andma nüüd sõna Olivier Messiaenile, kuna oleme ammendanud esimese küsimuste ja vastuste ringi. Dialoog Olivier Messiaeniga OLIVIER MESSIAEN Kangelast ei kritiseerita! Seetõttu soovin ma küsida vaid mõned küsimused. Kuid ma ei sooviks, kallis sõber, et need küsimused näiksid teile taktitutena. Kui nad teid pahandavad, palun öelge. Need ei ole päris küsimused, vaid pigem palved võimaldada teil selgitada oma mõtet. Selle asemel, et pidada hiilgavat sissejuhatavat kõnet, nagu mu kolleegid, soovin ma küsida teilt oma küsimused lihtsalt üksteise järel. See oleks kergem teile, mulle, meile kõigile. Esimene küsimus: teie väitekirja leheküljel 13 ja ka mitmes kohas raamatus Muusika.Arhitektuur näite te viitavat ajaloole ning eriti muusika algusele, heliridade, laadide ja konstrueeritud heliridade sünnile. Enne neid heliridu (ja te ise tunnistate seda) olid kasutusel ainult tetrakordid. Aga kas te pole mõelnud, et inimkonna väga varastel algusaegadel oli kõigepealt "karje"? Rõõmukarje ja valukisa: väljenduslik keel (nimetagem seda muusikaliseks). Lisaks muude helide tajumine ja imiteerimine: tuul, vesi, linnulaul. Jäljendav keel, mis on samuti enamasti muusikaline ja mida leidub ka primitiivses onomatopoeetikas. Süntaktiline kõnekeel ja organiseeritud muusikaline fraas tekkisid palju hiljem ning koos sellega esialgsed, "ajavälised" (nagu te seda kutsute) heliread, laadid ja skaalad. Miks olete peatunud heliridade materjalil, välistades kõik ülejäänu? IANNIS XENAKIS Ei, mitte sugugi. Te sooviksite, et räägiksin sellest kohe? Õige, ma ei ole läinud kaugemale, kuid mitte ignorantsusest. Ma ei tea, mis viiks paleontoloogilise ürginimese mõistuseni miljon või kaks või isegi kolmkümmend miljonit aastat tagasi, nagu on äsja avastatud. Meil pole mingit võimalust tunnetada tema mõtlemise vorme. Kui ma vaatan läinud sajanditele praegusest, kuna ma kuulun sellesse, võin ma järelikult rääkida ainult asjadest, mis on mulle arusaadavad. Möönan, kahtlemata on puuduseks suutmatus tegelda sügavamate küsimustega, mille te tõstatasite. Lisaks, mis tähendab "imiteerida", mis tähendab "karjuda", mis eelneb süntaksile enne kõiki reegleid, enne konstruktsioone, ükskõik kui väikesed nad olla võisid? Näiteks, on juba vormitaju, kui keskkonna strukturaalsest visioonist lähtuvalt võib möönda, et inimene eksisteeris asjana iseeneses. Loodus ja selle keskkond olid midagi väljaspool teda ning see, mida ta oma meeltega tajus, oli järelikult imiteeritud. Tõenäoliselt võime imiteerida tuule müha, rahet või äikest jne. oli võime konstrueerida, ehkki primitiivselt, aga siiski piisavalt keeruliselt. Tänapäeva teadus (öeldes teadus, pean ma silmas teaduslikku mõtlemist) omab lihtsat ülevaadet inimese teatud vaimsetest struktuuridest ainult väga väikese aja ulatuses. Lisa on tulemas, kuid sellest on keeruline rääkida, võin rääkida ainult asjadest, mis on selgelt välja kujunenud ja nähtavad. Seetõttu alustasin tetrakordiga, mis viitab juba üpris arenenud konstruktsioonitasandile. Lisaks on tetrakord materjali silmas pidades osa kultuurilisest, teaduslikust või organisatoorsest lähenemisviisist. Siiski muudes väga vanades tsivilisatsioonides, palju vanemates kui Kreeka tsivilisatsioon, nagu Jaapan, Hiina või Aafrika, (Egiptusest teame me liiga vähe), on erinevad lähenemised, milles tetrakordi ei esinenud. Näiteks nō muusika intervall on kvart. Me võime öelda, et kvart on teatud tüüpi universaalne reaalsus, aga kvardi sisemine konstruktsioon on midagi spetsiifilisemat kui kvardi konstruktsioon kolmandal või neljandal sajandil enne Kristust Kreekas. Kuna tetrakordid olid diatoonilise süsteemi aluseks, võib kogu muusikat kuni meie ajani vaadelda ajaloolise ja musikoloogilise jadana, mis võimaldab meile edasisi üldistusi. Mida ei saa öelda varasema perioodi kohta (mida ma kutsun loogikaeelseks, kuigi muusikas see ei ole mitte sugugi loogikaeelne). Mida te rääkisite, on fundamentaalne, sest kui me soovime uurida põhjalikumalt tänapäeva struktuure puudutavaid küsimusi, oleks vaja liikuda tagasi või pigem distantseeruda neist struktuuridest, neist muusikalistest mõistetest, mis pealegi juhiksid meid muusikaväliste lahendusteni. Vaadakem asju täiesti uue silma või kõrvaga, uute vahenditega. See on vormide tajumine. Võttes vastu (ja tegelikult me võtame) signaale tähtedevahelisest galaktilisest kosmosest, on vaja teada, kuidas eristada neid mürast (nagu Michel Serres varem ütles), näha, kas nad on struktureeritud, kas nad on koherentsed ning kas see koherentsus on mõistuslik või mitte. Mõistuslikkuse puhul pean ma silmas, kas nad on pärit looduslikust allikast, niiöelda loodusest endast, või on nad pärit teiselt olendilt, kes võib sarnaneda inimesega. On vaja minna tagasi kõigi tsivilisatsiooni ja koolitusega omandatud struktuuride ning mõtlemise vormide eelsesse aega ning taastada ratsionaalsuse-eelne, loogika-eelne, strukturaalsuse-eelne, süntaktilisuse-eelne situatsioon. Ma ei tea, kas vastasin teie küsimusele. OLIVIER MESSIAEN See on väga ilus vastus. Aga te ütlesite ka, et minevik on olemas tulevikus ja tulevik minevikus. Seetõttu lubasin ma endale puudutada mõningaid valdkondi, kus meie teadmised on võimetud. Teine küsimus, absoluutselt isiklik: Te teate niisama hästi kui mina, et teatud arv objekte annab teatud arvu permutatsioone ja mida rohkem objektide arvu suurendada, seda rohkem suureneb permutatsioonide arv koos kiiruse ja hulgaga, mis võivad paista disproportsioonaalsetena. Niisiis kolm objekti annab kuus permutatsiooni, kuus objekti seitsesada kakskümmend, ning kaksteist objekti (kui ma ei eksi) nelisada üheksakümmend seitse miljonit üks tuhat kuussada permutatsiooni [tegelikult 12!= 479001600, tlk]. Eeldame, et need objektid vastavad kestustele ning ma sooviksin neid kestusi üles kirjutada, selleks et teada, milline žest või liikumine neid ajas tekitab. Siin on olnud palju juttu tagurpidi liikumisest: see on aga vaid üks liikumisi, üksainus liikumine keset tuhandeid teisi. Ning selle permutatsioonid järgivad originaalset trajektoori. Ent kõik muud permutatsioonid? Ma ei suuda üles kirjutada miljoneid ja miljoneid permutatsioone ... ja veel kirjutada neid välja, selleks et neid tunda ja armastada (rõhutan verbi armastama!). Teie puhul võib masin anda miljoneid permutatsioone mõne minuti jooksul: see on külm ja mõttetu nimekiri. Kuidas oskate te teha valikut selles tohutus võimaluste maailmas ilma lähedase teadmise või armastuseta? IANNIS XENAKIS Näib, et teie viimases küsimuses on koos kaks küsimust. Esiteks küsimus armastusest, hea küll. Teiseks võimalik valik keset suurt hulka võimalusi ... OLIVIER MESSIAEN Usun, et vastate härra d’Allonnes’i esimesele küsimusele ... IANNIS XENAKIS Võib-olla. Ma ei tea. Niisiis küsimus millegi armastamisest, sellepärast et seda kasutada, eeldab loomulikult eelnevat taltsutamist. Vahendite taltsutamine või "enda poole võitmine" määravad armastuse ja mittearmastuse, armastuseni viib selle järeldus. OLIVIER MESSIAEN Ma väljendusin puudulikult. Tahtsin öelda "teadma!" Teadma tõelise ja emotsionaalse tarkusega, väljaspool armastust või vihkamist ... IANNIS XENAKIS Jah, see on emotsionaalne külg, tarkuse kaasnähe, valu või vastupidi rõõm või kaks koos, millest ühte võiks näiteks väljendada armastusega ilusasse naisesse. Kuid valdama midagi väljaspool armastust või vihkamist on üks vorme ja ehk ainus võimalik tarkuse vorm. Kui ma vaatan tähistaevasse, armastan ma seda teatud moel, sest ma tean sellest teatud moel, aga kui ma soovin teada järgmistel astrofüüsika tasanditel, võib see toimuda ilma armastuseta. Armastus võiks siin ülenduda pigem teatud tüüpi ilmutuseks, mida selle kaasnähu tõttu nimetatakse armastuseks. Järelikult, ma võin menetleda asjade olemuste endiga ilma neid isiklikult otseselt omamata, tingimusel et ma kujutlen ja tunnen neid samal viisil. See on vastuse algus teie küsimusele, mille ma leian olevat fundamentaalse. Kõik see tähendab, et kui ma olen ka võimetu valitsema teatud ilmingut, ma olen võimeline leidma tõe, mis on tänu teatud vahetule ilmutusele omane kujuteldavale või vaadeldavale nähtusele. Seejärel võin ma aktsepteerida ja kasutada seda nagu enda oma. Kui ma lindistan heli, mille ma leian olevat huvitava, ma ei tea täpselt, mis selles helis on. Ma tajun asju, mis mind huvitavad ja ma kasutan neid. Seepärast ei saa ma selles helis armastada asju, mis on nii rafineeritud, et ma ei suuda neid täielikult tajuda. Ma ei ole teadlikult või mitteteadlikult võimeline neid nimetama, aga ma aktsepteerin tervikut kui niisugust, sest ma olen sellest võlutud. OLIVIER MESSIAEN Te olete võlutud, kuna selles on ilmutus! IANNIS XENAKIS See on õige, jah. OLIVIER MESSIAEN Ilmutus on nagu armastusse langemine, nagu välgunool. See on romantiline inspiratsioon. IANNIS XENAKIS Jah, ma ei eita seda põrmugi. Vastupidi. OLIVIER REVAULT D’ALLONNES Ma ei teadnudki, et sa oled romantik, Iannis! (naerab) IANNIS XENAKIS Ma ütlesin varem (või võib-olla ma ei öelnud ka), et kunsti vallas on selleks ilmutus. Filosoofias, tarkuses on see sama. Jah, ilmutus on absoluutselt asendamatu. See on inimese üks karkudest. Tal on kaks karku: ilmutus ja järeldus. Ja kunstis kehtivad mõlemad. Teaduses on üks, mis võtab teiselt eesõiguse, tuletamine. Jõudes teie küsimuse teise osa juurde, kuidas toimub valik suurest hulgast võimalustest? Hästi, selleni jõudmiseks on palju teid. Ma võin ette kujutada – kui ma ei suuda, vajan selle jaoks masinat - ma võin ette kujutada ja mõistuslikult teha valiku. Selle valiku tegemiseks on mitu teed. Õige, kui on vaja kontrollida üksikuid helisid või täpsemalt helikõrgusi, on lihtne jätkata juhuslikul või intuitiivsel moel, otse. Aga kui on küsimus suures hulgas helides, oleks otstarbekas laenata teistest valdkondadest. Kui ma vaatlen väikest arvu inimesi, näen ma neid üksikisikutena, näen nende suhteid, nende tunnuseid, nende seoseid ruumi ja ajaga, nende personaalset füsiognoomiat jne. Aga rahvahulga puhul ei suuda ma enam eristada üksikuid inimesi, sest neid on liiga palju. Vastupidi, mida ma näen, on aspektid, rahvahulga tunnused. Kui ma vajan suurt hulka võimalusi, pean ma kasutama suurte arvude omadusi: näiteks tihedus, korra või korratuse kõverad, ruum, heliruumi jaotus (helikõrgus, aeg, kord, korratus jne. parameetrid), selles leiame me võimalikud töövahendid valiku tegemiseks. Ma ei ole öelnud, et see kehtiks kõigi valikute kohta, aga me võime sellega kõrvaldada päris suure arvu ilmseid võimatusi, valides samas ääretu arvu elementide vahel. Olen jõudmas põhimõtteni, et inimene, kui tihedus on liiga suur, on võimetu ütlema: "jah, ma pean silmas seda objekti seal". Suurearvulise valiku tõttu on sellistele hetkedele omane teatud kõhklus, sest siis on olulised muud karakteristikud. Sama nähtus tekkis, kui gaaside kineetilise teooria jaoks pakuti välja tõenäosusarvutus. Igal juhul oli see pisut erinev, kuna selle puhul oli arvutamise ja mitte psühholoogia probleem. Jõudsime gaaside kineetilise teooriani, kontseptsioonideni, mis võimaldasid paljudel erinevatel teadustel, mitte ainult termodünaamikal, teha suure hüppe edasi. Usun, et nii toimub ka kunsti-, tunde- ja aistilises vallas. Olen ma vastanud teie küsimusele? Olen ma teinud seda igas suhtes? OLIVIER MESSIAEN Jah, jah. Kolmas küsimus (absoluutselt ebadiskreetne ja kui te ei soovi vastata, võite te seda omal äranägemisel teha!). Raamatus "Muusika.Arhitektuur" tsiteerite te Parmenidese võrratut teksti, mida on üldiselt rakendatud universumi kohta ja mis sisaldab teiste hulgas mõistet "olemine" või olemise kvaliteet.* Seda teksti optimeerides võib eristada mõningaid sõnu: "see on", "sündimata", "hävimatu", "vankumatu", "lõputu", "jagamatu, katkematu". Uurinud teoloogiat, võin ma kasutada neid ainult Jumala kohta, kuna need väljendavad vaid jumalikke tunnuseid. Ometi selgitate te seda teksti energia ja energia jäävuse terminitega. Olen vägagi teadlik, et üks uutest teooriatest seletab universumi algust plahvatusega, kinnitades, et universum sai alguse fantastilisest põlemisest, mis eeldab energeetilist jõudu, millel endal võivad olla arvestatavad jumalikud tunnused. Aga ma pean teie Parmenidese selgitust täiesti erinevaks. Võite te rääkida meile, miks olete eelistanud energiat? IANNIS XENAKIS Parmenidese "Olemisest" on esimesi tekste, milles ta proovis hõlmata "reaalsust". Aga et seda teha, oli ta sunnitud ennast sellest lahti rebima ning looma teatud abstraktse definitsiooni, isegi kui see räägib tavakogemusele vastu. See võimaldas Aristotelesel öelda, et Parmenides oli hull. Õige, sest mida Parmenides ütles "olemise" kohta, vastas sellele, mida võib öelda (nagu te ise just ütlesite) ainult jumala kohta. Aga teisalt, kui me ei mõtle teoloogiale või usule, vaid püsime valdkonnas, mis on, ma usun, sama fundamentaalne ja Parmenidese mõistes palju universaalsem, ei anna tekst mingit viidet jumalale. Ta ei räägi sellest midagi. Ta ütleb lihtsalt, see on "olemine". Ta räägib ainult "olemisest", "olemisest" kui "olemasolust", mitte aktiivsest "olemisest". Seetõttu ei pane ta mõistet "olemine" infinitiivi. Nii vastuoluline, kui Parmenidese suund suhtes reaalsusega ka ei paistaks, leian ma selle olevat ühe ilmutuslikest sädemetest keset inimmõtlemise konflikti, sel ajal kui kõik teised proovisid inimesi pika aja jooksul probleemidesse mässida. Nüüd on aga Parmenidese mõistele "olemine" olemas spektraalne vastus, vastastikune sõltuvus, mille ma tekitan olemise ja energia vahele, kuna leian selle olevat lähemal teaduslikule sisule, mida ta kirjeldab. Sest tegelikult on energia miski, mis täidab maailma. Energia jäävuse põhimõte on loomulikult vaid üks põhimõtteid, aga see-eest selline, mis vastab "olemise" sellisele definitsioonile. Seetõttu olen ma proovinud leida vaste looduses, pidades silmas täppisteadusi, füüsikat. Kahtlemata ei ole see arvestatav vastus, vaid lihtsalt võrdlus, mille ma teen. Ma ei saa öelda, see on just "olemine", kuid see näib kahtlaselt meenutavat määratlust või täpsemalt kontseptsiooni energiast, mis maailma täidab. Energia jäävuse põhimõtte kohaselt energia ei alga ega lõpe, sellel ei ole lõppu ega algust. Algaatomite seisukohalt on see muidugi veidi vastuolus plahvatusteooriaga meie ülimalt kondenseeritud universumi alguses. Aga mul on võimalus mõelda sellest kui ajutisest teooriast, nagu on kõik teooriad... Parmenidese "olemise" ja energia võrdlus analoogia on ainult teatud määral. Tegelikult on Jumala tunnused identsed "olemise" tunnustega, järelikult võib inimeses leida sama loogikat. OLIVIER MESSIAEN Nüüd neljas küsimus ... IANNIS XENAKIS Kui lubate lõpetada Parmenidesega, sooviksin mainida ühte teist fundamentaalset asja, mille võib leida ühest tema fragmendist: küsimuse olemise ja mõtlemise ekvivalentsusest, mis on samuti üks pika aja jooksul inimmõtte suunajaid. Ühes kuulsaks saanud värsis, mille Platon taasesitab oma "Riigis", ütleb Parmenides: "Tema jaoks on sama olla ja mõelda." Niisiis on lause struktuur sümmeetriline tegusõna "on" suhtes. "Olemise" tähenduses olla ning mõelda on seesama. Ma näen siin sümmeetriat. Hiljem tekib ebasümmeetria, kui Descartes sedastab: "Ma mõtlen, järelikult olen". Neid kahte lauset võrreldes on kummaline tähelepanek (mis, ma usun, on vajalik), kuna see on pika aja jooksul täpselt sama mõttesuund. Ma ei tea, kas Descartes teadis ... BERNARD TEYSSÈDRE See ei ole põrmugi seesama. IANNIS XENAKIS Ei, "ma mõtlen, järelikult olen" on asümmeetriline ja kui võtame solipsistid, näiteks Berkeley, on meil teine inversioon, mis meenutab Descartes’i, aga on teise tähendusega. Niisiis objektiivne reaalsus, "olemine", ei ole veel kõik, kuid pole midagi muud kui mõtlemine. "Olemine" ja mõtlemine on võrdsed väljaspool ükskõik millist reaalsust. Kui Descartes on realist, muutub Berkeley oma solipsismiga äkki abstraktseks ja kõik taandub "mõtlemisele". Hiljem tuli muidugi üheksateistkümnenda sajandi filosoofia marksistlike arutluskäikudega, mis tunnistavad inimesest sõltumatut objektiivsust ja samuti täppisteadus, mis on kaheldav oma klassikalise mehhaanika teooriate mälestusväärse läbikukkumisega. Ja see jätkub! Seetõttu ütlevadki tänapäeva teadlased: "Kõik toimub justkui ..." OLIVIER MESSIAEN Neljas ja viimane küsimus: teie raamatu "Formaliseeritud muusika" prantsuskeelse tõlke viimase peatüki, mille te olete lisanud oma väitekirja toimikule, alates kaheksandast leheküljest, tutvustate te mitmeid tõenäosusele põhineva jaotuse meetodeid mikrokompositsiooni jaoks. Tsiteerin, meetod 4: "Juhuslik muutuja liigub kahe elastse peegelduva barjääri vahel". Kuna see on väga poeetiline, langesin ma unistuste sügavikku ... Hiljem annate te arvulise seletuse, mida ma ei suuda mõista. Võiksite te seletada seda protsessi uuesti koos mõne muusikalise näitega, võib-olla mõnega teie teoste hulgast? IANNIS XENAKIS Neljas meetod viitab põhihüpoteesile, mis algab eelmisel leheküljel 145, "Uued tõenäolisele jaotusele põhinevad ettepanekud mikrokompositsiooni jaoks." Seal on juttu rõhk-aeg-ruumist, rõhust, mida meie kõrva trumminahk võtab teatud aja jooksul atmosfääriõhust vastu. Arvestades, et sellel rõhul on suuremaid või väiksemaid arvudes väljendatavaid väärtusi, võime me viia rõhu vastavusse noodiga helikõrgusteljel ja kirjutada see noodijoonestikule. Aja funktsioonina võime me saada passaaži, valiku helikõrgusi, mis vormivad jätkuva meloodilise kõvera. Perioodilise rõhk-aeg ruumi puhul (on olemas kasti, saehamba või sinusoidi kujulisi helilaineid) kordub helilaine identselt ja süstemaatiliselt. Aga kui kordumine ei ole perioodiline, tekivad kõverad, mis looklevad erinevalt. Me võime ette kujutada, et selle kõvera veab tasandile sujuvalt liikuv punkt nii helikõrgus-aeg-ruumis kui ka rõhk-aeg ruumis sammugi tagasi liikumata, jõudes oma trajektoori definitsiooni seisukohalt sama tulemuseni. Need trajektoorid vastavad reeglitele, mis määravad punkti liikumise. Perioodilised funktsioonid alluvad väga rangetele reeglitele, mis kehtivad nii meloodiate kui ka mürade puhul. Samas tõenäosusteooriad ja selle matemaatilised kombinatsioonid võivad vastupidi toota vägagi suvalisi trajektoore, mis ei kordu iial ja mis vastavad palju rikkamatele meloodiatele ja kõladele. Kuna tõenäolised trajektoorid võivad omandada ükskõik milliseid väärtusi, võib liikuv punkt ületada kuulmispiire. Teisisõnu, helirõhk-aeg-ruumis võib esineda helirõhkusid, mis võrduvad aatompommi plahvatusega! Seetõttu on vaja sobimatuid kolossaalseid tõenäolisi energiaväärtusi piirata! Nii on ka püssitorusse kanaliseeritud kuuliga, mis püsib püssitoru seinte vahel. OLIVIER MESSIAEN Neid kutsute te barjäärideks ... IANNIS XENAKIS Need on elastsed barjäärid ... OLIVIER MESSIAEN Mis peegeldavad ... IANNIS XENAKIS Sest nad peegeldavad sissepoole, järgides elastsete pindade peegeldamise reegleid, kadudeta, energiat neelamata. Teisisõnu trajektoor, mis on loodud tõenäolise stohhastilise protsessi käigus ning valitud barjäärideni jõudes põrkub otsekui peeglist. Täpselt samuti toimub see meloodilise intervalli inversiooni puhul. Meloodia inversiooni puhul peegeldub intervall horisontaalses peeglis, asetsedes retrograadis suhtes ajateljega, mis omakorda peegeldub vertikaalses peeglis. Need on samad lihtsad printsiibid, mida võib leida kõikjal, ka muusikas. Seoses gravitatsiooniväljadega võime me ette kujutada mittepeegelduvaid pindu ning igat liiki jõude (loomulikult mõiste abstraktses tähenduses). OLIVIER MESSIAEN See kõik on imeline ... Kui palju ma ka tüli tegin, ma lõpetasin. Kuid enne, kui kõneles Olivier Revault d’Allonnes, ei soovinud ma sekkuda. Kuna ta pidas nii hiilgava kõne, ei julgenud ma teda katkestada! Ehk sooviks ta nüüd esitada mõne oma puhtalt muusikalise küsimuse, kuna mul on õnn viibida kohal? OLIVIER REVAULT D’ALLONNES Mina isiklikult jäin hätta. Xenakis ei rääkinud midagi! OLIVIER MESSIAEN Mitte pahatahtlikkusest vaid uudishimust, sümpaatiast ja imetlusest ... OLIVIER REVAULT D’ALLONNES Kord soovisin, et Xenakis räägiks oma muusika stiilist ning ta andis vägagi rahuldava ja ammendava vastuse. Ta ütles: "Kuula, mul pole midagi lisada. Kuula, ja kui sa aru ei saa, kuula veelkord. Ja siis, meeldigu see, kui see sulle meeldib." OLIVIER MESSIAEN Selles on teatud tagasihoidlikkust, mis mind isiklikult üllatab, kuna mul pole sama elukutse kui temal. Mina õpetan juba nelikümmend aastat konservatooriumis kompositsiooni ning olen kulutanud oma aega muusikateoste lahtikruvimisele, püüdes välja nuputada, mis neis toimub... Need asjad, millest te ei julgenud rääkida, mis teid ehmatasid—mina tegelesin kõige sellega pikki päevi... IANNIS XENAKIS See on õige, mäletan väga hästi. Olin teie muusikaanalüüsi loengutes ning mis mind kõige rohkem huvitasid, olid eelkõige loengud, milles te jäite tehnika teema juurde... (naerab) sest kõik muu päädis lausega: "nagu me juba tõdesime, see on ilus, kas pole?" OLIVIER MESSIAEN Tegelikult ei öelnud ma seda kuigi tihti. Ma vaikisin! IANNIS XENAKIS See on õige, küll harva, kuid te ütlesite seda mõnikord. Aga seda kõike ütlesite te stiili probleemi kohta. Ning kuna stiil ei ole juba ammu enam tehnika küsimus, on midagi muud. Minu jaoks viitab stiil lisaks tehnikale ka muusika "lõhnadele", ning mis on ilmselt veelgi huvitavam, paljudele lisatasanditele. OLIVIER MESSIAEN Jah, aga väljaspool kõiki struktuure näib mulle, et iga üksikisik ja muusik eraldi (kuna me räägime muusikast) mõistab seda, mida meie kutsume filosoofiliselt "tema äpardusteks", tema "nippideks", tema isiklikeks harjumusteks. Teine või kolmas Xenakis, kes sooviks proovida kirjutada Xenakise muusikat teie asemel, kasutades samu struktuure, ei saavutaks kindlasti samu tulemusi. Niisiis eksisteerib küsimus isiklikust stiilist. IANNIS XENAKIS Jah, möönan, et ... OLIVIER MESSIAEN On võimalik kohe ära tunda Xenakise muusika. Mitte ainult glissandode või permutatsioonide tõttu, seda on võimalik ära tunda teatud kõla, teatud orkestratsioonilaadi, teatud helide jaotuse tõttu, mis erinevad kõigist teistest. IANNIS XENAKIS Vastus Olivier Revault d’Allonnes’i küsimusele oleks ehk järgmine: elus on kaks tegevuse liiki, asju teha ja neid analüüsida. Minu jaoks on parim analüüs asju teha, teisisõnu, ma keeldun analüüsist - psühhoanalüüsist, kui soovite - enesevaatluse meetodina. Kui ennast neisse valdkondadesse juba sisse mässida, teadmata, mida on tarvis avastada, on risk langeda auku, kohutavasse lõksu. On taktika, miks ma jään kindlaks öeldes, et "asi", muusika ise, ei ole ammendav, vastandina analüütilisele diskursusele, mis on ammendav. OLIVIER MESSIAEN Ja siiski küsitlen mina iga päev sfinksi, kuna juhendan analüüsõpetuse kursust ning pole sugugi õnnetu. See ei sega mind teha muusikat! IANNIS XENAKIS Kas ei anna te väljaspool tehnilisi küsimusi teisi vastuseid? OLIVIER MESSIAEN Ma käsitlen ainult tehnilisi küsimusi. IANNIS XENAKIS Jaa ... OLIVIER MESSIAEN Loomulikult ei lubaks ma endale püstitada eesmärke väljaspool puhtalt muusikalist tegelikkust, kuna oleksin selleks kahtlemata võimetu. Kui ma seda teeksin, siis ainult väga juhuslikult. IANNIS XENAKIS Aga mida te silmas pidasite, kui rääkisite muusikalisest tehnikast? Kas see ei ole siis küsimus proportsioonidest, kestustest, kombinatsioonidest? OLIVIER MESSIAEN Ma räägin sageli kestustest, harmooniast, laadidest, värvidest. Ma tean, te ei usu ... IANNIS XENAKIS Minu meelest on see juba väljaspool tehnikat. OLIVIER MESSIAEN Orkestratsioon on minu meelest ka tehnika küsimus. IANNIS XENAKIS Järelikult on need asjad, millest võib rääkida. OLIVIER MESSAEN Muusikalisest tehnikast: täielikult ja puhtalt ning ainuüksi. Mulle näib, et seda üritas Olivier Revault d’Allonnes teilt küsida ... OLIVIER REVAULT D’ ALLONNES ... nagu ka seda, mis järgneb tehnikale ja rõhutab tehnikat. Ma ei usu, et paljastaksin erilise saladuse jutustades, et nägin ükskord Xenakist tema töölaua taga teose kallal töötamas. Tehtut üle vaadates peatus ta ühel detailil, öeldes "oi ei, see kisub küll õudseks" ning muutis seda. On see siis tehnika? (naerab) Ma usun, et nii on kõigi heliloojatega. MICHEL SERRES Ühesõnaga, oleme tagasi valiku küsimuse juures. IANNIS XENAKIS Jah, juhusliku, intuitiivse valiku. MICHEL SERRES ... mida võib soovi korral nimetada inspiratsiooniks, aga mis tähendab valikut. OLIVIER REVAULT D’ALLONNES Vältides nii sukeldumist subjektiivsuse mudastesse sfääridesse? IANNIS XENAKIS Kas muusika tegemisel pole mitte parim sukelduda just nimelt sellesse? OLIVIER REVAULT D’ALLONNES Valida keset ääretut hulka võimalusi näib Olivier Messiaenile raske probleemina. Tegelikult töötab iga meeleelund—kõrv, silm, ka kompamine—täpselt samal viisil, võttes vastu määratu koguse informatsiooni, kontrasteerides olemuslikult määravad elemendid (tõestades seega valiku tegemise tehnilist probleemi), valides ühelt poolt miljonite sinu ees olevate võimaluste hulgast ja teiselt poolt püstitades subjektiivse probleemi, otsekui "rusikas silmaauku": "see on õudne". See on täpselt sama asi. "Rusikas" või kõrv või silm funktsioneerivad selles suhtes täpselt samuti kui arvuti, võttes vastu viiskümmend miljonit bitti informatsiooni, korrastades seda ja andes laitmatult edasi. Järelikult puudub vastuolu selle, mida te kutsute jõuks, inspiratsiooniks, sündmuseks, "aistinguks" ja teiselt poolt probleemi vahel, mille te leidsite olevat nii keerulise, valiku tegemise ääretu hulga elementide hulgas. Nii töötab see elavas organismis. IANNIS XENAKIS Isegi hulgateoorias on kuulus Zermelo aksioom, mis postuleerib: antud hulgast võime me valida elemente kas juhuslikult või tänu "ilmutusele". See on matemaatika ja matemaatikat on siinjuures kasutatud täielikult, ma julgeksin öelda, esteetilisena. Probleem on selles ja filtriteks on arvutid. OLIVIER MESSIAEN Simulaatoriteks. IANNIS XENAKIS Valikusimulaatoriteks, sisaldades reegleid valiku tegemiseks. Inimene teeb kõrva ja meeltega palju keerukamaid valikuid kui suudab teha tänapäeva arvuti. Teisisõnu, valiku simuleerimine ja automatiseerimine tänapäeva tehnikaga on ikka veel väga maha jäänud võrreldes inimese võimetega. OLIVIER REVULT D’ALLONNES Jah, me ei tea ikka veel, kuidas arvutit juhtida. Närvilõpmed teevad seda, teadmata, kuidas nad seda teevad. OLIVIER MESSIAEN Võin tuua ühe näite. Kui ma kirjutan üles linnulaulu, teen ma seda paberi ja pliiatsiga. Mõnikord mu naine saadab mind ja lindistab needsamad laulud, mille ma olen üles kirjutanud. Seejärel, kui me istume kodus ja kuulame, mis on lindile jäänud, saan ma aru, kui halastamatu on masin. See on salvestanud kõik, kaasa arvatud õudse müra, millel pole mingit seost sellega, mida ma otsimas olin. Ma ei kuulnud neid mürasid: ma kuulsin ainult lindu. Miks ma ei kuulnud neid teisi mürasid? See see on, see "miks"? Sest mu kõrv töötas loomulikult filtrina. IANNIS XENAKIS Seda võib nimetada arukaks või suunatud kuulmiseks. See vastab ühele valikukriteeriumile, mida te teadmatult rakendasite iseenda suhtes, sest te soovisite kuulda ainult linnulaulu keset metsa mürasid. OLIVIER MESSIAEN Minu tähelepanu oli suunatud lindudele ja ma kuulsin neid, aga ma kuulsin neid, välistades ebameeldivad helid, nagu mööduvad autod või lennukid ... IANNIS XENAKIS Välistades teised helid. Veelgi enam, informatsiooniteoorias kõik, mis pole soovitud või valitud signaal, heidetakse kõrvale kui müra. OLIVIER MESSIAEN Me kuuleme, mida me tahame kuulda. MICHEL SERRES Me kuuleme signaale. IANNIS XENAKIS Jah. Ja raskus mõnda teost hinnates on eelkõige valida, mis on oluline. Seetõttu kuulates Bachi teost, mida on mängitud juba sadu, tuhandeid kordi, võib see paista sõltuvalt valikutest, mida sa antud hetkel teed, täiesti erinevana, kui sa oled harjunud kuulma. Huvitav ei ole ainult teos iseeneses, vaid ka kuulaja individuaalne ja isiklik valik. Miks Newton, saades äkki vopsu ninale kukkuvalt õunalt, hüüdis: "Leidsin! Heureka!" OLIVIER REVAULT D’ALLONNES Kõik see räägib meile rohkemal või vähemal määral, kuidas sina teed valikuid, aga mitte seda, kuidas sa otsustad, mis on "õudne" või vastupidi. Kellelt võime me seda küsida kui mitte teilt, heliloojad? OLIVIER MESSIAEN Enne, rääkides struktuurist, mainisime Bachi fuugasid. Tänapäeval ei ole midagi strukturaalsemat ja (vabandage mind) igavamat kui akadeemiline fuuga. Bach kirjutas tuhandeid fuugasid; neid oli kõikjal, kõigis tema teostes, tema kantaatides, passioonides, missades, oreli- ja klahvpilliteostes. Need fuugad ei ole iial struktuureeritud nii nagu akadeemilised fuugad ja nad erinevad kõigist teistest samal perioodil kirjutatud fuugadest, sest nad järgisid teatud meloodilist rõõmu ja harmoonilist kontrolli, mis oli omane ainult "papa" Bachile. IANNIS XENAKIS Jah, usun, probleem on selles. OLIVIER MESSIAEN Läheksin veel kaugemale. Kui Bachil oleks olnud pisutki sellest, mis on teil. Mõnikord on tal lisakohustused! Näiteks teatud koraalides on selleks koraalimeloodia, mida Bach ei puudutanud, sest see oli püha tekst. Ta jättis selle nagu see oli. See oli tahtlik valik. Madalaimas bassis on ostinato, mis on samuti tahtlik. Sisemistes häältes kromatism: jälle tahtlik ja järelejätmatu. Kolm ülestikust ülesannet seletavad modernsete akordide ja kontrapunkti tavatut kokkupõrget, mille võiks peaaegu allkirjastada Debussy. See on ehk üheks võimaluseks mõista, kuidas struktuur võib sünnitada midagi uut ja personaalset. IANNIS XENAKIS Tänapäevases valguses ei ole fuuga totaalne struktuur, see sisaldab vabu osi ning üksikuid rohkemal või vähemal määral jälgitavaid selgelt defineeritud skeeme. Kuid nende skeemide raames asuvad "andmesisestused", nagu neid nimetatakse tänapäeva informaatikas, mis võimaldavad saada samade skeemide põhjal erineva tulemuse. Neisse vabadesse andmesisestustesse võivad olla kaasatud suured, kõige laiemas mõttes vabad infomäärad ning vastandlikud ülesanded. Aga neid skeeme võib süsteemi või automaatika omaduste funktsioonide autonoomia tõttu üle kanda ja just selles ilmneb fuuga mõjukas üleolek oma aja teaduslikust mõtlemisest, kuna fuuga pakub süsteeme, mida tolleaegne teadus ignoreeris. Alles veidi aega tagasi hakkas teadus süstemaatiliselt tegelema süstemaatiliste meetoditega, teisisõnu stohhastilise või deterministliku kellavärgiga. MICHEL SERRES Ei. Seitsmeteistkümnendal sajandil, pisut enne, kui Bach kirjutas fuugasid või koolis nõuti fuugade kirjutamist, tegeles kogu teaduslik mõte automaatidega. Lõpuks on see teaduse ja kunstide kaasaegsuse demonstratsiooniks. IANNIS XENAKIS Jah, sul on õigus, ka Descartes räägib sellest palju. MICHEL SERRES Just, Descartes ... Olivier de Serres. IANNIS XENAKIS Aga abstraktset automaatikat ei pakkunud välja keegi muu kui muusikud. MICHEL SERRES Just, jah ... võimalik ... mängutoosid olid moes. IANNIS XENAKIS Ning tulemusi, mida pakkus absoluutne automaatika, materialiseerisid muusikud nendega mängides. MICHEL SERRES Jah, õige, nad olid teadusest ees, nagu tavaliselt. BERNARD TEYSSÈDRE Ent tulgem tagasi meie teema juurde ... kummaline, fuugas ei ole minu arvates huvitav mitte abstraktne automaatika, vaid nimelt vaba osa, milles Bach suutis rakendada oma isiklikku geeniust. IANNIS XENAKIS Jah, kuid enam ei ole võimalik välistada fakti, et võrreldes teiste muusikavormidega on fuugal ülimalt kompaktne allstruktuuriga vorm, millele võib lisada teisi "vorme". Loomulikult, tulemused ei oleks samad, kui selles puuduksid need allstruktuurid, see skeem. BERNARD TEYSSÈDRE Aitab. Kui debatt Olivier Messiaeniga keskendus põhiliselt muusikale, usun ma, et arutelu Michel Ragoniga tegeleb üksikasjalikumalt arhitektuuriprobleemidega. Dialoog Michel Ragoniga MICHEL RAGON Arutelu käigus on tsiteeritud tihti Xenakise raamatut "Muusika.Arhitektuur". See on üks kahest raamatust, millesse on kogutud kõik Xenakise tekstid, teine on "Formaliseeritud muusika". Selle raamatu pealkiri "Muusika. Arhitektuur" on tabav, kuna need kaks loovvaldkonda, muusika ja arhitektuur, on Xenakise töös tihedalt seotud. Kui mingil perioodil olid need kaks valdkonda Xenakisel mingil perioodil lahus, siis nüüd on nad taas täielikult ühinenud. Nad olid eraldi ajal, mil me teadsime Xenakisest vähe, siis kui Xenakis oli Le Corbusier’ kaastöötajana niiöelda "puhas" arhitekt. Xenakis töötas Le Corbusier’ juures kaksteist aastat. Te teate, kui töötada teise arhitekti, ülemuse huvides, siis kõik, mida sa teed, kõike, mis on loodud ülemuse käe all, peetakse iseenesestmõistetavalt ülemuse omaks. Seetõttu soovin ma pöörata tähelepanu kahele Le Corbusier’ allkirjastatud projektile, mille kallal tegelikult töötas Xenakis üksi. Pean silmas Tourette’i nunnakloostri fassaadi aastast 1954. On piisavalt lihtne veenduda, et selle autoriks on Xenakis, kuna tegu on arhitektuuriga, mis näeb välja nagu partituur. Samuti Philipsi paviljoni aastast 1956 võib kutsuda "muusikaliseks reservuaariks." Need kaks Le Corbusier’ büroos Xenakise osalusel loodud projekti on Le Corbusier’ enda poolt algusest peale tunnistatud Xenakise töödeks. Meie käsutuses on kaks Le Corbusier’ teksti, millele on viidatud ka raamatus "Muusika.Arhitektuur", mis annavad nende tööde puhul tunnistust Xenakise kaalukast panusest. Mainisin seda möödaminnes, kuna mõned arhitektid eitavad Xenakise õigust pidada omaks Le Corbusier’ allkirjastatud töid. Olles vähem rojalist kui tema õpilased või jüngrid, on Le Corbusier kindlalt kinnitanud, et nimetatud tööd kuuluvad Xenakisele. Ning siis veel polütoobid! Olivier Revault d’Allonnes on kirjutanud ammendava raamatu polütoopidest, mis räägib neist paremini kui mina suudaksin. Selles läbipaistvas helendavate punktide toe ülesannet täitvas terastross-arhitektuuris struktureerib valgus ruumi üürikeste konstruktsioonidena, on arhitektuuriks valgus ise. See on samuti oluline osa Xenakise arhitektuuriloomingust ja antud juhul arhitekti töö sügavaimast seosest muusiku tööga. Niisiis on see Xenakise korduv utoopia totaalsest etendusest. Kahtlemata see on totaalne etendus, mille tunnistajateks me võisime olla imetoredal ööl Persepolises, kui kanti kahtsada viitkümmet tõrvikut, millele on samuti sageli viidatud. Aga vaimustuda võib ka Xenakise uuest särava ämblikuvõrgu sarnase lõuendi ideest üle linnade ja maade, ühendamas maad ja kuud valgustatud hõõgniitidega, loomas kunstlikke virmalisi ... Kõik need on asjad, millest ta räägib, millest teie, Iannis Xenakis, räägite meile oma väitekirja toimiku kokkuvõttes. Kuid on olemas ka teie töö teine aspekt, mille ma usun olevat rohkem teada ning mistõttu sooviksin ma peatuda sellel. Viitan teie tulevikuarhitektuuriprojektile, teie utoopilisele arhitektuurile. Minnes tagasi teie raamatu "Muusika.Arhitektuur" peatüki juurde pealkirjaga "Kosmiline linn", sooviks ma küsida sellel teemal mõned küsimused, kuna sellised on mängureeglid. Tsiteeriksin mõningaid lõike teie tekstist "Kosmiline linn". Te alustate küsimusega, kas poleks aeg valida linnade arhitektuurilise detsentraliseerimise või tsentraliseerimise vahel. Ning te soovitate kategooriliselt tsentraliseerida, mida keegi ei tohiks ka pidada vääraks. Teisisõnu, te olete vastu lineaarse linna teooriale, mille üks autoreid on Le Corbusier, süüdistades seda naiivsuses ja pakute välja võimaluse konstrueerida vertikaalseid, tihedaid linnu, mis ulatuks kolme, kohati isegi viie tuhande meetri kõrgusele. Niisiis mitte väga suuri üleni metallist linnu, teatud tüüpi hiiglaslikke pilvelõhkujaid, mis sisaldaks täielikku linna morfoloogiat. Nagu te ütlete, te leiate, et kontsentratsioon on inimkonnale eluliselt vajalik, täielikult on vaja muuta praegusi urbanistlikke ja arhitektuurseid ideid ning asendada need uutega. Sellest minu esimene küsimus, kuigi see tekst on üsna vana, pärinedes aastast 1964. On võimalik, et te olete seda edasi arendanud. Tänane kokkusaamine on võimaluseks teiega pisut vestelda ja teid küsitleda. Lõpuks on mul võimalus küsida teilt mõned küsimused, mida ma soovisin küsida juba ammu. Usute te ikka veel sellesse kaksteist aastat tagasi välja töötatud tsentraliseerimise ideesse? Kas te leiate selle olevat veel vajaliku, kui elektrienergia jaotamine või looduslik, nagu näiteks päikese- või tuuleenergia võimaldavad detsentraliseerimist, millel pole midagi ühist mineviku detsentraliseerimisega minevikus? Teisisõnu, kui kultuur ise võib olla tänu elektroonilistele vahenditele lihtsalt detsentraliseeritav? Usute, et selline keerukas tsentraliseerimine on ikka vajalik? Või on see idee võrreldes aastaga 1964 iganenud? IANNIS XENAKIS Leian, et tsentraliseerimine, pigem inimese eluasemete ja inimsuhete tsentraliseerimine, mida ma eelistaksin kutsuda "tihenemiseks", on eelkõige ajalooline paratamatus, mida me võime leida nii linnaehituses kui ka inimelamute kõigis vormides, aga ka inimestevahelistes sidemetes, kultuuris, kõikjal. Mis teeb selle järjest vajalikumaks tänapäeval, on hajutatud linnadest moodustuva planetaarsele ruumile sarnaneva otsekui nahkja kile pealetung, mis hävitab loomuliku keskkonna [valglinnastumine, tlk]. Tegelikult eksisteerib kaks tendentsi: tihenemine kuni kompaktsuse (suurima võimaliku tiheduseni) ning tsentrifugaalne hajumise tendents, mille puhul eelistatakse võimaluse korral tagasi pöördumist maaelu juurde keset rohelist loodust. Kui see ei ole aga võimalik, luuakse see kunstlike vahenditega. Need on kaks loomulikku tendentsi, kuid kompaktsuse tendents kujuneb paratamatult olulisemaks, kuna industriaalajastul toimub Maa rahvastiku plahvatuslik tihenemine. Ka teine tendents on loomulik, sest see vastab mineviku nostalgiale ning praegune linn on kaugel loomulikust keskkonnast, mida inimese keha ja vaim vajavad. Tegelikult need kaks tendentsi võitlevad. Kusjuures küllastatuse (või kompaktsuse) tendents on võidukas nii majanduslikel, kui ka muudel erinevatel põhjustel. Nõustun praegugi sellega, mida ma pakkusin välja aastal 1964. Olen veendunud, et see on lahendus, ehkki ajutine, aga palju huvitavam ja vähem kriminaalne kui hajutatus üle maakera pinna. Tihenemine ei tähenda, et ma välistaksin inimese privaatsuse, tema õiguse eralduda indiviidina selles üüratus tarus, mida tänapäevane linn on. Ma leian vaid, selle asemel et laiuda üle pinna, mis loob inimtegevuses kontaktiprobleeme, peaksime organiseerima linna vertikaalselt. See ei ole põrmugi uus mõte, kuna väiksemas ulatuses eksisteeris see väide juba kahekümnendatel, mil esitati küsimus "aedlinna" (nagu neid siis nimetati) ja "vertikaalse linna" vahelisest valikust. Le Corbusier oli üks vertikaalse linna kaitsjatest. Aga need vertikaalsed linnad kujutasid siis ainult puhtaid ja lihtsaid elamuid, mitte kogu linna. Nad ei hõlmanud linna kõiki funktsioone, kui mina leian, et peaksime seda mõtet tehnilistel ja inimsuhetest tulenevatel põhjustel avardama kõikidele linna funktsioonidele ning ka selleks, et põhjalikumalt tajuda, mis jääb meist pärandina maailma maha ja seetõttu, et selline süsteem võimaldaks ehitada linnu elamiskõlbmatusse, liiga kuuma või ka liiga külma kliimasse, nii ülerahvastatud kui ka kõrbealadele. Ma usun, et vastasin teie esimesele küsimusele. MICHEL RAGON See tekst on kirjutatud kaksteist aastat tagasi kaasaegsena teistele tekstidele, teistele paralleelteooriatele, näiteks Yona Friedmani "linn õhus", Nicolas Schöfferi "küberneetiline linn" või Paul Maymonti asustatud püramiidid. Kuidas seostaksite te ennast nende tulevikuarhitektuuri teooriatega, mis sündisid teie teooriaga üheaegselt? IANNIS XENAKIS Võrreldes minu omaga leian nad olevat arglikud! Tegelikult on nad suhteliselt redutseeritud skaalaga suurekontsentratsioonilised ekstrapolatsioonid, käsitledes üldiselt vaid individuaalelamuid ja mitte linna tervikuna. MICHEL RAGON Usun, et mitte keegi enne meie aega ei ole visandanud kolme, nelja või viie kilomeetri kõrgust konstruktsiooni. Kuni teieni oli kõige utoopilisemaks vertikaalse linna suunaliseks progressiooniks Frank Lloyd Wrighti 1660 meetri kõrguse torni projekt. IANNIS XENAKIS Jah, kuid see l660-meetrine torn oli bürooehitis, millel oli kaks viga: esiteks, see polnud piisavalt kõrge ja teiseks, see oli tuletis oma pindstruktuurist, mis oli konstrueeritud "portikusena"), transformeerudes lõpuks otsekui l660 meetri kõrguseks obeliskiks. MICHEL RAGON See on õige, see oli teatud tüüpi obelisk, samal ajal kui teie olete leidnud oma projektile ülimalt huvitavad vormid. IANNIS XENAKIS See toimus otsekui ilmutusena. Olin just kavandamas Philipsi paviljoni, mis on vormitud S-kõverpinnnana. Eindhoveni lähedal Hollandis toimunud laboratoorsete katsete tulemusena ma taipasin, et S-kõver on ülimalt vastupidav ja selle vorm ei hävine. Need katsed teostati, kuna algsed teoreetilised arvutused nii materjali tugevuse kui ka elastsuse kohta ei andnud võimalust asju lõpuni läbi näha ning jäid suured ebakindluse marginaalid. Katsed näitasid S-kõverpindade geomeetriast tulenevat ülimat vastupidavust. Need olid "PH-d" ehk hüperboolsed paraboloidid. On oluline valida tasandist piisavalt kauge S-kõver. Siis ma leidsin otstarbekana kasutada seda pinnastruktuuri geomeetrilist omadust ning sellest tulenevalt planeerida linn, mitte obeliski või pilvelõhkuja, nagu me näeme siin Pariis või Ühendriikides, vaid pideva S-kõvervormina. Need oleksid ruumilised kelmed laiusega sada või sada viiskümmend meetrit, loomulikult aukudega ja läbipaistvad, tagades ventilatsiooni, läbinähtavuse, valguse ja muu... On olemas linnu kõrguses kaks tuhat meetrit, Mexico ja Bogota. See on täielikult elamiskõlbulik kõrgus. Muidugi, viis tuhat meetrit on erinev, kuna õhu hõrenemine muutub kriitiliseks. Keegi ei tea täpselt, mis hakkab toimuma. Aga tänapäeva tehnoloogiaga on nagu lennukis võimalik saavutada piisav hermeetilisus, temperatuuri kontroll ning õhuvahetus. Lõppude lõpuks linn nagu see sarnaneks lihtsalt inimese rõiva avardamisega. Inimene ei tundnud väga pikka aega riietust. Rõivad kannab ta alles umbes kümme tuhat aastat, mitte rohkem. Enne oli ta riieteta, alasti. Hiljem pani ta selga individuaalsed personaalsed rõivad. Ta töötab hommikust õhtuni paigas, kus ka meie õigupoolest nüüd oleme, kus ei ole õhku ja kus ta ei näe päevavalgust. Enamus inimesi töötab nii kontorites ja vabrikutes. Selline keskkond võib olla inimese tervisele vägagi kahjulik, kuid mõeldes tänapäeva tehnoloogiale ning tehnoloogiale lähitulevikus, need probleemid lahendatakse selliselt, et igaüks riietab linna enda jaoks ise, saavutades nii suurema füüsilise, kontseptuaalse, mentaalse ja spirituaalse vabaduse. See eeldab lihtsalt tänaste tehniliste võimaluste ekstrapolatsiooni, laiema skaala kasutamist. Linn, mille mina välja pakun, ei ole mõeldav piiratud kapitalistliku süsteemi tingimustes. Siiski võib seda realiseerida paljurahvuseliste koosluste või ka tsentraliseeritud riikide (nagu näiteks Prantsusmaa) poolt, mis suudavad neid ehitades vältida munitsipaalsüsteemi. Seda tüüpi üksuste projekteerimisega suudaks tegelda vaid mitmete kümnete miljonite elanikega riigid või ka üksikud rahvusvahelised korporatsioonid, kasutades selleks kas kõrbelisi, kuumi ja niiskeid ekvatoriaalseid või väga külmi piirkondi nagu Siber, Alaska või Põhja-Kanada. MICHEL RAGON Kas need pole mitte energiapiirangud, mis teevad keeruliseks juba mõttegi sellises mahus kütmisest? IANNIS XENAKIS Loomulikult on see seotud energiaprobleemidega. Kuid juba praegu on olemas materjale ja isolatsioonisüsteeme, mis võivad oluliselt vähendada soojuse ja energia kadusid. Ma ei usu, et tehnilised takistused oleks tõelisteks takistusteks. Suurimad takistused kuuluvad kahte kategooriasse. Kõigepealt organisatsioon, kuna linn on organisatsioon ... MICHEL RAGON Ma olin selleni jõudmas. Olin just ütlemas, et te peaksite sellist vertikaalset linna organiseerides järgmisena ette nägema elektroonilise halduse ja otsustamise süsteemid. Kuigi Nicolas Schöfferi "küberneetilises linnas" leiame me samuti usu küberneetilistesse ja elektroonilistesse haldusese ning otsustamise süsteemidesse. Kas te ei harrasta mitte usku, mis minu jaoks näib ohtlikuna, arvestades teaduse poliitilist neitsilikkust? Seda kohtab muuseas aeg-ajalt teie kirjutistes. IANNIS XENAKIS Ma ei tea, mida Nicolas Schöffer täpselt ütleb. Ma usun, ta tegeleb pigem küberneetika müstifitseerimisega... MICHEL RAGON Jah, ta läheb kaugemale kui teie: see muutub tõepoolest teatud müstikaks. IANNIS XENAKIS Praegu on infotöötlus või haldussüsteemid üpris mahajäänud ja primitiivsed. Automaatsele haldusele võib hetkel usaldada vaid üksikuid kontrolliülesanded. Aga see on ka miski, mis töötab. Näiteks linna valgusfoorid on muutunud järjest enam ja enam automatiseerituks, reageerides ümbritsevate tänavate vastureaktsioonile, see on fakt. MICHEL RAGON Selline automatiseerimine on peaaegu alati repressiivne. IANNIS XENAKIS Seisame silmitsi kahe probleemiga: esiteks organisatsiooni ning teiseks palju sügavama sotsiaalse struktuuri probleemiga. Rääkides organisatsioonist on ilmne, et linn, mis koondab viie tuhande meetri kõrgusena miljoneid inimesi, ei saa olla läbini ette planeeritud, sest see kujutaks riski luua surnud linn. Nii juhtus Detroidi, Le Havre’i, Brasília ja Chandigarh’iga. Nad ei tööta, sest nad olid planeeritud laboratooriumis - pean silmas arhitektuuribürood - järgides kas traditsioonilisi joonestuslaua reegleid või mõnikord isegi revolutsioonilisi ideid. Ei ole võimalik võtta arvesse kogu linna tema komplekssuses tuginedes vaid üheleainsale ajule. Küll on aga võimalik tekitada raam, niiöelda konteiner, jättes defineerimata ja määramata sisu. See annaks piisava vabaduse, et sisu võiks areneda järk-järgult. Peaks olema arusaadav, et sellist linna ei ole võimalik püstitada viie või kümme aastaga, on vaja pühendada kakskümmend või kolmkümmend aastat ainuüksi konstruktsioonile. Niisiis mitte linna ennast ei kavandata ette kakskümmend või kolmkümmend aastat, aga "konteinerit", teisisõnu fundamentaalstruktuuri, mis peab selle kõrguse saavutama. Teisalt peaks see võimaldama vigade parandust, arengut, ka vastuolusid, mis ilmnevad linna arengu käigus jätkuvalt. Järelikult on absoluutselt vajalik kujutada ette teatud määral mobiilset arhitektuuri. Vihjeid sellisele ideele võib leida Jaapani arhitektuuris, mis võimaldab erinevatest funktsioonidest sõltuvalt ruumi või hoone transformatsioone. MICHEL RAGON Nagu te äsja rõhutasite, on sisemine nomaadlus võimalik tänu mobiilse arhitektuuri permutatsioonidele. IANNIS XENAKIS Linna materiaalsest aspektist rääkides ei rääkinud ma sisemisest nomaadlusest, rääkisin lihtsalt nomaadlusest. Me võime anda linnaalale või -piirkonnale ühe või teise, näiteks tööstuse funktsiooni ning muuta see mõne aja pärast elamu- või pargifunktsiooniks jne. See on linna materiaalse sisestruktuuri mobiilsuse küsimus. Mis puutub teise keerulisemasse takistusse, inimelamu funktsiooni selles konteineris: on ülimalt vajalik jätta vabadus või pakkuda välja piisavalt vaba plaan, mis kindlustaks selle valdkonna autonoomse arengu, et vastuolud oleks kõrvaldatavad, vorm oleks muudetav. (Ma ei ütlegi, et konflikte võiks välistada või absorbeerida. See on utoopia, mis ulatub üheksateistkümnendasse sajandisse, kui mitte varasemasse aega.) MICHEL RAGON Te kirjutate ka: "Kuna see linn", teie linn, "on kujundatud, järgides universaalset tehnikat, oleks see võrdselt kasutatav populatsioonide puhul kaugel põhjas (või lõunas), troopikas või kõrbetes." Teisisõnu, see tekst paistab mulle ohtliku tehnokraatliku usuna universaalsesse või tüüpilisse inimesse. See on väga levinud idee, mida võib leida Le Corbusier’l, samuti Gropiusel. Ja kuna eksisteerib universaalne, "tüüpiline" inimene, järeldavad arhitektid, et sellisele inimesele on võimalik konstrueerida tüüpilist ja universaalset arhitektuuri: usk, millest me oleme nüüdseks peaaegu toibunud. IANNIS XENAKIS Jah, see on nimelt tehnoloogia, mis loob teatud universaalsuse, aga ma imestan, kui oleksime päriselt lahti öelnud ideest või vaimsusest. Kui te võtate arvesse, mil määral tehnoloogilised vahendid on levinud... Vägagi primitiivsete ühiskondade keskustes on olemas elekter, erinevad energialiigid ja energiatransformatsioonid, kuid ka institutsioonid—millised vahendid on praegusel ajal koolidel, ülikoolidel, käsiraamatud igal pool kuhu vaatad. Teaduslik kirjandus ja laboratooriumid on samad, riietus on sama, isegi kui need ühiskonnad on erineval ajaloolisel arenguastmel. Nüüdsel ajal on inimesed harva riietatud rahvariietesse, fakt, mille on põhjustanud üldine erinevat liiki põhjustest tulenev universaliseerumine. Teisalt, ma ei ole tehnokraat, kaugel sellest. Vastupidi. Kuigi ma leian, et praeguse aja tehnoloogiat peaks kasutama ja rakendama. Igal väitel on vähemalt kaks aspekti: must ja valge. Sama on tuumaenergiaga. On uskumatu ime, et inimene on suutnud näha ja tungida mateeria mikrokosmosesse ja ära kasutada, mida ta seal leidnud on. Samuti on täiesti normaalne leida kõrvalekaldeid inimloomuse selles osas, mis puudutab inimese kaasasündinud konfliktsust, niisiis küsimust individuaalse ja sotsiaalse võitlusest. MICHEL RAGON Lõpuks, viimane küsimus: kuhu paigutate te ennast arhitektina, olete ikkagi arhitekt, luues näiteks ülitihedas seoses muusikaga projekteeritud arhitektuuri George Pompidou keskuse esisele väljakule Pariisis, niisiis muusikalisi polütoope? Samuti konstrueerisite te hiljuti eramu muusik François-Bernard Mâche’le. Kuidas seostate te oma arengut teie endise tööandja Le Corbusier’ga, kes on tänapäeval vaielnud paljude teie kolleegide ja arhitektuuriteoreetikutega? IANNIS XENAKIS Esiteks, seos arhitektuuriga... Otsustades luua ainult muusikat, olin ma väga hädas, sest arhitektuur oli minu jaoks väga oluline. Kuid nii ma tegin, sest pidin valima. Kas teha teadust või hakata ärimeheks. Kuuekümnendatel läksin ma arhitektide büroodesse ja ütlesin: "Siin ma olen! Esitlen ennast arhitektina, kes sooviks teha koostööd, aga ei taha olla ori, tahan uurida." See oli võimatu. Te teate väga hästi, et üldiselt on väga vähe võimalusi tegelda arhitektuuriuurimusega. Seepärast piirasin ma ennast muusikaga, kus kõigist raskustest hoolimata võin ma pühenduda kunsti uurimisele. Nii öelnud ja teinud, olen ma alati valmis looma arhitektuuri, kui vaid saan. Näiteks see Beaubourg’i "vidin" — kavandasin teisaldatava struktuuri, mida võib hoida üleval mitu kuud ja võtta seejärel selga koos laserite ja elektrooniliste välklampide etendusega, nagu Cluny’s, ainult võimsama. Sellel on tekstiilstruktuur, mis seetõttu eeldab mõningaid arhitektuurseid põhilahendusi. Teisalt seoses Le Corbusier’ga ma ei tea, kas on palju teisi arhitekte, kes oleks saanud teha seda, mida ma nimetaksin kunstiliseks väljenduseks. Erinevalt üksikutest ideedest, mida arhitektil või urbanistil ikka leidub, on see midagi vägagi kompleksset, pärinedes erinevatest allikatest ja suundadest. Marseille projekti ühe perekonna sahtelkorteriga võib loomulikult vaielda ja see on ka vaid üks võimalikke lahendusi. Ei saa aga öelda, et see oleks ainus lahendus. Lisaks, Le Corbusier on tõendanud seda ise, kavandades igat tüüpi maju. Kuid tema kunstilisi ja arhitektuurseid kvaliteete, mida leiab praktiliselt kõigis tema töödes, ei ole võimalik vaidlustada. Ideed tulevad ja lähevad, aga kunstifakt jääb. See on üks ajaloo õppetunde, nagu rõhutas Marx antiikkunsti vaadeldes. Ta ütles midagi sellist, kuidas tsivilisatsiooni ja lääne kultuuri alguses on orjade ühiskonnad kõigele vaatamata loonud teoseid, mis mõjutavad meid tänapäevani? See on kunstifakti kaasasündinud ime ja vastus varasemale arutelule, küsimustele, mida esitasid Olivier Messiaen ja Revault d’Allonnes. Le Corbusier’d võib teatud asjades vägagi kritiseerida. Tegin seda isegi. Kuid usun, ta on üks meie aja suuremaid arhitekte. Neid ei ole tänapäeval kolmkümmend kuus, neid ei ole ehk ühtegi. MICHEL RAGON Mul ei ole rohkem küsimusi. Kuigi ma nokkisin teid pisut tehnokraatlikkuse pärast, ei saa ma jätta rõhutamata, et kõigis teie tekstides on ülistatud eelkõige kunsti. Kuuldes pidevalt kunsti surmast, on selline kunsti ülistamine tänapäeval vägagi ebaharilik ja tähelepanuväärne. Samuti tundub teie kunstnik-algataja definitsioon olevat minu jaoks midagi väga olulist. Rõhutan veelkord kõigis teie tekstides, teie mõtlemises seda, mida te mitte enda kohta, aga seoses sellega, milles teie töid võiks süüdistada, kutsute "külmaks tuleks". Olen teid alati näinud niiöelda "külma tulena". See on mind alati võlunud, nii teie muusikas kui ka teie arhitektuuris. Teie tulise imetlejana pean suureks auks olla täna siin, mitte teie kohtunikuna, vaid teid tervitamas. Dialoog Michel Serresiga BERNARD TEYSSÈDRE Annaksin nüüd sõna Michel Serresile. MICHEL SERRES Ma ei usu, et ruum oleks ühiskonna kuvandiks ainult arhitektuuris. Näiteks täna on selle laua taga imetleja ja selle ees looja. Ei ole minu viga, et selline on ülikooli kuvand. Ülikool on osaline väitekirjas, kuid mitte, loomingus. Kuna meie ees on kordki nii looming kui ka väitekiri, äratab see nii palju imetlust, et ma sooviks tervitada seda nähtust, mida esineb nii harva meie institutsioonide üldises mõtteruumis. Seetõttu olen imetleja, kes soovib esitada küsimusi. Tuleksin tagasi matemaatika ja muusika seoste juurde. Väitekirja kokkuvõtte leheküljel 14, rääkides kunstnik-algatajast, pakute te välja globaalse idee üldisest morfoloogiast. Mis on üldine morfoloogia? IANNIS XENAKIS Hästi, igas inimtegevuse vallas kujuneb nagu mingi vahuna vorm. Olen märganud mõningaid kujundeid, mõningaid vorme, mis kuuluvad kas abstraktse loogilis-matemaatilise või konkreetsema füüsikalise spekulatsiooni hulka, sisaldades nii atomaarseid kui ka subatomaarseid ilminguid või geneetika geomeetrilisi väljundeid, nagu molekulaarsed keemilised reaktsioonid. Samas need kujundid, need vormid, mis kuuluvad nii paljudesse erinevatesse valdkondadesse, omavad nii kütkestavaid kokkulangevusi kui ka mitmekesisust ning võivad selgitada teisi valdkondi nagu näiteks kunstilist tegevust. MICHEL SERRES Mis aastal te seda kirjutasite? Kas hiljuti? IANNIS XENAKIS Oh! Ma ei tea, mitmed aastad tagasi. MICHEL SERRES Kaks küsimust või allküsimust. Artikli lõpulõigus, kus te tutvustate üldist morfoloogiat, kasutate te näitena selgroogsete vormide evolutsiooni. IANNIS XENAKIS Selgroogsed on jah üheks näiteks. MICHEL SERRES See on väga hea näide. Kellelgi enne Xenakist oli ka idee üldisest morfoloogiast, kuid vaid bioloogias. Geoffroy Saint-Hilaire’l oli idee üldisest tasandist, mida võib projitseerida kõigile selgroogsetele ning veelgi üldisemalt tervele loomariigile. Aga praegusel hetkel on veel keegi, kes töötab mõttega üldisest morfoloogiast sellisel viisil, et teie mõte morfogeneesist langeb kokku juba töötava teadusaspektiga: pean silmas René Thom'i. Nagu ikka, on muusik esirinnas. IANNIS XENAKIS Seda parem! Thom võiks ka sõna võtta kunstivallas ja mitte ainult füüsikas. Aga ma usun, sellel ideel on muudes vormides palju eelkäijaid? MICHEL SERRES Geoffroy oli esimene, kas pole? IANNIS XENAKIS Ma ei tea. Seda võib leida juba antiikajast, kui esimest korda rakendati arhitektuuris ideed inimese vormiproportsioonidest. See on lokaalse morfoloogia juhtumiks. MICHEL SERRES See lokaalne morfoloogia ei ole Xenakise mõttes üldine morfoloogia. IANNIS XENAKIS Kuid ma leian, et on hädavajalik luua kõigi võimalike vormide kõigi tahkude teatud tüüpi konvergents, mis eeldaks teadmisi kõigis neis erinevates teadustes. MICHEL SERRES Kas teie sedalaadi morfoloogia projektil oli ka matemaatiline raam? IANNIS XENAKIS Oh ei! Mitte põrmugi ... MICHEL SERRES Topoloogia? IANNIS XENAKIS Topoloogia? Topoloogia, millises mõttes? Kuna topoloogia on matemaatikas üks fundamentaalsemaid teadusi... MICHEL SERRES Kindlasti, mis puudutab vorme. IANNIS XENAKIS Mis puudutab vorme, aga mitte ainult vorme, ka matemaatilist filosoofilist mõtlemist, kas te ei arva? See on pidevuse, katkevuse, kokkupuute ja sidususe probleem. MICHEL SERRES Raamid. IANNIS XENAKIS Jah, raamid ning järelikult vormid. Topoloogia on tõenäoliselt olulisim tööriist, kuigi ma arvan selle olevat tänapäeval veel üpris tahumatu. Liiga ebatäiusliku selliste keeruliste ülesannete jaoks nagu pilveformatsioonid või populatsioonivormid. MICHEL SERRES Kuid idee üldisest morfoloogiast sai alguse just siis, kui töötati selliste probleemide kallal nagu pilveformatsioonid. Mis puutub teie esimesse lisasse, nimekirja muusika ja matemaatika arengu kokkupuutepunktidest, olen teiega nõus ja sooviks lisada vaid üht. Kui te räägite, et enne meie ajaarvamist eksisteeris midagi sellist nagu pillikeele pikkuse ja helikõrguse võrdlev analüüs, eeldan ma teid viitavat Pythagorasele ja pütagoorlaste koolkonnale. Tänapäeval on järjest levinum veendumus, et tol ajal ei eksisteerinud analoogiat esimeste muusikaliste intervallide ja matemaatilise teooria vahel. Pigem arvatakse, et see on rohkem põhjuse ja tagajärje küsimus, tähendades seda, et tänu muusikale arenes idee naturaalarvude poolrühmast ja murdudest ning jagatistest. Kui see oli põhjuseks, võis muusika olla matemaatilise teooria matriitsiks. IANNIS XENAKIS Jah, see on arheoloogia probleem. MICHEL SERRES Taas on muusikaline mõtlemine esirinnas. Millises mõttes te leiate, et fuuga on automaat: fuuga on abstraktne automaat, mis on loodud kaks sajandit enne teadust automaatidest [edaspidi 'automaatika', tlk]?" Ma usun, see pole õige. Arvan, et automaatika esineb samal ajal, kui mitte varem. IANNIS XENAKIS Oh ei, mitte automaatika. Automaatika sündis 20. sajandil. MICHEL SERRES Mitte automaatika, vaid automaatide konstrueerimine. IANNIS XENAKIS See on erinev, kuna automaatide kasutamine pärineb vähemalt Aleksandriast. MICHEL SERRES "Tuhandes ja ühes öös" on näiteks automaatsed purskkaevud, veemasinad. IANNIS XENAKIS Jah, aga "Tuhat ja üks ööd" pärineb 12.sajandist, kuid automaate kasutati palju varem. Aleksandria perioodil tunti juba Heronit ja esimest aurumasinat. MICHEL SERRES Jah, samuti Archytuse tuvi. IANNIS XENAKIS Need kõik on konkreetsed leiutised, mis jäid alles materiaalsele tasandile. Ma usun, muusika oli see, mis nad abstraheeris. MICHEL SERRES Niisiis, miks on fuuga automaat? IANNIS XENAKIS Ma leian, et fuuga vastab rohkemal või vähemal määral teadusliku automaadi definitsioonile, mis sündis kahekümnendatel tänu Wienerile ja küberneetikale. Selle võib kokku võtta järgmiselt: automaat on põhjuste ja tagajärgede võrgustik, sündmuste teatud viisil paaride või paljukordsete paaridena seotud temporaalne ahel. Automaat võib olla suletud. Piisab ühendamisest energiaallikaga, kui see töötab tsükliliselt. Automaat võib olla ka suhteliselt avatud, täiendatud andmete sisestamise ja väljastamise võimalusega, näiteks juhthoobade abil. Ning vaatamata oma sisemisele jäikusele iga kord, kui sisestatakse uued andmed, võib automaat produtseerida erineva tulemuse. MICHEL SERRES Tema süntaks on korduv, tema töö aga mitte. IANNIS XENAKIS Jah, tema süntaks on korduv. Miks? Sest ta on sisestruktuurilt jäik. MICHEL SERRES Kas fuuga süntaks on alati püsiv? IANNIS XENAKIS Fuuga ei moodusta sellist absoluutset automaati, ta on suhteline automaat, eriti kui võrrelda teaduse poolt uuritava automaatikaga, mis on suhteliselt range võrreldes muusikalisega. Kui ma räägin muusikalisest automaadist, on ka menuett automaat. Muusikalise avastuse spetsiifiliseks väärtuseks oli luua esimene abstraktne automaat, isegi kui see ei tooda midagi peale muusika. MICHEL SERRES Kas aeg on sellises muusikas pöörduv või mitte? IANNIS XENAKIS Hästi, see on probleem ajast üldisemalt. Inimeste, ka muusikute meeltes valitseb segadus. Fakt, et asjad võivad korduda, kogemused või sündmused toimuda uuesti, pakub inimestele teatud turvalisust, vaatamata sellele et aeg ise iial ei kordu. MICHEL SERRES Mõnikord me puutume kokku pöörduva ajaga. IANNIS XENAKIS Milline aeg on pöörduv? MICHEL SERRES Planetaarne tsirkulatsioon. IANNIS XENAKIS Aeg ei ole pöörduv, pöörduv on aja liikumine. Aeg ise (minu teada on see mingi postulaat) ehk ajaline voog ei liigu tagasi. MICHEL SERRES Igal juhul on see väga uus avastus. IANNIS XENAKIS Et aeg ei liigu tagurpidi? MICHEL SERRES Absoluutselt. IANNIS XENAKIS Aga on ju nii loomulik mõelda, et aeg ei liigu tagurpidi. Herakleitos ütles muuseas sama. Aja pöörduvus võiks olla olemas, kui universumi liikumine oleks pendeldav, tõmbuks kokku ja laieneks taas. Rääkides näiteks ajavahemikest, need on kommutatiivsed, vahetatavad. Ma võin võtta ajavahemiku nüüd või hiljem ja vahetada selle teise ajavahemikuga. Aga üksikud hetked, millest need ajavahemikud koosnevad, ei ole pöörduvad, nad on absoluutsed, see tähendab, nad kuuluvad aega, mis tähendab, on midagi, mis kaob aja kulgedes lõplikult. See vastab Piaget’ uurimustele, milles jälgiti katseliselt laste õppimise faase ajas. MICHEL SERRES Pean silmas Xenakist ja mitte Piaget’. IANNIS XENAKIS Aa! MICHEL SERRES Jah, kuna te pakute välja stohhastikal põhinevaid teoseid, puudutab see aja probleemi. IANNIS XENAKIS Jah. MICHEL SERRES Milliseid seoseid võite te komponeerides tekitada korra ja korratuse vahele? IANNIS XENAKIS Kord ja korratus? MICHEL SERRES Tean, mis on korratus, kuna ma tean, kuidas te sellega ümber käite. Aga mis on kord, mis on teie süntaks? IANNIS XENAKIS Hästi, sellel on mitu tahku. Ma võin näiteks öelda: eksisteerib kord, kuna eksisteerib sümmeetria. MICHEL SERRES Nii see on, võitsin juba sümmeetriaga. IANNIS XENAKIS Jah, sellega te võitsite, muidugi. Aga see ei ole võit, see on küsimus sõnavarast. MICHEL SERRES Ei. Ei, ma võitsin, see tähendab, me tulime tagasi aja küsimuse juurde. Kui eksisteerib sümmeetria, võib eksisteerida ka pöörduvus ... IANNIS XENAKIS Ei, sest kord võib esineda ajavälistes asjades. On vaja teha selget vahet, mis toimub ajas ja mis väljaspool aega. Võtkem näiteks kõige lihtsam juhtum: rühm klaveriklahve. Niisiis on meil intervallid, mis korduvad, aga ei kordu iial ajas, nad on fikseeritud. Klaveri klahvid on liikumatult klaveri küljes. MICHEL SERRES Seetõttu on need klahvid väljaspool aega? IANNIS XENAKIS Jah, väljaspool aega. MICHEL SERRES Süntaks on väljaspool aega? IANNIS XENAKIS Jah. MICHEL SERRES Ma kahtlen selles! IANNIS XENAKIS Selles eksisteerib sümmeetria, kuna eksisteerivad suhted, järelikult eksisteerib kordumine. MICHEL SERRES Jah. Siis järjestus on väljaspool aega? IANNIS XENAKIS On mõningaid järjestusi, mis võivad olla väljaspool aega. Kui ma rakendan seda ideed aja puhul, võin ma saada ikka sellesama järjestuse, aga mitte tõelises, aja voolamise tähenduses, sest ajavool ei ole iial pöörduv. Ma võin selle saada väljamõeldud ajas, mis põhineb mälule. MICHEL SERRES Kas klaver on mälu? IANNIS XENAKIS Jah, see on materialiseerunud mälu. MICHEL SERRES Materialiseerunud mälu. Küsimus oleks siis järgmine: kas te võite saavutada pöördumatu voo? IANNIS XENAKIS Muidugi ma võin, kuna ma pole gaas, ja samal ajal olen ma Maxwelli deemoni poolt kurjast vaimust vaevatud. MICHEL SERRES Maxwelli deemon loob järjestuse. IANNIS XENAKIS Maxwelli deemon võib asju ümber pöörata. MICHEL SERRES Siin me oleme. Niisiis, muusikas on olemas pöörduvaid struktuure. IANNIS XENAKIS Nad on pöörduvad ajaväliselt. MICHEL SERRES Kas Maxwelli deemon töötaks ajaväliselt? IANNIS XENAKIS Valisin Maxwelli deemoni, kuid see ei muuda iseenesest veel aja voo suunda. On hästi mõistetav, kuidas see toimib. Näiteks kui edastada valguse voog ütleme laserile, laseri valgus, olles teatud tingimuste tõttu organiseeritud ja korrapärane, on selline, et sellesse sekkub justkui Maxwelli deemon. Sest vastupidisel juhul võiks meil olla ükskõik milline korrastamata valgus. Aga see kehtib ainult mõistete või asjade puhul, mis vastavalt definitsioonile võivad olla pöörduvad. Aeg ise ei ole pöörduv, ma väidan seda. MICHEL SERRES Xenakis, nagu ükskõik kes, on seda tõestanud. Triivimine korra ehk struktuuri ja korratuse vahel on üks teie heliloomingu saladusi. Kas olete nõus? IANNIS XENAKIS Jah. MICHEL SERRES Esimene välja pakutud füüsikateoreem puudutas võnkuvat pillikeelt. Kas mitte võnkuv pillikeel pole pöörduv ilming? IANNIS XENAKIS Ajavälised positsioonid on pöörduvad. MICHEL SERRES Mida te kutsute ajavälisteks positsioonideks? Ma ei mõista. IANNIS XENAKIS Ruumiintervalle, näiteks pillikeele positsioone. Need on pöörduvad, sest nad kuuluvad ruumi, mis ei ole ajaline. MICHEL SERRES Järelikult nagu kell! IANNIS XENAKIS Järelikult nagu kell. MICHEL SERRES Tegelikult kell, nagu võnkuv pillikeel, loendab aega. Võnkuv pillikeel võib olla aja loenduriks. See on mõõtmine. IANNIS XENAKIS See on aja loendamine, mis tugineb mitte aja, vaid positsioonide pöörduvusele. Selles on põhiidee. Nagu ütles Herakleitos, keegi ei või elada samas hetkes kaks korda. Keegi proovis viisteist aastat tagasi tõestada aja pöörduvust, kasutades mikrofüüsika paarsuse ideed, aga meil pole katseandmeid, keegi pole seda veel demonstreerinud ... MICHEL SERRES Teatud määral on muusikas küsimus soovis võidelda pöördumatu ajalise muutuse vastu? IANNIS XENAKIS Kui soovite. MICHEL SERRES Suutsime seda teemat veidi üldistada ning liikuda tehnika juurest komponeerimise juurde. Kas eksisteerib suhe glissandode ja eelnimetatud pöörduvuuse vahel? See näib mulle vägagi tähtsana. Hiljem näete, miks. IANNIS XENAKIS Ma ei tea, kas glissandol on sellega otsene seos või mitte. MICHEL SERRES Kas nõustute, et glissando on teie heliloomingu oluline element? IANNIS XENAKIS Jah. MICHEL SERRES Miks te valisite glissando? IANNIS XENAKIS Võib-olla Eukleidese geomeetria mõjul. Kuna glissando on millegi täpne, kuid hoomamatu muutus ajas, see tähendab, ta on lakkamatu, võimatu tajuda, sest inimene on katkeline olevus. Ta ei ole katkeline mitte ainult oma tajus ja valikutes, vaid kõiges. Pidevus on miski, mis tema eest jätkuvalt põgeneb. See on Zenoni problemaatika, muutus iseeneses, meie tajus ja meie valikutes, igavene võitlus püüda ette kujutada pidevat liikumist. Nii toimub muuseas eriti matemaatikas. Matemaatika alustas esmalt ainult katkelisusega, jõudes pidevuseni palju hiljem. MICHEL SERRES Need on kaks elementi teie töös, mis panevad mind mõtlema pöördumatusele. Esimene on tõenäosusfunktsioonide abil korra ja korratuse vahel triivimine ning teine järjekindlalt kasutatud glissandoelement. IANNIS XENAKIS Jah. MICHEL SERRES Niisiis, Xenakise muusika ei vasta enam pöördumatuse vastu võitlemise definitsioonile, mis oli sedastatud varem, kui te aktsepteerisite pöördumatut muutust neis kahes fundamentaaltehnikas. Kas teie muusika pole mitte erinev kui kõik teised nimelt selles suhtes, et see tõendab viimaks lõplikult aja pöörduvust? Vastandina muule muusikale. IANNIS XENAKIS Naasen tagasi selle juurde, et ma ei usu aja, reaalse aja, ajavoo pöörduvusse. Ma arvan, on võimatu luua tagurpidi aega. MICHEL SERRES Jah, nii see on. IANNIS XENAKIS Kuna aeg on pöördumatu. Ajavoos tehtud otsused on, kui lubate, pöörduvad. Võtkem näiteks lihtne asi nagu kestus. Kestus on miski, mis võib liikuda ajas, olla pöörduv, kommutatiivne. Kestusel on loomulikult alati ajaga sama suund (mis ei või olla ajavoole vastupidine). Teisisõnu, kui ma kirjutan, kavandan, või kujutan aega spetsiaalselt visuaalselt, panen ma selle koordinaatteljele nagu füüsikud, nagu muusikud (kõigepealt muusikud ja hiljem füüsikud). On oluline, et muusikud olid noodikirjaga esimesed, kes leiutasid kartesiaanliku representatsiooni põhimõtte. Hea küll. Ajavoogu peaks kujutama sirgena, mis definitsiooni kohaselt peaks olema pidev. Ma paigutan sellele sirgele punktid. Need on ajahetked. Kahe punkti vaheline erinevus on kontseptsioon, mis tuleneb võrdlemisest ja müstilistest otsustest, mida ma teen aprioorsena aktsepteeritava ajavoo reaalsuse kohta, mida ma. Vahemaa kahe punkti vahel identifitseeritav kestusena. Kestuse võin ma asetada ükskõik kuhu, kuna see on pöörduv. Kuid ajavoog ise on pöördumatu. Ning kui ma joonestan risti horisontaalse ajateljega ruumitelje ja paigutan sellele helikõrgused, siis madalast punktist kõrgemasse punkti paremal võin ma liikuda ainult ühtviisi: alt üles ja vasakult paremale. See ongi pöördumatus. MICHEL SERRES Oleme jõudnud pöördumatuse mõisteni, mis iseloomustab teie muusikat kahe tehnilise meetodi puhul: ühelt poolt triivimisel järjestuse ja järjestamatuse vahel ning teiselt poolt glissandode kasutamisel. Mis mind niisiis üldiselt hämmastab, nii teie muusikas ja kui ka teie arhitektuuris, on teie maailmanägemuse teine konstant, joonpinnad, PH-d, hüperboolsed paraboloidid. Millest selline püsivus joonpindade juures? IANNIS XENAKIS Ilmselt paljudel põhjustel. MICHEL SERRES Olge vastates väga ettevaatlik, sest antud [küsimus] on täpselt vastupidine sellele, millest räägiti varem. Varem räägiti triivimisest juhuse suunas, kui meie alustasime joonpindade juures püsimisest, mis tähendab korduvate struktuuride uuenemist. IANNIS XENAKIS Jah, see on teatud määral teistsugune mõttesuund. See on pidevuse ja katkevuse probleem, mis põhineb lineaarsetel elementidel. Joon on ilmselt rohkem pidevuse baaselement, pidevuse väljendus. MICHEL SERRES Kas see ei tulene mitte lihtsalt tehnilisest teostusest? Kuna kergem on töödelda joonpindu. IANNIS XENAKIS Ei, neid on võimatu töödelda, nad on S-kõverad, vaja on ... MICHEL SERRES Jah, kuna nad reeglipärased, olid teil paratamatult PH-de ehk hüperboolsete paraboloidide jaoks valmis lõpututest sirgetest koosnevatest pindadest valmis raamid. IANNIS XENAKIS Jah, aga kuna tegu on S-kõveratega, on ruum väändunud ja tavaline sirgete poolt moodustuvatest pindadest raam sobib S-kõveraga väga puudulikult. Kui konstrueerida "moondunud" raamistik, nagu näiteks paatidel, maksaks see liiga palju. MICHEL SERRES Mingem tagasi joonpindade ja olukorra juurde, mis lubavad meil ... joonpind võib tuleneda sirgest. IANNIS XENAKIS Jah, sirges on midagi ülimalt paeluvat. Päikesekiir on iseenesest paeluv. Päikesekiirt võib näha, kui see piilub läbi pilvede. Päikesekiired, mis koonduvad maapinna lähedal, on tegelikult paralleelsed. Laserkiire sirge on midagi absoluutset, samuti silulaua tera sirge. Niisiis looduses eksisteerib sirge. Aga iseseisva mõistusliku entiteedina on see ülimalt paeluv kiiruse, suuna ja pidevuse seisukohalt. Pidevuse seisukohalt on võimatu ette kujutada midagi lihtsamat kui sirge. Sest näiteks kõvera puhul võib ette kujutada jõude, mis seda toodavad, kõiksuguseid keerdusid ja väändeid, samal ajal kui sirge on üks, vaba, identselt korduv. Vabandage mind, ma ei lõpetatud veel joonpindadega. Joonpind on arenenud sirgest kolmes mõõtmes (glissando on kahes dimensioonis sirge). Sirge võimaldab meil kujundada väga lihtsate ja kontrollitavate elementide abil väga keerulisi vorme. MICHEL SERRES Minimaalse tehnika juures maksimaalne teostus... IANNIS XENAKIS Tulemuslikkuselt. MICHEL SERRES Jah, nõus... Viimane küsimus oleks järgmine, soovin sellega lõpetada: teie raamatu "Formaliseeritud muusika" alguses on mul teiega veel üks kana kitkuda seoses informaatikutega, kuna tuleb teha vaja teha vahet informaatika ja informatsiooniteooria vahel. IANNIS XENAKIS Head ja pahad! MICHEL SERRES Räägime lõpuks korrastamatusest. Asi puudutab termodünaamilist korrastamatust, aga ka müra. Järelikult on see sama asi. Niisiis viimane küsimus: seoses Xenakisega on kaks asja, mida ma ei suuda ühendada. Esiteks, teatud reeglipäraste invariantide lumm, teisisõnu joonpinnad ning lisaks süntaktilised invariandid ja invariantsus üldisemalt. Lühidalt, korduv süntaks. Teiseks lummus, mis viitab teie termodünaamilistele eeldustele, mürale jne., ning glissandod, mis on selle elemendid—teisisõnu vastandlik eeldus, eeldus "liuguda" või liuelda pöördumatult korrastamatuse, müra suunas. Kuidas selgitaksite te seda süntaksi invariantsuse ja korrastamatuse suunas triivimise lummust? Kas muusikat võib selliselt defineerida? IANNIS XENAKIS Ei, sest korrastamatus on korrastatuse, mis antud juhul tähendab kordumist, eituseks. Niisiis on korrastamatus perioodilisuse tähenduses pöörduv. (Perioodilisus on pöörduv vastavalt oma definitsioonile). Soovin sellega öelda, mis ei ole essentsiaalselt ajaline, on pöörduv. Objekte võib selles mõttes järjestada kuidas tahes, kuna definitsiooni kohaselt on nad väljaspool aega. Nii suhestuvad need kaks poolust pidevalt korrastatuse või korrastamatusega, kehastudes perioodilisuses. Kes ütleb "perioodiline", ütleb samas "invariantne". On terve rida võimalikke kahe pooluse vahelisi astmeid, mis minu meelest moodustavad teatud mentaalse kategooria. Seda kategooriat võib leida läbi kogu ajaloo, ka filosoofiast ja täppisteadustest. See on üks minu muusika põhilisemaid eeldusi. MICHEL SERRES Viimane kokkuvõttev küsimus: kas müras võib olla korrastatust? IANNIS XENAKIS Jah. On huvitav, et me võime simuleerida müra, mis füüsikaliselt on mitte iial identselt korduv rõhuvariatsioon. Seda võib tekitada kas katoodtorude või arvutitega. Ometi asub kuulaja korruse kõrgemal, kui ta tegelikult peaks asuma individuaalsel mikroskoopilisel alatasandil, et tajuda müra makroskoopilise kogumina nagu keegi, kes valitseb regulaarsust, korda! MICHEL SERRES Nii, vastus on nüüd käes, see on lihtsalt suurepärane. Te teate, et kõik küsimused, mida ma äsja esitasin, pöörlevad ümber probleemi, kas müras leidub korrastatust? Teie muusika avastas selle esimesena. IANNIS XENAKIS Suur tänu. Dialoog Bernard Teyssèdrega BERNARD TEYSSÈDRE Hästi, kuna on jõudnud kätte hetk lõpetada kaitsmine ja kuna komme (või protokoll) annab lõppsõna komisjoni esimehele, palun lubada mind, kallis Iannis Xenakis, väljendada rõõmu ja erutust nähes teid esitlemas seda väitekirja. Eeskätt isiklikel põhjustel. Ma ei suuda iial unustada teie üllatust ja ühtlasi skeptitsismi, kui ma soovitasin teil mõned aastad tagasi taotleda õppe-ja teadusosakonnalt korralist professuuri Plastiliste Kunstide ja Kunstiteaduse Koolis, kus ma olin siis direktoriks. Neis uutes raamides ehitasite te järjekindlalt üles pedagoogilise idee, millest kasvasid välja teie magistri- ja doktoriseminarid "Formaliseerimine ja programmeerimine visuaalsetes kunstides ja muusikas." Samuti ei unusta ma teie üllatust, kui ma kokkuleppel meie mõlema sõbra Olivier Revault d’Allonnesiga soovitasin teil esitada väitekiri riikliku doktorikraadi saamiseks ning ühendada selleks partituurid ja tekstid, mida me täna arutame. Mul on isiklikke põhjusi esitada samu põhimõttelisi küsimusi, mida Michel Serres tõstatas varem. Nagu tema, olen ka mina rahul, et kõrge tasemega uurijatele omistakse riiklik doktorikraad hoolimata faktist, et nende elukäigus ja koolituses pole midagi "sorbonnilikku". Ehkki praeguseks on seda praktiseeritud juba välismaa ülikoolides, eriti Ameerikas, on sellest hoolimata Prantsusmaal see tendents alles uus. Mäletan umbusku, millega ma põrkasin kokku isegi aastatel 1969-1970, kui kaitsmist vajas ainuüksi idee, et muusik või skulptor võiks saada järgmise Sorbonne’i professori koha õpetamaks ajalugu või filosoofiat. Põhjendati, et ülikool pole loodud kunstnikele. Aga miks mitte? Mulle näib, et sestpeale on liigutud otsejoones selles suunas. Ammu ei ole enam ülikoolides üksnes muusikateaduse, kinematograafia ja kunstiajaloo programme, vaid muusika, kino- ja kujutava kunsti programmides on kombineeritud teooria ja praktika. Kunstiliidest ei ole enam praktiseeritud mitte ainult reflektiivse teoretiseerimise kasu huvides, nagu see toimus veel lähiminevikus. Seda diskursuse tüüpi on sageli surutud ka ajaloo alla. Vähemalt viie aasta jooksul on ülikoolides algatatud kunstiinimestega komplekteeritud programme alustades algtsüklist kuni mitmesuguste diplomite või magistrikraadideni, teise astme ametikoolitusest kuni pedagoogise koolituse ja niiöelda "agregaatideni." Sellised isikud nagu Michel Butor, Maurice Lemaitre, George Charbonnier ja Frank Popper on nüüdseks riikliku doktorikraadiga. Freskomaalija Jose Balmes või teatrimees Jacques Clancy õpetavad oma ala välislektoritena ning käesolev kaitsmine omab selles suhtes olulisimat tähendust. Teie väitekiri, kallis Iannis Xenakis, on tõeline väitekiri selle sõna kõige pühitsetumas - peaaegu keskaegses tähenduses. Olles esimene omataoline, murrab see takistusi teiste kaitsmiste või "toimikväitekirjade" teelt: mingiski suhtes pole see kogum kokkusobimatuid plaanipäratuid töid. Vastupidi, see küünib esile oma sügava ühtsuse poolest, kuna esitatud tekstid ja nende juurde kuuluvad partituurid, koonduvad ümber tänase väitluse aluseks oleva põhiteema: kunstide ja teaduse sulam (ja mitte "liit"). Kas ei viita see pigem teatud kunstikontseptsioonile? Või teatud teadusekontseptsioonile? Ma möönan, et ma usun seda. Aga nimelt seetõttu, et teie väitekiri on tõeline väitekiri, teisisõnu: see ei ole mõne kitsa detaili õpetlaslik uurimisraport, nagu sageli juhtub, vaid originaalne teooria, argumenteeritud ja samas vaidlustatav — taas nagu keskajal, kui "doktorid" ründasid nii Duns Scotust kui ka Occami Williamit. Ma sooviksin vaadelda üht asja, siiski põgusalt, et mitte edasi lükata juba üpris pika kokkusaamise lõppu. Kasutades ainult ühte teie toimiku kirjalikest tekstidest, "Formaalset muusikat", soovin ma heita valgust teisele küljele latentsetest hüpoteesidest, millele teie väitekiri tugineb. Need seostavad ja iseloomustavad teie töö filosoofilisi valikuid, täiesti isiklikke valikuid, kehtides sellesama koherentsuse tõttu. Ehk ma eksin, Xenakis, aga mulle paistab, et üks teie üldistustest erineb teistest, mitte vastuolulisuselt, vaid ei rohkem ega vähem kehtivana kui teised. Esitaksin sellele mõne vastuväite, mis on ehk aluseks või mis mulle paistab aluseks olevat tajumata või teadvustamata põhihüpoteeside rühmale, millele väitekiri põhineb. Täpsustan ette rutates, ma ei soovi käsitleda kõiki vastuväiteid (vähemalt nende ekstreemsel kujul). Siiski näib mulle, et üks mängureegleid on "mängida kuradi advokaati", ärgitada teid reageerima ja loota, et oma vasturünnakuga suudate te selgitada oma seisukohti. Puudutagem niisiis äärmusi, et paremini hinnata, kuidas ja kuivõrd on teie seisukohad teie enda omad. See aitab mind hajutada oma nõrkusest tingitud ebamugavustunnet ning hakata vastu esteetilisele teooriale, mis väidab end olevat üldkehtiv ning kõrvaldada süüdistus "kultuurilises imperialismis". Isiklikult leian teie töö peamise väärtuse "Formaliseeritud muusikas", mida võiks võrrelda aksiomaatikaga Hilber’i või Paeno’ tähenduses, mis tähendab rajada muusikas piiravate tõkendite lisamise abil teatud universaale, mida võib määratleda nii, et teatud tüüpi muusikat (mitte kõike) võib tuletada osade kooslusena. Neid tõkendeid (teisisõnu helistikke, laade, seeriaid) võib determineerida heliuniversumina, milles võib eristada muusikaliste võimaluste välju. Ma ütlen universum ja mitte "pluriversum." Leian, et "Formaliseeritud muusika" (kuigi Xenakise mõtlemine on sealt alates arvatavasti arenenud), paistab mulle lahendusena, justkui peituks seal lootus kõikehõlmavale teooriale katta lünkadeta kõikmõeldavate valdkondade rühm, olles justkui Einsteini ammune unistus universaalsest relatiivsusteooriast, ületades kvantmehhaanikas ja termodünaamikas isegi Gödeli teoreemi ja olles midagi enamat kui lihtsalt kogum protseduurilisi reegleid. Ma aiman, et Xenakis on defineerinud "universumi süsteemi" ja seetõttu näib tema väitekiri isegi enam fundamentaalne, kuna see on tõeline väitekiri, vastates tingimustele, mille on loonud suur arv muusikateoseid. Siiski lubab teie väitekiri eksisteerida teistel väitekirjadel kõrvuti teie omaga, mida võiks käsitleda alusena teiste muusikaloomigule. Lahkudes üldiselt tasandilt jõuan ma spetsiifilisemate küsimusteni ja üritan näidata, et Xenakise teoorias on vähemalt kaks postulaati ja mitu valikut, millest ühed on metodoloogilised ning teised selgelt subjektiivsed. Esimene postulaat oleks järgmine: "Formaliseeritud muusikas" näivad ajalugu ja kultuur degradeeruvat taustaks, jättes uurimise puhul eelisõiguse loogilis-matemaatilistele invariantidele. Xenakise muusikateooriale võiks ehk leida teatud kontseptuaalseid ekvivalente seriaalses, süstemaatilises või programmeeritud maalikunstis sarnaselt Vasarely optiliste efektide kombinatsioonidele. Ma imestaksin siiski, kui kaitstav stohhastilise jaotuse hüpotees võiks oma lähtekohtade ja trajektooride puhul tuua kaasa absoluutseid tõenäosuslikke ekvivalentse. Vastupidi, kõrgemate selgroogsete anatoomia ja embrüoloogia näitavad, et geneetilise koodi determinatsioonid ei ole evolutsiooni käigus "rikastunud" infopanga "rikastumise" tähenduses. Samuti näitavad nad, et närvisüsteemi, eriti ajukoorekeskuste areng ilmneb neuronite vohamise ja sünoptiliste sidemete suhtelise ebapüsivusena. Teisisõnu, inimesele teada olevaid arhailisemaid imetajaid (ehk eelnevate eeskirjade loomingut) ei oleks üldse tekkinud. Viidates võrgustikkude ja võimalike seoste arvukusele oleks nad isegi oluliselt taandarenenud. Teatud juhuslikud teedrajavad tulemused, kontrollitud aleatoorika: mitte seetõttu, et puuduksid determinandid, vaid seetõttu, et neid juhivad muud kui geneetilised determinandid—teisisõnu, kuna õppimise roll kaugeneb jätkuvalt puhtast ja lihtsast küpsemisest. Veel enam, õppimine on tingitud kontekstist, mida võib kvalifitseerida ajaloolisena (sõna üldises tähenduses), alates embrüonaalsest tasandist perekonna ja koolisituatsioonide kaudu sotsiaalkultuurilise keskkonnani. Te imestate, milleni ma välja jõudsin? Niisiis: eelnevalt kindlaks määratud elementide seos, kaasa arvatud formaliseeritavad invariandid (need, mida Xenakis formaliseeris) ühelt poolt ning teiselt poolt kimp kultuurilisi ja ajaloolisi äpardusi, millest üksikisik ei suuda vabaneda. Näib, et seda tuleks arvestada. Seoses geneetilise lao või Counot’ järgi "võimaluste" seeriatega banaalseimas tähenduses moodustab selline tuletamine sõltumatute kausaalsete ahelate kokkupuutepunkte. Ja mis teeb need võimaluste seeriad pidevalt juhitavate ahelate asemel korratuks hajumiseks, on see, mis peitub suhteliselt konstantses sotsiaalkultuurilises kontekstis. Ma imestan, kas nende tingimuste puhul on võimalik püstitada fiktiivset väidet amneesiast (nagu Xenakis oma raamatus palju kordi teeb)? Kas on kasulik arvestada inimese kui "amneesiahaigega", tabades teda täpselt tema taju ilmnemise hetkel, abstraheerides tema individuaalse mineviku? Või vastupidi, kas ei oleks vajalik möönda, et puhtalt stohhastiline jaotus on muusikalisest valdkonnast peaaegu välistatud, kuni seal puuduvad kas alguspunktide või trajektooride tõenäolised ekvivalendid? Teisisõnu, kas on võimalik eristada loogilis-matemaatilisi invariante, kui muusikaline kogemus ei suuda integreerida erinevate sotsiaalkultuuriliste või ajalooliste ettekirjutuste determinante? Kas mu küsimus on selge, Xenakis? IANNIS XENAKIS Võib-olla, ma ei tea. BERNARD TEYSSÈDRE Võtan oma küsimuse kokku järgmiselt: "Formaalne muusika" näib mulle tõrjuvat oletuse tõenäosuste ekvivalentsusest, kuna lahkumise punktis või teekonda läbides, niisiis ajal, kui inimese fülogenees, embrüoloogia ja psühholoogia esindavad sellist ekvivalentsust, on see printsiibina välistatud. On tõsi, et eksisteerib palju piiravaid geneetilisi predeterminatsioone, mis vastupidiselt närvikanalite tekkimisele moodustuvad suures osas sotsiaalses kontekstis individuaalse kogemuse käigus. Näib vajalikuna tunnustada Xenakise teooriat, mis eeldab inimese "amneesiat". Teisisõnu inimest, kellel puudub ajalugu hetke enne munaraku viljastumist. IANNIS XENAKIS Ma ei tea, kas ma olen seda öelnud. Ma ei usu. BERNARD TEYSSÈDRE Ent hüpotees amneesiast esineb tihti. Näiteks leheküljel 35: "Eeldame, et ülalpool määratletud punkti M võib vaadelda teistsugustel tingimustel teisiti, kui ta allutada mäluta aleatoorika seadusele." Leheküljel 185: "Me hakkame endale ette kujutama, et kannatame äkilise amneesia all määral, mis küünib kompositsiooni mentaalsete operatsioonide allikateni ning vabastama end üldistest printsiipidest, mis kehtivad kogu muusika puhul." IANNIS XENAKIS Ah jaa! Kuid see on vaid provisoorne tööhüpotees, reflektsioon. Ma ei räägi amneesiast bioloogilises mõttes. Räägin amneesiast seoses mentaalse pingutusega, et mõista sügavamaid fakte, eristada seda, mis on see, mis kuulub vabade ja mis tingimuslike asjade hulka, mida võetakse vastu peamiselt sotsiaalkultuurilise faktina. BERNARD TEYSSÈDRE Soovin öelda, et sotsiaalkultuuriline tingitus võib olla mitte ainult millegi ekstensioon, mis ise võib olla liidetud algselt võrdselt võimalikena arvesse võetud tõenäosustega, vaid vastupidi, seda moodustavate suhete endi võrgustik. Ja kõike seda kombel, et me ei või iial alustada absoluutsest "eikellegimaast", "puhtalt lehelt", vaid vastupidi, ülimalt kihiliselt maastikult. IANNIS XENAKIS Jah, aga see "ülimalt kihiline" ei ole millegagi tõestatud. See on tõepoolest kõigis valdkondades üks uuringute fundamentaalsemaid teemasid. Bioloogias või geneetikas näiteks on väga vähe teada rohkemal või vähemal määral välja töötatud ja keeruliste vaimsete struktuuride pärilikkusest. On fakt, et tänu pärilikkusele me pole taimed või mineraalid. Oleme inimesed, kes sarnanevad silmade, elundite poolest üksteisega. Aga seda, mis toimub ajus, me ei tea. Kuna me ei tunne pärilikkuse rolli, milles võiks eristada "kategooriaid." Me ei tea, kuidas sündis kausaalsuse põhimõte või miks see sündis. Veel enam, see põhimõte on ekvivalentne referentsiaalse arutluskäiguga. Veelgi enam, tähendus, mille me anname ajale, ajavoole, sõltub mitte ainult kogemusest, vaid ka meie aju ehitusest. Me ei tea, millal need konstruktsioonid sünnivad: kas pärast või enne sündi tuhandeid või miljoneid aastaid tagasi. Keegi ei suuda otsustada. Vastupidi, praegu võime me öelda vaid seda, et meie teadvuses on determineerimata osa. Miks me võime seda öelda? Kuna on nii palju kultuure, nii palju lähenemisi reaalsusele, nii palju reaktsioone enne objektiivset universumit (kui selline eksisteerib!). See paljus võimaldab kõrgematel tasanditel suuremat vabadust. Seepärast antud juhul, miks me ei võiks muuta asju, mis paistavad praegu muutmatu ja universaalsena? Kujutagem ette ajavoogu nagu me seda ette kujutame, kaasa arvatud selle korrapärased struktuurid, mis on meie teadmiste aluseks ja mis on osa meie igapäevasest elust, olgu me tuumafüüsikud või muusikud. Kas see ajavoo kontseptsioon on absoluutne või muutuv? Selleks, et määratleda asjade tüüpe ning kõrvaldada kogu hariduse või sotsiaalkultuurilise traditsiooni tolm, on vaja oletada, püstitada aeg-ajalt ekstreemseidki hüpoteese nagu näiteks amneesia. See on lihtsalt töövahend. BERNARD TEYSSÈDRE Ma olin väga üllatunud, Xenakis, kui te viitasite Kreeka muusikale kui toitvale huumusele, millest meie lääne traditsioon on arenenud. Ma imestaksin, kui see pole ka huumus, millest on arenenud Xenakise universaalne muusikateooria. Julgen öelda sama, mida Olivier Messiaen ütles radikaalselt erinevate struktuuride võimaluse kohta, need ei räägi vastu ka mulle. Ma sooviks meenutada teile oma väidet: teades, et geneetiline kood on ülimalt puudulik võrreldes arvukate neuronitevaheliste sünapsidega, säravad trajektoorid nende individuaalse arengu käigus koos arengu endaga, olles tingitud suures osas sotsiaalkultuurilisest kontekstist. Miks tertsil põhinev akord, mida vaadeldi "dissonantsena" keskajal, muutus "konsoneerivaks" Bachi või Rameau ajal punktis, kus suur või väike terts defineerib "perfektse akordi", mis on kas mažoorne või minoorne? Minu järeldus on, et esialgne ekvivalentsuse postulaat, mida tõenäoliselt pole tegelikkuses vastuvõetavalt olemas ja mis degradeerib muusika lisakulturisatsioonilisse või ajaloolisse sekundaarsesse rolli, ühendades selle lihtsalt loogilis-matemaatiliste invariantidega, võib olla väga ohtlik hüpotees. Ma ei ole sugugi kindel, et me võime isegi heli tajumise tasandil kõrvaldada muusikakultuuri. IANNIS XENAKIS Hästi, ronides redelit mööda ülespoole ja vaadates ajaloole teatud kõrgusest võime me veenduda, et palju on toimunud. Selleks, et näha selgemalt, oleks vaja kõrvaldada just need sotsiaalkultuurilised kogemused. Kui see on tehtud, võime me lõpuks leida asju, mis on iseseisvad, mis on õppimise teel omandatud või permanentsed, kujutades enesest aja või ruumi invariante. Seetõttu avastame me äkki universaalse "personaalsuse" heliridade puhul, mis näivad olevat maailma arengu käigus muutunud ainult veidi. Selline universaalne "isikupära" on näiteks intervallil kvart. Otsekui juhuslikult alustas Aristoxenus oma muusikateooriaga sellest, et rääkis puhtast kvardist. Siiski, ta ei defineerinud seda intervalli matemaatiliselt, kuna ta ei põhjendanud nagu pütaagorlased, kuigi ta tundis matemaatikat ja pütagoreismi. Aga ta võttis puhast kvarti põhiintervallina ning alustas oma uurimusi sellest. Veel enam, meie kohtume puhta kvardiga kõigis kultuurides üle maailma. Kõrgemal tasandil vastab see teatud muusikalisele konstandile. Aga selleks, et mõista, on vaja teha plats puhtaks kõigist kõrvalnähtustest, kõigist ühele või teisele muusikakultuurile omastest värvingutest, sõnadest kurb ehk minoorne või mažoorne tonaalsus. See näide on ilmselt üpris triviaalne. Täpselt samuti teisel tasandil, öeldes «muusika on meloodiline», «peab olema meloodiline», «peab olema polüfooniline», ei oska me enam kujutleda mõnda teist muusikat väljaspool seda konteksti. See on eelarvamus, mis tuleneb meie sotsiaalkultuurilistest kontseptsioonidest. Mida peaksime kõigest sellest vabanemiseks tegema, et rajada fundamentaalne mõtlemine? Üheksateistkümnenda sajandi matemaatikud ja loogikud näitasid meile ühe tee, saades matemaatikas lahti sõnadest ja asendasid need sümbolitega. Et näha selgemalt. BERNARD TEYSSÈDRE Ma ütlesin seda kõigepealt ja kindlasti on see üks liik meile kättesaadavast aksiomaatikast. Vabandage mind, olen kohustatud kiiremini edasi liikuma, sest aega pole jäänud palju ja mul on teile veel palju küsimusi. Sooviksin jätta selle teema ja minna teise punkti juurde, milleks on minu arvates teie teine postulaat, mida võiks nimetada "komponeeritud hajutatuse" printsiibiks. "Formaliseeritud muusikat" lugedes võime tõdeda, et vähemalt metodoloogiliselt eelistate te elemente, helisid või graanuleid või graanulite pilvi või loogikaklasse või ka organogramme. Ma imestan, millisel määral (ja seda ma teilt küsingi) sobib see eelistus kokku lihtsaimate tajuandmetega, mõtlen neid, millele tugines Gestalt-teooria peaaegu sajand tagasi. Teie raamatus on seda tõlgendatud üldiselt järgmiselt: niipea, kui teatud arv helide koostisosi on eraldatud ja määratletud baaselementidena, asetuvad need baaselemendid suhtesse muusika kuulamiskogemusega (järgides mudelit, mis rakendab Fechneri seadust, kasutades sündmuse varianti aistilise ergutamise logaritmina). Kuidas sobib see kokku von Ehrenfelsi juba aegunud reflektsiooniga vägagi banaalsele transpositsioonikogemusele? On võimalik, et muusikalises fraasis, mida on kõigepealt kuuldud C-duuris ja siis näiteks fis-mollis, ei peaks kahel rühmal olema ühiseid füüsikalisi elemente. Siiski, mõlemad on tajutavad otsekui "sama muusikalise fraasina", lihtsalt transponeeritud kahte erinevasse helistikku. Kuidas võib seda seletada, et neid kuuldakse vähemalt analoogse kui mitte identsena? Lähtekohana kasutatud elementide asemel (osakesed või osakeste pilved või loogilised klassid jne.) ei suuda me ette kujutada suhteid endid, näiteks jõudmist esimesse ja mitte teise selle suhte äärmusse? Kas mitte see ei sunni teid kasutama oma muusikas glissandosid? Teie glissandode kasutamine räägib teie teooriale peaaegu vastu: te ei kasuta enam elemente kui lähtekohti, vaid pigem nende suhteid, intervalle ning seoses intervallidega võime me öelda, et heligraanulid mängivad lihtsate "teetähistena" teisejärgulist rolli glissando kahe äärmise punkti vahel, samal ajal kui glissando ise on ainus tajutav reaalsus? IANNIS XENAKIS Jah, see on väga hea küsimus. Õige, muusikas tähendavad sõnad "kompositsioon" ja "komponist" asjade ühendamist. Järelikult need asjad juba eksisteerivaid ja on juba teatud viisil defineeritud. BERNARD TEYSSÈDRE See annab sünteesi ees eelise analüüsile. Igal juhul see, kuidas "elemente" algselt esitletakse, näib meetodi kirjelduse enda strukturaalsest aspektist vastuolulisena. IANNIS XENAKIS See ei eelda tingimata seda, kuid eeldab midagi muud. See eeldab materiaalset universumit, milles helilooja mõjutab suhteid, struktuure, konstruktsioone, arhitektuure. Aga tõesti ainult teatud punktini, kuna on terve valdkond muusikat nagu ka taju, mis on täielikult tundmatu. Suurem osa "Formaliseeritud muusikast" tugineb teadaolevate heliobjektide organiseerimisele, teine osa aga (viimane peatükk) võtab arvesse teatud tüüpi globaalse taju. Öeldes globaalne taju, pean ma silmas mitte molekulide, objektide, mida helilooja kasutab luues rohkemal või vähemal määral arenenud organisme, puudumist, vaid võimalikult täpsete olukordade magmat (katkelisi rõhuväärtusi), mis on võimeline omandama kriteeriumitele vastavaid vorme, mille ta ise loob. Viimane peatükk tähistab teist, täielikult vastupidist lähtekohta sellele, millest te äsja rääkisite. Kui ma kõnelesin siin innukalt katkelistest asjadest, siis seetõttu, et rääkides näiteks helirõhkudest, räägime me katkevusest. Lõpuks, rääkides muusikaajaloost, kas minevikust või olevikust, on see lihtsaim, otseseim ja põnevaim lähenemisviis. Töötades kas taju või otsustega, oleme me rohkem kodus ja vabamad pigem katkevate kui pidevate objektide puhul, mis mingilgi moel ei välista määratlematuid või defineermatuid objekte. BERNARD TEYSSÈDRE Ma ei viidanud mingilgi viisil sellele, mis on defineerimatu. Ütlesin vaid, et meloodiat võib transponeerida sellisel moel, et ükski tema füüsikalistest elementidest ei jää samaks, aga see on tajutav siiski "sama meloodiana". Seisukoht, mis on pärit helivormide vaatlemisest, nii nagu sisuline täius on totaalselt erinev seisukohast, mis saab alguse heligraanulitest või graanulite pilvedest, enne kui luuakse suhe nende pilvede vahel. Öelda, et vastupidine on õige, tooks kaasa aistiliste stiimulitega segadusse aetud taju. IANNIS XENAKIS Hea küll, ma ei näe ... BERNARD TEYSSÈDRE Kuna mitte ükski aistilistest stiimulitest ei jääks samaks, kas neid võiks tajuda samal viisil? IANNIS XENAKIS Jah, aga tähelepanu. Sa räägid erinevatest tasanditest. Kui sa ütled, et noodid on erinevad, hea küll. Kuid meloodias ei ole ainult noodid, on nootide vahelised seosed, niisiis intervallid jms. BERNARD TEYSSÈDRE Täpselt seda ma ütlesin: teatud "molekulaarsest" seisukohast võime me vastustada "suhtelisi" seisukohti, mille kohaselt need kurikuulusad molekulid võiksid lihtsalt olla seoste kaugeimad punktid. IANNIS XENAKIS Loomulikult! Raamatus "Formaliseeritud muusika" olen ma töötanud tasandite vaheliste seostega (mõlemad mitmuses), eriliselt kõrgemate tasandite ning lisaks elementidega! BERNARD TEYSSÈDRE Olgu nii. Mingem edasi teise küsimuse juurde, millel on pisut tegemist sellega, mida räägiti varem stiili mõiste kohta. Ma imestaksin, et sinu teoreetilistes töödes ja heliteostes ei ole antud eelisõigust küllastatusele: teisisõnu, teatud valikuvõimalusele või subjektiivsele maitsele tihedusest, täitumusest, mitte aga heliruumi hõrendamisest. Rabav on lugeda "Formaliseeritud muusikat" alates leheküljelt 56: "Ergoodiline printsiip sedastab, et operatsiooni kapriisne efekt, mis sõltub juhusest, on reguleeritav aina enam ja enam, kui operatsiooni korrata." Kuid on nimelt võimalik, et stiili olemuseks on ergoodilise põhimõtte juhuslikkus. On võimalik, et selleks on subjektiivne valikuvõimalus või isiklik maitse, mis ajendab Xenakist valima pigem küllastatud kui hõrendatud heliruumi, valides harvade üksiknähtuste asemel suuri hulki, nagu Leibnitz ütles, mille defineerimine eeldab lõputut analüüsi. Kahtlemata prevaleerib soov kontrollida heliruumi küllastatust, välistades ökonöömsuse põhimõtte (aga ökonöömsuse põhimõte on ju ka jõu eelduseks). Me võime väga hästi ette kujutada vastupidist valikuvõimalust, mis paistaks silma ohjeldamatu juhuse harvaesinevate individuaalsuste eelistamise suhtes. Kokkuvõttes, John Cage või Marietani valik on täiesti vastandlik Xenakise valikule. IANNIS XENAKIS Ma arvan, sa ajad mitu asja segi. Vabanda mind seda sulle ütlemast. Tulles tagasi ergoodilisuse juurde: seal esitatud definitsioon on üksnes matemaatiline ning seda ei ole öelnud mina. BERNARD TEYSSÈDRE Tean seda väga hästi. IANNIS XENAKIS Tuginesin väga olulisele prantsuse matemaatikule, kes kirjutas Markovi ahelatest neljakümnendatel, Maurice Frechet’le. Temal on ergoodiliste protsesside, ergoodilisuse definitsioon. Kuid see piiritleb vaid ühe minu töö aspektidest. Teiselt poolt, kui räägime juhusest, peame olema väga ettevaatlikud. BERNARD TEYSSÈDRE Rohkem, kui lihtne tõsiasi kasutada tõenäosuslike arvutuste printsiipi, näib mulle korduv valik suurte arvude kasuks loovat eelduse kontrollida pigem rohkeid kui harvu sündmusi, mis eraldi võetuna ei oleks juhitavad. IANNIS XENAKIS Aga ma teostasin terve uurimuse harvadest sündmustest ja hõrenemisest Achorripis’es ning teistes lugudes. See on küsimus tihedusest ja tihedus on mõiste, mida ma käsitlen pikalt ja põhjalikult "Formaliseeritud muusikas". BERNARD TEYSSÈDRE Kas sa ei eelista oma muusikas pigem fortissimot ja pianissimot ebamäärasematele nüanssidele, pigem ääretuid helimasse kui tühjust või vaikust, pigem intensiivset emotsionaalset laengut kui meditatiivset avarust? IANNIS XENAKIS See on õige, ma ei ole kirjutanud palju hõredat muusikat. BERNARD TEYSSÈDRE Tõepoolest mitte palju hõredat muusikat. Ega ka muusikat, mis püüaks tabada üksikuid sündmusi, nagu Olivier Messiaen on kasutanud linnulaulu või nagu John Cage kasutab seitsme raadio juhuslikku konflikti, igaüks edastamas erinevat programmi. Nendes muusikatüüpides on ruumi harvaesinevatele kohtumistele, selle asemel et toimuks katkematu ülimalt tõenäoliste kokkupõrgete otsimine, nagu paistab mulle raamatust "Formaliseeritud muusika" (isegi kui olete seda hiljem muutnud). IANNIS XENAKIS See on palju keerulisem. Kõigepealt, "ülimalt tõenäolisel" on tähendus vaid suhtes tõenäolise jaotusega a priori ning suhtes teatud täpselt defineeritud sündmuste rühmaga. Õnneliku või ettenägematu juhuse mõiste on tõenäosusteoorias fundamentaalseks. Mis on ülimalt tõenäoline, ei räägi vastu sellele, mis on ülimalt juhuslik ja muutub ennustatavaks ning pole enam juhuslik mitte ainult stohhastiliselt, vaid viimaks ka statistiliselt. Järelikult, millal iganes sündmus teatud rühmas toimub, kõik kulgeb, otsekui oleksime juhusliku sündmuse lävel. See ilmub ootamatult ja on seetõttu range perioodilisuse mõttes "harv". Me võime korraga sisse lülitada mitu raadiot, aga kohe, kui nad on sisse lülitatud, leiame me end "sündinud fakti" ees ja tulemusena tühistab ettemääratus juhuse. Sel juhul toimub kõik, isegi kui see on lokaalselt juhuslik, otsekui oleksime me üldiselt ennustatava ilmingu lävel, defineerides seda, mis on ülimalt tõenäoline. Sel moel on need kaks lähenemisteed ekvivalentsed. Minu puhul on tunduv erinevus selles, et ma proovin luua mitte ainult sündmuste ahelaid, vaid ka sündmusi endid kombel, mis oleks ennustamatuse ja juhuse seisukohast palju usaldusväärsemad ja homogeensemad. Teisalt, rariteedi mõiste on suhtes võimalike olukordade ja nende koosluste kordumisega. Mingi sündmuse paljud või vähesed kordumised on rariteedi tiheduse või hõreduse mõiste tõttu tõlgendatavad ajas. Seda enam, et "Formaliseeritud muusika" teine peatükk algab üksikute sündmuste ja nende töötlemisega. BERNARD TEYSSÈDRE Selle asemel, et neid välistada, te tegelete nendega ... IANNIS XENAKIS Ei, mitte sugugi ... BERNARD TEYSSÈDRE ... või degradeerite neid tagaplaanile ... IANNIS XENAKIS Ei, sest tehnika seisukohast alustan ma Poissoni definitsiooniga, mis tegeleb just nimelt harvaesinevate sündmustega, mis on samuti integreeritud minu teostesse. Niisiis harv sündmus on harv vaid suhtes ajaga. On hetki, mil harv sündmus võib olla taotluslikult tihe ja sage. Tegelikult, kui valitud ajaühik on piisavalt väike, võivad teatud muusikateose vältel toimuvad sündmused näida toimuvat harva. Teisalt, kui valitud ajaühik on piisavalt pikk, võivad samad sündmused näida tihedamad või üksteisele lähemal, kuigi nad on jaotatud samal kombel ja võivad tekitada samasuguseid juhuslikke konflikte. Kvalitatiivselt eksisteerib seesama fenomen. Nagu asetaksite te Geigeri loenduri radioaktiivse allika lähedusse või liigutaksite selle kaugemale: tõenäosusjaotus on sõltumatult distantsist (ajaühikust) sama. Ilming on sama. See on sama seadus. BERNARD TEYSSÈDRE Jah, aga palun vabandage mind, kui naasen tagasi selle juurde, mida Michel Serres varem ütles, kui ta püstitas probleemi, kordan, me võime ette kujutada erinevaid muusikutüüpe, kes ei pakuks välja luua korda mürast, aga vastupidi püüaks eristada harva, individuaalse sündmuse kui niisuguse, näiteks John Cage või Marietan. Mitte julgustamaks kedagi eristama harva sündmust korrastumatusest, aga vastupidi aktsepteerima seda individuaalse sündmusena, mille suhtes ammendav analüüs oleks lõpmatult keeruline. IANNIS XENAKIS Seda ma üritasingi öelda. BERNARD TEYSSÈDRE Aga miks Xenakis ja mitte keegi teine ei suuda seda valitseda? Taas kord leiame me end isikliku stiili probleemi juures, mida me juba käsitlesime ... IANNIS XENAKIS Vaadelgem harva sündmust teiste sündmuste koosluse raames ning rakendagem hõrenemise saavutamiseks ajasuhteid. Kindlasti võite te leida üksiku harva sündmuse. Aga kui te kujutate sündmuste kooslust ette globaalselt, paistavad harvad sündmused palju paremini kompleksse keskkonna taustal. Loogiline, see on küsimus helisündmust ümbritsevast vaikusest vasakul ja paremal, aga mitte see ei ole põhiline. Küsimus on skaalas, mis vastab tähelepanu määrale, mida sellisele sündmusele osutatakse, järelikult tähtsuse astmele, mida sa otsustad sellele anda, mis on esteetilisele ettekirjutusele põhinev otsus. Ei looduses ega inimese mõtlemises, ei ruumis ega ajas pole midagi ainukordset. Vastupidi, sündmuse perioodilisus (kõige laiemas tähenduses) ja tema korduvus kas iseeneses või oma keskkonnas on täiesti loomulik ja vastupidine oleks mõeldamatu. BERNARD TEYSSÈDRE Kindlasti, ometi on sinu esialgsesse elementide valikusse segatud teatud üldise tasandi piirang, mis tähendab, et valitud maatriks ei sisalda enam vaid seetõttu kogu võimaluste täiust, et eelnevalt on kokku lepitud orkestri olemasolus. Need eelvalikud ei luba meid enam kaasata kõigi võimalike helide hulka, mõne kuulaja köhimist või saalis lendavat põrnikat, ja selle kaudu integreerida sumin või köhimine osaks muusikast, nagu taotles John Cage, püstitades teistsuguse muusikalise põhimõtte, erineva teie omast. IANNIS XENAKIS Hea küll, ma räägin sulle, miks. Lihtsalt väljendudes meie kõigi igapäevaelus esineb juhuslikke helisid, mis on banaalsed ja tüütud. Ma ei ole huvitatud banaalsuse reprodutseerimisest. BERNARD TEYSSÈDRE Olen täielikult nõus, sooviksin rõhutada, et sinu puhul on see esteetilise valiku küsimus. OLIVIER REVAULT D’ALLONNES Siiski ma arvan, et "Formaliseeritud muusika" leheküljel 114 on seoses muusikalise strateegia ja Duelliga võimalik vastuse element, mis sunnib nõustuma sellega, mida Teyssèdre ütleb. Leheküljel 113-114 nimetad sa kuut võimalikku sündmust: heligraanulite pilv, jätkuvad keelpillid, perkussiivsed helid jne. ning vaikus on kuues ja ühtlasi viimane sündmus. Ma ei sooviks sellest esialgu midagi järeldada. Siis, leheküljel 114 (Väärtuste tabel) ja leheküljel 115 (Maatriks M2) mainid sa ainult viit sündmust, esimest viit, mis on helisündmused. Vaikus on kadunud ja ei ilmu uuesti enne kui lehekülje allosas (Maatriks M2, lk. 115). Kuid siis lähed  sa vaikusest niiöelda vaikselt mööda, paigutadese selle taas vaid teise tabelisse (M2)? Sa ütled: "Sissejuhatus vaikuse liikumisele (VI) muudetuna (Ml) ja tulemuste maatriks (M2)" (lk. 115). Ja nüüd viitan ma lehekülje 114 allosale "Formaliseeritud muusikas", kus erinevad sündmused on hinnatud "hea", "hea+" jne. ning kus vaikus saab hindeks "ajutine" või "hinnang puudub". Kokkuvõttes, sa ei armasta vaikust. IANNIS XENAKIS Vaikus on banaalne. BERNARD TEYSSÈDRE Ma ei taha ületada selle debati aega. On selge, et härra Revault d’Allonnes ei suuda viljakalt võistelda Iannis Xenakise avatud perspektiividega. Ja kindlasti ka mina mitte. Mis puutub minusse, mis mind veidi hirmutab, on see, et need viljakad perspektiivid võivad paista väljastpoolt vaadates imperialistlikena. Tahaksin öelda, et ainult väga personaalne muusikateooria, mis toetub väga personaalsele muusikauurimisele võib teada, kuidas murda katki sellest erinevaid, rääkimata opositsioonilistest muusikateooriatest. Ka arvutiga programmeeritud seriaalne maalikunst ei muuda vanemat juhuslikku maalimistehnikat, ei Michaux "informaalseid" tehnikaid ega Pollocki "action painting'ut." Maaliline maalimine "Supports/Surface" mõttes ei degradeeru dadaistlikus tähenduses mittemaalimise tõttu marginaalseks. Ma ütleks nagu Heideggergi, kuna metafüüsika on ühe idee eksperimendiks, siis see doktriinide kobar, mille üle me äsja diskuteerisime, moodustub pigem muusikalisest metafüüsikast kui muusikateadusest. Stsientismi seisukohast on Iannis Xenakis seadnud teatud teadusliku eesmärgi. Kui me soovime, võib esitatud korpus olla teaduslik, aga selle korpuse põhiline eesmärk ei ole samast kategooriast kui korpus ise, kuna seda mõjutab isikliku subjektiivse stiiliküsimuse koefitsient, mille üle me oleme arutlenud. Mulle näib, et taas korduvad valikukriteeriumid: valikud, mis toetavad seda väitekirja, ning mida seesama väitekiri edaspidi toetab, vormides märkamatult teatud hulga põhihüpoteese. Kindlasti arvestaks ma Xenakise teoreetiliste kirjutistega nagu Alberti uurimusega, nagu teatud tüüpi "seadustatud konstruktsiooniga", "seadustatud" eeldades, et see ei muutu normatiivseks ning aktsepteerib teisi konstruktsioonimeetodeid, mis eksisteerivad seda eitades sellega paralleelselt ning et neid võib vaadelda võrdselt legitiimsetena. Muidugi, enne kui seda väita, oleks vaja arendada ka teisi teemasid. Ma ei tee seda ajapuuduse tõttu. Siiski sooviksin ma põgusalt arutleda ajalise ja ajavälise suhte probleemide üle. See näib mulle seadvat kahtluse alla teatud filosoofia ajast, kontseptsiooni, mis kõigub ühelt poolt Aristotelese õpetuse järgijate idee ajast kui liikumise väärtusest ning teiselt poolt, kahtlemata erineva, aja kui sündmuse neljanda mõõtme mõiste vahel. See ei too taas mingil juhul kaasa selgust vanasse Bergsoni paradoksi: aeg versus kestus. Küsimuse all on aeg, mis kulgeb lineaarselt, korrapäraselt. Aeg, mis kuulub samasse süsteemi ideega Leibnizi monaadist (matemaatilisest funktsioonilaiendist) või Hegeli kontseptsiooniga sfäärist, mis on alati olemas iseenesest, metoodilises tsüklis iseenesest lahutamatu. See on läänemaailma, emakese Kreeka ajamõiste, kus aeg kujunes kõigepealt esimeses ja siis teises oma kahest küljest: loogikas ja retoorikas. Vastavalt sellisele kontseptsioonile on võimalik mõelda muusikast kui "diskursusest". Mõtestades ümber Barbaud’ lause, kes kinnitas end olevat valmis "mitte-Beethovenlikuks muusikaks", ütleksin ma, et kooskõlas nii Kreeka kui ka lääne traditsiooniga pakub Xenakis välja aksioomi beethovenliku muusika üldistusest. On see ainus võimalik muusika? Ma toon esile Barbaud’, aga kas me ei võiks samuti esile tuua jaapani gagaku, kõik-juba-koos, sama-ümber-sama sära, kõike seda loogilis-retoorilise ahela asemel, milleks on lääne muusikaline "diskursus", liikumine ühest sellestsamast teise sellesamani? Ja minnes tagasi algusesse: kuna me veendusime, et me võime püsida Lääne "diskursuse" raames, kuidas võime me lepitada neid kahte äärmust pendulaarse ostsillatsiooni tingimustes: mõnikord on aeg "sündmuse neljandaks mõõtmeks" ja mõnikord "liikumise väärtuseks"? Teisel juhul on olulisemaks liikumine, ning olemata sündmuste toimumisel üks koordinaatidest, ei erine aeg sellest, mis teda loetleb? IANNIS XENAKIS Ma usun, et rääkisime sellest varem, see on meetrika. On olemas vahetu ajavoog ning meetrika, konstruktsioon, mille inimene ajast loob. Sellest me ei pääse. Kas muusik või füüsik, see toimub sarnaselt. Ma vastaksin ühele teisele asjale: mingil juhul ei soovi ma välistada teisi muusikalisi lähenemisteid ega soovi tõesti, et süüdistaksite mind minu tegevuse tõttu imperialismis. BERNARD TEYSSÈDRES Ei, ei. Xenakis pole sugugi imperialist. Seda võiks arvata tema täppisteadusliku lähenemise tõttu. Kui ta töötab oma muusikaga, jääb ta jääb sügavalt humanistlikuks, lubades isiklikul stiilil särada kunstniku "ego" kaudu. Tema valikud on õiged ja tema muusika suurepärane. Kas ei põhine need valikud lisaks täppisteadustele jõulise, huvitava ja initsitatiivika isiksuse poolt tehtud idiosünkraatilistele valikutele? Sub- Xenakis, kes sooviks rakendada Xenakise teadust, omamata Xenakise isikut, ei suuda iialgi muusikaliselt luua rohkem kui sub-Xenakis. Kas ei võimalda need hästi põhjendatud valikud eksistterida koos irratsionaalsel või põhjendamatul osal? Võtkem näide, mis illustreerib selgelt erinevust kahe laia haardega isiksuse vahel: kui Barbaud võtab appi arvuti, on muusikateoseks programm ise. Me võime kuulda kõlamas suurt kogust samast programmist pärinevaid versioone, ilma et ühtki neist versioonidest oleks võimalik teisele eelistada, kuna kogu töö eksisteerib siinpool oma kuuldavaid variante. Kuid mulle näib, et Xenakise kõrv ei saaks hinnata kõiki versioone võrdsetena, ta leiaks teatud arvu "eelistatavaid" versioone ning partituurid fikseeriksid siis neid, mille kõlaline tulemus oli "eelistatud". Välja arvatud polütoobid, kas see pole enamasti mitte nii? IANNIS XENAKIS Aga see on minu õigus, minu privileeg, minu ülesanne eelistada üht asja teisele. BERNARD TEYSSÈDRE Kahtlemata, kuna teie isiksus nii määrab. Siiski, teie maksiim ei ole põrmugi iseenesestmõistetav: riskides ennast korrata, Barbaud’l ei oleks eelistusi. Ta looks programme ja iga tulemus on ekvivalentne teistega. Xenakis, see on tema õigus, eelistab. IANNIS XENAKIS Aga see on loomulik. See on absoluutselt normaalne. BERNARD TEYSSÈDRE Sinu sõna jääb viimaseks. Komisjon lahkub nüüd nõu pidama. (Pärast põgusat arutelu komisjon naaseb ning komisjoni esimees teatab, et Iannis Xenakisele omistatakse humanitaarteaduste doktori kraad hindega "väga hea".) Järelsõna Matemaatika mängib Xenakise muusikas keskset rolli filosoofilise katalüsaatori, kõlalise või visuaalse struktuuri formaalse suunamise töövahendina. Xenakis kasutab mõnede oma partituuride loomiseks ka arvutit. Muusik ja arhitekt, täppisteadlane ja filosoof, kes on valinud oma doktoriväitekirja pealkirjaks kunstide ja teaduse "sulami". Selles raamatus on trükitud tema täielik väitekirja kaitsmine koos žürii küsimuste ja vahemärkustega. Ei ole üllatav, et Olivier Messiaen käsitleb muusikalise kompositsiooni, Michel Ragon arhitektuuri ning Michel Serres matemaatika ja täppisteaduste aspekti. Sunnitud rääkima endast ja oma muusikast, näitab Xenakis, et tema ettevalmistus on nii filosoofiline kui ka täppisteaduslik, mis on, nagu me kõik teame, erandlik. Me õpime paremini tundma meest, kelle kohta Antoine Golea kirjutas: "Xenakis on ehk üks kütkestavamaid, teravamaid ja ka provotseerivamaid figuure kahekümnenda sajandi muusikas." Tsiteerigem ka Claude Levi-Straussi, kes Quinzaine Litteraire küsimusele Xenakisest vastas: "Olen väga tundlik tema kirjutiste suhtes, leian need olevat teaduslikud, arukad ja peened."

Prantsuskeelne originaal ARTS / SCIENCES ALLIAGES ARTS / SCIENCES ALLIAGES Iannis XENAKIS Olivier MESSIAEN Michel RAGON Olivier REVAULT D’ALLONNES Michel SERRES Bernard TEYSSÈDRE Arts/sciences. Alliages, par Iannis XENAKIS Avec la collaboration d’Olivier MESSIAEN, Michel RAGON, Olivier REVAULT D’ALLONNES, Michel SERRES, Bernard TEYSSÈDRE Imprimé en Belgique par Casterman, s.a., Tournai, août 1979. N° Impr. 4126. N° Édit. 6112. Dépôt légal 4" trimestre 1979; D. 197910053/105. ISBN 2-203-23170-X Toute reproduction, même partielle, de cet ouvrage est interdite. Une copie ou reproduction par quelque procédé que ce soit, photographie, microfilm, bande magnétique, disque ou aut:e, constitue une contrefaçon passible des peines prévues par la loi du Il mars 1957 sur la protection des droits d’auteur. TABLE DES MATIÈRES AVERTISSEMENT 7 EXPOSÉ LIMINAIRE DE IANNIS XENAKIS 9 _ Philosophie sous-tendue Il _ Concrétions 19 DIALOGUE AVEC _ OLIVIER REVAULT D’ALLONNES 27 _ OLIVIER MESSIAEN 47 _ MICHEL RAGON 73 _ MICHEL SERRES 91 _ BERNARD TEYSSÈDRE 111 ANNEXE 139 Nouvelles propositions sur la microstructure des sons 139 _ Bibliographie 151 AVERTISSEMENT Ce texte est l’enregistrement de la soutenance de thèse effectuée par Iannis Xenakis le 18 mai 1976 à la Sorbonne. Le jury était présidé par Bernard Teyssèdre, professeur d’esthétique à Paris 1 - Sorbonne et composé de Olivier Messiaen, professeur au Conservatoire national de musique; Michel Ragon, professeur à l’École nationale supérieure des arts décoratifs; Olivier Revault d’Allonnes, professeur à Paris 1 - Sorbonne (directeur de la recherche et rapporteur); Michel Serres, professeur à Paris 1 - Sorbonne. EXPOSÉ LIMINAIRE DE IANNIS XENAKIS Philosophie sous-tendue[1]l Les univers des musiques classique, contemporaine, pop, folklorique, traditionnelle, d’avant-garde, etc., semblent former des unités en soi, parfois fermées, parfois s’interpénétrant. Ils présentent des diversités incroyables, riches de créations nouvelles, mais aussi de fossilisations, de ruines, de déchets, tout cela en formations et transformations continues, tels les nuages, si différenciés et si éphémères. Cela s’explique par la proposition que la musique est un phénomène culturel, donc subordonné à un instant de l’histoire. Pourtant, on peut distinguer des parties qui sont plus invariantes que d’autres et qui forment ainsi des matériaux de dureté et de consistance consécutives aux diverses époques des civilisations, matériaux qui se meuvent dans l’espace, créés, lancés, entraînés, par les courants des idées, se heurtant les uns aux autres, s’influençant, s’annihilant, se fécondant mutuellement. Mais de quelle essence ces matériaux sont-ils faits? Cette essence, c’est l’intelligence de l’homme, en quelque sorte solidifiée. L’intelligence qui quête, questionne, infère, révèle, échafaude à tous les niveaux. La musique et les arts en général semblent nécessairement être une solidification, une matérialisation de cette intelligence. Naturellement, cette intelligence, quoique humainement universelle, est diversifiée par l’individu, par le talent qui distancie l’individu des autres. Le talent est donc une sorte de qualification, de gradation de la vigueur et de la richesse de l’intelligence. Car elle est, au fond, le résultat, l’expression de milliards d’échanges, de réactions, de transformations énergétiques des cellules du cerveau et du corps. On pourrait, à l’image de l’astrophysique, dire que l’intelligence est la forme que prennent les actes minimes des cellules dans leurs condensations et leurs mouvements, tels les soleils, les planètes, les galaxies, les amas de galaxies, issus de ou se réduisant à la poussière interstellaire froide. Cette image, toutefois, est inversée (au moins sur un plan), car cette poussière froide en se condensant, devient chaude à l’inverse de l’intelligence qui est un résultat froid des échanges entre les cellules chaudes du cerveau et du corps, un "feu froid". Ainsi les couleurs, les sons, le relief, sont des condensations dans notre système sens-cerveau. De ce système, un aspect brutal et parfaitement superficiel, extérieur, est perçu et saisi au niveau conscient. Les vibrations périodiques du milieu électromagnétique de la lumière ou de l’air sont inaccessibles à la conscience mais magnifiquement (dans des limites, certes) bien suivies et converties par nos sens et notre cerveau dont les sens sont le prolongement. Les conversions, d’autre part, s’opèrent sur plusieurs niveaux, de celui de la perception immédiate à celui de la comparaison, de l’appréciation, du jugement. Comment, pourquoi tout cela se produit-il? C’est un mystère, élaboré comme chez les animaux depuis des millions et des millions d’années. De même, prenons un exemple qui a l’air d’être évident, celui des échelles en musique. Il y a eu, en Occident tout au moins, des condensations de plus en plus fortes : la quarte Juste et ses tétracordes, et peut-être la quinte juste, d’abord, dont les origines sont parfaitement Inconnues, puis l’octave, ensuite la construction des "systèmes" par juxtapositions de tétracordes qui ont engendré les échelles de l’Antiquité, dont l’échelle diatomque des touches blanches du piano est une survivance; puis l’échelle chromatique à tempérament égal et enfin la continuité dans l’ensemble "hauteurs du son". Il ressort de cet exemple que la musique est une forte condensatrice, peut-être plus forte que les autres arts. C'est. pourquoi je donne un tableau comparatif2 entre certaines conquêtes réalisées par la musique et quelques reallsations par les mathématiques, telles que l’histoire nous les enseigne. Ce tableau montre un des chemins que la musique a pris dès, l'origine (dès l’Antiquité), et qu’elle a gardé avec une fidehte remarquable à travers les millénaIres avec une forte accélération au xxe siècle ce qui prouve que loin d’être une mode, cette faculté de condensation vers l’abstrait est une nature profonde qui lui appartient sans doute plus à elle qu’à d’autres arts. Par consequent, Il semble qu’un type nouveau de musicien soit nécessaire, celui de l’artiste-concepteur de nouvelles formes abstraites et libres, tendant vers des complicatIons puis vers des généralisations sur plusieurs niveaux de l’organisation sonore. Par exemple, une forme, une construction, une organisation bâtie sur des chaînes de Markov ou sur un complexe de fonctions de probabilités interliées, peut être transportée simultanément sur plusieurs niveaux de micro-, méso- et macrocompositions musicales. On peut d’ailleurs étendre cette remarque au domaine visuel, par exemple, dans un spectacle fait avec des rayons lasers et des flashes électroniques comme celui du Polytope de Cluny [2]. Rien ne nous empêcherait de prévoir désormais une nouvelle relation entre arts et sciences, notamment entre arts et mathématiques dans laquelle les arts «poseraient» consciemment des problèmes pour lesquels les mathématiques devraient et devront forger de nouvelles théories. L’artiste-concepteur devra posséder des connaissances et de l’inventivité dans des domaines aussi variés que la mathématique, la logique, la physique, la chimie, la biologie, la génétique, la paléontologie (pour l’évolution des formes), les sciences humaines, l’histoire, en somme une sorte d’universalité, mais fondée, guidée, orientée par et vers les formes et les architectures. Il est d’ailleurs temps de fonder une nouvelle science de "morphologie générale" qui traitera des formes et des architectures, de ces diverses disciplines, de leurs aspects invariants et des lois de leurs transformations, qui parfois ont duré des millions d’années. La toile de fond de cette science nouvelle devra être faite des condensations réelles de l’intelligence, c’est-à-dire de l’approche abstraite, dégagée de l’anecdotique de nos sens et de nos habitudes. Par exemple, l’évolution formelle des vertèbres des dinosauriens est un des documents paléontologiques à verser aux dossiers de la science des formes. Plongeons maintenant dans le système fondamental sur lequel repose l’art. L’art participe du mécanisme inférentiel qui constitue les planches sur lesquelles se meuvent toutes les théories des sciences mathématiques, physiques, et celles des êtres vivants. En effet, les jeux des proportions réductibles à des jeux de nombres et de métriques dans l’architecture, la littérature, la musique, la peinture, le théâtre, la danse, etc.; les jeux de continuité, de proximité, dans le temps ou hors-temps, d’essence topologique, se font tous sur le terrain de l’inférence, au sens strict de la logique. A côté de ce terrain, et en activité réciproque, existe le mode expérimental qui dénie ou confirme les théories créées par les sciences, y compris par la mathématique. Car la mathématique a aussi montré que depuis les géométries non euclidiennes et les théorèmes comme ceux de Gôdel, elle n’est qu’expérimentale, mais selon un terme beaucoup plus long que celui des autres sciences. C’est l’expérience qui fait et défait les théories, sans pitié, sans considération pour elles. Or, les arts aussi sont régis d’une manière plus riche et complexe encore, par le mode expérimental. En effet, il n’y a pas, il n’y aura jamais sans doute, de critères objectifs de vérité absolue et éternelle de validité ou de vérité d’une œuvre d’art, tout comme aucune "vérité» scientifique n’est définitive. Mais, en plus de ces deux modes, l’inférentiel et l’expérimental, l’art vit dans un troisième, celui de la révélation immédiate, qui n’est ni inférentielle ni expérimentale. La révélation du beau se fait d’emblée, directement, à l’ignorant du fait de l’art, comme au connaisseur. C’est ce qui fait la force de l’art et, semble-t-il, sa supériorité sur les sciences car, vivant dans les deux dimensions de l’inférentiel et de l’expérimental, l’art en possède une troisième, la plus mystérieuse de toutes, celle qui fait que les objets d’art échappent à toute science de l’esthétique, tout en se permettant les caresses de l’inférentiel et de l’expérimental. Mais d’un autre côté, l’art ne peut vivre que par le mode de la révélation. Il lui faut, l’histoire de l’art de tous les temps, de toutes les civilisations nous le montre, il lui faut, il a un besoin impérieux d’organisation (y compris de celle du hasard), donc d’inférence, et de sa confirmation, donc de sa vérité expérimentale. Pour rendre plus évidente cette trinité des modes de l’art, imaginons que dans un avenir lointain le pouvoir d’action de l’artiste augmente comme jamais auparavant dans l’histoire (c’est le chemin qui suit l’humanité dans la création et la dissipation des quantités d’énergie croissantes). En effet, il n’y a aucune raison pour que l’art ne sorte, à l’exemple de la science, dans l’immensité du cosmos, et pour qu’il ne puisse modifier, tel un paysagiste cosmique, l’allure des galaxies. Ceci peut paraître de l’utopie, et en effet c’est de l’utopie, mais provisoirement, dans l’immensité du temps. Par contre, ce qui n’est pas de l’utopie, ce qui est possible aujourd’hui, c’est de lancer des toiles d’araignées lumineuses au-dessus des villes et des campagnes, faites de faisceaux lasers de couleur, telles un polytope géant : utiliser les nuages comme des écrans de réflexion, utiliser les satellites artificiels comme miroirs réfléchissants pour que ces toiles d’araignées montent dans l’ espace et entourent la terre de leurs fantasmagories géométriques mouvantes; lier la terre à la lune par des filaments de lumière; ou encore, créer dans tous les cieux nocturnes de la terre, à volonté, des aurores boréales artificielles commandées dans leurs mouvements, leurs formes et leurs couleurs, par des champs électromagnétiques de la haute atmosphère excités par des lasers. Quant à la musique, la technologie des haut-parleurs est encore embryonnaire, sous-développée, pour lancer le son dans l’espace et le recevoir du ciel, de là où habite le tonnerre. Mais le son eii rase-mottes, dans les villes et les campagnes, est déjà possible grâce aux réseaux nationaux des alarmes antiaériennes par haut-parleurs. Ils suffirait de les affiner[3]• Si l’économie des pays n’était pas torturée par les besoins stratégiques et l’armement, c’est-à-dire le jour où les armées des nations se seront dissoutes dans de simples polices non répressives, alors, financièrement, l’art pourra survoler la planète et s’élancer dans le cosmos. Car, technologiquement, ces choses sont faisables aujourd’hui. Dans ces types de réalisations artistiques, planétaires ou cosmiques, il est évident qu’il est indispensable que l’artiste, par conséquent l’art, soit à la fois rationnel (inférentiel), technicien (expérimental) et talentueux (révélateur); trois modes indispensables, coordonnés, qui éviteraient des échecs fatals, étant données les dimensions de ces projets et les risques très grands d’erreurs. Cette complexité plus grande du système fondamental des trois modes qui régissent l’art, conduit à la conclusion qu’il est plus riche et plus vaste et qu’il doit forcément prendre la tête dans la création des condensations et des concrétions de l’intelligence. Donc, servir de guide universel aux autres sciences. Concrétions Mon travail, depuis déjà plus de vingt ans, s’est efforcé, inconsciemment d’abord, puis de façon de plus en plus consciente, de remplir cet espace philosophique de l’intelligence qui se concrète, par des cailloux de couleur que sont les œuvres musicales, architecturales, visuelles et mes écrits, à la manière d’un artisan mosaïste. Ces cailloux, au début très isolés, se sont trouvés rassemblés par plages de parentés, d’affinités, mais aussi d’oppositions, formant graduellement des figures de cohérences locales, puis des champs plus vastes s’interpellant par les questions et les réponses données. La mathématique y joue un rôle essentiel en tant que catalyseur philosophique, comme outil de mise en forme des édifices sonores ou visuels, mais aussi comme tremplin d’auto-libération. Ici je ne tracerai que les questions fondamentales et, en vis-à-vis, les réponses données par des œuvres que j’ai produites, sans toutefois entrer dans le détail et dans les dédales de leur élaboration. En outre, nombre de questions sont liées entre elles et présentent des intersections appartenant à un même domaine philosophique. Par exemple: causalité - déterminisme continuité, indéterminisme (hasard) - existentialité - déterminisme, etc. C’est pourquoi aussi, une œuvre (réponse) à elle seule peut donner des réponses à un faisceau de questions. C’est un peu comme si l’on se trouvait en présence de sons-questions riches en harmoniques, dont on considérerait tel ou tel harmonique comme fondamental, suivant la quête du moment. De plus, je ne nommerai que les quelques œuvres du dossier de la thèse. Questions -> Réponses existentialité -> ST/lO-l, 080262 temps, hors-temps -> Nomos gamma causalité -> ST/IO-l, 080262, Nomos gamma, Tourette (façades) répétition ou pas de modules inférence -> Nomos gamma, ST/IO-l, 080262 connexité -> Empreintes (arborescences), Metastasis (formes de glissandi), Pavillon Philips (coque, formes de droites) compacité -> Metastasis, Pavillon Philips, Nomos gamma indéterminisme pur -> ST/IO-l, 080262, système stochastique libre déterminisme impur -> Stratégie (théorie de jeux), Syrmos (chaînes de Markov) déterminisme pur -> Nomos gamma (groupes) identité (similitude, équivalence) -> Toutes les œuvres. Les spectacles visuels des Polytopes reprennent les questions et les réponses posées et données en musique, cette fois avec les lasers, les flashes électroniques et les espaces. Ce qui est remarquable à constater, c’est que l’on trouve ces questions à tous les niveaux de la composition sonore ou visuelle, c’est-à-dire depuis le plan de la grande forme (macro-composition) jusqu’à celui de la synthèse des sons par ordinateur et conversion numérique-analogique (micro-composition), mais aussi aux niveaux intermédiaires. "Les voies du haut ou du bas ne font qu’une». Je disais donc que tout le travail que j’ai fait depuis tant d’années est une sorte de mosaïque de cohérences hiérarchisées. Au sommet de la hiérarchie je placerai la philosophie. Philosophie, dans quel sens? Au sens de l’élan qui nous pousse vers la vérité, la révélation, la recherche, la quête dans tout, par l’interrogation, par la critique systématique, âpre, pas seulement dans des domaines spécialisés, mais dans tous les domaines possibles. Ceci conduit à l’ensemble de la connaissance, mais qui devrait être active, au sens du faire. Ce n’est pas une connaissance passive mais une connaissance qui se traduit dans les actes de création, je répète: dans tous les domaines. Suivant les méthodes que j’examinerai tout de suite, on peut séparer, diviser ce tableau de cohérence, cette mosaïque, cette table, en trois catégories, ou trois chapitres, le premier étant la méthode qui permet d’arriver à cette connaissance active par la création, et qui implique l’inférence, c’est-à-dire la raison, la logique, etc., par la démonstration théorique. Suivant ce critère, il y a des aspects de l’activité et de la connaissance qui sont partiellement inférentiels, entièrement inférentiels et expérimentaux, et d’autres qui sont encore inconnus. Dans le domaine des partiellement inférentiels, je placerai les arts. Les arts participent à l’inférence. On construit, par conséquent, on peut enchaîner d’une manière raisonnée et démontrer jusqu’à un certain point. Par contre, les sciences de l’homme et les sciences de la nature, physique, mathématique, logique, sont entièrement inférentielles et aussi expérimentales. Il est nécessaire de bâtir une théorie et de vérifier cette théorie par l’ expérience. Dans le domaine des arts, on peut bâtir, partiellement, par inférence, mais l’expérimentation n’est pas immédiate car il yale problème esthétique et il n’y a pas de démonstration possible de la valeur esthétique des choses. Et je laisserai la porte ouverte sur toutes les méthodes qui ne sont pas encore connues ou découvertes par le cheminement de la pensée de l’homme. Comme corollaire à cette discrimination des arts, on peut dire que les arts sont plus libres, puisque les arts participent aussi bien à l’opération inférentielle qu’à l’expérimentation, l’expérience; et c’est peut-être ambitieux de le dire, mais les arts pourraient éventuellement guider les autres secteurs de la pensée de l’homme, c’est-à-dire que, à mon avis, je plac’erai les arts en tête des activités de l’homme, de manière à ce qu’ils baignent toutes ses activités, dans le domaine scientifique comme dans la vie quotidienne. Je descends dans l’échelle en disant qu’après, il y a une catégorie de questions que l’on peut se poser, qui ont été éludées en quelque sorte par l’histoire, et que l’on peut découvrir à nouveau et se poser, c’est-à-dire une sorte de fragmentation des directions dans un sens créatif de la philosophie. Parmi ces catégories, il y a l’existentialité (l’ontologie, la réalité), la causalité, l’inférence même, la contiguïté ou la connexité, la compacité, l’ubiquité temporelle ou spatiale, prises comme conséquences de nouvelles structures mentales éventuelles. Il y a aussi le déterminisme et son pôle extrême l’indéterminisme, etc. Je reprends en quelque sorte certaines des catégories de la pensée qui ont été énoncées plus ou moins consciemment et systématiquement depuis Aristote, très importantes, et qui sont laissées un peu de côté ou reprises, éventuellement par la psychologie expérimentale (Jean Piaget) et par certaines branches de la mathématique moderne. Ces catégories de pensées-questions reçoivent, peuvent recevoir, et c’est ce que je me suis efforcé de faire en musique, des familles de solutions. Je me reprends, j’espère que je suis clair. Je veux dire que la pensée de l’homme a essayé de répondre à ces questions, et elles sont multiples, en donnant des réponses provisoires avec certaines familles de solutions, surtout notamment en ce qui concerne le déterminisme. Ici, je veux ouvrir une parenthèse : la causalité, par exemple, est une des formes vécues de la vie, se rapportant à cette question fondamentale du déterminisme qui, lui, peut être considéré comme un aspect nuancé différentiel de l’indéterminisme. On peut même affirmer, ce que je n’ai pas énoncé plus tôt, que l’ordre ou le désordre font partie de l’indéterminisme. La connexité ou la continuité aussi sont d’autres facettes de ce bi-pôle déterminisme-indéterminisme. Je reprends la suite de ce que je disais, que les solutions et les procédures pouvant donner des réponses aux catégories de questions fondamentales sont, d’une manière très schématique bien sûr, définies par quelques sous-chapitres, quelques paragraphes. Par exemple, la pensée probabiliste avec, d’une part, son extrême que j’appelle la stochastique libre ou sans mémoire, avec, d’autre part, les chaînes markoviennes qui acceptent une certaine causalité, un certain déterminisme élémentaire, qui est en amont de celui-ci. Mais, au cœur de la pensée probabiliste et de l’indéterminisme, il y a ce qu’on peut appeler la symétrie ou la périodicité qui est une autre façon de définir, de parler de cette pensée; la symétrie ou la périodicité, c’est-à-dire le retour cyclique d’événements, de procédures, etc., peut se concrétiser au bas de l’échelle déterminisme-indéterminisme par des structures de groupes. Entre les deux, il y a ce qu’on pourrait appeler une phase hybride ou mixte dont l’une des formes intéressantes est la théorie des jeux. Plus bas, aux paliers inférieurs de la mosaïque, en réponse à ces thèmes, à ces façons de penser qui ont été posées aussi par d’autres sciences, y compris par la musique, on trouve des œuvres particulières qui sont des réflexions sur ces questions et des tentatives de solution. Je ne veux pas en faire l’énumération, car ce serait trop fastidieux. Mais par exemple, je peux dire que le thème de la stochastique libre est traité dans une pièce comme Achorripsis, qui a été formulé par la suite en un programme machine, programme qui représente un système stochastique libre. Ce programme a permis de faire des œuvres comme ST/lO, ST/48 pour orchestre, mais aussi d’entrer dans le domaine de la microstructure des sons, dans la synthèse des sons par ordinateur. D’ailleurs ce même programme est utilisé depuis quelques années, tant aux États-Unis qu’en Europe (Suède, France, etc.), dans d’autres studios que le CEMAMu[4] ainsi que par d’autres compositeurs. Dans le domaine de la stochastique markovienne, il y a des pièces comme Analogiques, Syrmos pour cordes. Dans celui des jeux: Stratégie, Linaia-Agon, etc. Dans les systèmes symétriques, périodiques, il y a Akrata, Nomos Alpha, Nomos Gamma, Persephassa, œuvres composées sur des structures de groupes. Je ne fais qu’énoncer les œuvres principales. Dans le rapport que j’ai remis au jury, et au début de mon exposé, il y a un peu plus de détails sur les autres réalisations visuelles, comme les Polytopes ou sur ce que j’ai pu faire en architecture. En continuant de cette façon, on arrive au bas de l’escalier où se trouve l’espace pression-temps du son. On pourrait dire des choses analogues dans le domaine du visuel, ce qui fait que les questions posées au niveau des microstructures, c’est-à-dire, au niveau de l’élément supérieur des macrostructures peuvent être vues, résolues ou traitées avec des procédures et des pensées équivalentes au niveau primordial qui est la pression en fonction du temps quant à l’oreille, ou les actions électromagnétiques quant à l’œil dans le spectre visible. On peut résumer en disant que tout ce qui a trait aux macrostructures et aux problèmes fondamentaux les plus généraux, se retrouve à tous les niveaux intermédiaires des structures, médio-structures, méso-structures, jusqu’au bas de l’échelle qui se confond avec l’action quantique, dirais-je, sur ces deux sens, vision, audition. Je vous ai donné, je crois, un aperçu très général du fil conducteur de tout ce travail, sans parler du travail lui-même. Bernard TEYSSÈDRE. - Je vous remercie beaucoup, Iannis Xenakis. Il est certain que votre exposé a été bref et qu’il peut apparaître complexe car il est sursaturé. J’espère que la discussion qui va avoir lieu maintenant éclairera la présentation que vous avez faite. Elle est, je le répète, précise pour ceux qui connaissent déjà bien votre travail. Elle risque de paraître un peu floue à d’autres, justement parce que trop de matières sont exposées à la fois. Je crois que Revault d’Allonnes, qui est le rapporteur de votre thèse, pourrait intervenir tout de suite. DIALOGUE AVEC OLIVIER REV AULT D’ALLONNES Olivier REVAULT D’ALLONNES. - Effectivement, par une bizarrerie administrative, je me trouve être le directeur de recherches. En réalité, le directeur des recherches de Iannis Xenakis est Iannis Xenakis lui-même. Il s’est très bien débrouillé. Je me trouve être aussi, au moment de la soutenance, le rapporteur, et devant une masse aussi considérable de recherches et d’œuvres, le rapporteur se sent assez petit; ce que je crois pouvoir être, c’est un spectateur parmi d’autres, et un spectateur fasciné par l’ensemble des travaux de Xenakis. Il y a untitre, choisi par Xenakis, pour présenter ses œuvres théoriques fondamentales, et à l’appui de ces œuvres théoriques, un certain nombre de documents qui sont les partitions musicales de quelques-unes des œuvres qu’il a citées à l’instant même, plus des croquis, dessins, schémas, relevés d’architecture, etc. Ce titre général définit non seulement le dossier, mais aussi l’ensemble de l’œuvre artistique de Xenakis, à savoir: Arts/sciences. Alliages. Xenakis présente quelques-uns de ses alliages, et vient de nous dire d’une manière très dense dans quel sens on pourrait entrevoir les alliages en question. "L’art", ce terme renvoie chez Xenakis à l’artifex, au créateur. Cet homme qui a une certaine attitude devant le monde, une certaine vision du monde, ressent la hantise permanente de quelque chose qu’il y a à faire. Depuis près de vingt ans, je ne l’ai jamais vu autrement qu’en proie à une sorte de démon créateur. La science, c’est quelque chose qui, chez lui, accompagne indissolublement ce démon créateur. Xenakis veut faire quelque chose, mais ne veut pas faire n’importe quoi. Il veut toujours composer une œuvre déterminée, œuvre qui à un certain niveau, le niveau proprement esthétique, se communique elle-même : vous allez au concert, vous écoutez du Xenakis; mais l’œuvre, à un autre niveau, peut être communiquée d’une autre façon, par un langage analytique, rationnel, qui simultanément analyse cette œuvre et la justifie. Dans des livres comme ceux qu’il présente aujourd’hui, à savoir: Musique. Architecture 1 et, peut-être surtout, Musiques formelles 2 , on voit que des œuvres sont analysées, décortiquées et qu’en même temps elles sont justifiées, légitimées. Xenakis dit pourquoi il a voulu faire ceci et comment il l’a fait, mais le pourquoi est au moins aussi important que le comment. Les "alliages" du reste, ces alliages qui ne vont pas sans problème, pour moi du moins, sont les œuvres architecturales, musicales, polytopiques, mais ils comprennent aussi le travail théorique que nous avons sous les yeux. Je voudrais laisser à plus compétent que moi le soin de réfléchir sur l’art et sur la science, pour poser à Xenakis des questions concernant les alliages. La première question sera celle-ci : Xenakis propose dans son œuvre théorique de lutter contre la séparation actuelle des arts et des sciences, de créer une sorte de circulation de la pensée, une fécondation mutuelle de la pensée scientifique et de la pensée artistique. Pour ce faire, Xenakis s’appuie à la fois sur une vision du passé et sur des réalisations actuelles. La vision du passé, nous la voyons réapparaître tour à tour dans chacun de ses ouvrages, et même dans l’exposé qu’il vient de faire: les périodes les plus heureuses de fécondation mutuelle des arts et des sciences ont été des périodes comme par exemple l’Antiquité grecque, la Renaissance italienne, l’Age classique, où artistes et savants s’ignoraient moins que de nos jours, d’où une nostalgie tout à fait légitime de la circulation entre l’art et la science. Or, actuellement, les services que peuvent se rendre les arts et les sciences me semblent fort inégalement répartis et fort inégalement possibles. J’ai l’impression que les sciences peuvent apporter aux arts, et particulièrement à la musique, infiniment plus de services, plus d’éclairages, plus de fécondation, que la musique ne le peut faire pour la connaissance scientifique. Par exemple, l’application à la musique du calcul stochastique, ou l’application de la théorie des cribles que Xenakis a affinée pour l’appliquer au problème de l’échelle des hauteurs , ~ont de nature à renouveler la musique et même, comme Il est dit dans la première partie de Musique. Architecture, de renouveler la musicologie; mais d’un point de vu~ purement mathématique, ces instruments, je le crams, ne présentent aucun intérêt particulier, aucune fécondité, aucune nouveauté, aucune difficulté à surmonter, et par conséquent, aucune découverte nouvelle à faire. De même, l’utilisation des ordinateurs a certainement posé des problèmes, mais des problèmes tout à fait classiques de programmation et d’informatique; bref, des problèmes qui sont actuellement assez parfaitement maîtrisés. Il n’en est pas de même évidemment dans l’autre sens. On pourrait dire aujourd’hui que, et une grande partie de l’œuvre de Xenakis l’a montré, la pensée musicale n’a pas encore, n’a pas assez utilisé toutes les ressources des mathématiques. Quand Xenakis s’est aperçu que pour un mathématicien, les échelles de hauteurs constituent un ensemble ordonné, une échelle abélienne, cette définition, triviale comme disent les mathématiciens, lui a mis pour ainsi dire la puce à l’oreille. Tiens, il y a des ensembles ordonnés, donc il y a peut-être des ensembles qui ne sont pas ordonnés. Il Y a une échelle abélienne, n’y a-t-il pas une échelle qui ne le serait pas? On comprend très bien comment la pensée musicale est ici fécondée par les mathématiques, mais étant donné, je dirais, le niveau mathématique assez élémentaire de ces concepts, l’intérêt est nul pour les mathématiques. Si l’on peut rêver, par conséquent, d’échange entre les arts et les sciences, il faudrait constater que de nos jours, les termes de l’échange semblent fort inégaux. D’où ma question: comment peut-on espérer, de nos jours, capter l’intérêt des savants, et essayer de percevoir ces nouvelles structures mentales auxquelles Xenakis faisait lui-même allusion à l’instant même? L’utilisation de la science par l’art profite plus à celui-ci qu’à celle-là. Ce déséquilibre est-il un mal? Si oui, peut-on le combattre? Ma deuxième question sera simplement dérivée de la première. La proposition de circulation et d’alliage n’est qu’une proposition, c’est-à-dire qu’il ne s’agit pas d’une situation actuellement réalisée; c’est un souhait; l’alliage a quelque chose d’utopique, c’est-à-dire de créateur. Il est expérimenté, pour ainsi dire, par la fécondité de l’œuvre de Xenakis, mais peut-il prétendre se répandre dans la société, peut-il prétendre devenir sinon la loi unique, au moins l’un des moments de ces rapports de l’art et de la science? La proposition d’alliage suppose-t-elle que la science de son côté, l’art du sien, aient quelque chose qui serait un sens qui leur serait propre, une sorte de vérité en soi? Ou bien l’art de son côté, la science du sien, ne seraient-ils pas porteurs d’autre chose que d’eux-mêmes? Seraient-ils issus d’ailleurs, d’un quelque part situé ailleurs que dans les axiomatiques auxquelles nous aimons les référer? Autrement dit, existe-t-il entre les arts et les sciences une union purement technique, ou bien y a-t-il finalement une division sociale (et si oui, laquelle) qui se cacherait derrière cette division technique? Je ne pense d’ailleurs pas particulièrement ici à une différence de classe entre les intellectuels et les manuels. Lesquels, du reste, seraient les uns et lesquels les autres? Il s’agit bien plus d’une division, d’une séparation entre les fonctions. La science est tournée vers l’action dite rationnelle, sur la nature et sur l’homme; elle se dit dans le réel. L’art est tourné vers la création d’objets imaginaires: en les détournant partiellement l’un et l’autre, en les retournant l’un vers l’autre, est-ce que Xenakis propose quelque chose qui est immédiatement réalisable, ou bien quelque chose qui, pour se réaliser, présuppose des transformations, notamment sociales, beaucoup plus profondes? En somme, les sciences ont donné aux hommes une certaine maîtrise sur les choses. Xenakis propose maintenant, en quelque sorte, de maîtriser cette maîtrise, ét qu’elle serve aux hommes au lieu de se servir des hommes. Alors, est-il concevable que ce renversement des termes, qui circule à travers toute l’œuvre de Xenakis, se limite finalement aux seuls domaines de la science et des arts ? La troisième question va revenir vers l’esthétique. L’opinion est, hélas, très répandue, que Xenakis ferait composer sa musique par des ordinateurs. Cette opinion n’est que l’un des aspects de l’idéologie scientiste et techniciste répandue dans toute la société. Quand on y regarde de plus près, on s’aperçoit que cela n’a pas de sens évidemment. Dans Musiques formelles [3] , on trouve mê~e une formule admirable: "Dans ce domaine, il se trouve que les ordinateurs peuvent rendre ce~ns ~e~ices". Cela veut dire qu’on peut ne pas pouvOlr beneficier de ces "services». Ce fut le cas de Metastasis, créée en 1954 et où je revois encore Xenakis calculant tout "à la main», comme il disait, avec une patience, il faudrait dire une obstination incroyable, réalisant en plusieurs mois de travail acharné ce qu’un ordinateur peut faire au maximum en quelques heures. Bon, on a alors là pour des mois de travail au crayon: si on le peut, on prendra donc une machine qui f~ra. les chose.s beaucoup plus vite et beaucoup mieux. MaIS il ~ a aUSSI, plus ~d, dans la production musicale de Xenakis des œuvres faItes elles aussi "à la main", des œuvres qu’on peut appeler artisanales des œuvres dans lesquelles il ne s’est pas servi d’ordinateur pour des raisons que Xenakis saura peut-être nous donner. Je pense par e~emple ~ Nuits" ~~ 1967, et beaucoup plus récemment a Evryalt, de 1 ete 1973. Ces œuvres, j’essaie encore depuis deux ans d’analyser leur partition. Or, sur le plan, j’allais dire de la beauté disons de la réussite esthétique, il est faux, selon mon g~ût du moins, que de ces œuvres-là soien~ .les moindres. Si je ne parviens pas à analyser la partItIon d’Evryali, évidemment, je dois incriminer d’abord .~es propres limites. Je n’en rougis pas, car c’est une partItIon particulièrement difficile. Mais enfm, faut-il aussi incriminer autre chose? Non pas, certes, un supplément d’âme, mais n’y aurait-il pas dans cette partition l’éclatement de ce qu’on peut appeler provisoirement un style xénakien, style dont Xenakis parle fort peu, style que fmalement il a pu contraindre les ordinateurs à respecter, style que le profane ne retrouve évidemment que dans l’écoute musicale. Xenakis en parle à peine dans son œuvre théorique. Par pudeur? Par modestie? Je ne sais pas. Quelquefois une allusion, une petite phrase qui émerge, sur la beauté de tel ou tel dispositif, de tel ou tel résultat, sur l’absurdité ou la bassesse de ce que Xenakis appelle quelque part "les bas-fonds de l’intelligence musicale". De ce style xénakien, tu parles fort peu. Tu peux répondre que tu en laisses le soin à tes historiographes. Ds te remercient de ta confiance; ils te remercient sans doute moins de ton silence! Si tu pouvais les aider un petit peu, ils te seraient encore plus reconnaissants. Est-ce sortir des limites de cette thèse, Arts/sciences. Alliages, que de n’accorder aux techniques qu’un rôle second et asservi par rapport à des intuitions ou à des intentions esthétiques qui, certes, vont vers des alliages ou même ressortissent entièrement aux alliages, mais ne se réduisent pas à ces alliages. [puudub prantsuskeelses originaalis] En somme, qu’est-ce qui préside à tout cela, qu’est-ce qui, comme on disait jadis, "inspire» l’ensemble de ces démarches? Nous débordons peut-être ici certaines limites, mais enfin, il serait un peu paradoxal d’avoir en face de soi un Xenakis qui, en raison de la situation, est quelque peu tenu de répondre (ri~es), et de ne pas lui demander ce qui se passe, ou ce qUI se protège derrière la forteresse des sciences, derrière la façade des ordinateurs. Comment se fait-il que Xenakis se raconte et nous raconte toute cette merveilleuse puissance du savoir à laquelle je crois, jusqu’à un certain point seulement, et d’un autre côté, qu’il compose les plus éclatantes de ses œuvres tout simplement avec un papier et un crayon? Si tu veux, où réside dans ce domaine ce qui aurait profondément et totalement changé, depuis Bach ou Mozart par exemple? Iannis XENAKIS. - La dernière question, à mon avis très importante, serait que j’ai été taxé parfois de calculant, de mathématicien, de sec, et ceci par opposition à musicien. Elle est périmée maintenant. Il semble qu’aujourd’hui je ne rencontre plus d’opposition à ce sujet. Même les musiciens me considèrent comme un musicien! C’est une parenthèse que je veux ouvrir. Pour la première fois, je me tiens dans une institution aussi "respectable" que l’Université de Paris et même à la Sorbonne. Jusqu’ici, j’étais toujours une sorte de marginal et je régularise un petit peu une situation nouvelle qui se crée (puisque j’enseigne maintenant à Paris-I), avec cette soutenance de thèse. C’est vrai que presque tous mes écrits se rapportent à des questions qui peuvent être démontrables, qui peuvent être exprimées dans un langage que j’espère tout le monde comprend, que ce soit ici, au Japon, en Amérique, chez les Esquimaux même ... Par contre, la partie qui n’est pas exprimable, elle ne peut être dite que par l’art lui-même, la musique elle-même ou par l’expression architecturale ou par l’expression visuelle et là-dessus, je ne sais pas s’il y a beaucoup de discours possibles, en dehors du discours «j’aime ça" ou «j’aime pas ça", ou "c’est beau", ou «c’est laid", ou "c’est dégueulasse" ou "c’est formidable", "intéressant", etc. C’est vrai que l’on retombe dans le problème de l’esthétique ou de la psychologie, mais que dire sur les agencements, sur les sonorités, etc., en dehors du langage technique ou analogique ou proportionnel ou architectural. Que peut-on dire? Il n’y a pas de langage qui pourrait cerner ces questions en dehors des questions de construction, de structure, donc de proportions, de règles, de lois. Mais je suis d’accord avec toi: il y a autre chose dans la musique, dans n’importe quelle musique, même dans la plus "laide» d’ailleurs, mais ce quelque chose, on ne peut le distinguer, on ne peut le discerner, on ne peut pas en parler. Ce sont des traits qui ne sont pas descriptibles pour l’instant. C’est l’objet artistique qui doit les dire. Voilà pourquoi c’est une sorte d’aspect amputé... Non? Olivier REVAULT D’ALLONNES. - C’est habile... Iannis XENAKIS. - Comment: c’est habile? Olivier REVAULT D’ALLONNES. - Tu me dis que tu ne peux pas répondre et pourtant tu fais toi-même des rapprochements entre des structures des œuvres du passé et un certain nombre de goûts de l’époque ... Iannis XENAKIS. - Je peux le faire ... je peux parler de structures, c’est ce que je viens de dire, mais je ne peux pas parler de la valeur d’une chose et de questions qui ne sont pas immédiatement perceptibles à travers la structure. Par exemple, tu as dit que j’ai fait des calculs soit avec des ordinateurs, soit à la main, mais de tout ça, il y a quand même un style qui se dégage, indépendamment des calculs. Je suppose que le style veut dire quelque chose qui est en dehors des calculs, qui est métacalcul. Olivier REV A UL T D’ALLONNES. - Ou infracalcul,je ne sais pas ... Iannis XENAKIS. - Ou infra, moije dirais méta ou derrière, ce qui revient au même! Je pourrais même généraliser ici, j’oserais ça, même n’importe quel choix présuppose un choix arbitraire. Car, il n’y a pas de construction faite par l’homme, qui ne soit pas en un certain point arbitraire. L’acceptation de lois qui régiraient la construction d’une chose est déjà un acte arbitraire. En mathématique, on rencontre cela, lorsque les mathématiques modernes ainsi que les mathématiques antiques posent arbitrairement des axiomes puis, seulement en un deuxième temps, emploient la logique formalisante et construisent tout leur édifice. L’ensemble des axiomes posés à la base de la pyramide, ou à son sommet, à son sommet puisque, pour moi, la base est inversée, c’est-à-dire que la pointe se trouve sur terre et la base dans le ciel, puisqu’on y a plus de place et qu’elle peut grandir ... Alors, l’ axiomatique est un choix, un choix qui est arbitraire. L’est-il complètement? Oui, mais en faisant d’abord la part à certaines nécessités théoriques ajoutées aux conditionnements de l’expérience vécue et historique. Olivier REVAULT D’ALLONNES. Il n’empêche qu’il y a un parallèle que tu fais toi-même. Je crois que c’est dans la dernière édition de Musique. Architecture et aussi à la fin de ton rapport de thèse, entre une histoire de la pensée mathématique d’une part et une histoire des formes musicales d’autre part; et pratiquement un troisième élément, un troisième parallèle qui bien entendu n’est pas tout à fait parallèle, qui est l’histoire du goût musical. De même que la fugue est une structure musicale de l’époque. de la fugue et que tes œuvres musicales sont typiquement des œuvres du xxe siècle. Bien entendu, il y a l’individu Xenakis, mais il me semble que l’arbitraire n’est pas total. Iannis XENAKIS. Je crains là qu’on ne s’éloigne un petit peu de la question que tu avais posée tout à l’heure, car ce que tu dis est une question de la musicologie et des formes ou mieux encore, une science des formes et de révolutions dans.le temps historique. Si la fugue était, à un moment donné, quelque chose de fondamental, elle ne l’était pas avant sa découverte, avant qu’elle ne s’impose! Elle l’est beaucoup moins aujourd’hui. C’est sûr. Donc, c’est un problème d’abord de technique car, qu’est-ce que c’est que la fugue? C’est bien un ensemble de règles, et procédures, en vue de construire un édifice musical et cet ensemble de règles est né; par conséquent, il n’existait pas avant! Et il n’existe plus au sens large, du point de vue création, maintenant. Ceci montre bien son caractère, au moins partiellement arbitraire. Olivier REVAULT D’ALLONNES. - La question ne portait pas sur la fugue, elle portait sur ton œuvre. Iannis XENAKIS. - Si je tente de m’expliquer dans des livres, des articles ou des conférences sur telle ou telle technique employée, c’est parce que c’est de cela que je peux parler facilement. Ou si je fais aussi de l’ enseignement, c’est pour amener les gens à rentrer dans ces questions-là, mais je ne dis pas tout, même si je le sens ou perçois, parce que je ne sais pas comment le dire. Alors je fais entendre et voir des résultats, éventuellement. Voilà, pour résumer un peu ma réponse. Je n’ai pas répondu à l’autre question peut-être... Olivier RE VAULT D’ALLONNES. - Oui, peut-être ... On voudrait te demander: pourquoi y aurait-il un certain décalage des arts par rapport aux sciences, et dans quelle mesure n’y aurait-il pas plutôt un apport unilatéral, dirigé des sciences vers les arts, plutôt que l’inverse? C’est une question, et la deuxième est : si cet alliage des sciences et des arts, que tu proposes, est quelque chose d’utopique, donc de créateur, est-ce que ça n’implique pas autre chose qu’une simple transformation dans le domaine ou des arts et des sciences, c’est-à-dire une transformation, disons, presque de civilisation. Iannis XENAKIS. - C’est parfait, parce que j’ai noté à peu près la même chose! Je reprends la première question d’Olivier Revault d’Allonnes qui dit qu’il y a un retard ... à sens unique plutôt et pas dans le bon sens ... pourquoi les routes se sont-elles rétrécies avec le temps? Je crois que c’est une question de civilisation. L’Antiquité avait aussi créé cette circulation entre les arts et les sciences. On voit Polyclète qui, avec son canon, essayait d’appliquer la géométrie à la sculpture, circulation qui se faisait de même dans l’architecture, dans la peinture et dans la musique; les textes d’ Aristoxène et des autres qui sont venus par la suite. La Renaissance a redécouvert, je pense que c’était ça son point fondamental, l’unicité de l’homme. L’homme est quelque chose d’unique, d’un. Il n’y a pas plusieurs hommes, il n’yen a qu’un et cet homme recouvre toutes les possibilités de la pensée et de l’activité et par conséquent, l’interpénétration des sciences et des arts. D’autre part, les arts aussi ont, à certains moments cruciaux de l’histoire, fait des apports dans le domaine de la pensée scientifique, d’une manière directe ou indirecte. C’est ce que je me suis efforcé de montrer dans le tableau que j’ai ajouté au dernier chapitre de Musique. Architecture, en faisant le parallèle entre le développement de la pensée musicale et de la pensée surtout mathématique. Car, ce qui est curieux et qui saute aux yeux immédiatement, c’est que la musique est beaucoup plus proche des mathématiques que les autres arts. Pourquoi? Je ne vais pas le montrer maintenant. Je peux néanmoins dire que l’œil est le plus rapide, qu’il est beaucoup plus immédiat, en prise directe avec la réalité, tandis que l’oreille, étant moins agile et plus en retrait, exige de la pensée de réfléchir, par conséquent d’être plus abstrait, et donc de se créer des bases qui soient plus abstraites et qui soient ainsi beaucoup plus proches de la mathématique. Et c’est dans cet ordre d’idée que j’ai essayé de montrer comment cette espèce de "vrille" entre la musique, la théorie musicale, une partie donc de la musique, et la théorie des mathématiques s’enroulent l’une sur l’autre, quoique parfois elles cheminent parallèlement, sans s’enrouler du tout. Aujourd’hui, nous sommes en retard dans le domaine artistique. Or, déjà avant de quitter l’école polytechnique d’Athènes, quand j’étudiais les procédures de composition, j’étais frappé par la pauvreté de la pensée "combinatoire» de la musique, y compris celle de la musique sérielle que j’étudiai plus tard. Je vais ici rendre hommage à Olivier Messiaen : c’est le seul qui avait une pensée complètement ouverte dans ce domaine-là et qui ait posé des bases avec son travail, entre autres, sur les "interversions". Je dirais plus: par son côté artistique. Mais ceci est une autre facette, qui n’appartient pas à celles des structures. Aussi, pour prendre un autre exemple, les modes à transposition limitée d’Olivier Messiaen étaient une amorce du travail sur les échelles, quoique sans généralisation, mais laquelle amorce devait me permettre d’aboutir aux principes durs des structures mentales des musiciens, de leur manière de penser et d’agir. Et lorsque, il y a déjà plus de quinze ans, je suis tombé sur des problèmes d’échelles, issus de mes problèmes en composition musicale, en les travaillant, j’ai été conduit à les résoudre à l’aide de mathématiques presque toutes faites, ce qui a donné la théorie des cribles. Ce n’est pas l’inverse, je n’ai presque jamais fait l’inverse. Mais à côté de ce que la mathématique d’aujourd’hui offre à l’artiste, ce n’est vraiment rien, c’est minime. Qu’est-ce qu’il faut donc faire? Eh bien, à mon avis, il faut une transformation concrète de la formation, aussi bien du musicien, de l’artiste que du scientifique. Cette formation ne doit pas se faire trop tard. Elle doit se faire déjà à l’école primaire, sinon à la maternelle. Et c’est tout le problème de l’éducation, du système d’éducation, de la formation de l’homme, du petit de l’homme, jusqu’à son adolescence, et plus loin même, jusqu’à sa mort, qui est en cause. Or, cette séparation du littéraire ou de l’artiste d’avec le scientifique se fait très tôt et on l’enseigne dès le biberon. Ce qui fait qu’il Y a un retard puisqu’il n’y a pas de communication du tout, mais cette absence de circulation, de contacts, se fait lourdement sentir. C’est pour ça d’ailleurs que j’ai accepté d’enseigner, de faire des conférences et des séminaires. Aussi, maintenant, nous sommes en train, au CEMAMu, de faire un effort en utilisant la technologie la plus avancée de l’informatique, de faire un effort dans la direction de la pédagogie pour essayer de révolutionner l’approche de la musique et de mettre ensemble des problèmes de composition et de pensée musicale avec des problèmes de la pensée mathématique que l’enfant apprend forcément par ailleurs dès l’âge de cinq, six ou sept ans, et des problèmes aussi de l’espace, de la vision. Je pense que c’est le nœud du problème, c’est le nœud de la survie de l’homme, dans un lieu harmonieux, avec ses contradictions naturellement, mais un lieu beaucoup plus riche qu’en ce moment. Donc, c’est un résidu de l’histoire récente, cette différentiation. Car, l’artiste s’est écarté petit à petit, a fait une sorte de sélection. Il a marché dans un seul des aspects de l’art : l’aspect indicible justement. Bernard TEYSSÈDRE. -Je crois que Michel Serres voudrait intervenir à propos de certains points. Michel SERRES. - J’ai envie de soutenir la thèse à la place de Xenakis et de répondre juste une minute à Olivier Revault d’Allonnes. Celui-ci pose le problème des échanges entre les sciences et les arts. Il pose la question de savoir si l’échange est déséquilibré, c’est-à-dire si vous avez emprunté des techniques à certaines régions des mathématiques, et inversement s’il est vrai que les mathématiques n’ont rien emprunté à la musique. La thèse inverse dirait que la musique est en avance, que la musique de Xenakis est en avance; je ne pose pas le problème du point de vue de l’échange, qui est un point de vue marchand, ni du point de vue des techniques scientifiques, et voici pourquoi: autre chose est de dire qu’on emprunte des techniques à une localité donnée de la science, autre chose est de dire que par sa musique, Xenakis présente une idée générale de la pensée scientifique, parce que le monde scientifique a changé, et que personne ne s’en est aperçu et peut-être même pas les savants. Ce qui a changé, ce n’est pas qu’on ait fait de la théorie des groupes à la place de l’algèbre combinatoire ou qu’on ait fait de la théorie de l’information à la place des transformées de Fourier. Ça, ce n’est pas important. Ce qui est important, c’est que quelque chose, qu’on appelle le «paradigme» , se soit complètement transformé. Un monde nouveau, un monde scientifique nouveau, a surgi dès la deuxième moitié du xxe siècle. Or, le premier à l’avoir dit, ce n’est pas un philosophe, ce n’est pas un scientifique, ce n’est pas un épistémologue, c’est Xenakis. C’est Xenakis qui le premier a fait voir ce qu’était un signal qui se détachait sur le fond, c’est Xenakis qui le premier a utilisé non pas telle ou telle technique mathématique, mais les plus importantes et les plus significatives d’entre elles. Dire qu’il y a retard n’a de sens que si on pose le problème sur des échanges locaux. Si on interroge la vision globale on la trouve chez Xenakis. Cette vision générale de la science et ce paradigme, tous les discours traditionnels nous les masquent. Non, Xenakis, vous êtes en avance et merci pour cette avance. (Rires et bravos ... ) Olivier REV AULT D’ALLONNES. - Michel Serres vient de montrer que l’esprit de nombreux savants peut être ouvert par des démarches du type de celle de Xenakis. Je n’en ai jamais douté. Ma question initiale portait sur ce que la musique par exemple peut apporter non aux savants, mais à la science. C’est là que je voyais un décalage, non pas un quelconque "retard», du reste, car par rapport à quel calendrier idéal pourrions-nous le définir? Reste enfin le problème des conditions sociales de 1’"alliage" en question. Iannis XENAKIS. - Bon, merci infiniment, ça répond à la première question (rires). Je ne peux pas mieux dire. La deuxième question est la "transformation sociale" . Naturellement c’est une question ... Mais je ne sais pas de quelle transformation sociale il s’agirait dans ce cas-là, parce que parmi toutes les transformations sociales qui se sont produites dans le monde entier, ce problème-là est resté absent. On n’a pas répondu à ce problème, et je pense que je reviendrai à ce que j’ai dit tout à l’heure: la transformation sociale qui aborderait la coexistence et l’interpénétration de ces aspects de la vie humaine, très tôt dans l’éducation de l’homme, serait la transformation sociale souhaitée. Olivier REV AUL TD’ALLONNES. - ... en passant par la pédagogie, mais il est quand même clair, me semble-t-il, que ça n’est pas innocemment ou par hasard que la pédagogie, telle qu’on la pratique dans notre société, fabrique d’un côté, comme tu disais, des littéraires, et d’un autre côté des scientifiques. Iannis XENAKIS. - Oui, il est certain que si on fabrique des scientifiques seulement, c’est probablement parce que, d’abord, il Y a une question de temps, de spécialisation. Mais je crois que l’on peut dépasser ce stade. Moi-même j’ai fait au moins deux métiers à la fois, et je pense que c’est très possible même d’en faire trois et pas seulement en surface, mais en poussant ces métiers vers la recherche. C’est aussi une question d’asservissement ... Je ne dirais pas de lutte de classe parce que c’est beaucoup plus nuancé que cela, et plus complexe, mais il va sans dire que c’est une question de ramification de l’organisation de l’homme qui produit des manchots spirituels, et mentaux. Ça c’est sûr. Ce sont des maladies qui, à mon avis, peuvent être dépassées. Comment aboutir à ce changement radical de la pédagogie, mais aussi de l’environnement social. Ça c’est une réforme que la politique devrait entreprendre au lieu de poser seulement des questions de salaire et de machins techniques, d’améliorations, de progrès social. C’est surtout de ce point de vue qu’est l’accomplissement de la totalité de l’homme. Je pense que l’art a son rôle à jouer en mettant tout ensemble; et la science d’ailleurs aussi. Ce qu’a dit Michel Serres est vrai : à la base de l’art, mais de la science également, il y a toute cette vision qu’on appellerait la vision du xxe siècle, qui est une totalité et qui est l’espoir, qui devrait être l’espoir de l’humanité. Bernard TEYSSÈDRE. - Eh bien, peut-être devons-nous donner la parole à Olivier Messiaen, puisque nous avons parcouru le cycle des premières questions et des premières réponses. DIALOGUE AVEC OLIVIER MESSIAEN Olivier MESSIAEN. On ne peut pas critiquer un héros! Je vais donc seulement poser quelques questions. Mais je ne voudrais pas, cher ami, que ces questions soient indiscrètes. Si elles vous déplaisent, vous le direz. Ce ne sont pas de vraies questions, plutôt des demandes d’éclaircissement, pour vous permettre de préciser votre pensée. Au lieu de faire un exposé brillant comme mes confrères, je vais simplement vous poser mes questions les unes après les autres. Ce sera plus facile pour vous, pour moi, pour tout le monde. Première question: à la page 13 de votre thèse, et aussi dans plusieurs endroits du livre Musique. Architecture, vous semblez ramener l’histoire et surtout les débuts de la musique à la naissance des gammes, des modes, des échelles. Avant ces échelles, et vous le reconnaissez vous-même, on utilisait seulement des tétracordes. Mais ne pensez-vous pas qu’au tout début de l’humanité, il y a eu d’abord le cri? Le cri de joie, le cri de douleur: c’est le langage exclamatif (aussi bien parlé que musical). Puis l’écoute et l’imitation d’autres sons, le bruit du vent, le bruit de l’eau, le chant des oiseaux, etc. : c’est le langage imitatif (qui est surtout musical et qu’on trouve cependant aussi dans les onomatopées primitives). Beaucoup plus tard sont venus les langages parlés syntaxiques et la phrase musicale organisée, et avec elle le préalable, le «hors-temps» comme vous l’appelez: des gammes, des modes, des échelles. Pourquoi vous arrêtez-vous à ce matériau de la gamme, à l’exclusion de tout le reste? Iannis XENAKIS. -Non, pas du tout. Vous voulez que j’en parle tout de suite? C’est vrai que je ne suis pas allé plus loin, peut-être par ignorance. Je ne sais pas ce qui s’est passé dans la tête de l’homme paléontologique d’il y a un million d’années ou deux millions d’années ou trente millions d’années, comme on vient de le découvrir. On ne connaît pas du tout sa forme de pensée et si c’est depuis ce ~iècle que je regarde les siècles du passé, c’est parce que j’appartiens à ce siècle et, par conséquent, ne peux parler que de choses qui me sont compréhensibles. l’avoue que c’est sans doute un manque que de ne pouvoir entrer plus profondément dans ces questions que vous avez soulevées. D’ailleurs, que veut dire «imiter», que veut dire "s’exclamer", qui sont avant la syntaxe, avant la règle, avant la construction, avant les structures, si petites soient-elles? C’est déjà une annonce de reconnaissance, de forme, donc une vision structurelle de l’environnement, en admettant que l’homme était une sorte d’objet en soi, la nature et son environnement quelque chose d’en dehors de lui et que, par conséquent, il y avait une imitation de ce qu’il percevait par ses sens. Je pense que, là aussi, on peut probablement dire que le fait d’être en mesure d’imiter le bruit du vent, le bruit de la grêle, ou de la foudre, etc., était une façon de construire, primitive peut-être, je n’en sais rien, mais déjà très complexe. La science d’aujourd’hui, quand je dis la science, c’est la pensée scientifique, a touché du doigt certaines des structures mentales de l’homme depuis quelque temps seulement. D’autres vont venir, mais il est difficile d’en parler; je ne parle que de choses qui sont relativement bien formulées, bien visibles. C’est pour cela que j’ai commencé avec les tétracordes qui sont déjà à un stade assez avancé de construction et je dois ajouter aussi que les tétracordes font partie d’une démarche culturelle ou scientifique ou d’organisation, c’est-à-dire d’un matériau. Il y en a également dans d’autres civilisations, comme celle du Japon, ou celle de la Chine ou celle d’Afrique, très anciennes, même plus anciennes peut-être (l’égyptienne on ne la connaît pas bien) que la civilisation grecque et qui ont d’autres approches où les tétracordes n’y sont pas. Par exemple, dans la musique du Nô, il y a la quarte, on peut dire que la quarte juste est une sorte de réalité universelle, mais la construction intérieure de la quarte est une chose peut-être spécifique du tem~s du Ille ou IVe siècle avant l’ère chrétienne dans le domame grec. Comme ce sont les tétracordes qui ont été à la base du système diatonique et donc de toute la musique postérieure jusqu’à l’époque actuelle, c’est ce fIl conducteur historique et musicologique qui nous permet de faire des extrapolations, beaucoup plus que les périodes antérieures que j’appellerais pré-logiques, bien. qu’elle~ ne soient pas du tout pré-logiques dans le domame musIcal, j’entends. Et ce que vous nous dites est fondamen~ parce que, aujourd’hui, si on veut aller plus !,rofond~ment dans ces questions mêmes de structures, il faudraIt revenir ou plutôt s’éloigner de ces structures-là, de ces concepts que nous avons de la musique, comme d’ailleurs il y aurait tendance de le faire maintenant pour des raisons tout à fait étrangères à la musique. Or, regardons les choses d’un œil ou d’une oreille tout à fait nouvelle, avec des outils nouveaux. C’est la reconnaissance des formes. Si on recevait, on reçoit d’ailleurs, des signaux de l’espace intrastellaire, galactique, eh bien, il faudrait pouvoir savoir les distinguer du bruit comme disait Michel Serres tout à l’heure, pour voir s’ils sont ordonnés, s’ils ont une cohérence, et si cette cohérence est significative ou pas. Si elle est significative, c’est-à-dire si elle a des sources naturelles, je veux dire de la nature ou si elle a des sources d’autres êtres, qui se rapprocheraient de l’homme, n’est-ce pas, de ce type-là. Pour ce faire, il faut aller bien avant toutes les structures, toutes les formes de pensée que nous avons reçues par la civilisation et par l’école, et donc revenir à des situations; se reformer complètement et revenir à des situations pré-rationnelles, pré-logiques, pré-structurelles, pré-syntaxiques. Je ne sais pas si j’ai répondu à votre question. Olivier MESSIAEN. C’est une très belle réponse. Mais vous avez dit aussi que le passé était dans l’avenir, et l’avenir dans le passé, c’est pourquoi je me suis permis de toucher à des régions où notre connaissance défaille ... Deuxième question, tout à fait personnelle: vous savez comme moi qu’un certain nombre d’objets donne un certain nombre de permutations, et que plus le nombre d’objets augmente, plus le nombre de permutations augmente, avec une rapidité et des quantités telles que cela peut paraître disproportionné. Ainsi, trois objets comportent six permutations, six objets en donnent 720, et douze objets en donnent (si je ne me trompe) 497.001.600. Supposez que ces objets soient des durées: il me faut écrire ces durées afin de savoir quel geste, quel mouvement elles vont accomplir dans le temps. On a beaucoup parlé de mouvement rétrograde ces temps-ci : ce n’est qu’un mouvement, un seul mouvement parmi des milliers d’autres, et sa permutation suit le trajet original. Et toutes les autres permutations? Je ne peux pas écrire des millions et des millions de permutations ... et cependant il me faut les écrire pour les connaître et pour les aimer! (j’insiste sur le verbe aimer!) Pour vous, une machine vous donne en quelques minutes des milliards de permutations de durée: c’est une liste froide et non explicite. Comment faites-vous pour choisir aussitôt, sans connaissance et sans amour, dans ce monde immense de possibilités? Iannis XENAKIS. - Il y a deux questions, je crois, groupées dans votre question: la première, c’est la question de l’amour; bien. La deuxième, c’est le choix possible parmi une très grande quantité de possibilités ... Olivier MESSIAEN. - Et je crois que vous allez répondre à la première question d’Olivier Revault d’Allonnes ... Iannis XENAKIS. Peut-être, je ne sais pas. Alors la question d’aimer, pour utiliser quelque chose, naturellement il faut l’apprivoiser. L’apprivoiser veut dire vivre avec, et vivre avec veut dire l’aimer et aussi ne pas l’aimer. Car aimer amène son corollaire. Olivier MESSIAEN. - Je me suis mal exprimé, je veux dire connaître! Connaître d’une connaissance réelle et affective, par l’amour ou la détestation ... Iannis XENAKIS. Oui, c’est le côté affectif, l’épiphénomène de la connaissance, c’est avec la douleur ou, au contraire, avec la joie ou les deux ensemble, quand on aime une belle femme par exemple. Mais la possession de quelque chose qui est impliqué par l’amour ou par la haine est peut-être une forme de la connaissance et, par conséquent, la seule possible. Lorsque je regarde le ciel étoilé, je l’aime d’une certaine façon parce que je le connais d’une certaine façon; mais si je dois connaître des étapes successives de l’astrophysique, eh bien, c’est peut-être sans amour, c’est le dépassement de l’amour par une sorte de révélation qui est au-delà de cet épiphénomène qu’est l’amour. Par conséquent, je peux manier des concepts des choses en soi sans en être le possesseur direct. A condition que je puisse d’une certaine façon les concevoir et les sentir du dedans. C’est une amorce de réponse à votre question qui est fondamentale à mon avis, ce qui fait que, même si je ne suis pas capable de dominer un certain phénomène, je suis capable d’obtenir, par une sorte de révélation en direct, une vérité qui est dans le phénomène que je conçois ou que j’observe. Donc, je l’accepte et je l’utilise en soi. Lorsque j’enregistre sur un magnétophone un son qui m’intéresse, je ne sais pas exactement ce qu’il y a dans ce son. J’aperçois certaines choses qui m’intéressent, et je l’utilise. Donc je ne peux pas aimer les choses qui sont à l’intérieur d’une manière trop fine puisque je ne les perçois pas totalement. Je ne suis pas capable, consciemment ou inconsciemment, de les nommer et je l’accepte globalement, en soi, parce que je suis attiré par cela. Olivier MESSIAEN. - Vous êtes attiré, donc il y a une révélation! Iannis XENAKIS. - C’est ça, voilà. Olivier MESSIAEN. - Une révélation, c’est comme un coup de foudre, c’est comme l’amour. C’est l’inspiration des romantiques. Iannis XENAKIS. - Oui. Je ne le nie pas du tout, au contraire. Olivier REY AULT D’ALLONNES. - Je ne te saValS pas romantique. (Rires.) Iannis XENAKIS. - J’ai dit au début, ou peut-être ne l’ai-je pas dit, que dans le domaine artistique, il y a la révélation. Dans la philosophie et dans la connaissance, de même. Oui, la révélation est absolument indispensable. Elle est une des béquilles de l’homme. Il y a deux béquilles, la révélation et l’inférence. Et dans le domaine artistique, les deux sont valables. Dans le domaine scientifique aussi c’est l’une qui prime sur l’autre, c’est l’inférence. Pour en venir à la deuxième partie de votre question, c’est-à-dire: comment choisir dans une grande richesse de possibilités?, eh bien, là, il y a plusieurs façons de faire. Je peux imaginer, et je n’ai pas besoin de la machine pour cela, je peux imaginer et réaliser le choix mentalement. Il y a plusieurs façons de faire ce choix. C’est vrai que lorsqu’on a quelques sons ou, pour préciser, quelques hauteurs à contrôler, il est facile de le faire d’une manière arbitraire ou intuitive, immédiatement. Mais, lorsqu’il s’agit de grandes quantités de sons, eh bien, c’est là où des emprunts à d’autres domaines de la pensée peuvent être utiles. Lorsque je regarde un petit nombre d’individus, je les vois en tant qu’individus, je vois leurs relations, leurs caractéristiques, et leurs relations dans l’espace ou dans le temps, leur physionomie propre, etc. Mais s’il y a foule, alors je ne peux plus distinguer les individus, parce que trop nombreux. Par contre, ce que je peux voir, ce sont les aspects, les caractéristiques de la foule. Il faut faire en sorte que, si j’ai besoin d’un grand nombre de possibilités, je puisse utilis.er les caractéristiques du grand nombre, qui sont par exemple des traits de densité, d’ordre ou de désordre, de r~partition dans l’espace à trois dimensions, de répartitIon dans les espaces sonores, comme dans la dimension de la hauteur, la dimension du temps, la dimension de l’ordre ou du désordre, etc., et alors il y a des outils possibles qui permettent de faire certains choix. Je ne dis pas tous les choix, mais de déblayer quand même pas mal dans l’impossibilité de choisir parmi un si grand nombre d’éléments. Car je me base sur l’incapacité de l’homme lorsque la densité est grande, trop forte pour pouvoir dire: "oui, il s’agit de cet objet et il est là". Un certain flou dans le choix est permis à ce moment-là, parce que d’autres caractéristiques sont importantes. C’est le même phénomène qui s’est produit lorsque l’on a introduit le calcul des probabilités en théorie cinétique des gaz. Toutefois, c’était un peu différent, c’était un problème de calcul et non pas un problème psychologique et on est arrivé à la théorie cinétique des gaz, c’est-à-dire à des concepts qui ont permis à toutes sortes de sciences, pas seulement à la thermo-dynamique, d’aller beaucoup plus en avant. Je crois que dans le domaine artistique et sensoriel, et sensuel aussi, c’est ce qui se passe. Est-ce que j’ai répondu? Ça vaut quelque chose? Olivier MESSIAEN. - Oui, oui. Troisième question (celle-là est tout à fait indiscrète et si vous ne voulez pas répondre, vous ferez à votre guise !). Vous citez, dans Musique. Architecture, un texte magnifique de Parménide, que l’on applique généralement à l’univers et qui contient entre autres la notion de "l’étant", ou qualité de ce qui est. En résumant ce texte à l’extrême, j’y trouve ces quelques mots: il est, inengendré, indestructible, imperturbable, sans fin, il est à la fois un, continu. Pour moi qui ai fait de la théologie, ce texte ne peut s’appliquer qu’à Dieu, car il n’exprime que des attributs divins. Or, vous expliquez ce texte par l’énergie et la conservation de l’énergie. Je sais bien que l’une des nouvelles théories de la création de l’univers est la théorie de l’explosion qui affIrme que l’univers commença par une fantastique déflagration, ce qui suppose au départ une force énergétique qui pourrait être encore un attribut divin. Mais je pense que votre explication de Parménide est toute différente. Pouvezvous nous dire pourquoi vous avez choisi l’énergie? Iannis XENAKIS. "L’étant» de Parménide est un des premiers textes où il essaye de cerner le réel. Mais, pour le cerner, il est obligé de s’en détacher et de faire une sorte de définition abstraite qui est même en contradiction avec l’expérience quotidienne; c’est ce qui a permis à Aristote de dire que Parménide était un fou. C’est vrai que ce que dit Parménide sur "l’étant" correspond à ce que l’on pourrait dire (que vous avez bien dit d’ailleurs) sur un dieu unique. D’un autre côté, si on ne pense pas à la théologie ou à une religion quelconque, mais si on reste dans le domaine qui, je crois, est à la fois fondamental et beaucoup plus universel, celui de Parménide, le texte ne dit en rien que c’est un dieu. Il ne dit rien du tout. Il dit seulement que c’est un être, il parle seulement de l’être, de l’être en tant qu’existence, pas de l’être actif, en tant qu’être agissant, c’est pour cela qu’il met la notion de l’être au participe et non "l’étant" à l’infinitif. Je pense que cette direction de Parménide, aussi contradictoire soit-elle avec la réalité, est une des lumières de la pensée de l’homme dans sa détresse pour arriver à cerner ses problèmes, à travers les âges. Maintenant, il n’y a plus qu’une sorte de réponse fantomatique cet "étant» de Parménide, soit le rapprochement que j’ai fait avec l’énergie parce que je n’ai trouvé que cela dans le domaine scientifique comme explication du monde qui se rapproche de ce contenu. Parce que, en effet, l’énergie est une chose qui remplit le monde. Le principe de la conservation de l’énergie n’est qu’un principe bien sûr, mais qui colle, oui, à cette définition de "l’étant". Donc c’est dans le domaine de la nature, du côté scientifique, du côté de la physique que j’ai essayé de donner une réponse. Elle n’est pas exclusive du tout, c’est une sorte de rapprochement que je fais. Je ne dis pas que c’est ça "l’étant", mais ça rappelle étrangement la définition, ou plutôt la conception de l’énergie qui remplit le monde, qui n’a pas eu de début ni de fin puisqu’à cause du principe de la conservation de l’énergie, il n’y a pas pu avoir de début ni de fin. Or ceci, bien sûr, est un peu en contradiction avec la théorie de l’explosion d’un atome originel, à l’origine de notre univers condensé" à l’extrême. Mais il m’est permis de penser que ce n’est qu’une théorie provisoire, comme toutes les théories ... Ce rapprochement de "l’étant» de Parménide avec l’énergie n’est qu’une sorte d’analogie. En fait, les attributs de Dieu et de "l’étant» sont identiques car, sous-jacente, se trouve la même logique de ‘homme. Olivier MESSIAEN. - Alors la quatrième question ... Iannis XENAKIS. - Si vous permettez, pour en terminer avec Parménide, je voudrais parler d’une autre chose fondamentale que l’on trouve dans un de ses fragments. Il s’agit de l’équivalence entre l’être et la pensée, qui est aussi un fIl conducteur pour la pensée de l’homme à travers les âges. Parménide dit dans un vers, qui est resté fameux et qui a été reproduit par Platon dans La République: "Car c’est la même chose, être et penser". Or, la structure de la phrase est une structure symétrique par rapport au verbe est. Être, c’est-à-dire "l’étant", et la pensée sont la même chose. C’est là que je vois la symétrie. Chez Descartes, longtemps après, il y a une dissymétrie lorsqu’il dit "Je pense donc je suis". C’est curieux, lorsqu’on les rapproche et je crois que c’est nécessaire, car c’est la même préoccupation de l’homme à travers les âges. Je ne sais pas s’il connaissait. .. Bernard TEYSSÈDRE. - Ce n’est pas du tout la même. Iannis XENAKIS. - Non, elle est dissymétrique: "Je pense donc je suis" et si on va chez les solipsistes, Berkeley par exemple, là il y a une autre inversion qui rappelle celle de Descartes, mais qui est dans un autre sens, c’est-à-dire que la réalité objective, «l’étant» peut ne pas être du tout, mais peut n’être que la pensée, c’est-àdire il y a une identité de "l’étant» avec la pensée, hors d’une réalité quelconque. Si Descartes est réaliste, Berkeley devient tout à coup abstrait avec son solipsisme, et tout se ramène à la pensée. Depuis, il y a eu, bien sûr, la philosophie du XIXe siècle, avec les discussions marxistes, qui a admis une objectivité indépendante de l’homme, ainsi que la science qui, elle, est ambiguë à cause des échecs retentissants des théories successives de la mécanique classique, etc. Et ça continue! C’est pour cela que les scientifiques disent aujourd’hui: "Tout se passe comme si ..." Olivier MESSIAEN. - Quatrième question, et c’est la dernière : pages 8 et suivantes de la traduction en français du dernier chapitre de votre livre Musiques formelles (édition anglo-américaine), que vous avez inclus dans les documents joints à votre thèse 1, vous donnez plusieurs méthodes de microproposition basées sur les distributions de probabilités, et je lis, méthode 4 : "La variable aléatoire se déplace entre deux bornes élastiques réfléchissantes." Je répète, car c’est une phrase extraordinaire: «La variable aléatoire se déplace entre deux bornes élastiques réfléchissantes." C’est très poétique et cela m’a plongé dans un abîme de rêverie ... Après vient l’explication chiffrée que je n’ai pas comprise. Pouvezvous nous donner une autre explication de ce procédé, avec un exemple musical concret, peut-être dans une de vos œuvres? Iannis XENAKIS. Cette méthode 4 se rapporte à l’hypothèse de base qui est dans les pages précédentes à partir de la page 145, "Nouvelles propositions dans la. microcomposition basées sur les distributions de probabilités". Ça se rapporte à l’espace pression-temps, la pression que vous recevez de l’air atmosphérique sur votre tympan au cours du temps. Alors si on considère que la pression prend des valeurs plus ou moins fortes, exprimées par des nombres, nous pouvons faire correspondre la pression à des notes placées sur l’axe des hauteurs et on pourrait l’écrire sur une portée. Nous obtiendrons un cheminement, la variation de la hauteur en fonction du temps, en forme de courbe mélodique continue. Dans le cas de l’espace pression-temps, si elle est penodique (elle peut former soit une onde carrée, soit une onde triangulaire, soit une onde sinusoïdale, etc.), la forme d’onde se répète identique à elle-même tout le temps. Mais, si la variation n’est pas périodique, elle épousera des courbes possédant n’importe quelle sinuosité. On pourrait imaginer que cette courbe est décrite par un point mobile se déplaçant dans un plan, sans jamais rebrousser chemin, soit dans l’espace hauteur-temps, soit dans celui de pression-temps, ce qui revient au même du point de vue de la définition de son cheminement. Ces cheminements dépendront évidemment des lois qui animeront le point mobile. Les fonctions périodiques sont des lois très contraignantes et correspondent à des mélodies ou à des sons ennuyeux. Par contre les lois des probabilit~s et leurs combinaisons mathé~atiques, peuvent produITe des cheminements très libres et qui ne se répéteront jamais, correspondant à des mélodies ou à des sons beaucoup plus riches. Seulement, ces cheminements probabilistes peuvent prendre n’importe quelle valel!r. Par conséquent, ils peuvent faire sortir le point mobile hors des faibles limites de l’oreille, c’est-à-dire que, dans le cas de l’espace pression-temps, il peut arri~er. à des pr~ssions de bombe atomique! Il faut donc h~Iter les crOIssances intempestives, ces énergies probabilIstes c~l~ssales ! C’est exactement le cas de la balle qui est canalIsee par le canon du fusil en la faisant ricocher d’un point à l’autre de la paroi interne. Olivier MESSIAEN. C’est ce que vous appelez les bornes ... Iannis XENAKIS. - Ce sont des bornes élastiques ... Olivier MESSIAEN. - Elles sont réfléchissantes ... Iannis XENAKIS. - Parce qu’elles réfléchissent vers l’intérieur et suivent la loi de la réflexion plane élastique, sans perte, sans absorption d’énergie. C’est-à-dire que le cheminement créé par le processus probabiliste, stochastique, est réfléchi comme par l’effet d’un miroir lorsqu’il atteint les barrières choisies. Si vous voulez, c’est exactement le cas de l’inversion des intervalles mélodiques. Dans l’inversion mélodique, les intervalles sont réfléchis dans un miroir horizontal, placé sur l’axe des temps et dans la rétrogradation, c’est une réflexion dans un miroir vertical. Ce sont les mêmes principes très simples qui existent partout, même en musique. A présent, on peut imaginer des parois non réfléchissantes avec des champs de gravitation. Enfin, toutes sortes de forces au sens abstrait bien sûr. Olivier MESSIAEN. - C’est tout à fait merveilleux ... Alors, en ce qui me concerne, j’ai terminé, mais tout à l’heure je ne suis pas intervenu quand Olivier Revault d’Allonnes parlait. Il faisait un exposé tellement beau que je n’ai pas osé l’interrompre! Peut-être pourrait-il reprendre quelques-unes de ses questions proprement musicales puisque j’ai la chance d’être là? .. Olivier REVAULT D’ALLONNES. - Personnellement j’ai échoué. Il n’a pas parlé! Olivier MESSIAEN. - Ce n’est pas par méchanceté, c’est par curiosité, par sympathie, par admiration aussi... Olivier REVAULT D’ALLONNES. -Je voulais que Xenakis parle de son style de compositeur et il m’a fait la réponse à la fois la plus satisfaisante et la plus hermétique. Il m’a dit: "Écoute, je n’ai rien à ajouter, écoute, et si tu n’as pas compris, ré-écoute". "Et puis aime, si tu aimes". Olivier MESSIAEN. - Il y a là une certaine pudeur qui personnellement m’étonne parce que je n’ai pas le même métier que lui. Je fais une classe de composition au Conservatoire, où, depuis quarante ans, je passe mon temps à décortiquer les œuvres musicales, à essayer de savoir ce qui se passe à l’intérieur ... Ces choses dont vous n’osez pas parler, qui vous font peur, je m’en occupe toute la journée ... Iannis XENAKIS. - C’est vrai, je m’en souviens très bien. J’étais dans votre classe d’analyse musicale, et ce qui m’avait le plus intéressé c’était justement le discours que vous teniez à propos des techniques ... (rires) parce que le reste se ramène à : "Nous disions, c’est beau ça, n’est-ce pas?" Olivier MESSIAEN. - Je ne le disais pas tellement, j’étais silencieux! Iannis XENAKIS. - C’est vrai, c’était rare, mais vous le disiez parfois. Mais c’est tout ce que vous disiez sur le problème du style. Ou alors, le style c’est plus dans le sens de la technique, et alors c’est autre chose. Mais pour moi le style se rapporte aussi bien à la technique, (aussi ce qui est peut-être plus intéressant) "qu’aux paIfums" de la musique, sur plusieurs étages d’ailleurs. Olivier MESSIAEN. - Oui, mais en dehors de toute structure, il me semble que chaque individu et chaque musicien en particulier (puisqu’on parle de musique), possède ce que nous appelons en philosophie, "ses accidents», ses tics, ses habitudes personnelles. Un deuxième ou. un troisième Xenakis qui essaieraient de faire du Xenakis à votre place, avec les mêmes structures, n’obtiendraient certainement pas le même résultat. Il y a donc une question de style personnel. Iannis XENAKIS. - Oui, alors là j’avoue que ... Olivier MESSIAEN. - On reconnaît la musique de Xenakis tout de suite. Pas seulement parce qu’il y a des glissandi ou des permutations, on la reconnaît à une certaine sonorité, à une certaine façon d’orchestrer, à une certaine façon de disposer les sons, qui diffère de celle des autres. Iannis XENAKIS. - Peut-être que la réponse à la question de Revault d’Allonnes est la suivante : dans la vie il y a deux façons de procéder, l’une c’est de faire les choses et l’autre de s’analyser. Or, la meilleure analyse pour moi c’est de faire les choses, c’est-à-dire que je nie l’analyse, la psychanalyse, si vous le voulez, en tant que méthode d’introspection. D’autant plus que, si on touche à ces domaines, on ne sait pas ce que l’on va découvrir et on risque de tomber dans des trous, des pièges épouvantables. Donc, c’est une tactique, et c’est pour ça que je persiste à dire que c’est la "chose", la musique même qui, elle, n’est pas hermétique, contrairement à la parole analytique qui, elle, est hermétique. Olivier MESSIAEN. - Et pourtant, moi j’interroge le sphinx tous les jours, puisque je fais une classe d’analyse, et je n’en suis pas plus malheureux. Ça ne m’empêche pas de faire de la musique! Iannis XENAKIS. - En dehors des questions techniques, est-ce que vous ne donnez pas d’autres réponses? Olivier MESSIAEN. - Je ne m’occupe que des questions techniques. Iannis XENAKIS. - Alors ... Olivier MESSIAEN. - En dehors du fait musical pur, bien entendu, je ne me permettrais pas de faire des rapprochements dans les intentions parce que j’en serais bien incapable. Ou si je l’ai fait, ils sont tout à fait occasionnels. Iannis XENAKIS. - Mais quand vous dites technique musicale, ça se rapporte à quoi? Ce sont bien des proportions, des durées, des combinaisons? Olivier MESSIAEN. -Durées, harmonies, modes, couleurs, j’en parle beaucoup, je sais que vous n’y croyez pas ... Iannis XENAKIS. - C’est déjà d’un domaine hors technique à mon avis. Olivier MESSIAEN. - L’orchestration aussi, pour moi c’est de la technique. Iannis XENAKIS. - C’est-à-dire que ce sont des choses dont on peut parler. Olivier MESSIAEN. - C’est de la technique, proprement et purement et complètement musicale. C’est là-dessus que Revault d’Allonnes a essayé de vous interroger, me semble-t-il. Olivier REVAULT D’ALLONNES. - Et sur ce qu’il y a à côté, en dessous, après la technique. Je ne crois .pas trahir un secret en disant que j’ai vu Xenakis un Jour devant sa table. Il avait sous les yeux une partition d’une œuvre en gestation et il a regardé, arrêté par un détail. Il a dit: "Oh non, ça va faire moche", et il l’a enlevé. Alors c’est de la technique, ça? (Rires.) Je crois que ça arrive à tous les compositeurs. Michel SERRES. - En un mot, revenons à la question du choix. Iannis XENAKIS. Oui, du choix arbitraire, intuitif, etc. Michel SERRES. - Qu’on peut appeler l’inspiration si on veut mais qui reste un choix. Olivier REVAULT D’ALLONNES. - Alors, nous évitons là de plonger dans les régions boueuses de la subjectivité? Iannis XENAKIS. - La meilleure façon de s ‘y plonger n’ estelle pas de faire, justement, de la musique? Olivier REV AULT D’ALLONNES. - Le choix entre un nombre très élevé de possibilités a paru à Olivier Messiaen un problème très difficile, mais en fait un organe des sens, n’importe lequel, l’oreille, l’œil, m,ême, le .toucher,. fonctionne exactement comme ça, c est-a-dlre reçOIt une quantité énorme d’informations de so~e que ce qu~ vous opposez, à savoir le problème techmque du ChOIX, du choix entre les millions de possibilités que vous avez d’une part, et d’autre part le problème subjectif de dire (comme on dit "au pif") "ça c’est moche", c’est exactement la même chose. Le pif justement, ou l’oreille ou l’œil fonctionnent très exactement comme l’ordinateur, c’est-à-dire qu’ils reçoivent cinquante millions d’informations qu’ils trient et transmettent exactement. Par conséquent, il n’y a pas d’opposition entre ce que vous appelez la puissance, l’inspiration, l’événement, la sensorialité, et d’autre part ce problème qui vous paraît très difficile du choix entre une énorme quantité d’éléments. C’est ainsi que ça fonctionne, dans le vivant. Iannis XENAKIS. - Il y a même, dans la théorie des ensembles, le fameux axiome du choix de Zermelo, qui postule qu’on peut choisir d’une manière arbitraire ou à l’aide de la "révélation" un élément dans un ensemble donné; c’est de la mathématique et la mathématique tient ici un langage tout à fait esthétique si j’ose dire. C’était le problème; et les machines à calculer sont des fIltres. Olivier MESSIAEN. - Des simulateurs. Iannis XENAKIS. - Des simulateurs de choix, qui ont des règles pour pouvoir choisir. L’homme, avec son oreille et ses sens, fait des choix beaucoup plus complexes que ne peut faire l’ordinateur actuellement, c’est-à-dire que la simulation des choix est encore à son balbutiement avec la technologie actuelle, l’automatisation des choix est encore très rudimentaire par rapport à l’homme. Olivier REV A UL T D’ALLONNES. - Oui, on ne sait pas comment la commander. Les terminaux sensoriels le font, sans le savoir, mais ils le font. Olivier MESSIAEN. -Je vais vous donner un exemple concret. Quand je note des chants d’oiseaux, je les note avec un papier et un crayon. Ma femme m’accompagne quelquefois, elle enregistre au magnétophone ces mêmes chants que je suis en train d’écrire. Or quand j’écoute, en rentrant à la maison, ce qu’a pris le magnétophone, je m’aperçois qu’il a fait les choses impitoyablement, il a tout pris, aussi bien des bruits horribles qui n’ont aucun rapport avec ce que j’étais venu chercher. Ces bruits je ne les avais pas entendus, je n’avais entendu que l’oiseau. Pourquoi n’ai-je pas entendu ces bruits-là? C’est ça, il y a un pourquoi, mon oreille a filtré bien sûr. Iannis XENAKIS. - C’est ce qu’on appelle l’écoute intelligente, l’écoute orientée. Ça correspond à un des critères de choix que vous vous êtes imposé sans le savoir d’ailleurs, parce que vous ne voulez écouter que les chants des oiseaux à travers les bruits de la forêt. Olivier MESSIAEN. - Mon attention était tournée vers les oiseaux et je les ai entendus, mais je les ai entendus à l’exclusion d’autres bruits mauvais comme les autos qui passent, ou les avions ... Iannis XENAKIS. - A l’exclusion d’autres bruits. D’ailleurs, en théorie de l’information, tout ce qui n’est pas le signal que l’on a voulu, que l’on a sélecté, on le refuse, comme étant du bruit. Olivier MESSIAEN. - On entend ce qu’on veut entendre. Michel SERRES. - On entend les signaux. Iannis XENAKIS. - Oui. Et la difficulté dans l’appréciation d’une œuvre quelconque, c’est de choisir exactement ce qui est important. C’est pour cela que, lorsque l’on écoute une œuvre de Bach qui est cent fois, mille fois écoutée, suivant le choix que vous faites à ce moment-là, elle peut vous paraître tout à fait différente de celle que vous aviez l’habitude d’entendre. Et ce n’est pas seulement l’intérêt en soi d’une œuvre, mais c’est aussi l’intérêt de ce choix individuel personnel, de l’auditeur. C’est pour ça que Newton, tout à coup, recevant la pomme sur le nez, a dit: "J’ai trouvé! Eurêka". Olivier REY AULT D’ALLONNES. - Tout ça nous dit à peu près comment tu conçois ce que c’est que le choix, mais pas ce que c’est que le moche, ou son contraire, et à qui le demander sinon à vous, les compositeurs? Olivier MESSIAEN. - Tout à 1 ‘heure, à propos de structure, nous avons parlé des fugues de Bach. Or, il n’y a rien de plus structurel et (excusez-moi) de plus ennuyeux qu’une fugue d’école. Bach a fait dans sa vie des milliers de fugues, il y en a partout, dans toutes ses œuvres, dans ses cantates, dans ses Passions, dans sa messe, dans ses œuvres d’orgue, dans ses œuvres de clavecin. Ces fugues n’ont jamais la structure des fugues d’école et elles sont différentes de toutes les autres fugues de la même époque, parce qu’elles possèdent une certaine joie mélodique et un contrôle harmonique qui n’appartiennent qu’au père Bach. Iannis XENAKIS. Oui, je crois que c’est là le problème. Olivier MESSIAEN. - Je dirai plus, dans le père Bach il y a un petit peu ce qu’il y a chez vous. Il y a parfois des volontés superposées! Par exemple, dans certains chorals, vous avez la ligne du choral à laquelle il n’a pas pu toucher parce que c’était un texte sacré. Il l’a laissée telle quelle. C’est une volonté. Dans la partie inférieure grave, il Y a un ostinato qui est aussi une volonté. Dans les parties centrales, il Y a des chromatismes; c’est également une volonté, il n’en démord pas. Les trois volontés superposées donnent des rencontres extraordinaires, des accords et des contrepoints presque modernes qui pourraient être signés Debussy. Voilà peut-être une façon de comprendre comment une structure peut faire jaillir quelque chose de nouveau, de personnel. Iannis XENAKIS. - Sur un plan plus actuel, une structure de fugue n’est pas totalitaire, c’est-à-dire qu’elle montre des parties floues, libres, et des schémas qui sont plus ou moins suivis. Mais, à l’intérieur de ces schémas, il y a des "données d’entrée» comme on dirait en informatique aujourd’hui, qui permettent d’obtenir de ces mêmes schémas des résultats différents. Et dans les données d’entrée qui sont libres, on peut mettre beaucoup de quantité d’intelligence au sens large et de volontés contradictoires. Mais les schémas peuvent se traduire par une sorte de système, ou comme on dit, d’automate, puisqu’ils fonctionnent seuls, et la grande avance de la fugue sur toute la pensée scientifique de son temps, c’était justement qu’elle proposait des systèmes que la science ignorait. C’est seulement depuis quelque temps que la science se préoccupe d’une manière systématique et avec ses méthodes propres de systèmes, c’est-à-dire d’horlogeries, stochastiques ou déterministes. Michel SERRES. - Non. Au XVIIe- siècle, un peu avant que Bach écrive des fugues ou avant que les écoles fassent faire des fugues, toute la pensée scientifique pensait aux automates. Finalement c’est une démonstration de contemporanéité entre les sciences et les arts. Iannis XENAKIS. Oui, vous avez raison, Descartes aussi en parle beaucoup. Michel SERRES. -C’est ça, Descartes ... Olivier de Serres. Iannis XENAKIS. - Mais l’automate abstrait n’était proposé que par les musiciens. Michel SERRES. - Ah bon, oui. .. c’est possible ... les boîtes à musique faisaient fureur. Iannis XENAKIS. -Et les produits que proposait l’automate abstrait, ce sont les musiciens qui les matérialisaient en les jouant. Michel SERRES. -Oui, c’est vrai, ils étaient en avance sur la science, comme d’habitude. Bernard TEYSSÈDRE. - Mais pour en revenir à notre propos, curieusement, ce qui est bien dans la fugue, à mon avis, ce n’est pas l’automate abstrait, c’est précisément les parties floues dans lesquelles Bach a pu introduire son génie personnel. Iannis XENAKIS. - Oui, mais il ne faut pas non plus ignorer le fait que nous avions là une forme très compacte, par rapport aux autres formes de la musique, d’une structure sous-jacente sur laquelle on peut ajouter des "formes". Naturellement, les résultats n’auraient pas été les mêmes s’il n’y avait pas eu ces structures sous-jacentes, ce schéma. Bernard TEYSSÈDRE. Eh bien, après que le débat avec Olivier Messiaen ait porté essentiellement sur la musique, je crois que celui avec Michel Ragon va porter plus particulièrement sur les problèmes de l’architecture. DIALOGUE AVEC MICHEL RAGON Michel RAGON. On a cité très souvent, dans le cours de ce débat, le livre de Xenakis : Musique. Architecture. C’est un des deux livres réunissant tous les textes de Xenakis; l’autre étant Musiques formelles. Si ce livre s’intitule Musique. Architecture, c’est justement parce que deux produits créatifs sont étroitement imbriqués dans l’œuvre de Xenakis: la Musique et l’Architecture. Si ces deux données ont été séparées chez Xenakis pendant un certain temps, elles sont maintenant tout à fait réunies. Elles ont été séparées dans une époque de Xenakis que l’on connaît moins, c’est-à-dire celle du Xenakis architecte pur, pourrait-on dire, le collaborateur de Le Corbusier. Xenakis a travaillé douze ans, je crois, chez Le Corbusier. Vous savez que lorsque l’on travaille chez un architecte, chez un patron, tout ce que l’on fait, tout ce que l’on produit chez ce patron, est évidemment récupéré par le patron. C’est pourquoi je voudrais attirer l’attention sur deux réalisations signées Le Corbusier, et pour lesquelles Xenakis a tout particulièrement travaillé. Il s’agit de la façade du Couvent de la Tourette en 1954, et il est assez facile de voir qu’il y a travaillé, puisque c’est une architecture un peu conçue comme une partition; puis le Pavillon Philips en 1956, dont on pourrait dire qu’il est un récipient à musique. Ces deux œuvres conçues avec la collaboration de Xenakis dans l’atelier de Le Corbusier, ont été d’ailleurs authentifiées par Le Corbusier lui-même comme étant une production Xenakis. A l’appui, nous disposons de deux textes de Le Corbusier cités dans Musique. Architecture[1], qui indiquent la part considérable prise par Xenakis dans cette création. Je dis cela en passant parce que certains architectes dénient à Xenakis le droit de s’approprier des œuvres signées Le Corbusier. Moins royaliste que ses élèves ou que ses disciples, Le Corbusier a, en fait, authentifié les œuvres en question comme étant des œuvres de Xenakis. Et puis il y a les Polytopes! Les Polytopes au sujet desquels Revault d’Allonnes a écrit un livre très copieux et qui en parle mieux que je ne pourrais en parler fort brièvement. Vous savez, c’est cette architecture transparente de cordes d’acier servant de support aux points lumineux, où la lumière est, elle-même, architecture, où la lumière architecture l’espace de dessins éphémères. Voilà aussi une autre part importante du travail d’architecte de Xenakis et, là, le travail d’architecte est mêlé étroitement au travail du musicien. Il y a aussi l’utopie d’un spectacle total qui revient très souvent chez Xenakis. C’est sans doute un spectacle total que l’on a pu voir en ce nocturne fabuleux de Persépolis, avec les 250 porteurs de torches si souvent cités. Mais aussi avec les idées plus récentes de Xenakis de lancer des toiles d’araignée brillantes au-dessus des villes et des campagnes, de lier la terre à la lune par des fIlaments de lumière, de créer des aurores boréales artificielles, toutes choses dont il parle, dont vous nous parlez dans le résumé de votre soutenance de thèse. Il y a enfin une autre partie de votre œuvre qui est, je pense, plus connue, c’est pourquoi je voudrais m’y attacher. Il s’agit de votre projet de prospective architecturale ou d’architecture utopique. Référons-nous au texte publié dans Musique. Architecture qui s’intitule "La Ville cosmique". A propos de ce texte, je voudrais vous poser, puisque telle est la règle du jeu, quelques questions. De ce texte de "La Ville cosmique", je vais citer des passages. Vous commencez par vous ~emander s’il faut opter pour la décentralisation de l’archItecture et la décentralisation de la ville, ou bien au contraire admettre cette centralisation. Et vous prenez un parti catégorique pour une centralisation que d’aucuns pourraient peut-être considérer comme abusive. C’est-à-dire que vous récusez la théorie des cités linéaires (Le Corbusier est un des auteurs de cette théorie), que vous qualifiez de naïveté, et que vous proposez de construire des v.illes ~ertical~s, étroites, qui puissent aller jusqu’à trOIs. mille, VOIre jusqu’à cinq mille mètres d’altitu~e, d~s ~illes donc ,peu épaisses, entièrement en métal, c est-a-dlfe des espec~s de gratte-ciel géants mais contenant toute la ~orphologle d’une ville. Vous considérez que la concentration est une nécessité vitale pour l’humanité, dites-vous, et qu’il faut changer complètement les idées actuelles sur l’urbanisme et l’architecture, pour les remplacer par d’autres. ?r, ce sera ma première question, ce texte est as~ez a~clen. !l date de 1964. Il est possible que vous ayez evolue depUIs lors. Cette séance, aujourd’hui, est une occasion de pouvoir bavarder un peu avec vous et de vous poser des questions. Elle me permet de vous poser q~elques questions que j’ai envie de vous poser .depUI~ longte~p~. Depuis douze ans, croyez-vous toujours a cette Idee d’une centralisation aussi poussée? Pensez-vous que cette centralisation soit toujours nécessaire? Pensez-vous qu’à une époque où l’électronique, la dispersio~ des énergies, où les énergies naturelles, comme le ~olalre ~t l’éolienne peuvent permettre justement une decentrallsation qui ne ressemble en rien aux dé~entralisati?ns du passé, c’est-à-dire où la culture elle-me me peut-etre décentralisée facilement avec l’électronique, pensez-vous que cette centralisation aussi poussée soit toujours nécessaire? Ou bien cette idée est-elle périmée depuis que vous l’avez créée en 1964? Iannis XENAKIS. - Je crois que la centralisation, que j’appellerai plutôt une densification de l’habitat humain et de ses relations humaines, est d’abord une nécessité historique que l’on voit à travers toutes les manifestations de la construction des villes et de l’habitat de l’homme et aussi bien dans ses relations, dans sa culture, partout. Ce qui rend la chose beaucoup plus nécessaire aujourd’hui, c’est l’envahissement de l’espace planétaire par les villes dispersées comme une pellicule qui détruit l’environnement. Il y a deux tendances, actuellement, l’une à une densification de compacité, densification plus grande et l’autre à une tendance centrifuge qui voudrait revenir à une sorte d’habitat rural au milieu d’une nature verdoyante, là où elle est possible, et si elle n’est pas possible, la faire d’une manière artificielle. Ce sont deux tendances qui sont naturelles, l’une comme l’autre, mais si la tendance à la compacité est une nécessité de l’ère industrielle en raison de la densification de plus en plus explosive de la population de l’homme sur terre, l’autre aussi est naturelle car elle correspond à des nostalgies du passé et également au fait que les villes actuelles sont loin de donner les conditions de nature que le corps de l’homme et son esprit réclament. Actuellement, ces deux tendances sont en lutte. En fait, c’est la tendance de la saturation (ou compacité) qui est la plus gagnante pour des raisons économiques et pour des raisons de toutes sortes. Je suis toujours en accord avec ce que J aVaiS propose en 964. Je suis persuadé que c’est une solution, provisoire d’ailleurs, qui est plus intéressante et moins criminelle que la dispersion sur la surface du globe. Une densification aussi grande ne veut pas dire que je refuse l’isolement de l’homme, sa possibilité de s’isoler en tant qu’individu, dans cette espèce de grande ruche que sont les villes actuelles. Seulement, je dis qu’au lieu de les étendre sur une surface qui pose beaucoup de problèmes de contacts pour les activités de l’homme, il faut les organiser de manière qu’elles soient à la verticale. Ce n’est pas une idée tout à fait nouvelle, puisqu’elle existait déjà d’une manière plus petite, si j’ose dire, dans la lutte qui s’était engagée dans les années vingt surtout lorsqu’il s’agissait de choisir entre les cités jardins, comme on disait à l’époque, et les cités verticales; ces cités verticales dont Le Corbusier était un des défenseurs. Mais ces cités verticales ne correspondaient qu’à l’habitat pur et simple, et non à la ville entière. Elles n’englobaient pas toutes les activités d’une ville, alors que moi je pense qu’on doit étendre ce principe à toutes les activités d’une ville pour des raisons techniques, pour des raisons de relations des hommes entre eux, pour des raisons aussi d’exploration de ce qui nous reste encore de l’espace terrestre, et aussi parce qu’un tel système permettrait d’installer des villes dans des climats vraiment impossibles à vivre actuellement, des climats très chauds, des climats très froids, qui sont soit surpeuplés, soit désertiques. Je crois que j’ai répondu à cette première question. Michel RAGON. - Ce texte date donc de douze ans. Il est contemporain d’autres textes, d’autres théories voisines, par exemple, la "ville spatiale" de Yona Friedman [l], ou la "ville cybernétique" de Nicolas Schôffer, ou encore les pyramides habitées de Paul Maymond. Comment vous situez-vous par rapport à ces théories de prospective architecturale qui sont nées à la même époque que votre théorie? Iannis XENAKIS. Je les trouve timides par rapport aux miennes! Ce sont en réalité des extrapolations à une échelle relativement faible de ce que devrait être une concentration très grande et elles ne se rapportent en général qu’à l’habitat et non à la ville comme un phénomène global. Michel RAGON. - Personne, avant nous, je crois, n’a jamais envisagé une construction qui puisse faire 3, 4 ou 5 kilomètres de hauteur. Le plus utopique, jusqu’à vous, dans cette progression de la ville verticale, c’était le projet d’une tour de 1.660 mètres par Frank Lloyd Wright. Iannis XENAKIS. - Oui, mais cette tour de 1.600 mètres était une tour d’affaires qui avait le défaut, d’abord de ne pas aller assez haut, et ensuite d’être subordonnée à sa structure portante, faite de "portiques» qui finalement transformait cette chose-là en une sorte d’obélisque qui montait jusqu’à 1.600 mètres d’altitude. Michel RAGON. - C’est vrai, c’était une sorte d’obélisque, alors que vous avez des inventions de formes extrêmement intéressantes dans votre projet. Iannis XENAKIS. C’est-à-dire que c’est venu tout à coup par une sorte d’illumination que j’ai eue en dessinant le Pavillon Philips formé de surfaces à douole courbure. Je me rendis compte, parce qu’on avait fait des expériences dans un laboratoire près d’Eindhoven en Hollande que c’était excessivement résistant et qu’on ne réussissait pas à détruire la forme. On fit cette expérience parce que les calculs basés sur la résistance des matériaux et la théorie de l’élasticité ne permettaient pas de tout prévoir jusqu’au bout, et qu’il restait des marges d’incertitude. L’expérience démontra l’extrême rigidité inhérente à la géométrie de ces surfaces à double courbure. C’était des PH (des paraboliques hyperboliques). L’essentiel est la double courbure bien choisie, c’est-à-dire celle qui est écartée suffisamment du plan. Et alors j’ai pensé que comme structure porteuse il fallait absolument utiliser cette propriété de la géométrie et faire une ville non pas en forme d’obélisque ou en forme de gratte-ciel, comme on les voit soit ici à Paris soit aux États-Unis, mais en forme continue, à double courbure. Ce sont des pellicules dans l’espace, d’une épaisseur de 100 ou 150 mètres, ajourées bien sûr et transparentes, pour laisser passer l’air et la vue, la lumière et tout... Et il y a des villes qui sont à 2.000 mètres, comme Mexico et Bogota. Donc, c’est une altitude qui est très habitable. A 5.000 mètres, bien sûr, c’est très différent car la raréfaction de l’air commence à être critique. On ne sait pas très bien ce qui se passe. Mais avec la technologie actuelle, il est possible, comme on fait dans les avions, d’obtenir une pressurisation suffisante ainsi qu’un renouvellement d’air, de température, etc. Au fond, une ville comme celle-ci serait une sorte d’élargissement du vêtement de l’homme. L’homme n’a pas eu de vêtements pendant fort longtemps. Il n’en porte que depuis peut-être 10.000 ans, pas plus. Avant il était à poil, nu. Il a mis un vêtement qui est personnalisé, individualisé. On travaille du matin au soir dans des espaces comme celui où nous sommes, par exemple, qui n’a pas d’air, qui ne voit jamais la lumière du soleil. La plupart des gens travaillent comme ça dans les bureaux, dans les usines. C’est un environnement qui peut être très méchant pour la santé de l’homme et je pense qu’avec la technologie actuelle et celle qui va venir tout de suite, ces problèmes-là seront résolus de manière à avoir un vêtement fait pour la ville elle-même, ce qui permettra une liberté beaucoup plus grande, physique et conceptuelle, mentale, spirituelle, etc. de l’homme. C’est tout simplement donc une extrapolation des possibilités de la technique d’aujourd’hui, utilisées à grande échelle. Une ville comme celle-ci ne peut pas être conçue dans le système capitaliste restreint. Elle pourrait être conçue, soit par des sociétés multinationales, soit alors par des Etats centralisés comme la France par exemple, qui pourraient les bâtir, mais hors du système des municipalités. Seulement un pays de plusieurs dizaines de millions d’habitants peut se permettre une telle programmation, ou encore une sorte de corporation internationale qui pourrait réaliser des unités de ce type, valables pour les endroits soit désertiq.ues, soit très chauds, excessivement chauds et humides, l’Equateur, le tour de l’Équateur, ou dans les régions très froides comme la Sibérie ou l’Alaska ou le Canada du Nord. Michel RAGON. - Est-ce qu’il n’existe pas des contraintes énergétiques de sorte qu’il paraît difficile de concevoir le chauffage d’un volume pareil? Iannis XENAKIS. - C’est lié, bien sûr, à des problèmes énergétiques. Mahs nous avons des matériaux maintenant et des systèmes d’isolation qui peuvent réduire de beaucoup les déperditions thermiques, calorifiques. Je ne pense pas que les obstacles techniques soient de vrais obstacles. Le plus grand obstacle, les plus grands obstacles sont de deux types. C’est d’abord l’organisation, car une ville est organisation ... Michel RAGON. - J’allais y venir, j’allais dire justement que pour l’organisation d’une telle ville verticale, vous envisagez des ensembles électroniques de gestion et de décision. Or, dans la "ville cybernétique" de Nicolas Schôffer, nous trouvons aussi cette croyance en la cybernétique et dans les ensembles électroniques de gestion et de décision. Est-ce que vous ne croyez pas, cela affieure parfois d’ailleurs dans vos écrits, est-ce que vous ne pratiquez pas une croyance qui me paraît dangereuse dans les vertus politiques de la science? Iannis XENAKIS. - Je ne sais pas exactement ce qu’a dit Nicolas Schôffer. Je crois qu’il fait une mystique de la cybernétique. Michel RAGON. - Oui, il va plus loin que vous, ça devient vraiment une sorte de mystique, en effet. .. Iannis XENAKIS. - Pour l’instant, l’informatique ou les systèmes de gestion sont assez rudimentaires, il faut bien le dire, et très grossiers. Seules quelques tâches pourraient être entreprises et prises en charge par des systèmes de gestion automatiques. Mais il y en a qui fonctionnent. Par exemple, les feux de circulation dans la ville qui tendent à devenir de plus en plus automatisés, avec des réactions, des contre-réactions de rue à rue, de quartier à quartier; ça c’est un fait. Michel RAGON. - Mais cette automatisation est presque toujours répressive. Iannis XENAKIS. - Alors, nous sommes devant deux problèmes : un problème d’organisation et ensuite un problème qui va beaucoup plus loin puisque c’est un problème de structure sociale. Quand je dis organisation, il est évident qu’une ville comme celle-là, qui doit comprendre sur 5.000 mètres d’altitude des millions d’individus, ne peut pas être conçue à l’avance parce qu’on risque de créer des villes mortes, comme ça a été le cas pour Detroit, pour le Havre, pour Brasilia et même Chandigarh, qui ne fonctionnent pas parce qu’elles ont été conçues en laboratoire, je veux dire dans les ateliers d’architecte suivant certaines règles issues de traditions de la planche à dessin ou même parfois d’idées révolutionnaires. Elles ne peuvent pas tenir compte de toute la complexité d’une ville du fait qu’elles sont issues d’un cerveau unique. Par contre, ce qui est possible c’est de donner le cadre, c’est-à-dire le contenant, et ne pas définir, déterminer le contenu, lui laisser une liberté suffisamment grande pour que le contenu puisse se développer au fur et à mesure. Il faut bien penser qu’une ville de cette sorte ne peut pas être édifiée en cinq ans ou en dix ans, mais peut prendre vingt ou trente ans de construction. Donc, ce n’est pas la ville elle-même qui sera dessinée à l’avance, en vingt ou trente ans, mais le contenant, c’est-à-dire la structure fondamentale qui doit s’élever à cette altitude. D’autre part, il faudrait permettre des aménagements, sinon des développements, sinon des contradictions qui se feront jour au fur et à mesure de l’élévation de cette ville. Par conséquent, il faut absolument concevoir une sorte d’architecture mobile. On trouve ça en germe dans les architectures japonaises, qui permettent de transformer des pièces ou des maisons pour des fonctions diverses. Michel RAGON. - Le nomadisme interne, dites-vous fort justement d’ailleurs, est possible par cette permutation de mobilité de l’architecture. Iannis XENAKIS. - Je n’ai pas encore parlé de nomadisme interne, j’ai simplement parlé de nomadisme, mettons matériel de la ville, c’est-à-dire qu’on puisse affecter des endroits, des régions de la ville, à telle ou telle fonction, à des usines, et les changer au bout d’un certain temps en habitat ou en parcs, etc. C’est une mobilité de la structure interne de la ville matérielle. En ce qui concerne le deuxième obstacle, le plus difficile, c’est celui de l’occupation par les hommes et par les fonctions humaines de ce contenant. Dans ce domaine-là, il faut absolument laisser la liberté, ou proposer un schéma suffisamment libre pour que cela puisse se développer d’une manière autonome, pour que les contradictions (je ne dis pas qu’elles vont être annulées ou absorbées, ceci n’existe pas, c’est une utopie qui nous vient du XIXe siècle, sinon de plus loin) puissent se déplacer, changer de forme. Michel RAGON. - Vous écrivez aussi: «Puisque cette ville, votre ville, sera façonnée par la technique universelle, elle sera également apte à loger les populations du grand nord ou sud, et celles des tropiques et des déserts.» C’est-à-dire qu’apparaît dans ce texte une croyance technocratique qui me paraît dangereuse en un homme universel, un homme type. C’est une idée qui est très répandue. On la trouve chez Le Corbusier, comme chez Gropius. Et puisqu’il y a un homme universel, un homme type, les architectes en déduisent que l’on peut construire une architecture type et universelle pour cet homme; croyance dont on est un peu revenu de nos Jours. Iannis XENAKIS. - Oui, c’est que la technologie impose une certaine universalité, mais je me demande si on en est revenu vraiment ou si ce n’est qu’en esprit, parce qu’il faut voir combien tous les moy.ens technologiques se répandent de plus en plus, au cœur des sociétés les plus primitives, avec l’électricité, avec les énergies, les transformations d’énergie; mais aussi les institutions qui font que partout on institue des écoles, des universités, des textes. Même s’ils sont différents sur le plan de l’histoire, les textes scientifiques sont les mêmes, les laboratoires scientifiques sont les mêmes et l’habillement est le même. On voit de moins en moins de gens habillés avec leur costume national et ceci t~nd à une universalisation de fait qui est due à toutes s’ortes de raisons. D’un autre côté, je ne suis pas du tout un technocrate, loin de là. Au contraire. Mais ceci ne veut pas dire qu’il ne faille pas utiliser et exploiter la technologie actuelle. Dans toute proposition il y a au moins deux aspects, le blanc et le noir. Dans l’énergie atomique c’est également la même chose. C’est un miracle remarquable que l’homme ait pu voir et entrer dans le microcosme de la matière et l’utiliser à son propre bénéfice. Maintenant, s’il y a des déviations, c’est tout à fait normal aussi, c’est dans la nature l’homme, c’est une contradiction qui est inhérente à l’ omme et c’est une question de lutte de l’individu et s~\ciale aussi. Mkhel RAGON. - Enfin, dernière question, comment vous sitQ.ez-vous en tant qu’architecte, puisque vous êtes toujours architecte, que vous avez réalisé une architecture destinée à être associée très étroitement à la musique sur l’esplanade du Centre Georges Pompidou à Paris, une architecture dans laquelle il y aura de la musique, et sans doute des Polytopes. Vous avez aussi construit récemment des maisons individuelles pour le musicien François Bernard Mâche. Comment vous situez-vous dans votre évolution par rapport à votre ancien patron Le Corbusier qui est très récusé aujourd’hui par beaucoup de vos confrères, et par beaucoup de théoriciens de l’architecture? Iannis XENAKIS. - D’abord par rapport à l’architecture. Quand j’ai décidé de faire de la musique uniquement, ce fut avec beaucoup de détresse; parce que l’architecture était très importante pour moi. Mais je l’ai fait parce qu’il fallait choisir. Ou bien la recherche ou bien devenir un homme d’affaires. J’avais fait les ateliers d’architectes dans les années soixante en disant : "Voilà! Je viens en tant qu’architecte vous proposer ma collaboration, mais je ne veux pas être le nègre, je veux faire de la recherche". Ça a été impossible. Vous savez très bien que ceci est vrai, dans la grande majorité, il y a très peu de cas de recherche dans l’architecture. Alors, je me suis cantonné dans la musique où je pouvais faire, malgré toutes les difficultés, de la recherche artistique. Ceci dit, je suis toujours prêt à faire de l’architecture et chaque fois que je le peux, j’en fais. Par exemple, avec ce "truc» de Beaubourg, j’ai dessiné une structure démontable i sera implantée pendant quelques mois et qui contien a les moyens de faire un spectacle avec des lasers et tfS flashs électroniques, comme à Cluny, mais amplifié. Et la structure est une structure textile qui implique donc des solutions architecturales fondamentales. D’un autre côté, par rapport à Le Corbusier, je ne sais pas s’il y a beaucoup d’architectes qui ont atteint ce que j’appellerai l’expression artistique. Indépendamment des idées sousjacentes qui sont chez un architecte, chez un urbaniste, ce sont des choses très complexes qui viennent de sources et de directions différentes. Le type de l’appartement de Marseille qui est une cellule, un habitat de cellule familiale, peut être contesté, bien sûr, et ce n’est qu’une des solutions possibles. On ne peut pas dire que ce soit la solution unique. D’ailleurs, Le Corbusier l’a montré luimême puisqu’il a fait toutes sortes de maisons. Par contre, ce qu’on ne peut pas lui contester, c’est sa qualité artistique et architecturale, qui existe pratiquement dans toutes ses œuvres. Et les idées passent, mais le fait artistique reste. C’est un des enseignements de l’histoire, comme l’avait très bien remarqué d’ailleurs Marx à propos de l’art antique. Il disait, approximativement, comment se fait-il qu’à l’orée de la civilisation, de la culture occidentale, malgré les sociétés esclavagistes, etc., il y ait eu des œuvres qui nous font de l’effet encore aujourd’hui? C’est un miracle inhérent au fait artistique et qui correspond à la discussion de tout à l’heure, et à la question qu’avaient posée Olivier Messiaen et Revault d’Allonnes. Donc, on peut critiquer Le Corbusier sur beaucoup de choses, je l’ai fait moi-même, d’ailleurs, mais je crois que c’est un des plus grands architectes de notre temps. Il n’yen a pas trente-six aujourd’hui, il n’y en a peut-être pas un. Michel RAGON. - J’en ai fini de mes questions et, puisque je vous ai chicané un peu du point de vue de la technocratie, je ne voudrais pas manquer de dire que dans tous vos textes, se trouve aussi un éloge de l’art, et que dans un temps où l’on parle surtout de mort de l’art, cet éloge de l’art est quelque chose de singulier, de remarquable, et aussi la définition de l’artiste-concepteur que vous donnez, me semble quelque chose d’extrêmement important. On reconnaît encore, dans tous vos textes, votre intelligence, et aussi ce que vous appelez, pas pour vous, mais qu’on pourrait vous retourner, un "feu froid". C’est un peu ainsi que je vous ai toujours vu, comme un feu froid. C’est ce qui m’a toujours donné cette fascination, à la fois pour votre musique, pour votre architecture. L’admiration très fervente que je vous porte fait que je considère comme un grand honneur aujourd’hui de pouvoir être là, non pas pour vous juger, mais pour vous accueillir. DIALOGUE AVEC MICHEL SERRES Bernard TEYSSÈDRE. - Maintenant je vais donner la parole à Michel Serres. Michel SERRES. - Je crois qu’il n’y a pas qu’en architecture que l’espace est l’image de la société. Par exemple, aujourd’hui, il y a un admirateur derrière la table et un créateur devant la table; ce n’est pas ma faute si c’est l’image de l’université. L’université favorise les thèses et ne favorise pas les œuvres. Pour une fois que nous avons comme thèse une œuvre, je voudrais saluer avec beaucoup d’admiration ce phénomène rare parmi le gaspillage d’intelligence qui se fait dans l’institution. C’est donc l’admirateur qui pose les questions. On reviendra tout à l’heure sur les rapports entre les mathématiques et la musique. A la page 14 de l’exposé de thèse que vous avez donné, à propos justement de l’artiste concepteur, vous proposez l’idée globale d’une morphologie générale. Qu’est-ce que cette morphologie générale? Iannis XENAKIS. Eh bien, dans chaque domaine de l’activité humaine, il y a une sorte d’écume qui est celle de la forme. J’ai remarqué des figures, des formes qui appartiennent, soit au domaine de la spéculation abstraite comme les mathématiques, comme la logique, soit aux spéculations plus matérielles comme celles de la physique, avec ses phénomènes soit subatomiques, soit atomiques, ou comme celles des expressions géométriques de la génétique ou des réactions de ses molécules chimiques. Or, ces figures, ces formes, qui appartiennent à tant de domaines disparates, ont des similitudes ou des diversités passionnantes et qui peuvent éclairer d’autres domaines, tels que ceux des activités artistiques. Mi~hel SERRES. - Vous avez écrit ça en quelle année? Mamtenant? lan~is XENAKIS. Oh! je ne sais pas, ça fait plusieurs annees. ~ichel SERRES. - Deux questions, ou deux sous-questIons. A la fin de l’article, à la fin du paragraphe où vous annoncez cette morphologie générale, vous prenez l’exemple de l’évolution formelle des vertébrés. Iannis XENAKIS. Des vertébrés, oui, c’est un exemple. Michel SERRES. - C’est un très bon exemple. Quelqu’un, av~nt Xenakis, a eu l’idée d’une morphologie générale m~Is. seulement dans la biologie, c’est Geoffroy SaintHIlaIre. Geoffroy Saint-Hilaire avait l’idée d’un plan général qui serait projeté dans l’ensemble des vertébrés puis, plus généralement, dans la totalité des animaux Mais actuellement, il y a quelqu’un qui s’occupe de cett~ ~~rphologie générale, c’est Thom, de sorte que votre Id~e de morphogenèse se rencontre avec une partie de la SCIence en marche. Comme d’habitude, le musicien était en avance. la~nis XENAKIS. - Tant mieux. Il faudrait aussi que Thom SOIt versé dans le domaine artistique, pas seulement dans le domaine physique. Mais je crois que cette idée est beaucoup plus antérieure sous une autre forme? Michel SERRES. - C’est Geoffroy, je crois, le premier, non? Iannis XENAKIS. - Je ne sais pas. Je crois qu’on peut en retrouver la trace dans l’Antiquité, par exemple lorsqu’on essayait de mettre l’idée de la proportion dans l’architecture, dans les formes de l’homme, c’est local. Michel SERRES. - C’est la morphologie locale, ce n’est pas la morphologie générale, au sens de Xenakis. Iannis XENAKIS. - Mais moi je pense qu’il est indispensable de faire une sorte de convergence de toutes les formes possibles, de partout, ce qui présuppose qu’il faut connaître toutes ces sciences disparates ... Michel SERRES. - Vous aviez une armature mathématique pour commencer le projet d’une morphologie de ce genre? Iannis XENAKIS. - Oh! pas du tout, non ... Michel SERRES. - Topologie? Iannis XENAKIS. - La topologie? La topologie, de quel point de vue? Parce que si la topologie est ~eut-~tre la science la plus fondamentale sur le plan mathematIque ... Michel SERRES. Sur le plan des formes, certainement. Iannis XENAKIS. - Sur le plan des formes, mais non seulement des formes, aussi de la pensée philosophique des mathématiques, vous ne croyez pas? C’est le problème de la continuité, de la discontinuité, des contacts, de la connexité. Michel SERRES. - Des bords. Iannis XENAKIS. - Oui, des bords, et par conséquent des formes. C’est probablement l’outil sous-jacent, mais je crois qu’il est assez grossier pour l’instant. Il est assez imparfait pour s’attaquer aux problèmes aussi complexes que sont les formes des nuages ou les formes des populations. Michel SERRES. - Mais c’est sur des problèmes comme la forme des nuages qu’on a commencé justement à avoir une idée d’une morphologie générale. Soit votre Annexe 1 sur le tableau des correspondances entre les développements de la musique et des mathématiques[1] : je suis d’accord avec vous, je voudrais seulement le compléter. Lorsque vous dites qu’avant notre ère, on avait eu quelque chose comme l’analyse comparée des longueurs, des cordes et des hauteurs des sons, vous pensez à Pythagore, je suppose, et à l’école pythagoricienne. On pense de plus en plus actuellement qu’il n’y a pas eu d’analogie entre l’invention des premiers intervalles musicaux et l’invention de la mathématique, mais cause et conséquence, c’est-à-dire que c’est par la musique qu’on a pu avoir l’idée de l’ensemble des nombres naturels mais aussi des rapports et des fractions. La musique aurait été la matrice de l’invention mathématique. Iannis XENAKIS. - Oui, ça c’est un problème d’archéologie. Michel SERRES. - Encore une fois, la pensée musicale est fondatrice. En quel sens dites-vous que la fugue est un automate, que "la fugue est un automate abstrait conçu deux siècles avant la science des automates»? Je crois que ce n’est pas vrai, je crois que c’est en même temps, ou un peu avant. Iannis XENAKIS. - Ah non, pas la science des automates, la science des automates est née au Xxe siècle. Michel SERRES. - Pas la science des automates, la réalisation d’automates. Iannis XENAKIS. - Ça fait une différence, parce que la pratique des automates date au moins du temps d’Alexandrie. Michel SERRES. - Il Y a dans les Mille et une Nuits, par exemple, des fontaines automatiques, des machines à eau. Iannis XENAKIS. - Oui, mais les Mille et une Nuits datent du XIIe siècle, or la pratique des automates en est bien antérieure. L’époque alexandrine avait déjà Héron et la première machine à vapeur. Michel SERRES. Oui, au moins la colombe d’Archytas. Iannis XENAKIS. - Mais c’était une préoccupation qui restait encore au stade matériel. L’abstraction est venue, je crois, du côté de la musique. Michel SERRES. - Alors, pourquoi la fugue est-elle un automate? Iannis XENAKIS. - Je pense qu’elle correspond plus ou moins à la définition de l’automate scientifique qui est né dans les années vingt, avec Wiener et la cybernétique, et qui peut être résumée de la manière suivante : un automate se présente comme un réseau de causes et d’effets, c’est-à-dire d’une chaîne temporelle d’événements, couplée ou multicouplée, multiplexée avec des libertés, éventuellement. Un automate peut être fermé. Il suffit de brancher l’énergie et il fonctionne cycliquement. Il peut être relativement ouvert avec des données d’entrée, des actions externes, à l’aide de boutons par exemple et, malgré une rigidité interne qui définit l’automate, il peut produire des résultats différents chaque fois que l’on change les données d’entrée. Michel SERRES. - Il est répétitif dans ses syntaxes et non pas répétitif dans ses performances. Iannis XENAKIS. Oui, il est répétitif dans ses syntaxes. Pourquoi? Parce qu’il a une rigidité interne structurelle. Michel SERRES. - Est-ce que la fugue est toujours stable dans sa syntaxe? Iannis XENAKIS. - Elle ne constitue pas un automate aussi absolu, elle l’est relativement, car les automates étudiés par la science sont encore des automates relativement rigides par rapport aux automates de la musique. Quand je dis automate de la musique, un menuet est un automate, déjà. Donc la valeur spécifique de l’invention musicale, c’est que c’est probablement la première qui a donné, qui a créé l’automate abstrait, c’est-à-dire qui ne produisait rien du tout, ne produisait que de la musique! Michel SERRES. - Est-ce que le temps de cette musique-là est réversible ou irréversible? Iannis XENAKIS. - Alors là, le problème serait celui du temps. Or, ici, il y a une sorte de confusion qui se passe dans la plupart des esprits de$-gens, y compris dans celui des musiciens. C’est que le fait de pouvoir répéter des choses, renouveler des expériences, ou des phénomènes, leur donne une sorte de sécurité envers le temps, qui lui, en fait, ne se répète jamais. Michel SERRES. - Quelquefois, il existe des temps réversibles. Iannis XENAKIS. - Quels sont les temps réversibles? Michel SERRES. - La circulation des planètes. Iannis XENAKIS. - Ce n’est pas le temps qui est réversible, c’est le mouvement qui est réversible. Le temps, lui, (à ma connaissance c’est une sorte de postulat) le flux temporel, ne revient pas. Michel SERRES. - En tous cas c’est une découverte très récente. Iannis XENAKIS. Que le temps ne revient pas? Michel SERRES. - Absolument. Iannis XENAKIS. - Mais il est tellement naturel de penser qu’il ne revient pas. Héraclite disait la même chose d’ailleurs ... Il y aurait réversibilité du temps éventuellement s’il y avait un mouvement pendulaire de l’univers qui se contracte et se dilate. Quand je dis, par exemple, que je prends des intervalles de temps : les intervalles de temps sont commutatifs. C’est-à-dire que je peux prendre des intervalles de temps et les prendre maintenant ou après et les commuter avec d’autres intervalles de temps. Mais les instants qui créent ces intervalles de temps ne sont pas réversibles, ils sont absolus, c’est-à-dire appartiennent au temps, c’est-à-dire qu’il y a une chose qui nous échappe complètement, car le temps court. Ceci correspond aux recherches qu’avait faites Piaget lorsqu’il avait vu les phases de l’apprentissage du temps chez l’enfant, expérimentalement. Michel SERRES. - Ce que j’ai dans l’esprit, ce n’est pas Piaget, c’est Xenakis. Iannis XENAKIS. - Ah! Michel SERRES. - Oui, lorsque vous amenez des compositions de type stochastique, par exemple, ça touche au problème du temps. Iannis XENAKIS. - Oui. Michel SERRES. - Quel est le rapport que vous faites entre ordre et désordre, lorsque vous composez? Iannis XENAKIS. - L’ordre et le désordre? Michel SERRES. -Je sais ce qu’est le désordre parce que je sais comment vous avez fait ça, mais l’ordre, qu’est-ce que c’est, quelle est votre syntaxe? Iannis XENAKIS. - Eh bien, il y a plusieurs facettes, par exemple, je peux dire qu’il y a ordre lorsqu’il y a symétrie. Michel SERRES. - Déjà ça y est, avec la symétrie, c’est gagné. Iannis XENAKIS. - Oui, vous avez gagné là, bien sûr. Il n’y a pas à gagner, c’est une question de vocabulaire. Michel SERRES. - Non, non, j’ai gagné, ça veut dire qu’on va revenir au temps. S’il y a symétrie, il peut y avoir réversibilité. Iannis XENAKIS. - Non, parce qu’on peut avoir de l’ordre dans des choses qui ne sont pas temporelles. C’est pour ça qu’il est absolument indispensable de distinguer entre ce qui est en temps et ce qui est hors-temps. Par exemple, je prends un ensemble de touches du piano, ce qui est un cas élémentaire, j’ai donc des intervalles qui se répètent, mais ils ne se répètent pas dans le temps, ils sont là, figés. Car les touches de piano sont sur un piano qui ne bouge pas. Michel SERRES. - Donc, ils sont hors du temps? Iannis XENAKIS. - Hors-temps, oui. Michel SERRES. - La syntaxe alors est hors du temps? Iannis XENAKIS. - Oui. Michel SERRES. - Je m’en doutais. Iannis XENAKIS. - Là, j’ai des symétries puisque j’ai des rapports, donc j’ai des répétitions. Michel SERRES. - Oui, alors l’ordre est en dehors du temps? Iannis XENAKIS. - Il existe des ordres qui peuvent être en dehors du temps. Maintenant, si j’applique cette idée au temps, je peux les obtenir aussi, mais pas dans le temps réel, c’est-à-dire dans le flux temporel parce que lui n’est jamais réversible, mais dans une fiction du temps qui est basée sur la mémoire. Michel SERRES. - Le piano est-il une mémoire? Iannis XENAKIS. Il est une mémoire matérielle, oui. Michel SERRES. - Une mémoire matérielle. La question serait la suivante : est-ce que vous obtenez de la dérive irréversible? Iannis XENAKIS. - Je le peux, bien sûr, puisque je ne suis pas un gaz et que je possède en même temps le démon de Maxwell en moi. Michel SERRES. Le démon de Maxwell fait de l’ordre. Iannis XENAKIS. - Le démon de Maxwell peut renverser les choses. Michel SERRES. - Nous y sommes maintenant. Donc il y a des structures réversibles dans la musique. Iannis XENAKIS. - Elles sont réversibles dans le sens du hors-temps. Michel SERRES. - Le démon de Maxwell ferait-il passer en dehors du temps? Iannis XENAKIS. - J’ai pris le démon de Maxwell, mais ce démon ne change pas l’ordre du flux temporel en soi. Il faut bien comprendre ce qui se passe. Par exemple, lorsqu’on dit qu’un flux lumineux, qui est passé dans certaines conditions et qui devient organisé, ordonné, donne le laser, la lumière laser, eh bien, c’est comme si on avait fait intervenir le démon de Maxwell là-dedans. Parce qu’autrement on n’aurait eu qu’une lumière. quelconque, désordonnée. Mais ceci ne s’applique qu’à des notions ou à des êtres qui peuvent être réversibles par définition. Le temps, lui, n’est pas réversible, j’insiste làdessus. Michel SERRES. - Si quelqu’un l’a montré, c’est bien Xenakis. La dérive de l’ordre ou de la structure au désordre, c’est quand même un des secrets de votre composition. Vous êtes bien d’accord? Iannis XENAKIS. - Oui. Michel SERRES. - Or, le premier théorème de physique fut proposé sur les cordes vibrantes. Une corde vibrante, n’est-ce pas un phénomène réversible? Iannis XENAKIS. - Les positions hors-temps sont réversibles. Michel SERRES. - Qu’est-ce que vous appelez position hors-temps? Je ne comprends pas. Iannis XENAKIS. - Les intervalles spatiaux, par exemple, les positions de la corde. Elles sont réversibles parce qu’elles appartiennent à l’espace qui n’est pas temporel. Michel SERRES. - C’est donc une horloge! Iannis XENAKIS. - C’est donc une horloge. Michel SERRES. - Effectivement, une horloge comme une corde vibrante font un comptage du temps. Une corde vibrante peut être un comptage du temps. C’est la mesure. Iannis XENAKIS. -C’est un comptage du temps, mais c’est un comptage du temps qui est fait, qui est basé sur la réversibilité des positions et non du temps, voilà l’idée fondamentale. Car, comme l’a dit Héraclite, personne ne peut revivre le même instant deux fois, quoique, en microphysique, on essaie de prouver la réversibilité du temps (on ne l’a pas encore démontré) avec la parité, par exemple, d’il y a quinze ans, que le temps même, peut être réversible, mais on n’a pas de données expérimentales ... Michel SERRES. - Les musiques en question sont un essai pour lutter contre l’irréversibilité temporelle. Iannis XENAKIS. - Si vous voulez. Michel SERRES. - On va pouvoir généraliser la chose peu à peu et passer de la technique à la composition. Est-ce que le glissando a un rapport avec ladite irréversibilité? Ce point me paraît vraiment très important, vous verrez pourquoi tout à l’heure. Iannis XENAKIS. - Je ne sais pas si le glissando a un rapport immédiat. Michel SERRES. - Vous êtes bien d’accord que le glissando est un élément important dans votre composition. Iannis XENAKIS. - Oui. Michel SERRES. Pourquoi avez-vous choisi le glissando? Iannis XENAKIS. - Peut-être une influence de la géométrie euclidienne. Peut-être du fait même que le glissando est une modification justement, de quelque chose dans le temps, mais imperceptible, c’est-à-dire qui est continue et qu’on ne peut pas saisir, car l’homme est un être discontinu. Non seulement il est discontinu dans ses perceptions, dans ses jugements, mais dans tout. La continuité est une chose qui lui échappe constamment. C’est une problématique zénonienne, le changement tout court, et c’est une sorte de lutte perpétuelle de notre perception et de notre jugement que d’essayer d’imaginer le mouvement continu. C’est ce qui s’est passé d’ailleurs, notamment en mathématiques. Elles ont d’abord commencé par le discret pour arriver à la continuité bien plus tard. Michel SERRES. - TI y a deux éléments dans votre travail qui m’amènent à penser à l’irréversibilité. La première c’est la dérive de l’ordre au désordre par les probabilités, et la deuxième c’est l’élément glissando utilisé constamment. lannÏs XENAKIS. - Oui. Michel SERRES. - Alors, la musique de Xenakis ne répond plus à la définition qu’on a donnée tout à l’heure, comme une lutte contre l’irréversible, puisque vous acceptez l’irréversible dans ces deux techniques fondamentales. Est-ce que votre musique n’est pas différente de toutes les autres en ce que, précisément, elle a admis pour toujours l’irréversibilité du temps? Contre toutes les autres. Iannis XENAKIS. Il faut que je revienne là-dessus parce que je ne crois pas à la réversibilité du temps, du temps réel, immédiat, du flux temporel. Je crois qu’on ne peut pas le faire revenir en arrière, le temps. Michel SERRES. - Oui, c’est ça. Iannis XENAKIS. - Donc il est irréversible. Ce qui est réversible, ce sont des jugements, si vous voulez, qu’on fait sur ce flux du temps. Prenons, par exemple, la chose la plus élémentaire qui soit, les durées. Une durée est une chose qu’on peut promener dans le temps, elle est donc réversible, commutative. Elle a toujours le même sens que le temps, bien sûr (une durée n’a pas de sens contraire au flux temporel). C’est-à-dire que si je voulais écrire, dessiner, ou plutôt figurer le temps visuellement, je l’aurais mis sur un axe comme font les physiciens, comme font les musiciens (les musiciens d’abord, puis ensuite les physiciens); il faut bien le dire, avec la portée par exemple, ce sont les musiciens qui avaient, les premiers, inventé la .représentation cartésienne. Bien. Le flux du temps serait représenté par une droite qui, par définition, est une ·continuité. Sur cette droite, je place des points. Ce sont les instants. La différence, entre deux points quelconques, est un concept issu des comparaisons, des jugements mystérieux que je porte sur la réalité du flux temporel que j’admets a priori. C’est cette différence qui est identifiée à la durée. C’est elle que je peux promener n’importe où. Elle est donc réversible. Mais, lui, le flux du temps, est irréversible. Et si je dessine dans un espace plan un axe sur lequel je porte des hauteurs, un axe qui soit normal à un axe des temps horizontal, alors, pour aller d’un point bas à un point haut qui se trouve à droite, je ne peux aller que dans un sens, de bas en haut et de gauche à droite. C’est ça l’irréversibilité. Michel SERRES. - On est arrivé à la notion d’irréversibilité qui caractérise votre musique, par deux méthodes techniques, la dérive de l’ordre au désordre d’une part et par l’utilisation des glissandi d’autre part. Ce qui m’a aussi frappé, à lire globalement, à la fois, votre musique et votre architecture, c’est un autre invariant de votre vision du monde: les surfaces réglées, c’est-à-dire les PH, l’hyperboloïde, etc. Pourquoi cette constance des surfaces réglées? Iannis XENAKIS. Pour plusieurs raisons, je crois. Michel SERRES. - Il faut faire très attention avant de ré pondre parce que c’est exactement le contraire de tout à l’heure. Tout à l’heure, il y avait une dérive vers le hasard, tandis qu’à partir de la constante des surfaces réglées, il y a une reprise de la structure répétitive. Iannis XENAKIS. - Oui, c’est un autre type de préoccupation. C’est un problème de continuité et de discontinuité, issu d’éléments de droite. La droite, c’est peut-être l’élément le plus primaire de continuité, de l’expression de la continuité. Michel SERRES. - Est-ce que ce n’est pas seulement le résultat de la technique du coffrage? Parce que les surfaces réglées, c’est plus facile à coffrer. Iannis XENAKIS. - Non, on ne peut pas les coffrer, parce qu’elles sont à double courbure, il faudrait... Michel SERRES. - Si, puisqu’elles sont réglées, vous avez forcément des coffrages faits de planches toujours droites sur un PH ou un hyperboloïde. Iannis XENAKIS. - Oui, mais comme c’est à double courbure, l’espace est tordu et le coffrage ordinaire, étant fait de planches planes, n’épouserait que très imparfaitement les formes à double courbure. Si l’on devait réaliser un coffrage «gauche» comme pour les bateaux, par exemple, cela coûterait beaucoup trop cher. Michel SERRES. - Revenons à nos surfaces réglées et à la situation qu’elles nous ont permis ... Une surface réglée peut être engendrée par des droites. Iannis XENAKIS. Oui, la droite a une fascination absolue. Un rayon de soleil est une chose fascinante en soi. On voit un rayon de soleil lorsqu’on le regarde à travers les nuages. Les rayons de soleil qui convergent vers le sol sont, en réalité, parallèles. La droite d’un rayon laser est quelque chose d’absolu, la droite d’un fù de maçon, c’est une chose absolue aussi. La droite, donc, existe dans la nature. Mais, en tant qu’entité intellectuelle, c’est la chose la plus fascinante du point de vue vitesse, du point de vue direction, et aussi du point de vue continuité. On ne peut pas imaginer quelque chose de plus simple, du point de vue continuité, qu’une droite. Parce que, dès que vous avez une courbe par exemple, on suppose les forces qui la produisent, et il existe toutes sortes de torsions, toutes sortes de courbes riches, tandis que la droite est une, sans forces se répétant identiquement. Excusez-moi, je n’ai pas fini avec les surfaces réglées. C’est la droite, dans trois dimensions, qui les engendre (le glissando étant une droite dans deux dimensions). Elle permet d’imaginer des formes très complexes avec des éléments très simples, contrôlables. Michel SERRES. - Le minimum de technique, le maximum de réalisations ... Iannis XENAKIS. - De résultats. Michel SERRES. - Oui, d’accord ... La question finale sera la suivante (je terminerai là-dessus) : page 8 de votre livre[2], vous avez encore maille à partir avec les informaticiens, mais il faut quand même distinguer entre l’informatique et la théorie de l’information. Iannis XENAKIS. - Les bons et les méchants! Michel SERRES. - Finalement, lorsqu’on parle du désordre, il s’agit du désordre thermodynamique, mais il s’agit aussi du bruit de fond. Par conséquent, c’est la même chose. Voici la question finale: il y a chez Xenakis deux choses que je n’arrive pas à mettre ensemble, d’abord une sorte de fascination pour les invariants réglés, c’est-à-dire les surfaces réglées, puis, pour les invariants syntaxiques, et ainsi de suite, l’invariance en général, bref, la syntaxe répétitive, et d’autre part, une fascination qu’indiquent vos préoccupations thermodynamiques, bruits de fond, etc., et les glissandi qui en sont des éléments, c’est-à-dire la préoccupation inverse, la préoccupation de glisser irréversiblement vers un désordre, vers le bruit de fond. Comment arrangez-vous cette fascination invariante sur la syntaxe et cette fascination vers la dérive, vers le désordre? Peut-être définit-on ainsi la musique? JanDis XENAKIS. - Non, parce que le désordre est une négation de l’ordre qui veut dire ici répétition. Le désordre donc, au sens de la périodicité, est réversible, bien sûr (une chose périodique est réversible, mais dans sa définition propre). Je veux dire par là que c’est ce qui n’est pas, par essence, temporel qui est réversible. Dans ce domaine, par définition hors temps, les êtres peuvent se placer dans n’importe quel ordre. C’est cette préoccupation constante de ces deux pôles, du désordre ou de l’ordre, personnifiés par la périodicité (quand on dit périodicité, on dit aussi invariant); c’est toute la gamme des· degrés possibles, d’un pôle à l’autre, qui constitue une sorte de catégorie mentale, à mon avis. C’est elle qui se trouve dans toute l’histoire, aussi bien de la philosophie que de la science, et qui est une des préoccupations sous-jacentes de la musique que j’ai faite. Michel SERRES. - Une dernière question corollaire: est-ce qu’il peut y avoir un ordre à partir du bruit? Iannis XENAKIS. - Oui. Et alors, ce qui est intéressant, c’est que le bruit qui, physiquement, est une variation de la pression qui ne se renouvelle pas identiquement (on peut le fabriquer soit avec des tubes cathodiques, soit à la machine à calculer) peut être simulé. Or, l’auditeur passe à l’étage au-dessus, il ne reste pas dans l’événement microscopiquement individuel de l’échantillon à l’étage inférieur, et il perçoit le bruit comme un tout macroscopiquement individuel, donc comme quelque chose qui possède une régularité, un ordre! Michel SERRES. ~ Alors la réponse peut maintenant se faire, elle est parfaitement générale. Vous savez que toutes les questions qui se posent actuellement se posent autour du problème: y a-t-il un ordre par le bruit? Or, c’est votre musique qui a découvert cela en premIer. Iannis XENAKIS. - Merci infiniment. DIALOGUE AVEC BERNARD TEYSSÈDRE Bernard TEYSSÈDRE. Eh bien, puisque le moment approche de conclure cette soutenance et puisque l’usage (ou le protocole) laisse les derniers mots au président du jury , permettez-lui, cher Iannis Xenakis, de vous dire sa joie, son émotion à vous voir présenter cette thèse. Ceci pour des raisons personnelles, d’abord. Je n’o~blie pas votre surprise, et presque votre scepticisme, quand je vous ai suggéré, voici quelques années, de poser votre candidature à un poste de professeur associé dans l’U .E.R. des Arts plastiques et Sciences de l’Art, dont j’étais alors le directeur. Vous avez progressivement mis en place, dans ce cadre nouveau pour vous, un enseignement qui aboutit à vos séminaires de second et troisième cycle: "Formalisation et programmation dans les arts visuels et en musique". Je n’oublie pas non plus, à nouveau, votre surprise lorsque, en accord avec notre ami commun Olivier Revault d’Allonnes, je vous ai engagé à présenter une thèse de doctorat d’État, en regroupant les partitions et les textes sur lesquels nous discutons aujourd’hui. Ici les raisons personnelles débouchent sur des questions de principe, celles mêmes qu’évoquait tout à l’heure Michel Serres. Comme lui, je suis heureux que des chercheurs de haute qualité, mais dont la carrière et la formation n’avaient rien de "sorbonicole", puissent désormais accéder au doctorat d’État. Cette situation est depuis longtemps acquise dans les universités étrangères, notamment américaines; en France pourtant, elle est toute nouvelle. Je me souviens de l’incrédulité que je rencontrais, dans les années 1969-1970 encore, en soutenant la seule idée qu’un musicien ou un sculpteur pût avoir sa place en Sorbonne aux côtés d’un docte professeur d’histoire ou de philosophie. L’Université n’est pas faite pour les artistes, m’objectait-on. Et pourquoi non? Il me semble que, depuis, ils y sont entrés de plein droit. Il n’existe plus seulement des formations en musicologie, en fùmologie, en histoire de l’art, mais des formations en musique, en cinéma, en arts plastiques, où la pratique et la théorie, intimement associées, vont de PaIr. La pratique artistique n’est plus, comme dans un passé récent, évacuée au seul profit du discours réflexif, lui-même souvent subordonné à l’hégémonie de l’histoire. Dans l’intervalle de moins de cinq ans, des "cursus» universitaires complets d’études artistiques ont été mis en place, du premier cycle à la licence, aux maîtrises et aux thèses, des IPES au CAPES et à l’agrégation. Des personnalités venues d’horizons très divers, par exemple Michel Butor, Maurice Lemaître, Georges Charbonnier ou Frank Popper, ont aujourd’hui leur doctorat d’État, un fresquiste comme José Balmès ou un homme de théâtre comme Jacques Clancy enseignent leur art au titre de maîtres de conférences associés, et c’est dans cette dynamique que la présente soutenance inscrit son plein sens. Votre thèse, cher Iannis Xenakis, est une thèse, une vraie thèse, au sens le plus consacré du terme - presque son sens médiéval. Elle l’est d’abord en ceci, qu’évitant l’écueil d’autres soutenances "sur dossier", elle n’ équivaut nullement à une collection, un peu au hasard, de travaux disparates; au contraire, elle se prévaut d’une unité profonde, puisque les textes présentés, avec les partitions qui les accompagnent, convergent autour d’un même thème fondamental, sur lequel a largement porté le débat: l’alliage (non pas «l’alliance») entre arts et sciences. Ne s’agirait-il pas plutôt d’une certaine conception de l’art? Et d’une certaine conception de la science? J’avoue que je le crois. Mais c’est par cela précisément, qu’en un second sens, votre thèse est vraiment une thèse : non pas une recherche érudite sur quelque point de détail, comme c’est très souvent le cas, mais une théorie originale, par conséquent discutable, et même contestable - à nouveau comme au Moyen-Age, au temps où les "docteurs" s’affrontaient autour de Duns Scot ou de Guillaume d’Occam. Et c’est à quoi je voudrais m’attacher, brièvement pour ne pas retarder l’issue de cette séance déjà longue. Je voudrais, en prenant à témoin un seul des ouvrages versés au dossier, Musiques formelles, faire apparaître l’en-deçà, les hypothèses latentes qui sous-tendent la thèse, qui fondent sa cohérence et aussi son caractère d’option philosophique: une option toute personnelle, valable de par cette cohérence même mais, me semble-t-il, je me trompe peut-être, Xenakis, valable parmi d’autres qui seraient différentes, qui d’aventure pourraient lui être contradictoires, et ni plus ni moins valable que ces autres options. Je vais porter à ce qui sous-tend, à ce qui me paraît sous-tendre, à cet ensemble peut-être inaperçu ou inavoué d’hypothèses souterraines sur lesquelles reposerait l’édifice de la thèse, un certain nombre d’objections. Je précise à l’avance que je ne les assume pas toutes (du moins sous leur forme extrême). Il me semble cependant que «jouer l’avocat du diable", afm de susciter vos réactions, vos répliques, dans l’espoir de vous amener à clarifier le point de vue qui vous est propre, fait partie des règles du jeu. Et puis, se porter 3.lnSI aux extremes, pour mIeux apprecler ou et Jusqu ou votre point de vue vous est propre, cela m’aidera à dissiper le malaise que j’ai la faiblesse de ressentir devant toute théorie esthétique qui se présenterait comme universellement valable, à évacuer les relents que je soupçonnerais d’un "impérialisme culturel". A ce propos, je dirai ceci: de la façon dont j’ai interprété votre ouvrage, Musiques formelles, j’ai trouvé en lui un intérêt majeur, comparable à celui d’une axiomatique au sens de Hilbert ou de Peano, et qui serait de fonder la musique sur un niveau de généralités tel qu’un certain nombre de musiques (non pas toutes) en seraient déductibles, en tant qu’ensembles partiels, par adjonction de contraintes restrictives qui les détermineraient. Ces contraintes, qui s’appellent par exemple tonalités, ou modes, ou séries, viendraient particulariser l’univers sonore, pour découper en lui le champ de musiques possibles. Je dis bien l’univers, non pas unplurivers. Et je veux dire que ce livre (mais peut-être la pensée de Xenakis a-t-elle évolué depuis) me paraît raisonner comme si on pouvait espérer une théorie totalisante, recouvrant sans lacune l’ensemble des domaines pensables comme si le vieux rêve d’Einstein d’une théorie unifiant la relativité généralisée, la mécanique quantIque et la thermodynamique était seulement en attente, comme si le théorème de Godel pouvait être surmonté et non pas seulement contourné par des artifices de procédure. Je crois déceler chez Xenakis un choix en faveur du "système de l’univers»; et en cela sa thèse me paraît d’autant plus fondamentale qu’elle est vraiment une thèse, en accord avec les conditions de production d’un nombre important d’œuvres musicales, une thèse qui cependant laisse subsister à côté d’elle d’autres thèses, susceptibles de fonder d’autres œuvres musicales. Quittant ce niveau de généralités, je vais passer à des questions plus précises, en tentant de faire appar~ître que la théorie de Xenakis comporte à tout le mOInS deux postulats et plusieurs options, les unes méthodologiques, les autres nettement subjectives. Le premier postulat serait celui-ci. Dans Musiques formelles, l’histoire et la culture me semblent rejetées en arrière-plan, au profit d’une recherche des invariants 10gico-mathématiques. A cet égard, peut-être la théorie musicale de Xenakis trouverait-elle des équivalents dans certaines conceptions de la peinture sérielle, ou systématique, ou programmée, par exemple dans un inventaire et une combinatoire des effets optiques selon Vasarely. Or je me demande si l’hypothèse d’une distribution stochastique, avec absolue équivalence des probabilités dans les points de départ et dans les voies de passage, peut être réellement soutenue. Au contraire, l’anatomie et l’embryologie des vertébrés supérieurs pourraient indiquer que le code des déterminations génétiques ne s’est pas tellement "enrichi" (au sens où "s’enrichit" une banque d’informations) au cours de leur évolution; que le développement du système nerveux, particulièrement des centres corticaux, s’est manifesté plutôt par une prolifération des neurones et par une relative labilité de leurs connexions synaptiques. En d’autres termes, des mammifères les plus archaïques à l’homme, le stock des régulations pré-établies n’aurait guère augmenté, il aurait même fortement décru si on le rapporte à la multiplication des réseaux de connexions possibles. Il en résulterait une sorte d’aléatoire dans le frayage des voies, pourtant un aléatoire orienté: non pas du tout qu’il manque de déterminations, mais parce qu’il est régi par des déterminations autres que génétiques, c’est-à-dire parce que de plus en plus la part de l’apprentissage s’étend aux dépens de la pure et simple maturation. Or, cet apprentissage est conditionné par un contexte qu’on pourrait qualifier, au sens le plus général, d’historique, à partir du milieu intra-utérin jusqu’à la vie familiale et scolaire, jusqu’à l’environnement socio-culturel. Vous vous demandez où je veux en venir? A ceci. Il faut tenir compte, me semble-t-il, de l’interférence entre des éléments pré-établis, qui comprendraient des invariants formalisables (ce sont ceux que formalise Xenakis), et d’autre part un faisceau d’accidents culturels ou historiques qui seraient inéliminables de l’homme individuel. Cette interférence-là constitue, par rapport au stock génétique, une série de "hasards", au sens le plus banal, celui de Cournot, l’entrecroisement de chaînes causales indépendantes. Et ce qui fait de cette série de hasards une chaîne continue, orientée, au lieu d’une dispersion erratique, c’est qu’elle est arrimée en permanence à un contexte relativement constant, d’ordre socio-culturel. En ces conditions, je me demande s’il est possible de maintenir (comme Xenakis le fait à maintes reprises dans son livre) la fiction de l’amnésie: est-il opportun de considérer l’homme comme "amnésique", de le situer dans l’instant de ses perceptions présentes en faisant abstraction de son passé individuel? Ou, au contraire, ne faut-il pas adme!tre qu’une répartition purement stochastique est presque exclue du domaine musical, puisqu’il n’y aurait pas d’équivalence des probabilités ni dans les points de départ, ni dans les voies de passage? Autrement dit, est-il possible d’isoler les invariants logiço-mathématiques, comme si l’expérience musicale n’intégrait des déterminations d’ordre différent, d’ordre socio-culturel, historique? Ma question est-elle claire, Xenakis? \annis XENAKIS. - Peut-être, je ne sais pas. Bernard TEYSSÈDRE. - Je résume mon argument: Musiques formelles me paraît présupposer une équivalence des probabilités à la fois quant aux points de départ et quant aux voies de passage, alors que la phylogenèse, l’embryologie et la physiologie humaine établissent qu’une telle équivalence est en principe exclue, s’il est vrai qu’il existe UJl nombre restreint de prédéterminations génétiques, et qu’au contraire les voies de frayage nerveux se constituent en grande partie au cours de l’expérience individuelle dans son contexte social. On serait obligé, pour accepter la théorie de Xenakis, de supposer l’homme "amnésique". C’est-à-dire l’homme qui n’a pas d’histoire depuis l’instant où l’ovule a été fécondé. Iannis XENAKIS. Je ne sais pas si j’ai dit cela. Je ne le crois pas. Bernard TEYSSÈDRE. - Mais l’hypothèse de l’amnésie intervient fréquemment. Par exemple, page 35 : "Nous supposerons que les points M définis plus haut puissent apparaître sans aucune nécessité autre que celle d’obéir à une loi aléatoire sans mémoire." Page 185 : "Nous commencerons par nous considérer brusquement amnésiques de manière à pouvoir remonter aux sources des opérations mentales de la composition et pour dégager des principes généraux valables pour toutes les musIques." Iannis XENAKIS. - Ah oui! Mais c’est une hypothèse provisoire de travail, de réflexion et ce n’est pas) dans le sens biologique que je parle d’amnésie. Je parle! d’amnésie dans un effort mental de détacher les faits profonds, de distinguer ce qui est de ce qui appartient au courant et au conditionnement que l’on reçoit, surtout du fait socio-culturel. Bernard TEYSSÈDRE. - Ce que je veux dire, c’est que le conditionnement socio-culturel ne serait pas seulement un surcroît, quelque chose qui viendrait se surajouter à des probabilités considérées comme au départ équiprobables, mais serait au contraire constitutif des réseaux de liaison eux-mêmes. De sorte qu’on ne partirait jamais d’une sorte de "no man’s land» absolu, d’une "table rase", mais au contraire d’un terrain hautement stratifié. Iannis XENAKIS. Oui, mais ce "hautement stratifié» n’est pas du tout prouvé. Justement c’est une des recherches fondamentales dans tous les domaines. Par exemple, en biologie et en génétique, on sait très peu de choses sur l’hérédité des structures mentales, plus ou moins élaborées et complexes. C’est un fait que l’hérédité aboutit à ce que nous ne soyons pas des plantes ou des minéraux. Nous sommes des hommes qui se ressemblent d’ailleurs, avec des yeux, des organes. Mais là où on ne sait pas du tout ce qui se passe, c’est dans la constitution de notre cerveau. Car on ne sait pas quelle est la part de l’hérédité dans ce qu’on pourrait appeler les catégories. On ne sait pas comment le principe de la causalité naît, pourquoi il naît. Ce principe, d’ailleurs, est équivalent au raisonnement référentiel. Ensuite, le sens qu’on donne au temps, au flux temporel, qui repose sur l’expérience mais aussi sur les constructions dures de notre cerveau qui sont faites on ne sait pas quand: est-ce après la naissance, ou est-ce bien avant, c’est-à-dire il y a des millions ou des milliards d’années. On ne peut pas en décider. Par contre, ce que l’on peut dire éventuellement, c’est que, effectivement, il y a une partie non déterminée dans notre mental. Pourquoi peut-on dire ça? Eh bien, parce qu’il y a tellement de cultures, tellement d’approches de la réalité, tellement de réactions devant un univers objectif (s’il existe)! Cette pluralité fait que sur des plans supérieurs, il y a une plus grande liberté. Alors, dans ce cas ne pourrait-on pas aussi changer les choses qui paraissent immuables pour l’instant, et qui semblent universelles? Considérons le flux du temps tel qu’on le conçoit et sa structure d’ordre qui est sousjacente à ce que nous connaissons, et qui fait partie de notre vie quotidienne, de celle des physiciens atomiques, ou de celle .du musicien. Ce concept du flux du temps est-il absolu ou serait-il modifiable? POlH" arriver à définir ces choses-là et aussi à en retirer toutes les scories d’une éducation ou d’une tradition socio-culturelle, il est nécessaire de supposer, de faire de temps en temps des hypothèses un peu extrêmes, comme l’amnésie par exemple. C’est simplement un outil de travail. Bernard TEYSSÈDRE. -J’ai été très frappé, Xenakis, quand vous avez fait référence à la musique grecque comme au terreau nourricier à partir duquel s’est développée notre tradition occidentale. Je me demande si ce n’est pas aussi le terreau à partir duquel se fonde la théorie de Xenakis sur la musique universelle. Et ce qu’a dit Olivier Messiaen sur les possibilités de structures radicalement différentes de celles-là ne me contredit sans doute pas. Je rappelle à nouveau mon argument : étant donné que la codification génétique est extrêmement insuffisante par rapport à la multiplicité des connexions synaptiques entre neurones, les voies de passage se fraient en très grande partie au cours du développement individuel, développement lui-même en très grande partie conditionné par le contexte socio-culturel. Pourquoi l’accord de tierce, qui était perçu comme "dissonant» au Moyen-Âge, est-il devenu au temps de Bach ou de Rameau à ce point "consonant" qu’une tierce majeure ou mineure définit "l’accord parfait» comme majeur ou mineur? l’en conclus que le postulat d’une équivalence initiale entre les probables n’est peut-être pas admissible, et que le fait de rejeter l’acculturation ou l’histoire de la musique au second plan pour s’attacher seulement aux invariants logico-mathématiques, pourrait être une hypothèse hasardée. Je ne suis pas sûr qu’on puisse éliminer le culturel du musical, même pas au niveau de la perception sonore. Iannis XENAKIS. - Eh bien, si on monte sur un escabeau et que l’on regarde l’histoire de cet escabeau, on voit qu’il y a beaucoup de choses qui se sont passées. Pour voir plus clair, il faudrait justement faire cette élimination des acquis socio-culturels. Si on la fait, on peut trouver éventuellement des choses qui sont indépendantes de ces acquis et permanentes, c’est-à-dire des invariants aussi bien dans le temps que dans l’espace. Et c’est pour cela que tout à coup on trouve, dans le cas des échelles ~u! changent un peu partout dans le monde, une personnalIte qui semble universelle, c’est l’intervalle de quarte. Comme par hasard, c’est par elle que commence la théorie musicale d’Aristoxène, il parle de la quarte-juste. Or il ne la définit pas mathématiquement car lui ne rai~onne pas en pythagoricien, quoiqu’il connaissait les mathématiques et le pythagorisme. Mais il considère la quarte-juste comme l’intervalle de base et c’est par elle qu’il commence son traité. Or, la quarte-juste, on la rencontre dans toutes les cultures du monde entier. Ceci correspond à une sorte d’invariant musical, à un plan supérieur. Mais il est nécessaire, pour s’en rendre compte, de faire table rase de tous les épiphénomènes .• de toutes les colorations qu’a telle ou telle culture musIcale lorsqu’on dit que c’est un mode mineur et triste ou que c’est un mode majeur. Cet exemple est très ~rivi~, évidemment. De même sur un autre plan, lorsqu on dIt que la musique est mélodique, doit être mélodiqu~, doit être polyphonique, et qu’on ne peut pas conceVOIr une autre musique en dehors de ce contexte. Ceci, c’est encore un parti pris qui nous vient de conceptions socioculturelles. Pour se dégager de tout ça, c’est-à-dire pour établir une pensée fondamentale, qu’est-ce qu’on doit faire? Les mathématiciens et les logiciens au XIXe siècle, en débarrassant les mathématiques du verbe et en créant la symbolique, ont montré le chemin et c’est bien dans ce sens-là que j’ai essayé de voir plus clair. Bernard TEYSSÈDRE. C’est ce que je disais au début, c’est bien une sorte d’axiomatique qui nous est proposée là. Excusez-moi, je suis obligé d’aller très vite parce qu’il nous reste peu de temps et j’ai encore beaucoup de questions à vous poser. Je laisse ce débat pour passer à un autre point. A un autre de vos postulats, selon moi. A celui qu’on pourrait appeler le principe "de dispersion composée". En lisant Musiques formelles, on peut penser que vous admettez une antériorité, tout au moins méthodologique, des éléments, disons des sons, ou des grains ou nuages de grains, ou des classes logiques, ou encore des cases d’organigramme, etc. Et cette antériorité, je me demande (c’est une question que je vous pose) dans quelle mesure elle est compatible avec les données les plus simples de la perception, avec celles qui ont fondé, depuis près d’un siècle, la Gestalttheorie. Généralement, dans votre livre, cela se traduit ainsi: un certain nombre de constituants du son ayant été isolés et considérés comme éléments de base, ces éléments fondamentaux sont mis en rapport avec l’audition musicale selon un modèle qui appliquerait la loi de Fechner, la sensation variant comme le logarithme de l’excitation. Comment cela est-il compatible avec les réflexions déjà anciennes de Von Ehrenfels sur l’expérience très banale de la transposition? Dans la mesure où une phrase musicale a été entendue dans la tonalité d’ut majeur, puis entendue, que sais-je, en fa dièze mineur, il se peut à la limite qu’aucun des éléments physiques ne soit commun aux deux ensembles, et cependant tous deux sont perçus comme "la même phrase musicale", seulement transposée en deux tons différents. Comment expliquer qu’ils soient entendus, sinon comme identiques, du moins comme analogues? Ne pourrait-on, au lieu de prendre pour points de départ les éléments (grains, ou nuages de grains, ou classes logiques, etc.), considérer que ce qui est premier, ce sont les relations et non pas les termes situés aux deux extrémités de ces relations? Ne serait-ce pas ce que suggère, dans votre propre musique, l’usage des glissandi? Votre usage des glissandi équivaudrait presqu’au contraire de ce qu’expose votre théorie: il ne prendrait plus pour points de départ les éléments, mais leur relation, leur intervalle, et par rapport à cet intervalle on pourrait dire que les grains de sons ne joueraient plus qu’un rôle secondaire de jalons entre les deux points extrêmes d’un glissando qui serait, lui, la seule réalité perçue? Iannis XENAKIS. - Oui, c’est une bonne question, celle-là, parce qu’il est vrai que dans le domaine de la musique les termes: composition, compositeur, indiquent celui qui met ensemble des choses, donc des choses préexistantes, définies d’une certaine façon. Bernard TEYSSÈDRE. Cela présuppose une primauté de l’analyse par rapport à la synthèse. Du moins, la manière dont des «éléments» sont d’abord présentés paraît contradictoire avec l’allure plutôt structurale du mode de présentation lui-même. Iannis XENAKIS. - Ça ne présuppose pas ça, nécessairement, mais ça présuppose autre chose, ça présuppose un univers matériel dans lequel le compositeur vient mettre des relations, des structures, des constructions, des architectures. Mais ceci est vrai jusqu’à un certain point, parce qu’il y a toute une partie qui est absolument inconnue, de la musique et aussi de la perception. Une grande partie de Musiques formelles est basée effectivement sur cette organisation d’objets sonores donnés, mais une autre partie (c’est le dernier chapitre) part d’une sorte de perception globale. Si je dis perception globale, c’est dans le sens où il n’y a pas les molécules, les objets que le compositeur vient mettre ensemble pour constituer des organismes plus ou moins évolués, mais un magma d’états ponctuels possibles (les valeurs discrètes de la pression), dans lequel il est capable de fabriquer des formes suivant des critères qu’il doit s’inventer lui-même. Le dernier chapitre est un autre point de départ tout à fait à l’opposé de ce que tu viens de dire. Si je me suis acharné à parler ici de choses discrètes, c’est que, au niveau des échantillons de la pression, il s’agit bien de choses discrètes. C’est parce que, fmalement, c’est également l’approche la plus facile et immédiate à faire et la plus riche, en ce qui concerne l’histoire de la musique, aussi bien du passé que d’aujourd’hui. On est plus familier, on est plus à l’aise avec des choses discrètes qu’avec des choses continues, aussi bien sur le plan de la perception que sur celui du jugement, mais cela n’exclut absolument pas les choses non défmies, les choses non définissables. Bernard TEYSSÈDRE. - Ce n’est pas du tout de cet indéfini que je parlais. Je disais qu’une mélodie est transposable sans qu’aucun de ses éléments physiques demeure identique, et cependant elle est reconnue comme "la même mélodie». Le point de vue qui part d’une forme sonore en tant que totalité signifiante est tout autre que celui qui part de grains de sons, puis de nuages de grains, avant d’établir une combinatoire entre ces nuages. Prétendre le contraire, ce serait confondre la perception avec ses stimuli sensoriels. Iannis XENAKIS. - Bien, je ne vois pas ... Bernard TEYSSÈDRE. - Qu’aucun des stimuli sensoriels ne soit le même, et que cependant ce soit la même perception ? Iannis XENAKIS. - Oui, mais attention, tu parles là de niveaux différents. Quand tu dis que les notes ne sont plus les mêmes, d’accord. Dans une mélodie il n’y a pas seulement que les notes, il y a les relations entre les notes, c’est-à-dire les intervalles, etc. Bernard TEYSSÈDRE. -Je disais précisément cela: qu’à un point de vue en quelque sorte "moléculaire", on peut opposer un point de vue "relationnel", selon lequel les fameuses molécules ne seraient que les points extrêmes des relations. Iannis XENAKIS. - Naturellement! Ce dont je traite dans ce livre-là, c’est des relations de niveaux, au pluriel, de niveaux supérieurs, au-dessus des éléments! Bernard TEYSSÈDRE. Soit. Passons à une autre question. Elle est un peu en rapport avec ce qu’on disait, tout à l’heure, sur la notion de style. Je me demande s’il n’y aurait pas, dans ton travail de théoricien et de compositeur, un privilège de la saturation, c’est-à-dire une sorte d’option, de goût subjectif, pour des espaces sonores denses, pleins, et non pas raréfiés. Il est frappant de lire, page 74, cette définition du principe ergodique : "L’effet capricieux d’une opération dépendant du hasard se trouve régularisé de plus en plus par une répétition suffisante de cette opération." Or, il se peut justement que le choix même du principe ergodique soit de caractère stylistique. Il se peut que ce soit une option subjective, un goût personnel qui pousse Xenakis à choisir des espaces sonores saturés, plutôt que raréfiés, à choisir plutôt des grands nombres que des individus rares, ceux dont, dirait Leibniz, la définition impliquerait analyse infinie. C’est sans doute par un principe d’économie (mais ce principe d’économie est aussi une revendication de pouvoir) que prévaut la volonté de maîtriser la saturation des espaces sonores. On peut très bien concevoir l’option inverse, qui serait le goût pour l’individu rare, pour le hasard non contrôlable. Bref, le choix de John Cage ou de Marietan, au pôle opposé du choix de Xenakis. Iannis XENAKIS. - Je crois que tu mélanges un peu plusieurs choses à la fois. Excuse-moi de te dire ça. Pour en revenir à l’ergodisme, la définition, là, est une définition des mathématiques, ce n’est pas moi qui l’ai dit. Bernard TYESSÈDRE. - Je le sais bien. Iannis XENAKIS. - Je l’ai prise dans le livre du mathématicien français très important qui a écrit sur les chaînes markoviennes dans les années quarante, Maurice Fréchet. Il a cette définition des processus ergodiques, de l’ergodicité. Mais ceci est tout à fait limité dans cette partie de mon travail. D’un autre côté, quand on parle de hasard, il faut faire bien attention. Bernard TEYSSÈDRE. - Il me semble plutôt que le choix répété en faveur des grands nombres, le simple fait de prendre pour principe le calcul des probabilités, implique une préférence pour une plénitude à maîtriser, par opposition à l’événement rare qui, lui, ne serait pas maîtrisable. Iannis XENAKIS. - Mais j’ai fait tout un travail, avec Achorripsis et d’autres compositions, sur l’événement rare et la raréfaction. C’est une question de densité, et la densité est une notion qui est traitée dans Musiques formelles, en long et en large. Bernard TEYSSÈDRE. - Est-ce que, par exemple, ta musique ne privilégie pas le fortissimo et le pianissimo, plutôt que d’impalpables nuances, les vastes masses sonores, plutôt que le vide ou le silence, la charge émotive intense, plutôt que le dénuement recueilli? Iannis XENAKIS. - Je n’ai pas fait beaucoup de musique raréfiée, c’est sûr. Bernard TEYSSÈDRE. - Non, pas beaucoup de musique raréfiée. Ni de musique qui s’attacherait à capter l’individuel, au sens d’Olivier Messiaen captant un chant d’oiseau, au sens de John Cage captant la rencontre fortuite de sept postes de radio qui transmettent des émissions différentes. Il y a place, dans ces musiques-là, pour les rencontres rares, au lieu qu’il me semble trouver, dans ce livre-ci, une recherche insistante (même quand ce serait pour s’en écarter ensuite) de rencontres hautement probables. Iannis XENAKIS. - C’est bien plus complexe. D’abord, le hautement probable n’a de sens qu’en rapport avec des distributions de probabilités connues a priori et concernant certains ensembles d’événements bien définis. La notion du fortuit, de l’imprévisible, est fondamentale pour la probabilité. Le hautement probable ne contredit pas le hautement fortuit et il ne cesse d’être fortuit et ne devient prévisible que stochastiquement, à la longue et statistiquement. Par conséquent, à chaque occurrence d’un événement pris dans un ensemble donné, tout se passe comme si nous nous trouvions devant un phénomène dû au hasard, inattendu, donc rare au sens strict de la périodicité. Par contre, faire marcher plusieurs postes à la fois, dès le moment où les postes sont ouverts, nous nous trouvons devant un fait accompli donc déterminé et vide de hasard. Dans ce cas, le fortuit naît au niveau des rencontres inattendues de chaînes d’événements propres à chacun des postes, qui, elles, sont plus ou moins fortement déterminées. Donc, tout se passe comme si nous étions devant un phénomène globalement prévisible, mais localement fortuit, ce qui constituerait la défmition du hautement probable. Les deux approches sont, en quelque sorte, équivalentes. La différence appréciable est que, dans mon cas, j’essaie de créer les chaînes d’événements mais aussi les événements, d’une manière plus fidèle et homogène avec l’idée de base qui est l’imprévisibilité, le fortuit. D’autre part, la notion de rareté est relative à un ensemble d’états possibles, et de leurs récurrences. Beaucoup ou peu de récurrences d’un événement donné, dans le temps, se traduisent par la notion de densité (de rareté). Or, le deuxième chapitre de Musiques formelles commence par les événements rares et leur traitement. Bernard TEYSSÈDRE. - Il en traite pour mieux les éliminer ... Iannis XENAKIS. Non, pas du tout... Bernard TEYSSÈDRE. - ... ou pour les reléguer au second plan ... Iannis XENAKIS. - Non, car du point de vue technique, c’est avec la formule de Poisson que je commence, qui justement traite des événements rares que j’intègre dans mes compositions. Ceci dit, les événements rares ne sont rares qu’en fonction de l’échelle temporelle. Et il arrive que les états rares puissent être jugés comme étant denses, fréquents. En effet, les événements d’une musique peuvent paraître agrégés d’une manière raréfiée, si l’unité temporelle choisie est suffisamment petite. Tandis que si l’unité temporelle est choisie suffisamment grande, les mêmes événements, disposés de la même façon, avec les mêmes rencontres fortuites paraissent plus rapprochés, plus denses. Donc le phénomène, qualitativement, reste le même. C’est comme lorsque l’on approche un tube Geiger d’une source radioactive ou qu’on l’en éloigne: c’est la même distribution de probabilités, indépendante de la distance (de l’unité temporelle). Le phénomène est le même. C’est la même loi. Bernard TEYSSÈDRE. - Oui, mais pardonne-moi si je reviens à ce qu’a dit tout à l’heure Michel Serres, quand il pos?it en problème : comment établir l’ordre à partir du bruit? Ce problème, c’est celui que tu assumes, il me ~mble, mais on peut tout aussi bien concevoir, je le repète, un type différent de musicien, celui de John Cage ou de Marietan, qui ne se proposerait pas d’établir l’ordre ~ partir du bruit, qui au contraire s’efforcerait de capter 1 ~vénement rare, l’individuel en tant que tel. Ne pas le faIre surgir du désordre, au contraire l’accepter comme un individu dont l’analyse exhaustive serait impossible, parce qu’infinie. Iannis XENAKIS. C’est ce que j’essaie de dire. Bernard TEYSSÈDRE. - Mais comment est-ce que ce Xenakis-ci, non pas un autre, a pu en sortir? Nous retrouvons le problème du style personnel dont nous parlions ... Iannis XENAKIS. - Considère des événements rares dans un ensemble d’autres événements, et applique le rapport temporel pour obtenir la raréfaction. Il est certain que tu trouveras des événements rares isolés. Mais si tu conçois l’ensemble des événements, globalement, les événements rares se dessineront sur un fond, au milieu d’un environnement qui, lui, est beaucoup plus complexe. Mettre un silence, autour, à gauche et à droite d’un événement, c’est une question tout à fait possible mais qui, logiquement, n’est pas fondamentale. C’est une question d’échelle, qui correspond au degré d’attention que tu portes sur cet événement, donc du degré de relief que tu désires lui donner et qui est une décision d’ordre esthétique. Mais dans la nature ou dans la pensée de l’homme, il n’y a rien qui soit unique dans l’univers et dans le temps. C’est-à-dire que, au contraire, la périodicité (au sens large) de l’événement, sa récurrence, en soi ou avec son environnement, est tout à fait naturelle, et même impensable autrement. Bernard TEYSSÈDRE. - Certes, mais dans le choix même des éléments que tu te donnes au départ, il est intervenu déjà une certaine restriction du champ global, c’est-à-dire que la matrice choisie ne comporte plus la totalité des possibles. Ne serait-ce que parce qu’il est convenu d’emblée qu’il y aura, par exemple, un orchestre. Ces choix préalables ne permettent plus d’incorporer parmi les sons possibles, que sais-je, la toux d’un auditeur enrhumé, ni le bruit d’une mouche qui volerait dans la salle; et alors, intégrer à la musique la mouche ou la toux, comme le ferait John Cage, cela relèverait d’un autre principe musical, différent du tien. Iannis XENAKIS. - Bien, je vais te dire pourquoi. Très simplement parce que, dans notre vie de tous les jours, nous avons tous ces bruits fortuits. Ils sont pleins de banalité et ils m’ennuient. Ça ne m’intéresse pas de reproduire des banalités. Bernard TEYSSÈDRE. -J’en suis bien d’accord; seulement, ce que je veux faire ressortir, c’est qu’à ton insu il s’agit d’un choix esthétique ... Olivier REVAULT D’ALLONNES. - Je crois quand même qu’il y a dans Musiques formelles, page 142, à propos de la stratégie musicale et de Duel un élément de réponse qui va dans le sens de ce que disait Teyssèdre. Lorsque tu donnes, page 141, les six événements, il peut se passer un nuage de grains, des tenues de cordes, des percussions, etc., et le silence est quand même le sixième et dernier événement. Je n’en tire aucune conclusion pour le moment. Or, à la page 142, tu ne parles que des cinq événements, des cinq premiers événements proprement sonores, le silence est parti, il n’apparaît qu’en bas de la page. Pourquoi, alors, ce silence l’as-tu, si j’ose dire, passé sous silence pendant plus d’une page, pour le réinjecter dans le deuxième tableau? Tu dis: "L’introduction de la tactique du silence 6 modifie la matrice précédente." Et maintenant je me reporte en bas de la page 141, alors que les différents événements peuvent avoir des mentions qui sont bien, très bien, etc., le silence, lui, est toujours "passable". En somme, tu n’aimes pas le silence. Iannis XENAKIS. - Le silence est banal. Bernard TEYSSÈDRE. -Je ne veux pas allonger démesurément ce débat. Il est clair que Revault d’Allonnes ne conteste en rien la fécondité des perspectives ouvertes par Xenakis. Et, certes, moi non plus. Ce que, pour ma part, je redoutais un peu, c’est que ces perspectives fécondes n’apparaissent, vues du dehors, comme "impérialistes". Je veux dire qu’une théorie musicale très personnelle, sous-tendant une recherche musicale très personnelle, ne saurait rendre caduques d’autres théories musicales, différentes si ce n’est opposées. De la même façon que la programmation de tableaux sériels pour ordinateurs ne rend pas désuète la peinture la plus accidentelle, une encre "informelle» de Michaux, une "action painting» de Pollock, et que la peinture-peinture au sens de Support/Surface n’a pas rejeté dans les limbes une non-peinture au sens dadaïste. J’en viendrai presque à dire que si, comme Heidegger le prétend, toute métaphysique est une expérience autour d’une idée, alors ce faisceau doctrinal sur lequel nous avons discuté constitue davantage une métaphysique de la musique qu’une science musicale. Car il implique, en deçà de sa scientificité, une certaine visée vers la science. Le corpus présenté a beau être aussi scientifique qu’on le veut, la visée sous-jacente au corpus n’est pas du même ordre que le corpus lui-même, et c’est peut-être là qu’intervient ce coefficient personnel, cette question subjective de style dont nous avons débattu. Il m’apparaît qu’à maintes reprises interviennent des critères de choix, de choix qui sous-tendent la thèse, et que par suite, cette thèse même a pour fondement secret un certain nombre d’hypothèses principielles. Je considérerais volontiers l’ouvrage de Xenakis à la façon du traité d’Alberti, comme une sorte de "construction légitime", légitime à condition de ne pas devenir normative et de laisser subsister hors d’elle, contre elle, d’autres modes de constructions aussi légitimes qu’elle. Bien sûr, avant de pouvoir dire cela, il aurait fallu développer d’autres thèmes, je ne l’ai pas fait, le temps m’a manqué. En quelques mots, j’aurais aimé discuter des problèmes posés par le rapport du en-temps et du hors-temps, parce qu’il me paraît mettre en jeu une certaine philosophie du temps, une conception qui oscillerait entre l’idée aristotélicienne du temps comme nombre du mouvement, d’un côté, et d’autre côté la notion, différente sans doute, du temps comme quatrième dimension d’un événement. Il ne s’agit nullement de reprendre la vieille antinomie bergsonienne : temps versus durée. Ce qui est en cause, c’est un temps comme dévidement ordonné, linéaire, un temps qui appartient au même système de pensée que la monade de Leibniz (déploiement d’une fonction mathématique) ou que le concept de Hegel (la sphère toujours-déjà-Ià de l’en-soi se déployant poursoi en cycle de la méthode). Ce temps-là, c’est celui de l’Occident, celui de notre mère la Grèce, où il a puisé l’une et l’autre de ses deux faces: la logique et la rhétorique. Selon une telle conception, la musique est pensable, est pensée comme «discours». Pour transposer une phrase de Barbaud, qui affirmait être en quête de "musiques non-beethovéniennes", je dirais que Xenakis, en accord avec la tradition grecque puis occidentale, nous propose une axiomatique de la musique beethovénienne généralisée. Serait-elle la seule possible? J’évoquais Barbaud, ne pourrait-on évoquer aussi le Gagaku japonais, le tout-déjà-ensemble, l’irradiation du même autour du même - au lieu de la chaîne logique-rhétorique qu’est le "discours» musical d’Occident, ce passage du même à l’autre-du-même? Et dès lors que, revenant à mon point de départ, on se maintiendrait à l’intérieur du «discours» d’Occident, comment concilier ces deux points extrêmes de son oscillation pendulaire, tantôt le temps comme "quatrième dimension de l’événement", tantôt le temps comme "nombre du mouvement"? Dans ce second cas, le mouvement serait le premier, et le temps, loin d’être l’une des coordonnées dans la série des événements, ne serait guère que ce qui la dénombre? Iannis XENAKIS. - On a parlé de cela, je crois, tout à l’heure, c’est la métrique. Il yale flux temporel, qui est une donnée immédiate, et il y a la métrique qui est une construction que l’homme fait sur le temps. Et on ne peut pas s’en échapper, qu’on soit musicien ou qu’on soit physicien, on passe par le même pont. Je te répondrai à une autre chose: je n’exclus pas du tout d’autres approches de la musique, et je ne veux pas du tout que tu me taxes d’impérialiste pour ce que j’ai fait. Bernard TEYSSÈDRE. - Non, non, Xenakis n’a rien d’un impérialiste. Il se peut même que, derrière son outillage hautement scientifique, quand Xenakis travaille à sa musique, Xenakis reste profondément humaniste: il laisse transparaître un style personnel, un Moi d’artiste. Ses choix sont bien fondés, puisque sa musique est d’excellente musique, mais sur quoi sont-ils fondés, si ce n’est, outre la science, sur une idiosyncrasie, sur les choix d’une personnalité puissante et riche en initiatives? Un sous-Xenakis qui appliquerait la science de Xenakis, sans avoir la personnalité de Xenakis, ne produirait jamais en musique que du sous-Xenakis. Ces choix si bien fondés ne laissent-ils pas subsister une part d’irrationnel, de non-fondé? Pour prendre un exemple, qui illustre bien l’écart entre deux personnalités, toutes deux de grande envergure, lorsque Barbaud recourt à l’ordinateur, l’œuvre musicale, pour lui, c’est la programmation même. On peut entendre une quantité de versions sonores issues du même programme, sans qu’aucune de ces versions soit préférable à aucune autre, puisque l’œuvre se situe en deçà de ses variantes audibles. Au lieu qu’à l’oreille de Xenakis, me semble-t-il, toutes les versions ne seront pas réputees équivalentes, il s’en trouvera un certain nombre de «préférables», et les partitions retiendront celles dont l’effet sonore aura été "préféré» ; n’est-ce pas (les Polytopes exceptés) souvent le cas? Iannis XENAKIS. - Mais c’est mon privilège, c’est mon devoir de préférer une chose à une autre. Bernard TEYSSÈDRE. Sans doute, puisque ainsi en décide ta personnalité. Ta maxime pourtant n’a rien d’une évidence : Barbaud, quitte à me répéter, ne préfère pas, il compose sa programmation et n’importe quelle audition est équivalente aux autres. Xenakis, lui, c’est son droit, a ses préférences. Iannis XENAKIS. - Mais c’est naturel, c’est tout à fait normal. Bernard TEYSSÈDRE. - Ce sera ton mot de la fin. Le jury va se retirer pour délibérer. (Après une brève délibération, le jury revient et son président annonce que le titre de docteur ès-lettres et sciences humaines est décerné à Iannis Xenakis avec la mention "Très honorable".) Dans la musique de Xenakis, la mathématique joue un rôle essentiel en tant que catalyseur philosophique, comme outil de mise en forme des édifices sonores ou visuels. Xenakis s’est également servi de l’ordinateur pour composer certaines de ses partitions. Ce musicien qui est aussi architecte, cet homme de science qui est aussi philosophe, a choisi pour thème de son doctorat ès lettres et sciences les cc alliages» entre les arts et les sciences. C’est la soutenance de ce doctorat, qui eut lieu à la Sorbonne, en 1976, que nous publions, avec les questions et les interventions des membres du jury. Nous ne nous étonnerons pas que celle d’Olivier Messiaen traite de la composition musicale, celle de Michel Ragon de l’architecture, celie de Michel Serres de la mathématique et des sciences. Sommé de s’expliquer sur sa musique, Xenakis démontre que sa culture est à la fois philosophique et scientifique, ce qui est, on le sait, exceptionnel. Ainsi connaîtra-t-on mieux celui à propos duquel Antoine Goléa a écrit: cc Xenakis, c’est peut-être la figure la plus attachante, la plus pathétique et aussi la plus exaspérante de la musique du xx& siècle." Citons aussi Claude Lévi-Strauss qui, interrogé sur Xenakis par la Quinzaine Littéraire, le 1 er août 1978, répondait: cc Je suis très sensible à ses écrits; je trouve que c’est savant, intelligent et subtil."

Google'i masintõlge ARTS/SCIENCES ALLOYS ARTS/SCIENCES ALLOYS Iannis XENAKIS Olivier MESSIAEN Michel RAGON Olivier REVAULT Of ALLONNES Michel SERRES Bernard TEYSSÈDRE Arts/sciences. Alloys, by Iannis XENAKIS With the collaboration of Olivier MESSIAEN, Michel RAGON, Olivier REVAULT Of ALLONNES, Michel SERRES, Bernard TEYSSÈDRE Printed in Belgium by Casterman, S.a., Turned, August 1979. N° Impr. 4126. N° Edict. 6112. Registration of copyright 4 " quarter 1979; D. 197910053/105. ISBN 2-203-23170-X Any reproduction, even partial, of this work is prohibited. A copy or reproduction by some process that it is, photography, microfilm, magnetic tape, disc or aut: E, constitutes a counterfeit liable to the sorrows envisaged by the law of It March 1957 on the protection of the royalties. CONTENTS PRELIMINARY WARNING 7 TALK OF IANNIS XENAKIS 9 _ underlain Philosophie It _ Concrétions 19 DIALOGUE WITH _ OLIVIER REVAULT Of ALLONNES 27 _ OLIVIER MESSIAEN 47 _ MICHEL RAGON 73 _ MICHEL SERRES 91 _ BERNARD TEYSSÈDRE 111 APPENDIX 139 New proposals on the microstructure of the sounds 139 _ Bibliographie 151 WARNING This text is the recording of the defence of thesis carried out by Iannis Xenakis on May 18, 1976 in the Sorbonne. The jury was chaired by Bernard Teyssèdre, professor of esthetics in Paris 1 - Sorbonne and was composed of Olivier Messiaen, professor with the national Academy of music; Michel Ragon, professor at the École Nationale Supérieure of decorative arts; Olivier Revault d' Allonnes, professor in Paris 1 - Sorbonne (director of research and rapporteur); Michel SERRES, professor in Paris 1 - Sorbonne. PRELIMINARY TALK OF IANNIS XENAKIS underlain Philosophy [1] L The universes of the classical musics, contemporary, pop, folk, traditional, of avant-garde, etc, seem to form units in oneself, sometimes closed, sometimes interpenetrating. They have incredible, rich diversities of new creations, but also of fossilizations, ruins, waste, all that in formations and continuous transformations, the such clouds, if differentiated and so transitory. That is explained by the proposal that the music is a cultural phenomenon, therefore subordinated to one moment of the history. However, one can distinguish from the parts which are more invariant than others and which thus form materials of consecutive hardness and consistency at the various times of civilizations, materials which are driven in space, created, launched, involved, by the currents of the ideas, running up the ones against the others, influencing oneself, destroying oneself, fertilizing oneself mutually. But of which gasoline these materials are they made? This gasoline, it is the intelligence of the man, to some extent solidified. The intelligence which searches, questions, infère, reveals, erects scaffolding on all the levels. The music and arts in general necessarily seem to be a solidification, matérialisation of this intelligence. Naturally, this intelligence, though humanly universal, is diversified by the individual, the talent which distancie the individual of the others. The talent is thus a kind of qualification, gradation of the strength and richness of the intelligence. Because it is, at the bottom, the result, the billion expression exchanges, reactions, energy transformations of the cells of the brain and the body. One could, with the image of astrophysics, statement which the intelligence is the form that take the acts tiny of the cells in their condensations and their movements, the such suns, the planets, the galaxies, the galaxy clusters, resulting from or being reduced to cold interstellar dust. This image, however, is reversed (at least on a plan), because this cold dust while condensing, becomes hot contrary to the intelligence which is a cold result of the exchanges between the hot cells of the brain and the body, a “cold fire”. Thus the colors, the sounds, the relief, are condensations in our system direction-brain. This system, an aspect brutal and perfectly surface, external, is perceived and seized at the conscious level. The periodic vibrations of the electromagnetic medium of the light or the air inaccessible to the conscience but (within limits, certainly) followed well and are magnificiently converted by our directions and our brain whose directions are the prolongation. Conversions, in addition, take place on several levels, of that of immediate perception to that of the comparison, the appreciation, the judgement. How, why all that it occurs? It is a mystery, elaborate as in the animals since million and million years. In the same way, let us take an example which seems to be obvious, that of the scales in music. There was, in Occident at least, of increasingly strong condensations: the perfect fourth and its tétracordes, and perhaps the perfect fifth, initially, whose origins are perfectly Inconnues, then the octave, then the construction of the “systems” by juxtapositions of tétracordes which generated the scales of the Antiquity, whose diatomque scale of the white keys of the piano is a survival; then the chromatic scale with equal temperament and finally continuity as a whole “heights of the sound”. It comes out from this example that the music is strong condensing, perhaps stronger than other arts. It is. why I give a table comparatif2 between certain conquests carried out by the music and some reallsations by mathematics, such as the history teaches them to us. This table shows one of the ways that the music took as of, the origin (as of Antiquity), and that it kept with a remarkable fidehte through the millenia with a strong acceleration at the xxe century what proves that far from being a fashion, this faculty of condensation towards the abstract is a major nature which undoubtedly belongs to him more with it that with other arts. Consequently, It seems that a new type of musician is necessary, that of the artist-originator of new abstract and free forms, tightening towards complications then worms of generalizations on several levels of the sound organization. For example, a form, a construction, an organization built on chains of Markov or a complex of functions of interliées probabilities, can be transported simultaneously on several levels of microphone, méso- and musical macrocompositions. One can extend this remark besides to the visual field, for example, in a spectacle made with laser beams and electronic flashes like that of Polytope of Cluny [2]. Nothing would prevent us to envisage from now on new relation between arts and sciences, in particular between arts and mathematics in which arts “would consciously pose” problems for which mathematics would have and will have to forge new theories. The artist-originator must have knowledge and inventiveness in fields as varied as mathematics, logic, physics, chemistry, biology, the genetics, paleontology (for the evolution of the forms), the social sciences, the history, all in all a kind of universality, but founded, guided, directed by and towards the forms and architectures. It is time besides to found a new science of “general morphology” which will treat forms and architectures, of these various disciplines, their aspects invariants and laws of their transformations, which sometimes lasted of the million years. The background of this new science will have to be made real condensations of the intelligence, i.e. approach abstracted, disengaged from anecdotic from our directions and our practices. For example, the formal evolution of the vertebrae of the dinosauriens is one of the paleontological documents to pour with the files of the science of the forms. Let us plunge now in the fundamental system on which art rests. Art takes part of the mechanism inférentiel which constitutes the boards on which all the theories of sciences mathematical, physical, and those of the alive beings are driven. Indeed, plays of the reducible proportions to sets of numbers and the metric ones in architecture, the literature, the music, painting, the theatre, the dance, etc; the plays of continuity, proximity, in time or out-time, of topological gasoline, are done all on the ground of the inference, in a strict sense of logic. Concurrently to this ground, and in reciprocal activity, exists the experimental mode which denies or confirms the theories created by sciences, including by mathematics. Because mathematics as showed as since the nonEuclidean geometries and the theorems like those of Gôdel, it is only experimental, but according to a term much longer as that of other sciences. It is the experiment which makes and demolishes the theories, without pity, without consideration for them. However, arts also are governed in a richer and complex way still, by the experimental mode. Indeed, there is not, it will be never undoubtedly, of objective criteria of truth absolute and eternal of validity or truth of a work of art, just like no scientific “truth” is final. But, in addition to these two modes, the inférentiel and the experimental one, art lives in a third, that of the immediate revelation, which is neither inférentielle nor experimental. The revelation of beautiful is made from the start, directly, with the ignoramus because of art, as the expert. It is what makes the force of art and, seems it, its superiority on sciences because, alive in two dimensions of the inférentiel and experimental, art has of it the third, most mysterious of all, that which does that the objets d'art escape any science from esthetics, while allowing the caresses of the inférentiel and the experimental one. But on another side, art can live only by the mode of the revelation. It needs, the history of the art of all times, of all civilizations shows it to us, it is necessary for him, it has an imperative need for organization (including that of the chance), therefore of inference, and its confirmation, therefore of its experimental truth. To make more obvious this trinity of the modes of art, let us imagine that in a remote future the capacity of action of the artist increases as ever before in the history (it is the way which follows humanity in the creation and the dissipation of the increasing quantities of energy). Indeed, there is no reason so that art did not leave, the science following the example of, in the vastness of cosmos, and so that it cannot modify, a such cosmic landscape designer, pace of the galaxies. This can appear Utopia, and indeed it is Utopia, but temporarily, in the vastness of time. On the other hand, which is not Utopia, which is possible today, it is to launch luminous cobwebs above the cities and the campaigns, made laser beams of color, a such giant polytope: to use the clouds like screens of reflexion, to use the artificial satellites as reflective mirrors so that these cobwebs go up in space and surround the ground of their moving geometrical phantasmagorias; to bind the ground to the moon by filaments of light; or, to create in all the night skies of the ground, at will, of the aurorae boreales artificial ordered in their movements, their forms and their colors, by electromagnetic fields of the upper atmosphere excited by lasers. As for the music, the technology of the loudspeakers still embryonic, is underdeveloped, to launch the sound in space and to receive it sky, of where the thunder lives. But the sound eii hedgehopping, in the cities and the campaigns, is already possible thanks to the national networks of anti-aircraft alarms by loudspeakers. They would be enough to refine them [3] • If the economy of the countries were not tortured by the strategic needs and the armament, i.e. the day when the armies of the nations will be dissolved in simple nonrepressive police forces, then, financially, art will be able to fly over planet and to spring in cosmos. Because, technologically, these things are feasible today. In these types of artistic achievements, planetary or cosmic, it is obvious that it is essential that the artist, consequently art, that is to say at the same time rational (inférentiel), technician (experimental) and talented (revealing); three essential modes, coordinated, which would avoid fatal failures, being given dimensions of these projects and very great risks of errors. This larger complexity of the fundamental system of the three modes which govern the art, conduit with the conclusion which it is richer and vaster and which it must inevitably take the head in the creation of condensations and concretions of the intelligence. Therefore, to be used as universal guide with other sciences. Concretions My work, since already more than twenty years, made an effort, unconsciously initially, then in an increasingly conscious way, to fill this philosophical space of the intelligence which is concreted, by stones of color which are musical works, architectural, visual and my writings, with the manner of a craftsman mosaïste. These stones, at the beginning very insulated, were gathered by beaches of relationships, of affinities, but also of oppositions, forming figures of local coherences gradually, then vaster fields challenging itself by the questions and the answers given. Mathematics plays an essential part as a philosophical catalyst there, like tool of working of the sound or visual buildings, but also like springboard of car-release. Here I will trace only the fundamental questions and, in opposite, the answers given by works which I produced, without however entering in detail and the mazes of their development. Moreover, a many questions are dependent between them and present intersections belonging to the same philosophical field. For example: causality - determinism continuity, indeterminism (chance) - existentiality - determinism, etc This is why also, a work (answer) with it only can give answers to a beam of questions. It is a little as if one were in the presence of sound-questions rich in harmonics, which one would regard such or such harmonic as fundamental, according to the search of the moment. Moreover, I will name only few works of the file of the thesis. Questions - > Réponses existentialité - > ST/lO-l, 080262temps, out-time - > Nomos gamma causality - > ST/IO-l, 080262, Nomos gamma, Tourette (frontages) repetition or not of modules inference - > Nomos gamma, ST/IO-l, 080262connexity - > Impressed (tree structures), Metastasis (forms of glissandi), House Philips (hull, forms of right-hand sides) compactness - > Metastasis, Philips House, Nomos gamma pure indeterminism - > ST/IO-l, 080262, stochastic system impure libredeterminism - > Strategy (theory of plays), Syrmos (chains of Markov) pure determinism - > Nomos gamma (groups) identity (similarity, equivalence) - > All works. The visual spectacles of Polytopes take again the questions and the answers posed and data in music, this time with the lasers, the flashes electronic and spaces. What is remarkable to note, it is that one finds these questions on all the levels of the composition sound or visual, i.e. since the plan of the great form (macro-composition) until that of the synthesis of the sounds by computer and digital-analogue conversion (microphone-composition), but also at the intermediate levels. “The ways top or bottom do only one”. I thus said that all work that I made since so many years is a kind of mosaic of hierarchical coherences. At the top of the hierarchy I will place philosophy. Philosophy, in which direction? Within the meaning of the dash which pushes us towards the truth, the revelation, research, the search in all, by the interrogation, criticism systematic, rough, not only in specialized fields, but in all the possible fields. This led to the whole of the knowledge, but which should be active, within the meaning of making. It is not a passive knowledge but a knowledge which is translated in the acts of creation, I repeat: in all the fields. According to the methods which I will examine immediately, one can separate, divide this table of coherence, this mosaic, this table, in three categories, or three chapters, the first being the method which makes it possible to arrive to this active knowledge by the creation, and who imply the inference, i.e. reason, logic, etc, by the theoretical demonstration. According to this criterion, there are aspects of the activity and knowledge which are partially inférentiels, entirely inférentiels and experimental, and others which are still unknown. In the field of partially the inférentiels, I will place arts. Arts take part in the inference. One builds, consequently, one can connect in a reasoned way and show up to a certain point. On the other hand, the social sciences and sciences of nature, physics, mathematics, logic, are entirely inférentielles and also experimental. It is necessary to build a theory and to check this theory by the experiment. In the field of arts, one can build, partially, by inference, but the experimentation is not immediate because there yale aesthetic problem and it is no possible demonstration of the aesthetic value of the things. And I will leave the door open on all the methods which are not yet known or are not discovered by the advance of the thought of the man. Like corollary with this discrimination of arts, one can say that arts are freer, since arts take part as well in the inférentielle operation with the experimentation, the experiment; and they is perhaps ambitious to say it, but arts could possibly guide the other sectors of the thought of the man, i.e., in my opinion, I plac' will erai arts at the head activities of the man, so that they bathe all his activities, in the scientific field as in the everyday life. I go down in scale while saying that after, there is a category of questions which one can put, which was eluded to some extent by the history, and that one can discover again and be posed, i.e. a kind of fragmentation of the directions in a creative direction of philosophy. Among these categories, there are the existentiality (ontology, reality), causality, the inference even, the adjacency or the connexity, compactness, temporal or space ubiquity, catches like consequences of new possible mental structures. There are also the determinism and its extreme pole the indeterminism, etc I take again to some extent some of the categories of the thought which were stated more or less consciously and systematically since Aristote, very important, and which is left a little on side or recoveries, possibly by experimental psychology (Jean Piaget) and by certain branches of modern mathematics. These categories of thought-questions receive, can receive, and it is what I endeavoured to do in music, of the families of solutions. I begin again myself, I hope that I am clear. I want to say that the thought of the man tried to answer these questions, and they are multiple, by giving provisional answers with certain families of solutions, especially in particular with regard to the determinism. Here, I want to make a digression: causality, for example, is one of the lived forms of the life, referring to this fundamental question of the determinism which, it, can be regarded as a differential moderate aspect of the indeterminism. One can even affirm, which I did not state earlier, that the order or the disorder belongs to the indeterminism. The connexity or continuity also is other facets of this Bi-pole determinism-indéterminisme. I take again the continuation of what I said, that the solutions and the procedures being able to give of the answers to the categories of fundamental questions are, in a very diagrammatic way of course, defined by some sub-chapters, some paragraphs. For example, the probabilistic thought with, on the one hand, its extreme that I call the stochastic free one or without memory, with, on the other hand, the Markovian chains which accept a certain causality, a certain elementary determinism, which is upstream of this one. But, in the middle of the probabilistic thought and the indeterminism, there is what one can call the symmetry or the periodicity which is another way of defining, to speak about this thought; symmetry or the periodicity, i.e. the cyclic return of events, procedures, etc, can be concretized with the bottom of the scale determinism-indéterminisme by structures of groups. Between the two, there is what one could call a hybrid or mixed phase of which one of the interesting forms is the game theory. Low, with the lower stages of the mosaic, in response to these topics, these ways of thinking which were posed also by other sciences, including by the music, one finds works particular which are reflexions on these questions and of the attempts at solution. I do not want to make the enumeration of it, because they would be too tiresome. But for example, I can say that the topic of stochastic free is treated in a part like Achorripsis, which was formulated thereafter in a program machine, program which represents a free stochastic system. This program made it possible to make works like ST/lO, ST/48 for orchestra, but also to enter the field of the microstructure of the sounds, in the synthesis of the sounds by computer. Moreover this same program has been used for a few years, both in the United States and in Europe (Sweden, France, etc), in other studios that CEMAMu [4] like by other type-setters. In the field of stochastic Markovian, there are parts like Analogiques, Syrmos for cords. In that of the plays: Strategy, Linaia-Agon, etc In the systems symmetrical, periodic, there are Akrata, Nomos Alpha, Nomos Gamma, Persephassa, works made up on structures of groups. I do nothing but state principal works. In the report/ratio that I gave to the jury, and the beginning of my talk, there are a little more details on the other visual achievements, like Polytopes or on what I could make in architecture. Continuously this way, one arrives at the bottom of the staircase where is space pressure-time of the sound. One could say similar things in the field of the visual one, with the result that the questions put on the level of the microstructures, i.e., on the level of the higher element of the macrostructures can be seen, solved or be treated with procedures and thoughts equivalent at the paramount level which is the pressure according to time as for the ear, or the electromagnetic actions as for the eye in the visible spectrum. One can summarize by saying that all that milked with the macrostructures and the fundamental problems most general, finds oneself on all the intermediate levels of the structures, médio-structures, méso-structures, until the bottom of the scale which merges with the quantum action, would say I, on these two directions, vision, hearing. I gave you, I believe, an outline very general of the discussion thread of all this work, without speaking about work itself. Bernard TEYSSÈDRE. I thank you much, Iannis Xenakis. It is certain that your talk was in short and that it can appear complex because he is supersaturated. I hope that the discussion which will take place now will clarify the presentation which you made. It is, I repeat it, precise for those which know your work already well. It is likely to appear a little fuzzy with others, precisely because too many matters are exposed at the same time. I believe that Revault d' Allonnes, which is the rapporteur of your thesis, could intervene immediately. DIALOGUE WITH OLIVIER REV AULT D' ALLONNES Olivier REVAULT Of ALLONNES. Indeed, by an administrative bizarrery, I am being the director of research. Actually, the director of research of Iannis Xenakis is Iannis Xenakis itself. He managed very well. I am being also, at the moment of defence, the rapporteur, and in front of such a considerable mass of research and works, the rapporteur feels rather small; what I believe capacity being, it is a spectator among others, and a spectator fascinated by the unit of work of Xenakis. There is untitre, chosen by Xenakis, to present its fundamental theoretical works, and in support of these theoretical works, a certain number of documents which are the musical partitions of some of works that it quoted at the moment even, more of the sketches, drawings, diagrams, statements of architecture, etc This title general defines not only the file, but also the whole of the artistic work of Xenakis, namely: Arts/sciences. Alloys. Xenakis presents some of its alloys, and has just said to us in a very dense way in which direction one could foresee alloys in question. “Art”, this term returns to Xenakis to the artifex, the creator. This man who adopts a certain attitude in front of the world, a certain vision of the world, feels the permanent obsession of something that there is to make. Since nearly twenty years, I never saw it differently than in prey with a kind of creative demon. Science, it is something which, at his place, accompanies this creative demon indissolubly. Xenakis wants to do something, but does not want to do anything. It wants to always compose a determined work, work which on a certain level, the properly aesthetic level, communicates itself: you go to the concert, you listen of Xenakis; but work, on another level, can be communicated in another way, by a language analytical, rational, which simultaneously analyzes this work and justifies it. In books as those which it presents today, namely: Music. Structure 1 and, perhaps especially, formal Musiques 2, one sees that works are analyzed, peeled and that at the same time they are justified, legitimated. Xenakis says why he wanted to do this and how he did it, but it why is at least as important as it how. The “alloys” of the remainder, these alloys which do not go without problem, for me at least, are works architectural, musical, polytopic, but they include as theoretical work as we have under the eyes. I would like to leave with more qualified than me the care to reflect on art and science, to put to Xenakis questions concerning alloys. The first question will be this one: Xenakis proposes in its theoretical work to fight against the current separation of arts and sciences, to create a kind of circulation of the thought, a mutual fecundation of the scientific thought and artistic thought. With this intention, Xenakis is based at the same time on a vision of last and current achievements. The vision of the past, we see it reappearing in turn in each one of its works, and even in the talk which it has just done: the happiest periods of mutual fecundation of arts and sciences were periods such as for example Greek Antiquity, the Italian Rebirth, the traditional Age, where artists and scientists were unaware of themselves less than nowadays, from where a completely legitimate nostalgia of circulation enters art and science. However, currently, the services which arts and sciences can render extremely unequally seem distributed and extremely unequally possible me. I have the impression that sciences can bring to arts, and particularly with the music, infinitely more services, more lightings, more fecundation, that the music it cannot make for scientific knowledge. For example, the application to the music of stochastic calculation, or the application of the theory of the screens that Xenakis refined to apply it to the problem of the scale heights, ~ont likely to renew the music and even, as It is known as in the first part of Music. Structure, to renew musicology; but of a purely mathematical point of vu~, these instruments, I it crams, do not present any particular interest, any fruitfulness, any innovation, any difficulty of surmounting, and consequently, any new discovery to make. In the same way, the use of the computers posed certainly problems, but of the completely traditional problems of programming and data processing; in short, of the problems which are controlled currently rather perfectly. It is not in the same way obviously in the other direction. One could say today that, and most of the work of Xenakis showed, the musical thought does not have yet, did not use all the resources of mathematics enough. When Xenakis realized that for a mathematician, the scales heights constitute an ordered unit, an abelian, this definition, commonplace scale as say the mathematicians, put so to speak the chip to him at the ear. Hold, there are ordered sets, therefore there are perhaps sets which are not ordered. It Y an abelian scale, isn't there has a scale which would not be it? One includes/understands very well how the musical thought is fertilized here by mathematics, but being given, I would say, the rather elementary mathematical level of these concepts, the interest is null for mathematics. If one can dream, consequently, of exchange between arts and sciences, it would have to be noted that nowadays, the terms of trade seem extremely unequal. From where my question: how can one hope, nowadays, to collect the interest of the scientists, and to try to perceive these new mental structures to which Xenakis even did itself allusion to the moment? The use of science by art benefits more this one than with that one. This imbalance is an evil? If so, can one fight it? My second question will be simply derived from the first. The proposal of circulation and alloy is only one proposal, i.e. it is not a question of a situation currently carried out; it is a wish; the alloy has something of utopian, i.e. of creator. It, so to speak, by the fruitfulness of the work of Xenakis, but can it is tested claim to be spread in the company, can it claim to become if not the single law, at least one of the moments of these reports/ratios of art and science? Does the proposal of alloy suppose that the science on its side, the art of his, have something which would be a direction which would be clean for them, a kind of truth in oneself? Or wouldn't the art on its side, the science of his, be carrying another thing only of themselves? Would they resulting, from one some share be located besides elsewhere than in the axiomatic ones to which we like to refer them? In other words, does there exist between arts and sciences a purely technical union, or is there finally a social division (and if so, which) which would hide behind this technical division? I do not think besides particularly here of a difference in class between the intellectuals and the handbooks. Which, of the remainder, would be the ones and which the others? It acts much more than one division, of a separation between the functions. Science is turned towards the action known as rational, on nature and the man; it is said in reality. Art is turned towards the creation of imaginary objects: by diverting them partially does one and the other, while turning over them one towards the other, Xenakis propose something which is immediately realizable, or something which, to be carried out, presupposes of the transformations, in particular social, much deeper? All in all, sciences gave to the men a certain control on the things. Xenakis proposes now, to some extent, to control this control, ét that it serf with the men instead of being useful itself of the men. Then, is it conceivable that this inversion of the terms, which circulates through all the work of Xenakis, is limited finally to the only fields of science and arts? The third question will return towards esthetics. The opinion is, alas, very widespread, that Xenakis would make compose its music by computers. This opinion is only one of the aspects of the scientistic ideology and technicist spread in all the company. When one looks at there more closely, one realizes that that obviously does not have a direction. In formal Musics [3], one finds mê~e an admirable formula: “In this field, it is that the computers can return ce~ns ~e~ices”. That wants to say that one can not pouvOlr profit from these “services”. It was the case of Metastasis, created in 1954 and where I still re-examine Xenakis calculating all “with the hand”, as he said, for a patience, he would be necessary to say an incredible obstinacy, carrying out in several months of keen work what a computer can do to the maximum in a few hours. Good, one has then there for months of work with the pencil: if it can, one will thus take a machine which will f~ra. chose.s much more quickly and much better. But it ~ also has, more ~d, in the musical production of Xenakis of made works they also “with the hand”, of works which one can call artisanal works in which it was not useful of computer for reasons that Xenakis will be able to perhaps give us. I think by e~emple ~ Nuits” ~~ 1967, and much more recently has Evryalt, of 1 summer 1973. These works, I have still tried for two years to analyze their partition. However, on the plan, I was going to say beauty say aesthetic success, it is false, according to my g~ût at least, that of these less works soien~ .les. If I do not manage to analyze the partition of Evryali, obviously, I must accuse initially. ~es clean limiting. I in reddened not, because it is a particularly difficult partition. But enfm, also should be accused another thing? Not, certainly, a supplement of heart, but would not be there in this partition the bursting of what one can temporarily call a style xénakien, style about which Xenakis speaks very little, style that fmalement it could force the computers to respect, style that the layman finds obviously only in musical listening. Xenakis hardly speaks about it in its theoretical work. By decency? By modesty? I do not know. Sometimes an allusion, a small sentence which emerges, on the beauty of such or such device, such or such result, on the nonsense or the lowness of what Xenakis calls the hollows some share “of the musical intelligence”. This style xénakien, you speak very little. You can answer that you in leashes the care your historiographers. Ds thank you for your confidence; they undoubtedly thank you less tone silence! If you could help them a little bit, they would be even more grateful to you. This is to leave the limits of this thesis, Arts/sciences. Alloys, to grant to the techniques only one role second and controlled compared to intuitions or to aesthetic intentions which, certainly, go towards alloys or even arose entirely with alloys, but are not reduced to these alloys. [puudub prantsuskeelses originaalis] All in all, what governs all that, what, as one said formerly, “inspires” the whole of these steps? We overflow perhaps here some limit, but finally, it would be a little paradoxical to have opposite oneself Xenakis which, because of the situation, is somewhat held to answer (ri~es), and not to ask him what occurs, or what is protected behind the fortress from sciences, behind the frontage of the computers. How is it only done that Xenakis is told and tells us all this marvellous power of the knowledge in which I believe, up to a certain point, and on another side, which it quite simply composes brightest of its works with a paper and a pencil? If you want, where resides in this field what would have radically and completely changed, since Bach or Mozart for example? Iannis XENAKIS. The last question, in my opinion very important, would be that I was taxed sometimes with calculating, of mathematician, dryness, and this in opposition to musician. It is now out-of-date. It seems that today I do not meet any more opposition on this subject. Even the musicians regard me as a musician! It is a digression which I want to make. For the first time, I am as held in a “sizeable” institution as the University of Paris and even in the Sorbonne. Up to now, I was always a kind of marginal and I regularize a little bit a new situation which is created (since I teach now in Paris-I), with this defence of thesis. It is true that almost all my writings refer to questions which can be demonstrable, which can be expressed in a language that I hope for everyone understands, that it is here, in Japan, in America, at the Eskimos even… On the other hand, the part which is not exprimable, it can be known as only by art itself, the music itself or by the architectural expression or the visual expression and on top, I do not know if there are many possible speeches, apart from the speech “I like that” or “I do not like that”, or “it is beautiful”, or “it is ugly”, or “it is disgusting” or “it is formidable”, “interesting”, etc It is true that one falls down in the problem of esthetics or psychology, but that to say on the fittings, sonorities, etc, apart from the technical language or analogical or proportional or architectural. What can one say? There is no language which could determine these questions apart from the questions of construction, structure, therefore of proportions, rules, laws. But I agree with you: there is another thing in the music, in any music, even in more “ugly” besides, but this something, one cannot distinguish it, one cannot distinguish it, one cannot speak about it. In fact features are not describable for the moment. It is the artistic object which must say them. For this reason it is a kind of cut down aspect… Not? Olivier REVAULT Of ALLONNES. It is skilful… Iannis XENAKIS. How: it is skilful? Olivier REVAULT Of ALLONNES. You say to me that you cannot answer and yet you do yourself of the bringings together between structures of works of last and a certain number of tastes of the time… Iannis XENAKIS. I can do it… I can speak about structures, it is what I have just said, but I cannot speak about the value about a thing and questions which are not immediately perceptible through the structure. For example, you said that I made calculations either with computers, or with the hand, but with all that, there is nevertheless a style which emerges, independently of calculations. I suppose that the style wants to say something which is apart from calculations, which is métacalcul. Olivier REV A UL T Of ALLONNES. Or infracalcul, I do not know… Iannis XENAKIS. Or will infra, moije would say méta or behind, which returns to same! I could even generalize here, I would dare that, even any choice presupposes an arbitrary choice. Because, there is no construction made by the man, who is not in a certain arbitrary point. The acceptance of laws which would govern the construction of a thing is already an arbitrary act. In mathematics, one meets that, when modern mathematics as well as ancient mathematics poses axioms arbitrarily then, only in the one second time, employs formalizing logic and builds all their building. The whole of the axioms posed at the base of the pyramid, or its top, its top since, for me, the base is reversed, i.e. the point is on ground and bases in the sky, since one has there more place and that it can grow… Alors, the axiomatic one is a choice, a choice which is arbitrary. Is it it completely? Yes, but by initially informing theoretical need certain added to conditionings of the lived and historical experiment. Olivier REVAULT Of ALLONNES. Nevertheless there is a parallel which you make yourself. I believe that it is in the last edition of Music. Structure and also at the end of your report/ratio of thesis, between a history of the mathematical thought on the one hand and a history of the musical forms on the other hand; and practically a third element, a parallel third which of course is not completely parallel, which is the history of the musical taste. Just as the running away is a musical structure of the time. running away and that your musical works are typically works of the xxe century. Of course, there is the Xenakis individual, but it seems to to me that the arbitrary one is not total. Iannis XENAKIS. I fear there that one does not move away a little bit from the question which you had put a few moments ago, because what you say is a question of musicology and forms or better still, a science of the forms and revolutions dans.le historical time. If the running away were, at a given time, something of fundamental, it was not it before its discovery, before it is not essential! It is it much less today. It is sure. Therefore, it is a problem initially of technique because, what is it that the running away? It is well a whole of rules, and procedures, in order to build a musical building and this whole of rules was born; consequently, there was not front! And there does not exist in the broad sense any more, from the creation point of view, now. This shows well its character, at least partially arbitrary. Olivier REVAULT Of ALLONNES. The question did not relate to the running away, it related to your work. Iannis XENAKIS. If I try to explain me in books, articles or conferences on such or such technique employed, it is because it is of that that I can speak easily. Or if I make also teaching, it is to lead people to return in these questions, but I do not say all, even if I feel it or perceive, because I do not know how to say it. Then I show to hear and results, possibly. Here, to summarize my answer a little. I did not answer the other question perhaps… Olivier RE VAULT Of ALLONNES. Yes, perhaps… One would like to ask you: there would why be a certain shift of arts compared to sciences, and up to what point there would not be rather a unilateral contribution, directed sciences towards arts, rather than the reverse? It is a question, and second is: if this alloy of sciences and arts, that you propose, is something of utopian, therefore of creator, that does not imply another thing that a simple transformation in the field or of arts and sciences, i.e. a transformation, say, almost civilization. Iannis XENAKIS. It is perfect, because I noted about the same thing! I take again the first question of Olivier Revault d' Allonnes who says that there is a delay… with single direction rather and not in the good direction… why the roads are they narrowed with time? I believe that it is a question of civilization. Antiquity had also created this circulation between arts and sciences. One sees Polyclète which, with its gun, tried to apply the geometry to the sculpture, circulation which was done in the same way in architecture, painting and the music; texts of Aristoxène and others which came thereafter. The Rebirth rediscovered, I think that it was that its fundamental point, the unicity of the man. The man is something of single, of one. There are not several men, it yen has only one and this man covers all the possibilities with the thought and the activity and consequently, the interpenetration of sciences and arts. In addition, arts also have, at certain crucial moments of the history, fact of the contributions in the field of the scientific thought, in a direct or indirect way. It is what I endeavoured to show in the table that I added to the final chapter of Music. Structure, by doing it parallel between the development of the musical thought and the especially mathematical thought. Because, which is curious and which jumps to the eyes immediately, it is that the music is much closer to mathematics than other arts. Why? I will not show it now. I can nevertheless say that the eye is fastest, that it is much more immediate, in direct catch with reality, while the ear, being less nimble and more in withdrawal, requires thought to reflect, consequently to be more abstract, and thus to create bases which are more abstract and which are thus much closer to mathematics. And it is in this order of idea that I tried to show how this species of “gimlet” between the music, the musical theory, a part thus of the music, and the theory of mathematics are rolled up one on the other, though sometimes they walk on in parallel, without being rolled up whole. Today, we are late in the artistic field. However, already before leaving the polytechnic school of Athens, when I studied the procedures of composition, I was struck by the poverty of the “combinative” thought of the music, including that of the serial music which I studied later. I here will pay homage to Olivier Messiaen: it is the only one which had a thought completely opened in this field and which posed bases with its work, inter alia, on the “inversions”. I would say more: by its artistic side. But this is another facet, which does not belong to those of the structures. Also, to take another example, the modes with transposition limited of Olivier Messiaen were a starter of work on the scales, though without generalization, but which starter was to enable me to lead to the hard principles mental structures of the musicians, in their manner of thinking and to act. And when, there is already more than fifteen years, I fell on problems from scales, resulting from my problems in musical composition, by working them, I was led to solve them using done everything mathematics almost, which gave the theory of the screens. It is not the reverse, I almost never made the reverse. But beside what the mathematics of today offers to the artist, it is really nothing, it is tiny. What is it thus necessary to make? Eh well, for my opinion, one needs a concrete transformation of the formation, as well of the musician, the artist of the scientist. This formation should not be done too late. It must be done already at the primary school, if not the nursery school. And it is all the problem of education, the system of education, training of the man, small of the man, until its adolescence, and further same, until its death, which is in question. However, this separation of the arts person or the artist of with the scientist is done very early and one teaches it as of the feeding-bottle. With the result that it Y has a delay since there is no communication of the whole, but this absence of circulation, contacts, is heavily felt. It is for that besides that I agreed to teach, to make conferences and seminars. As, now, we are in the train, in CEMAMu, to make an effort by using the most advanced technology data processing, to make an effort in the direction of pedagogy to try to revolutionize the approach of the music and to put together problems of composition and musical thought with problems of the mathematical thought as the child inevitably in addition learns as of the age from five, six or seven years, and of the problems also of space, of the vision. I think that it is the node of the problem, it is the node of the survival of the man, in a harmonious place, with his contradictions naturally, but a place much richer than in this moment. Therefore, it is a residue of the recent history, this differentiation. Because, the artist deviated gradually, made a kind of selection. He went in only one of the aspects of art: the inexpressible aspect precisely. Bernard TEYSSÈDRE. I believe that Michel Serres would like to speak on certain points. Michel SERRES. I want to support the thesis in the place of Xenakis and to answer just a minute Olivier Revault d' Allonnes. This one poses the problem of the exchanges between sciences and arts. It raises the question to know if the exchange is unbalanced, i.e. if you borrowed techniques from certain areas of mathematics, and conversely if it is true that mathematics did not borrow anything from the music. The opposite thesis would say that the music is in advance, that the music of Xenakis is in advance; I do not pose the problem from the point of view of the exchange, which is a commercial point of view, nor from the point of view of the scientific techniques, and here why: another thing is of saying that one borrows techniques from a given locality of science, another thing is of saying that by its music, Xenakis presents a general idea of the scientific thought, because the scientific world changed, and that nobody realized some and perhaps even not scientists. What changed, it is not that one made theory of the groups in the place of the combinative algebra or that one made information theory in the place of the transforms of Fourier. That, it is not important. What is important, it is that something, that one calls the “paradigm”, completely changed. A new world, a new scientific world, emerged as of second half of the xxe century. However, the first to have said it, it is not a philosopher, it is not a scientist, it is not a epistemologist, it is Xenakis. It is Xenakis which first showed it what was a signal which was detached on the bottom, it is Xenakis which first used it not such or such mathematical technique, but most important and most significant of them. To say that there is delay has direction only if one poses the problem on local exchanges. If one questions the global vision one finds it at Xenakis. This general vision of science and this paradigm, all the traditional speeches mask them to us. Not, Xenakis, you are in advance and thank you for this advance. (Laughter and cheers…) Olivier REV AULT Of ALLONNES. Michel Serres has just shown that the spirit of many scientists can be opened by steps of the type of that of Xenakis. I never doubted it. My initial question related to what the music for example can bring not to the scientists, but with science. It is there that I saw a shift, not any “delay”, remainder, because compared to which ideal calendar could we define it? Remain finally the problem of the social conditions of 1' “alloy” in question. Iannis XENAKIS. Good, thank you infinitely, that answers the first question (laughter). I cannot better say. The second question is the “social transformation”. Naturally it is a question… But I do not know which social transformation it would act in this case, because among all the social transformations which occurred in the whole world, this problem remained absent. One did not answer this problem, and I think that I will return so that I said a few moments ago: the social transformation which would approach the coexistence and interpenetration of these aspects of the human life, very early in the education of the man, would be the desired social transformation. Olivier REV AUL TD' ALLONNES. … while passing by pedagogy, but it is nevertheless clear, seems to to me it, that that is not innocently or by chance that pedagogy, such as one practises it in our company, manufactures on a side, as you said, of the arts persons, and another side of the scientists. Iannis XENAKIS. Yes, it is certain that if one only manufactures scientists, it is probably because, initially, it Y has a question of time, of specialization. But I believe that one can exceed this stage. Myself I made at least two trades at the same time, and I think that it is very possible to even make three of them and not only surfaces some, but by pushing these trades towards research. It is as a question of control… I would not say a fight of class because it is much more moderate as that, and more complex, but it goes without saying that it is a question of ramification of the organization of the man which produces spiritual penguins, and mental. That it is sure. In fact diseases, in my opinion, can be exceeded. How to lead to this radical change of pedagogy, but also of the social environment. That it is a reform which the policy should undertake instead of posing only of the questions of wages and technical things, improvements, social progress. It is especially from this point of view that is the achievement of the totality of the man. I think that art has its role to play by putting all ens emble; et la science d’ailleurs aussi. Ce qu’a dit Michel Serres est vrai : à la base de l’art, mais de la science également, il y a toute cette vision qu’on appellerait la vision du xxe siècle, qui est une totalité et qui est l’espoir, qui devrait être l’espoir de l’humanité. Bernard TEYSSÈDRE. Eh bien, peut-être devons-nous donner la parole à Olivier Messiaen, puisque nous avons parcouru le cycle des premières questions et des premières réponses. DIALOGUE WITH OLIVIER MESSIAEN Olivier MESSIAEN. On cannot criticize a hero! I thus only will put some questions. But I would not like, dear friend, that these questions are indiscreet. If they displease to you, you will say it. They are not true questions, rather requests for explanation, to enable you to specify your thought. Instead of making a talk shining like my fellow-members, I simply will ask you my questions the ones after the others. It will be easier for you, me, everyone. First question: on page 13 of your thesis, and also in several places of the book Music. Structure, you seem to bring back the history and especially the beginnings of the music to the birth of the ranges, the modes, the scales. Before these scales, and recognize it to you yourself, one used only tétracordes. But don't you think that with the whole beginning of humanity, there was initially the cry? The cry of joy, the cry of pain: it is the exclamative language (as well spoken as musical). Then the listening and the imitation of other sounds, noise of the wind, noise of water, song of the birds, etc: it is the imitative language (which is especially musical and that one however also finds in the primitive onomatopoeias). Many later came the syntactic spoken languages and the organized musical sentence, and with it the precondition, “out-time” as you call it: ranges, modes, scales. Why do you stop with this material of the range, other than all the remainder? Iannis XENAKIS. Not, at all. You want that I speak about it immediately? It is true that I did not go further, perhaps by ignorance. I do not know what occurred in the head from the paleontological man from a million years or two million years or thirty million years ago, as one have just discovered it. One knows at all his form of thought and if it is since this ~iècle that I look at the centuries of the past, it is because I belong to this century and, consequently, can speak only about things which are comprehensible for me. acknowledges that it is undoubtedly a lack which to be able to enter these questions more deeply only you raised. Moreover, that wants to say “to imitate”, that wants to say “to exclaim”, which is before syntax, before the rule, before construction, before the structures, if small are they? It is already an advertisement of recognition, form, therefore a vision structural of the environment, by admitting that the man was a kind of object in oneself, nature and its environment something of apart from him and that, consequently, there was an imitation of what it perceived by its directions. I think that, there too, one can probably say that the fact of being able to imitate the noise of the wind, the noise of hail, or the lightning, etc, was a way of building, primitive perhaps, I do not know nothing of it, but already very complex. The science of today, when I say science, it is the scientific thought, touched finger some of the mental structures of the man for some time only. Others will come, but it is difficult to speak about it; I speak only about things which are relatively well formulated, quite visible. Therefore I started with the tétracordes which are already at a rather advanced stage of construction and I must also add that the tétracordes belong to a cultural or scientific step or organization, i.e. of a material. There are of it also in other civilizations, like that of Japan, or that of China or that of Africa, very old, even older perhaps (the Egyptian woman one does not know it well) only Greek civilization and which have other approaches where the tétracordes are not there. For example, in the music of Nô, it there with the quad, one can say that the perfect fourth is a kind of universal reality, but the interior construction of the quad is a perhaps specific thing of the tem~s of Ille or IVe century before the Christian era in the Greek domame. As in fact the tétracordes were at the diatonic base of the system and thus of all the posterior music until the current time, it is this historical and musicologic discussion thread which enables us to make extrapolations, much more than the former periods which I would call prelogical, well. that elle~ is not at all prelogical in the musical domame, I hear. And what you say to us is fondamen~ because, today, if one wants to go more! , rofond~ment in these same questions of structures, it faudraIt to return or rather to move away from these structures, of these concepts which we have of the music, as besides there would be to now do it for completely foreign reasons with the music. However, let us look at the things of an eye or a completely new ear, with new tools. It is the pattern recognition. If one received, one receives besides, of the signals of space intrastellaire, galactic, eh well, it would be necessary to be able to know to distinguish them from the noise as said Michel Serres presently, to see whether they are ordered, if they have a coherence, and if this coherence is significant or not. If it is significant, i.e. if it has natural sources, I want to say nature or if it has sources of other beings, which would approach the man, this is not, of this type. With this intention, it is necessary to go well before all the structures, all the forms of thought which we received by civilization and the school, and thus to return to situations; to reform themselves completely and return to situations pre-rational, prelogical, pre-structural, pre-syntactic. I do not know if I answered your question. Olivier MESSIAEN. C' is a very beautiful answer. But you also said that the past was in the future, and future in the past, this is why I allowed myself to touch with areas where our knowledge weakens… Second question, completely personal: you know as me that a certain number of objects gives a certain number of permutations, and that the more the number of objects increases, the more the number of permutations increases, with a speed and quantities such as that can appear disproportionate. Thus, three objects comprise six permutations, six objects give 720 of them, and twelve objects give of them (if I am not mistaken) 497.001.600. Suppose that these objects are durations: it is necessary me to write these durations in order to know which gesture, which movement they will achieve in time. One spoke much about movement retrogresses these times: it is only one movement, one movement among thousands of others, and its permutation follows the original way. And all other permutations? I cannot write million and million permutations… and however I should write them to know them and to like them! (I insist on the verb to like!) For you, a machine gives you in a few minutes of the billion permutations of duration: it is a cold and nonexplicit list. How do you make to choose at once, without knowledge and love, in this immense world of possibilities? Iannis XENAKIS. There are two questions, I believe, grouped in your question: the first, it is the question of the love; well. The second, it is the possible choice among a very great quantity of possibilities… Olivier MESSIAEN. And I believe that you will answer the first question of Olivier Revault d' Allonnes… Iannis XENAKIS. Perhaps, I do not know. Then the question of liking, to use something, naturally it should be tamed. To tame wants to say to live with, and to live with wants to say to like it and also not to like it. Because to like brings its corollary. Olivier MESSIAEN. I badly expressed myself, I want to say to know! To know of a real and emotional knowledge, by the love or the detestation… Iannis XENAKIS. Oui, it is the emotional side, the epiphenomene of knowledge, it is with the pain or, on the contrary, the joy or both unit, when one loves a beautiful woman for example. But the possession of something which is implied by the love or hatred is perhaps a form of knowledge and, consequently, the only possible one. When I look at the starry sky, I like it in a certain way because I know it in a certain way; but if I must know successive stages of astrophysics, eh well, it is perhaps without love, it is the going beyond of the love by a kind of revelation which is beyond this epiphenomene which is the love. Consequently, I can handle concepts of the things in oneself without in being the direct owner. Provided that I can in a certain way of conceiving them and to feel them inside. It is starter of answer to your question which is fundamental in my opinion, with the result that, even if I am not able to dominate a certain phenomenon, I is able to obtain, by a kind of revelation on line, a truth which is in the phenomenon that I conceive or that I observe. Therefore, I accept it and I use it in oneself. When I record on a tape recorder a sound which interests me, I do not know exactly what there is in this sound. I see certain things which interest me, and I use it. Thus I cannot like the things which are inside a too fine manner since I do not perceive them completely. I am not able, consciously or unconsciously, to name them and I accept it overall, in oneself, because I am attracted by that. Olivier MESSIAEN. You are attracted, therefore there is a revelation! Iannis XENAKIS. It is that, here. Olivier MESSIAEN. A revelation, it is like a it, thunderbolt is like the love. It is the inspiration of the romantic ones. Iannis XENAKIS. Yes. I do not deny it at all, on the contrary. Olivier REY AULT Of ALLONNES. I saValS not romantic. (Laughter.) Iannis XENAKIS. I said to the beginning, or perhaps I said it, only in the artistic field, it there with the revelation. In philosophy and knowledge, in the same way. Yes, the revelation is absolutely essential. It is one of the crutches of the man. There are two crutches, the revelation and the inference. And in the artistic field, both are valid. In the scientific field also it is one which takes precedence over the other, it is the inference. To come to the second part of your question, i.e.: how to choose in a great richness of possibilities? , eh well, there, there are several ways of making. I can imagine, and I do not need the machine for that, I can imagine and carry out the choice mentally. There are several ways of making this choice. It is true that when one has some sounds or, to specify, some heights to be controlled, it is easy to do it in an arbitrary or intuitive way, immediately. But, when they are great quantities of sounds, eh well, it is where loans with other fields of the thought can be useful. When I look at a small number of individuals, I see them as individuals, I see their relations, their characteristics, and their relations in space or in time, their own aspect, etc But if there is crowd, then I cannot distinguish any more the individuals, because too much many. On the other hand, which I can see, they are the aspects, the characteristics of crowd. It should be made so that, if I require for a great number of possibilities, I can utilis.er the characteristics of the great number, which are for example features of density, order or disorder, of r~partition in space with three dimensions, of distribution in sound spaces, as in the dimension height, the dimension of time, the dimension of the order or of the disorder, etc, and then there are possible tools which make it possible to make certain choices. I do not say all the choices, but to clear nevertheless not badly in impossibility of choosing among a so great number of elements. Because I base myself on the incapacity of the man when the density is large, too strong to be able to say: “yes, it is about this object and he is there”. A certain blur in the choice is allowed this moment, because other characteristics are important. It is the same phenomenon which occurred when one introduced the theory of probability in kinetic theory of gases. However, it was a little different, it was a problem of calculation and not a psychological problem and one arrived at the kinetic theory of gases, i.e. with concepts which allowed all kinds of sciences, not only with thermodynamic, of going much ahead. I believe that in the field artistic and sensory, and sensual also, it is what occurs. Did I answer? Is that worth something? Olivier MESSIAEN. Yes, yes. Third question (that one is completely indiscreet and if you do not want to answer, you will make with your own way!). You quote, in Musique. Structure, a splendid text of Parménide, which one generally applies to the universe and which contains inter alia the concept of “being”, or quality of what is. By summarizing this text to the extreme, I find these some words there: it, is inengendré, indestructible, imperturbable, without end, it is at the same time one, continuous. For me which made theology, this text can apply only to God, because it expresses only divine attributes. However, you explain this text by the energy and the conservation of energy. I know well that one of the new theories of the creation of the universe is the theory of the explosion which affirms that the universe started with a fantastic deflagration, which supposes at the beginning an energy force which could be still a divine attribute. But I think that your explanation of Parménide is very different. Did Pouvezvous to say to us why you choose energy? Iannis XENAKIS. “Being It” of Parménide is one of the first texts where it tries to determine reality. But, to encircle it, it is obliged to be detached and make of it a kind of abstract definition which is even in contradiction with the daily experiment; it is what made it possible Aristote to say that Parménide was insane. It is true that what Parménide says on “being” corresponds so that one could say (that you said well besides) on a single god. On another side, if one does not think of theology or an unspecified religion, but if one remains in the field which, I believe, is at the same time fundamental and much more universal, that of Parménide, the text does not say in only it is a god. He does not say anything the whole. He says only that it is a being, he only speaks to be it, to be it as an existence, not to be it active, as being acting, therefore he puts the concept to be it with the participle and not “being it” with infinitive. I think that this direction of Parménide, so contradictory is it with reality, is one of the lights of the thought of the man in his distress to manage to determine its problems, through the ages. Now, there is no more that one kind of ghostly response this “being” of Parménide, is the bringing together which I made with energy because I found only that in the scientific field as explanation of the world which approaches these contents. Because, indeed, energy is a thing which fills the world. The principle of the conservation of energy is only one principle of course, but which sticks, yes, with this definition of “being”. Thus it is in the field of nature, the scientific side, the side of the physics which I tried to give an answer. It is not exclusive whole, it is a kind of bringing together which I make. I do not say that it is that “being it”, but that points out the definition curiously, or rather the design of the energy which fills the world, which had beginning neither of end since because of the principle of the conservation of energy, it could not there have beginning nor of end. However this, of course, is a little in contradiction with the theory of the explosion of an original atom, at the origin of our universe condensed” to the extreme. But it is allowed to me to think that it is only one provisional theory, as all the theories… This bringing together of “being” of Parménide with energy is only one kind of analogy. In fact, the attributes of God and of “being” are identical because, subjacent, is the same logic of `man. Olivier MESSIAEN. Then the fourth question… Iannis XENAKIS. If you allow, to finish some with Parménide, I would like to speak about another fundamental thing that one finds in one of his fragments. It is about equivalence between being it and the thought, which is also a discussion thread for the thought of the man through the ages. Parménide called in worms, which remained famous and which was reproduced by Plato in the Republic: “Because it is the same thing, being and to think”. However, the structure of the sentence is a symmetrical structure compared to the verb is. To be, i.e. “being it”, and the thought are the same thing. It is there that I see symmetry. At Descartes, a long time after, there is a dissymmetry when it says “I thus think I am”. They is curious, when they are brought closer and I believe that it is necessary, because it is the same concern of the man through the ages. I do not know if he knew. Bernard TEYSSÈDRE. It is not at all the same one. Iannis XENAKIS. Not, it is dissymmetrical: “I thus think I am” and if one goes in the solipsists, Berkeley for example, there there is another inversion which points out that of Descartes, but who is in another direction, i.e. objective reality, “being it” can not be whole, but can be only the thought, it is-àdire there is an identity of “being” with the thought, out of an unspecified reality. If Descartes is realistic, Berkeley suddenly becomes abstract with its solipsism, and all is reduced to the thought. Since, there was, of course, the philosophy of the XIXe century, with the discussions Marxists, which admitted an objectivity independent of the man, as well as the science which, it, is ambiguous because of the resounding failures of the successive theories of traditional mechanics, etc And that continues! Therefore the scientists say today: “All occurs like if…” Olivier MESSIAEN. Fourth question, and it is the last: pages 8 and following of the translation in French of the final chapter of your formal Musiques book (Anglo-American edition), which you in the documents joined to your thesis 1, you included give several methods of microproposition based on the probability distributions, and I read, method 4: “The random variable moves between two reflective elastic terminals.” I repeat, because it is an extraordinary sentence: “The random variable moves between two reflective elastic terminals.” It is very poetic and that plunged me in an abyss of daydream… After comes the quantified explanation which I did not include/understand. Pouvezvous to give us another explanation of this process, with a concrete musical example, perhaps in one of your works? Iannis XENAKIS. This method 4 refers to the basic assumption which is in the preceding pages starting from page 145, “New proposals in. microcomposition based on the probability distributions”. That refers to space pressure-time, the pressure which you receive from the atmospheric air on your tympanum in the course of time. Then if it is considered that the pressure takes more or less strong values, expressed by numbers, we can make correspond the pressure to notes placed on the axis heights and one could write it on a range. We will obtain a advance, the variation height according to time, in the shape of continuous melody curve. In the case of space pressure-time, if it is penodic (it can form either a square wave, or a triangular wave, or a sinusoidal wave, etc), the form of wave is repeated identical to itself all the time. But, if the variation is not periodic, it will marry curves having any sinuosity. One could imagine that this curve is followed by a mobile point moving in a plan, without never turning back, either in space height-time, or in that of pressure-time, which returns to same from the point of view of the definition of its advance. These routes will depend obviously on the laws which will animate the mobile point. The periodic functions are very constraining laws and correspond to melodies or tedious sounds. On the other hand the laws of the probabilit~s and their mathe~atic combinations, can produITe of the very free routes and which will never be repeated, corresponding to melodies or sounds much richer. Only, these probabilistic routes can take any valel! r. Consequently, they can make leave the mobile point out of the weak limits of the ear, i.e., in the case of space pressure-time, it can arri~er. with pr~ssions of atomic bomb! One thus needs h~Iter the inopportune growths, these probabilistic energies c~l~ssales! It is exactly the case of the ball which is canalIsee by the gun of rifle by making it rebound from one point to another of the internal wall. Olivier MESSIAEN. C' is what you call Iannis the terminals… XENAKIS. They are elastic terminals… Olivier MESSIAEN. They are reflective… Iannis XENAKIS. Because they reflect towards the interior and follow the law of the reflexion planes elastic, without loss, without energy absorption. I.e. the advance created by the process probabilistic, stochastic, is considered as by the effect of a mirror when it reaches the selected barriers. If you want, it is exactly the case of the inversion of the melody intervals. In the melody inversion, the intervals are considered in a horizontal mirror, placed on the axis of times and in retrogradation, it is a reflexion in a vertical mirror. In fact the same very simple principles exist everywhere, even in music. Now, one can imagine nonreflective walls with fields of gravitation. Lastly, all kinds of forces to the direction abstracts of course. Olivier MESSIAEN. They is completely marvellous… Alors, in what relates to me, I finished, but a few moments ago I did not intervene when Olivier Revault d' Allonnes spoke. It made a so beautiful talk which I did not dare to stop it! Perhaps could it take again some of its properly musical there questions since I have the chance to be? . Olivier REVAULT Of ALLONNES. Personally I failed. It did not speak! Olivier MESSIAEN. It is not by spite, it is by curiosity, sympathy, admiration also… Olivier REVAULT Of ALLONNES. I wanted that Xenakis speaks about its style of type-setter and it made me the most satisfactory answer at the same time and most hermetic. It said to me: “Listening, I do not have anything to add, listening, and if you did not include/understand, D-listening”. “And then likes, if you like”. Olivier MESSIAEN. - There is a certain decency which personally astonishes me because I do not have the same trade as him. I make class of composition with Academy, where, since forty years, I pass my time to peel works musical, to test to know what passes inside… These things about which you do not dare to speak, who frighten you, I occupy yourselves of it all the day… Iannis XENAKIS. It is true, I remember it very well. I was in your class of musical analysis, and what had interested me the most was precisely the speech which you held in connection with the techniques… (laughter) because the remainder is reduced to: “We said, it is beautiful that, isn't this?” Olivier MESSIAEN. I did not say it so much, I were quiet! Iannis XENAKIS. It is true, it was rare, but said it sometimes to you. But it is all that you say on the problem of the style. Or then, the style it is more in the direction of the technique, and then it is other thing. But for me the style refers as well to the technique, (also what is perhaps more interesting) “as with the paIfums” of the music, on several stages besides. Olivier MESSIAEN. Yes, but apart from any structure, it seems to to me that each individual and each musician in particular (since one speaks about music), has what we call in philosophy, “its accidents”, its tics, its personal practices. A second or. third Xenakis which would try to make of Xenakis in your place, with the same structures, would certainly not obtain the same result. There is thus a question of personal style. Iannis XENAKIS. Yes, then there I acknowledge that… Olivier MESSIAEN. One recognizes the music of Xenakis immediately. Not only because there are glissandi or permutations, one recognizes it with a certain sonority, a certain way of orchestrating, a certain way of laying out the sounds, which differs from that of the others. Iannis XENAKIS. Perhaps that the answer to the question of Revault d' Allonnes is as follows: in the life there are two ways of proceeding, one is to make the things and the other to analyze itself. However, the best analysis for me is to make the things, i.e. I deny the analysis, the psychoanalysis, if you want it, as a method of introspection. More especially as, if one touches with these fields, one does not know what one will discover and one is likely to fall into holes, terrible traps. Therefore, it is a tactic, and it is for that which I persist in saying that it is the “thing”, the music even which, it, is not hermetic, contrary to the analytical word which, it, is hermetic. Olivier MESSIAEN. And yet, me I question the sphinx the every day, since I make a class of analysis, and I am not more unhappy. That does not prevent me from making music! Iannis XENAKIS. Apart from don't the technical questions, you give other answers? Olivier MESSIAEN. I deal only with the technical questions. Iannis XENAKIS. Then… Olivier MESSIAEN. Apart from the pure musical fact, of course, I would not allow myself to make bringings together in the intentions because I would be quite unable. Or if I did it, they are completely occasional. Iannis XENAKIS. But when you say technical musical, that refers to what? It is many proportions, of the durations, the combinations? Olivier MESSIAEN. Durations, harmony, modes, colors, I speak much about it, I know that you do not believe… Iannis XENAKIS. It is already of a field except technique in my opinion. Olivier MESSIAEN. The orchestration also, for me it is technique. Iannis XENAKIS. I.e. these are things which one can speak. Olivier MESSIAEN. It is technique, properly and purely and completely musical. It is on top that Revault d' Allonnes tried to question you, seems to me it. Olivier REVAULT Of ALLONNES. And on what there is at side, in lower part, after the technique. I do not believe .pas to betray a secrecy by saying that I saw Xenakis one Day in front of his table. It had under the eyes a partition of a work in gestation and it looked at, stopped by a detail. It said: “Oh not, that will make bad”, and it removed it. Then it is technique, that? (Laughter.) I believe that that arrives at all the type-setters. Michel SERRES. In a word, let us return to the question of the choice. Iannis XENAKIS. Oui, of the choice arbitrary, intuitive, etc Michel SERRES. That one can call the inspiration if one wants but who remains a choice. Olivier REVAULT Of ALLONNES. There Then, we avoid plunging in the muddy areas of subjectivity? Iannis XENAKIS. The best way of S `of plunging Estelle there not to make, precisely, of the music? Olivier REV AULT Of ALLONNES. The choice enters a very high number of possibilities appeared in Olivier Messiaen a very difficult problem, but makes of it a body of the directions, any, the ear, the eye, m, ême, the .toucher. function exactly like that, C is-A-dlre receives an enormous quantity of information of so~e that this qu~ you oppose, namely the techmque problem of the Choice, of the choice between the million possibilities that you have on the one hand, and on the other hand the subjective problem of saying (as one says “to the conk”) “that it is ugly”, it is exactly the same thing. The conk precisely, or the ear or the eye functions very exactly like the computer, i.e. they receive fifty million information that they sort and transmit exactly. Consequently, there is no opposition between what you call the power, the inspiration, the event, the sensoriality, and in addition this problem which appears very difficult to you choice between an enormous quantity of elements. Thus that functions, in the alive one. Iannis XENAKIS. There is even, in the set theory, the famous axiom of the choice of Zermelo, which postulates that one can choose in an arbitrary way or using the “revelation” an element in a given unit; it is mathematics and mathematics speaks a completely aesthetic language here if I dare statement. It was the problem; and the calculating machines are filters. Olivier MESSIAEN. Simulators. Iannis XENAKIS. Simulators of choices, which have rules to be able to choose. The man, with his ear and his directions, fact of the choices much more complex than cannot currently make the computer, i.e. the simulation of the choices is still with its stammering with current technology, the automation of the choices is still very rudimentary compared to the man. Olivier REV A UL T Of ALLONNES. Yes, one does not know how to order it. The sensory terminals do it, without the knowledge, but they do it. Olivier MESSIAEN. I will give you a concrete example. When I note songs of birds, I note them with a paper and a pencil. My wife accompanies me sometimes, it records with the tape recorder these same songs that I am writing. However when I listen, while returning to the house, which took the tape recorder, I realize as it made the things pitilessly, it very took, as well of the horrible noises which do not have any relationship with as I had come to seek. These noises I had not heard them, I had heard only the bird. Why didn't I hear these noises? It is that, there is why, my ear filtered of course. Iannis XENAKIS. It is what is called intelligent listening, directed listening. That corresponds to one of the selection criteria that you asserted yourselves without the knowledge besides, because you want to listen to only the songs of the birds through the noises of the forest. Olivier MESSIAEN. My attention was turned towards the birds and I heard them, but I heard them with the exlusion of other bad noises as the cars which pass, or had them… Iannis XENAKIS. With the exlusion of other noises. Moreover, in information theory, all that is not the signal that one wanted, whom one selected, one refuses it, as being noise. Olivier MESSIAEN. One hears what one wants to hear. Michel SERRES. The signals are heard. Iannis XENAKIS. Yes. And the difficulty in the appreciation of an unspecified work, it is to choose exactly what is important. Therefore, when one listens to a work of Bach which is hundred times, thousand times listened, according to the choice which you make at this time, it can appear completely different to you from that which you had the practice to hear. And it is not only the interest in oneself of a work, but it is also the interest of this personal individual choice, of the listener. It is for that that Newton, suddenly, receiving apple on the nose, said: “I found! Eureka”. Olivier REY AULT Of ALLONNES. All that does the choice say to us about how you conceive what it is that, but not what it is that the ugly one, or its opposite, and with which to require it if not you, the type-setters? Olivier MESSIAEN. - All to 1 `hour, in connection with structure, we spoke about the runnings away of Bach. However, there are nothing more structural and (excuse me) more tedious than a running away of school. Bach made in its life of the thousands of runnings away, there is everywhere, in all its works, its cantatas, its Passions, its mass, its works of organ, its works of harpsichord. These runnings away never have the structure of the runnings away of school and they are different from all the other runnings away of the same time, because they have a certain melody joy and a harmonic control which belong only to the Bach father. Iannis XENAKIS. Oui, I believe that it is the problem there. Olivier MESSIAEN. I will say more, in the father Bach there is a little bit what there is on your premise. There are sometimes superimposed wills! For example, in certain chorals, you have the line of the choral to which it could not touch because it was a crowned text. It left it just as it is. It is a will. In the lower part engraves, it Y has a ostinato which is also a will. In the central parts, it Y has chromatisms; it is also a will, it in démord not. The three superimposed wills give extraordinary meetings, almost modern agreements and counterpoints which could be signed Debussy. Here is perhaps a way of including/understanding how a structure can make spout out something again, of personnel. Iannis XENAKIS. On a more current level, a structure of running away is not totalitarian, i.e. it shows parts fuzzy, free, and diagrams which are more or less followed. But, inside these diagrams, there are “data input” as one would say in data processing today, which make it possible to obtain these same diagrams of the different results. And in the data input which are free, one can in the broad sense put much quantity of intelligence and wills contradictory. But the diagrams can result in a kind of system, or like one says, of automat, since they only function, and the great advance of the running away on all the scientific thought of its time, it was precisely that it proposed systems which science was unaware of. It is only for some time that science is concerned with a systematic manner and with its own methods of systems, i.e. of clock industries, stochastic or deterministic. Michel SERRES. Not. Of the XVIIe- century, a little before Bach writes runnings away or before the schools make make runnings away, all the scientific thought thought of the automats. Finally it is a demonstration of contemporaneity between sciences and arts. Iannis XENAKIS. Oui, you have reason, Descartes also speaks much about it. Michel SERRES. C' is that, Descartes… Olivier de Serres. Iannis XENAKIS. But the abstract automat was proposed only by the musicians. Michel SERRES. Good Ah, yes. it is possible… the musical boxes made fury. Iannis XENAKIS. And the products which offered the abstracted automat, they are the musicians who materialized them by playing them. Michel SERRES. Yes, it is true, they had a lead over science, as usual. Bernard TEYSSÈDRE. But to return from there about us, curiously, which is well in the running away, in my opinion, it is not the abstracted automat, it is precisely the fuzzy parts into which Bach could introduce its personal genius. Iannis XENAKIS. Yes, but it should not either be been unaware of the fact that we had a very compact form there, compared to the other forms of the music, of a subjacent structure on which one can add “forms”. Naturally, the results would not have been the same ones if there had not been these subjacent structures, this diagram. Bernard TEYSSÈDRE. Eh well, after the debate with Olivier Messiaen related primarily to the music, I believe that that with Michel Ragon will relate more particularly to the problems of architecture. DIALOGUE WITH MICHEL RAGON Michel RAGON. On quoted very often, in the course of this debate, the book of Xenakis: Music. Structure. It is one of the two books joining together all the texts of Xenakis; the other being formal Musics. If this book is entitled Musique. Structure, it is precisely because two creative products are narrowly overlapping in the work of Xenakis: music and Architecture. If these two data were separate at Xenakis during a certain time, they are now completely joined together. They were separate in one time of Xenakis which one knows less, i.e. that of Xenakis pure architect, could one say, the collaborator of Corbusier. Xenakis worked twelve years, I believe, at Corbusier. You know that when one works in an architect, an owner, all that one does, all that one produces at this owner, is obviously recovered by the owner. This is why I would like to draw the attention to two signed achievements Corbusier, and for which Xenakis particularly worked. It is about the frontage of the Convent of Tourette in 1954, and it is rather easy to see that it worked there, since it is an architecture conceived a little like a partition; then the Philips House in 1956, which one could say that it is a container with music. These two works designed with the collaboration of Xenakis in the workshop of Corbusier, were authenticated besides by Corbusier itself as being a Xenakis production. In the support, we have two texts of Corbusier quoted in Musique. Structure [1], which indicates the considerable share taken by Xenakis in this creation. I say that while passing because certain architects deny in Xenakis the right to adapt signed works Corbusier. Less royalist than its pupils or than its disciples, Corbusier has, in fact, authenticated works in question as being works of Xenakis. And then there is Polytopes! Polytopes on the subject of which Revault d' Allonnes wrote a very copious book and which speaks about it better than I did not can speak about it extremely briefly. You know, it is this transparent architecture of steel cords being used as support with the luminous points, where the light is, itself, architecture, where the light structures the space of transitory drawings. Here is also another significant part of the work of architect of Xenakis and, there, the work of architect is mixed narrowly with work with the musician. There is also the Utopia of a total spectacle which very often returns to Xenakis. It is undoubtedly a total spectacle which one could see in this night fabulous of Persépolis, with the 250 carriers of torches so often quoted. But also with the more recent ideas of Xenakis of launching brilliant cobwebs above the cities and the campaigns, to bind the ground to the moon by filaments of light, to create aurorae boreales artificial, all things about which it speaks, of which you speak to us in the summary about your defence about thesis. There is finally another part of your work which is, I think, more known, this is why I would like to attach me to it. It is about your project of architectural futurology or utopian architecture. We with the text published in Musique refer. Structure which is entitled “the cosmic City”. In connection with this text, I would like to pose to you, since such is the rule of the game, some questions. This text of “the cosmic City”, I will quote passages. You begin with you ~emander if it is necessary to choose the decentralization of architecture and the decentralization of the city, or quite to the contrary to admit this centralization. And you take a categorical party for a centralization that of aucuns could perhaps regard as abusive. I.e. you challenge the theory of the linear cities (Corbusier is one of the authors of this theory), that you qualify naivety, and that you propose to build v.illes ~ertical~s, narrow, who can go up to three. thousand, Even up to five thousand meters of altitu~e, d~s ~illes thus, not very thick, entirely out of metal, C is-A-dlfe espec~s giant skyscrapers but containing all the ~orphologle of a city. You consider that the concentration is a vital need for humanity, say you, and that it is necessary to completely change the current ideas on town planning and architecture, to replace them by others. ? R, it will be my first question, this text east as~ez a~clen. ! L goes back to 1964. It is possible that you since then evolved/moved. This meeting, today, is an occasion to be able to chatter a little with to ask you and you questions. It enables me to ask you q~elques questions which I have desire for posing .depUI~ longte~p~ to you. Since twelve years, do you always believe has this Idea of such a thorough centralization? Do you think that this centralization is always necessary? Do you think that of one time when electronics, the dispersio~ of energies, where natural energies, as the ~olalre ~t the wind mill can precisely allow a decentrallsation which resembles of nothing the dé~entralisati? NS of the past, i.e. where culture it-me perhaps decentralized easily with electronics, do you think that this so thorough centralization is always necessary? Or is this idea out-of-date since you created it in 1964? Iannis XENAKIS. I believe that centralization, that I will rather call a thickening of the human habitat and his human relations, is initially a historical need as one sees through all the manifestations of construction of the cities and the habitat of the man and as well in his relations, in his culture, everywhere. What makes today the thing much more necessary, it is the invasion of planetary space by the dispersed cities as a film which destroys the environment. There are two tendencies, currently, one with a thickening of compactness, larger thickening and the other with a centrifugal tendency which would like to return to a kind of rural settlement in the middle of a green nature, where it is possible, and if it is not possible, to do it in an artificial way. These are two tendencies which are natural, one like the other, but if the tendency to compactness is a need for the industrial era because of the increasingly explosive thickening of the population of the man on ground, the other also is natural because it corresponds to nostalgias of last and also to the fact that the current cities are far from giving the conditions of nature that the body of the man and his spirit claims. Currently, these two tendencies are in fight. In fact, it is the tendency of the saturation (or compactness) which is more gaining for economic reasons and reasons of all kinds. I am always in agreement with what J aVaiS proposes into 964. I am persuaded that it is a solution, provisional besides, who am more interesting and less criminal than dispersion on the surface of the sphere. A as large thickening does not want to say as I refuse the insulation of the man, its possibility of insulating itself as an individual, in this species of large hive that are the current cities. Only, I say that instead of extending them on a surface which poses many problems of contacts for the activities of the man, they should be organized in manner that they are with the vertical. It is not a completely new idea, since it existed already in a smaller way, if I dare statement, in the fight which had begun in the Twenties especially when it was a question of choosing between the cities gardens, as one said at the time, and the vertical cities; these vertical cities whose Corbusier was one of the defenders. But these vertical cities corresponded only to the pure and simple habitat, and not to the whole city. They did not include all the activities of a city, whereas me I think that one must extend this principle to all the activities of a city for technical reasons, reasons of relations of the men between them, for reasons also of exploration of what still remains us of terrestrial space, and also because such a system would make it possible to install cities in climates really impossible to currently live, very hot climates, very cold climates, which are either over-populated, or desert. I believe that I answered this first question. Michel RAGON. This text thus goes back to twelve years. It is contemporary other texts, other close theories, for example, the “space city” of Yona Friedman [L], or the “cybernetic city” of Nicolas Schôffer, or the inhabited pyramids of Paul Maymond. How are you located compared to these theories of architectural futurology which were born at the same time as your theory? Iannis XENAKIS. I finds them timid compared to the miennes! They are actually extrapolations on a relatively weak scale of what should be a very large concentration and they refer in general only to the habitat and not to the city like a total phenomenon. Michel RAGON. Nobody, before us, I believe, forever considered a construction which can make 3, 4 or 5 kilometers height. Most utopian, to you, in this progression of the vertical city, it was the project of a tower of 1.660 meters by Frank Lloyd Wright. Iannis XENAKIS. Yes, but this tower of 1.600 meters was a tower of businesses which had the defect, initially not to go rather high, and then to be subordinated to its bearing structure, made “gantries” which finally transformed this thing into a kind of obelisk which went up up to 1.600 meters of altitude. Michel RAGON. It is true, it was a kind of obelisk, whereas you have inventions of extremely interesting forms in your project. Iannis XENAKIS. C'est-with-statement that it came suddenly by a kind of illumination that I had by drawing Philips the formed House of surfaces to douole curve. I realized, because one had made experiments in a laboratory close to Eindhoven in Holland that it was excessively resistant and that one did not succeed in destroying the form. This experiment was made because the calculations based on the resistance of materials and the theory of elasticity did not allow all to provide until the end, and that there remained margins of uncertainty. The experiment showed extreme rigidity inherent in the geometry of these surfaces curved in two planes. It was pH (the parabolic hyperbolic ones). Essence is the quite selected S curve, i.e. that which is sufficient isolated plan. And then I thought that as carrying structure it was absolutely necessary to use this property of the geometry and to not make a city in the shape of obelisk or the shape of skyscraper, as one sees them either here in Paris or in the United States, but in continuous form, with S curve. They are films in space, a 100 or 150 meters thickness, openwork of course and transparent, to let pass the air and the sight, the light and all… And there are cities which are with 2.000 meters, like Mexico City and Bogota. Therefore, it is an altitude which is very livable. With 5.000 meters, of course, it is very different bus the rarefaction of the air starts to be critical. One does not know very well what occurs. But with current technology, it is possible, like one makes on the aircraft, to obtain a sufficient pressurization as well as a renewal of air, temperature, etc At the bottom, a city as this one would be a kind of widening of the men's cloth. The man did not have clothing during strong a long time. He has carried from there only for perhaps 10.000 years, not more. Before it was with hair, naked. It put a clothing which is personalized, individualized. One works of the morning at the evening in spaces as that where we are, for example, which does not have air, which never sees the sunlight. The majority of people work like that in the offices, in the factories. It is an environment which can be very malicious for the health of the man and I think that with current technology and that which will come immediately, these problems will be solved so as to have a clothing made for the city itself, which will allow a freedom much larger, physical and conceptual, mental, spiritual, etc of the man. It is quite simply thus an extrapolation of the possibilities of the technique of today, used on a large scale. A city as this one cannot be designed in the restricted capitalist system. It could be conceived, either by multinationals, or then by States centralized like France for example, which could build them, but out of the system of the municipalities. Only one country of several tens of million inhabitants can allow such a programming, or a kind of international corporation which could carry out units of this type, valid for the places either désertiq.ues, or very heats, excessively hot and wet, Ecuador, the turn of Ecuador, or in the very cold areas like Siberia or Alaska or Canada of North. Michel RAGON. - Aren't there energy constraints so that it appears difficult to conceive the heating of a similar volume? Iannis XENAKIS. It is bound, of course, with energy problems. Mahs we now have materials and systems of insulation which can reduce much thermal losses, calorific. I do not think that the technical obstacles are truths obstacles. The largest obstacle, the largest obstacles are of two types. It is initially the organization, because a city is organization… Michel RAGON. I was going to come there, I were going to precisely say that for the organization of such a vertical city, you consider electronic sets of management and decision. However, in the “cybernetic city” of Nicolas Schôffer, we find also this belief in the cybernetics and in the electronic sets of management and decision. Don't you believe, that affieure sometimes besides in your writings, you do not practise a belief which appears dangerous to me in the political virtues of science? Iannis XENAKIS. I do not know exactly what Nicolas Schôffer said. I believe that it makes a mystic of cybernetics. Michel RAGON. Yes, it further goes than you, that becomes really a kind of mystic, indeed. Iannis XENAKIS. For the moment, the data processing or the systems of management are rather rudimentary, it should well be said, and very coarse. Only some tasks could be undertaken and taken of load by automatic systems of management. But there are some who function. For example, fires of circulation in the city which tend to becoming increasingly automated, with reactions, negative feedbacks of street with street, district with district; that it is a fact. Michel RAGON. But this automation is almost always repressive. Iannis XENAKIS. Then, we are in front of two problems: a problem of organization and then a problem which goes much further since it is a problem of social structure. When I say organization, it is obvious that city like that one, which must include/understand on 5.000 meters of altitude of the million individuals, can not to be conceived in advance because one is likely to create died cities, like that has be case for Strait, for Le Havre, for Brasilia and even Chandigarh, which do not function because they were conceived in laboratory, I want to say in the workshops of architect following certain rules resulting from traditions of the drawing board or even sometimes of revolutionary ideas. They cannot take account of all the complexity of a city owing to the fact that they result from a single brain. On the other hand, which is possible is to give the framework, i.e. the container, and not to define, determine the contents, to leave him a sufficiently large freedom so that the contents can develop progressively. It should well be thought that a town of this kind cannot be built in five years or ten years, but can take twenty or thirty years of construction. Therefore, it is not the city itself which will be drawn in advance, into twenty or thirty years, but the container, i.e. the fundamental structure which must rise at this altitude. In addition, it would be necessary to allow installations, if not developments, if not contradictions which will be done day progressively rise in this city. Consequently, it is absolutely necessary to conceive a kind of architecture mobile. One finds that germinates about it in Japanese architectures, which make it possible to transform parts or houses for various functions. Michel RAGON. The internal nomadism, you say extremely precisely besides, is possible by this permutation of mobility of architecture. Iannis XENAKIS. I did not speak yet about internal nomadism, I simply spoke about nomadism, put material city, i.e. one can affect places, areas of the city, with such or such function, factories, and change them at the end of a certain time into habitat or parks, etc It is a mobility of the internal structure of the material city. With regard to the second obstacle, most difficult, it is that of the occupation by the men and the human functions of this container. In this field, it is absolutely necessary to leave freedom, or to propose a sufficiently free diagram so that that can develop in an autonomous way, so that contradictions (I do not say that they will be cancelled or absorbed, this does not exist, it is a Utopia which comes us the XIXe century, if not moreover further) can move, to change form. Michel RAGON. You also write: “Since this city, your city, will be worked by the universal technique, it will be also ready to place the populations of the far North or south, and those of the tropics and the deserts.” I.e. appears in this text a technocratic belief which appears dangerous to me in a universal man, a standard man. It is an idea which is very widespread. One finds it at Corbusier, as at Gropius. And since there is a universal man, a standard man, the architects deduce from it that one can build a standard and universal architecture for this man; belief which one returned a little nowadays. Iannis XENAKIS. Yes, it is that technology imposes a certain universality, but I wonder whether one really returned from there or if it is only in spirit, because it should be seen how much all the technological moy.ens are spread more and more, in the middle of the most primitive companies, with electricity, with energies, the conversions energy; but as the institutions which make as everywhere schools are instituted, universities, texts. Even if they are different in the field of the history, the scientific texts are the same ones, the scientific laboratories are the same ones and clothing is the same one. One less and less sees the people equipped with their national costume and this t~nd with a universalization in fact which is due to all ortes of reasons. On another side, I am not at all a technocrat, far from there. On the contrary. But this does not want to say only one should not use and exploit current technology. In any proposal there are at least two aspects, the white and the black. In atomic energy it is also the same thing. It is a remarkable miracle which the man could see and enter the microcosm of the matter and to use it with its own benefit. Now, if there are deviations, it is completely normal also, it is in nature the man, it is a contradiction which is inherent in the omme and it is a question of fight of the individual and s~ \ ciale too. Mkhel RAGON. - Lastly, last question, how you as an architect sitQ.ez yourselves, since you are always an architect, that you carried out an architecture intended to be associated very narrowly with the music on the esplanade with the Center George Pompidou for Paris, an architecture in which there will be music, and undoubtedly of Polytopes. You also recently built houses for the musician François Bernard Mâche. How are you located in your evolution compared to your former owner Corbusier which is very challenged today per many of your fellow-members, and by much of theorists of architecture? Iannis XENAKIS. Initially compared to architecture. When I decided to only make music, it was with much distress; because architecture was very important for me. But I did it because it was necessary to choose. Either research or to become a businessman. I had made the workshops of architects in the Sixties while saying: “Here! I come as an architect to propose my collaboration to you, but I do not want to be the negro, I want to make research”. That was impossible. You know very well that this is true, in the great majority, there is very little case of research in architecture. Then, I confined myself in the music where I could make, despite everything the difficulties, of artistic research. This said, I am always ready to make architecture and each time I can it, I make some. For example, with this “trick” of Beaubourg, I drew a dismountable structure I will be established during a few months and which contien has the means of making a spectacle with lasers and tfS electronic flashes, as in Cluny, but amplified. And the structure is a textile structure which thus implies fundamental architectural solutions. On another side, compared to Corbusier, I do not know if there are many architects who reached what I will call the artistic expression. Independently of the subjacent ideas which are in an architect, at a town planner, in fact very complex things come from sources and different directions. The type of the apartment of Marseilles which is a cell, a habitat of family unit, can be disputed, of course, and it is only one of the possible solutions. One cannot say that it is the single solution. Moreover, Corbusier showed luimême since it made all kinds of houses. On the other hand, which one cannot dispute to him, it is its artistic and architectural quality, which practically exists in all its works. And the ideas pass, but the artistic fact remains. It is one of the lesson of the history, like had very noticed it besides Marx in connection with the Antique art. It, roughly, how is it made said that with orée of civilization, the Western culture, in spite of the slave companies, etc, there were works which make us effect still today? It is a miracle inherent in the artistic fact and which corresponds to the discussion of presently, and with the question which had put Olivier Messiaen and Revault d' Allonnes. Therefore, one can criticize Corbusier on many things, I did it myself, moreover, but I believe that it is one of the largest architects of our time. Perhaps there yen does not have thirty-six today, it is not one of them. Michel RAGON. I finished my questions of them and, since I baffled you a little from the point of view of technocracy, I would not like to miss saying that in all your texts, also a praise of art is, and that in a time when one speaks especially about dead about art, this praise of art is something of singular, remarkable, and also the definition of the artist-originator whom you give, seems to me something of extremely important. One still recognizes, in all your texts, your intelligence, and also what you call, not for you, but that one could turn over you, a “cold fire”. It is a little as I always saw you, like a cold fire. It is what always gave me this fascination, at the same time for your music, for your architecture. Very enthusiastic admiration that I carry to you makes that I regard as a great honor to today be able to be there, not to judge you, but to accomodate you. DIALOGUE WITH MICHEL SERRES Bernard TEYSSÈDRE. Now I will call on Michel Serres. Michel SERRES. I believe that there is not only structures about it that space is the image of the company. For example, today, there are an admiror behind the table and a creator in front of the table; it is not my fault if it is the image of the university. The university supports the theses and does not support works. For once we have like thesis a work, I would like to greet with much admiration this rare phenomenon among the wasting of intelligence which is done in the institution. It is thus the admiror who puts the questions. One will presently reconsider the relationship between mathematics and the music. On page 14 of exposed thesis that you gave, by the way precisely of the artist originator, you propose the total idea of a general morphology. What this general morphology? Iannis XENAKIS. Eh well, in each sphere of the human activity, there is a kind of scum which is that of the form. I noticed figures, forms which belong, either with the field of the speculation abstracted like mathematics, logic, or with the more material speculations like those of physics, with its phenomena or subatomic, or atomic, or like those of the geometrical expressions of the genetics or the reactions of its chemical molecules. However, these figures, these forms, which belong to so many disparate fields, have enthralling similarities or diversities and which can clarify other fields, such as those of the artistic activities. Mi~hel SERRES. You wrote that in which year? Mamtenant? lan~is XENAKIS. Oh! I do not know, that not made several years. ~ichel SERRES. Two questions, or two under-questions. At the end of the article, at the end of the paragraph where you announce this general morphology, you take the example of the formal evolution of the vertebrate ones. Iannis XENAKIS. Des vertebrate, yes, it is an example. Michel SERRES. It is a very good example. Somebody, av~nt Xenakis, had the idea of a general morphology m~Is. only in biology, it is Geoffroy SaintHIlaIre. Geoffroy Saint-Hilaire had the idea of a general plan which would be projected in the whole of vertebrate then, more generally, in the totality of the animals But currently, there is somebody which deals with cett~ general ~~rphology, it is Thom, so that your Id~e of morphogenesis meets with part of Science moving. As usual, the musician was in advance. la~nis XENAKIS. So much better. It would also be necessary that Thom Is versed in the artistic field, not only in the physical field. But I believe that this idea is much former in another form? Michel SERRES. It is Geoffroy, I believe, the first, not? Iannis XENAKIS. I do not know. I believe that one can find the trace in Antiquity of it, for example when one tried to put the idea of the proportion in architecture, in the shapes of the man, it is local. Michel SERRES. It is local morphology, it is not general morphology, within the meaning of Xenakis. Iannis XENAKIS. But me I think that it is essential to make a kind of convergence of all the possible forms, of everywhere, which presupposes that it is necessary to know all these disparate sciences… Michel SERRES. You had a mathematical reinforcement to begin the project of a morphology of this kind? Iannis XENAKIS. Oh! at all, not… Michel SERRES. Topology? Iannis XENAKIS. Topology? Topology, from which point of view? Because if topology is ~eut-~tre the most fundamental science on the mathematical level… Michel SERRES. On the plan of the forms, certainly. Iannis XENAKIS. On don't the plan of the forms, but not only of the forms, also of the philosophical thought of mathematics, you believe? It is the problem of continuity, discontinuity, the contacts, the connexity. Michel SERRES. Edges. Iannis XENAKIS. Yes, of the edges, and consequently of the forms. It is probably the subjacent tool, but I believe that it is coarse enough for the moment. It is enough imperfect to attack the problems as complex as are the shapes of the clouds or the shapes of the populations. Michel SERRES. But it is on problems as the shape of the clouds which one precisely started to have an idea of a general morphology. That is to say your Appendix 1 on the table of the correspondences between the developments of the music and mathematics [1]: I agree with you, I would like only to supplement it. When you say that before our era, there had been something as compared analysis lengths, of the cords and the heights of the sounds, you think of Pythagore, I suppose, and at the school pythagorician. One more and more currently thinks that there no was analogy between the invention of the first musical intervals and the invention of mathematics, but causes and consequence, i.e. it is by the music that one could have the idea of the whole of the natural numbers but also of the reports/ratios and the fractions. The music would have been the matrix of the mathematical invention. Iannis XENAKIS. Yes, that it is a problem of archaeology. Michel SERRES. Once again, the musical thought is founder. In which direction do say you that the running away is an automat, that “the running away is an abstract automat conceived two centuries before the science of the automats”? I believe that it is not true, I believe that it is at the same time, or a little front. Iannis XENAKIS. Ah not, not the science of the automats, the science of the automats was born at the Xxe century. Michel SERRES. Not the science of the automats, the realization of automats. Iannis XENAKIS. That made a difference, because the practice of the automats dates at least from the time of Alexandria. Michel SERRES. It Y has in Thousand and One Nights, for example, of the automatic fountains, the machines with water. Iannis XENAKIS. Yes, but Thousand and One Nights date from XIIe century, but the practice of the automats in is quite former. The time alexandrine had already Héron and the first steam engine. Michel SERRES. Oui, at least the dove of Archytas. Iannis XENAKIS. - But it was a concern which still remained at the material stage. The abstraction came, I believe, on the side of the music. Michel SERRES. Then, why the running away is an automat? Iannis XENAKIS. I think that it corresponds more or less to the definition of the scientific automat which was born in the Twenties, with Wiener and cybernetics, and which can be summarized in the following way: an automat is presented in the form of a complex of causes and effects, i.e. of a temporal of events, coupled or multicouplée chain, multiplexed with freedoms, possibly. An automat can be closed. It is enough to connect energy and it functions recurringly. It can be relatively open with data input, external actions, using buttons for example and, in spite of a rigidity interns which defines the automat, it can produce different results each time one changes the data input. Michel SERRES. It is repetitive in its syntaxes and not repetitive in its performances. Iannis XENAKIS. Oui, it is repetitive in its syntaxes. Why? Because it has a structural internal rigidity. Michel SERRES. Is the running away always stable in its syntax? Iannis XENAKIS. It does not constitute such an absolute automat, it is it relatively, because the automats studied by science are still relatively rigid automats compared to the automats of the music. When I say automat of the music, a minuet is an automat, already. Thus value specific of invention musical, it is that it is probably first which gave, which created the abstracted automat, i.e. which did not produce anything the whole, produced only music! Michel SERRES. Is the time of this music reversible or irreversible? Iannis XENAKIS. Then there, the problem would be that of time. However, here, there is a kind of confusion which occurs in the majority from the de$-people spirits, including in that of the musicians. It is that the fact of being able to repeat things, to renew experiments, or phenomena, gives them a kind of safety towards the time, which him, in fact, is never repeated. Michel SERRES. Sometimes, there is reversible times. Iannis XENAKIS. Which are reversible times? Michel SERRES. The circulation of planets. Iannis XENAKIS. In fact the time is reversible, it is the movement which is reversible. Time, him, (to my knowledge it is a kind of postulate) temporal flow, does not return. Michel SERRES. In any case it is a very recent discovery. Iannis XENAKIS. Que time does not return? Michel SERRES. Absolutely. Iannis XENAKIS. But it is so natural to think that it does not return. Héraclite said the same thing besides… There would be reversibility of time possibly if it there had a pendular motion of the universe which contracts and dilates. When I say, for example, that I take intervals of time: the intervals of time are commutative. I.e. I can take intervals of time and to take them now or afterwards and to commutate them with other intervals of time. But the moments which create these intervals of time are not reversible, they are absolute, i.e. belong to time, i.e. there is a thing which escapes to us completely, because time runs. This corresponds to research which Piaget had made when it had seen the phases of the training of time in the child, in experiments. Michel SERRES. What I have in the spirit, it is not Piaget, it is Xenakis. Iannis XENAKIS. Ah! Michel SERRES. Yes, when you bring compositions of the stochastic type, for example, that touches with the problem of time. Iannis XENAKIS. Yes. Michel SERRES. Which is the report/ratio which you submit between order and disorder, when you compose? Iannis XENAKIS. The order and disorder? Michel SERRES. I know what is the disorder because I know how you did that, but the order, what it is, which is your syntax? Iannis XENAKIS. Eh well, there are several facets, for example, I can say that there is order when there is symmetry. Michel SERRES. Already that is there, with symmetry, it is gained. Iannis XENAKIS. Yes, you gained there, of course. There is not to gain, it is a question of vocabulary. Michel SERRES. Not, not, I gained, that wants to say that one will return at time. If there is symmetry, there can be reversibility. Iannis XENAKIS. Not, because one can have order in things which are not temporal. It is for that that it is absolutely essential to distinguish between what is in time and what is out-time. For example, I take a whole of keys of the piano, which is an elementary case, I thus have intervals which are repeated, but they are not repeated in time, they are, fixed there. Because the keys of piano are on a piano which does not move. Michel SERRES. Therefore, they are out of time? Iannis XENAKIS. Out-time, yes. Michel SERRES. Is syntax then out of time? Iannis XENAKIS. Yes. Michel SERRES. I suspected it. Iannis XENAKIS. There, I have symmetries since I have reports/ratios, therefore I have repetitions. Michel SERRES. Yes, then the order is apart from time? Iannis XENAKIS. There are orders which can be apart from time. Now, if I apply this idea to time, I can obtain them also, but not in the real time, i.e. in temporal flow because is never reversible for him, but in a fiction of the time which is based on the memory. Michel SERRES. Is the piano a memory? Iannis XENAKIS. Il is a material memory, yes. Michel SERRES. A material memory. The question would be as follows: do you obtain irreversible drift? Iannis XENAKIS. I can it, of course, since I am not a gas and that I have at the same time the demon of Maxwell in me. Michel SERRES. Le demon of Maxwell made of the order. Iannis XENAKIS. The demon of Maxwell can reverse the things. Michel SERRES. We are there now. Thus there are reversible structures in the music. Iannis XENAKIS. They are reversible in the direction of out-time. Michel SERRES. Would the demon of Maxwell make pass apart from time? Iannis XENAKIS. I took the demon of Maxwell, but this demon does not change the order of temporal flow into oneself. It is necessary well to include/understand what occurs. For example, when it is said that a luminous flow, which passed under certain conditions and which becomes organized, ordered, gives the laser, the laser light, eh well, it is as if one had utilized the demon of Maxwell in it. Because differently one would have had only one light. unspecified, disordered. But this applies only to concepts or beings which can be reversible by definition. Time, is not reversible for him, I insist làdessus. Michel SERRES. If somebody showed, it is well Xenakis. The drift of the order or the structure to the disorder, it is nevertheless one of the secrecies of your composition. You agree well? Iannis XENAKIS. Yes. Michel SERRES. But, the first theorem of physics was proposed on the vibrating cords. Isn't a vibrating cord, a reversible phenomenon? Iannis XENAKIS. The positions out-time are reversible. Michel SERRES. What do you call position out-time? I do not include/understand. Iannis XENAKIS. Space intervals, for example, positions of the cord. They are reversible because they belong to the space which is not temporal. Michel SERRES. It is thus a clock! Iannis XENAKIS. It is thus a clock. Michel SERRES. Indeed, a clock as a vibrating cord make a counting of time. A vibrating cord can be a counting of time. It is measurement. Iannis XENAKIS. C' is a counting of time, but it is a counting of the time which is made, which is based on the reversibility of the positions and not of time, here is the fundamental idea. Because, like said it Héraclite, nobody cannot revive the same moment twice, though, in microphysics, one tries to prove the reversibility of time (it yet was not shown) with the parity, for example, of fifteen years ago, that time even, can be reversible, but there are not experimental data… Michel SERRES. The musics in question are a test to fight against the temporal irreversibility. Iannis XENAKIS. If you want. Michel SERRES. One will be able to generalize the thing little by little and to pass from the technique to the composition. Does the glissando have a relationship with the aforementioned irreversibility? This point really appears very important to me, you will see why presently. Iannis XENAKIS. I do not know if the glissando has an immediate report/ratio. Michel SERRES. You agree well that the glissando is a major element in your composition. Iannis XENAKIS. Yes. Michel SERRES. Pourquoi did you choose the glissando? Iannis XENAKIS. Perhaps an influence of the Euclidean geometry. Perhaps by the very fact that the glissando is precisely a modification, of something in the time, but unperceivable, i.e. which is continuous and which one cannot seize, because the man is a discontinuous being. Not only it is discontinuous in its perceptions, in its judgements, but in all. Continuity is a thing which escapes to him constantly. It is problems zénonienne, the very short change, and it is a kind of perpetual fight of our perception and our judgement which to try to imagine the continuous motion. It is what occurred besides, in particular in mathematics. They initially started with the discrete one to arrive at continuity well later. Michel SERRES. TI has there two elements in your work which lead me to think of the irreversibility. The first it is the drift of the order to the disorder by the probabilities, and the second it is the element glissando used constantly. lannÏs XENAKIS. Yes. Michel SERRES. Then, the music of Xenakis does not answer any more the definition that one gave a few moments ago, like a fight against the irreversible one, since you accept the irreversible one in these two fundamental techniques. Isn't your music different from all the others in what, precisely, it admitted for always the irreversibility of time? Against all the others. Iannis XENAKIS. Il is necessary that I return on top because I do not believe in the reversibility of time, of the time real, immediate, from temporal flow. I believe that one cannot make it retrogress, time. Michel SERRES. Yes, it is that. Iannis XENAKIS. Thus it is irreversible. What is reversible, they are judgements, if you want, that one makes on this flow of time. Let us take, for example, the most elementary thing which is, the durations. One duration is a thing which one can walk in time, it is thus reversible, commutative. It always has the same direction as time, of course (a duration does not have a contrary direction with temporal flow). I.e. if I wanted to write, draw, or rather to appear time visually, I would have put it on an axis as make the physicists, as make the musicians (musicians initially, then then physicists); it should well be said, with the range for example, they are the musicians who had, the first, invented the Cartesian .representation. Well. The flow of time would be represented by a line which, by definition, is a · continuity. On this line, I place points. They are the moments. The difference, between two unspecified points, is a concept resulting from the comparisons, mysterious assessments which I make on the reality of temporal flow that I admit a priori. It is this difference which is identified at the duration. It is it whom I can walk anywhere. It is thus reversible. But, him, the flow of time, is irreversible. And if I draw in a plane space an axis on which I carry heights, an axis which is normal with an axis of horizontal time, then, to go from a low point to a high point which is on the right, I can go only in one direction, upwards and from left to right. It is that the irreversibility. Michel SERRES. One arrived at the concept of irreversibility which characterizes your music, by two technical methods, drift of the order to the disorder on the one hand and by the use of the glissandi on the other hand. What also struck me, to read overall, at the same time, your music and your architecture, it is another invariant of your vision of the world: regulated surfaces, i.e. pH, the hyperboloid, etc Why this constancy of regulated surfaces? Iannis XENAKIS. Pour several reasons, I believe. Michel SERRES. It is necessary to pay great attention before D to lay because it is exactly the opposite of presently. A few moments ago, there was a drift towards the chance, while to leave the constant of regulated surfaces, there is a resumption of the repetitive structure. Iannis XENAKIS. Yes, it is another type of concern. It is a problem of continuity and discontinuity, resulting from elements of right-hand side. The line, it is perhaps the most primary element of continuity, of the expression of continuity. Michel SERRES. Isn't it only the result of the technique of the formwork? Because regulated surfaces, it is easier to case. Iannis XENAKIS. Not, one cannot case them, because they are with S curve, it would be necessary… Michel SERRES. If, since they are regulated, you inevitably have formwork made of always right boards on a pH or a hyperboloid. Iannis XENAKIS. Yes, but as it is with S curve, space is twisted and the ordinary formwork, being made plane boards, would marry only very imperfectly the forms with S curve. If one were to carry out a “left” formwork as for the boats, for example, that would be too much expensive. Michel SERRES. Let us return on our regulated surfaces and with the situation that they allowed us… a regulated surface can be generated by lines. Iannis XENAKIS. Oui, the line has an absolute fascination. A sunbeam is an attractive thing in oneself. One sees a sunbeam when one looks it through the clouds. The sunbeams which converge towards the ground are, actually, parallels. The line of a laser beam is something of absolute, the line of a fù of mason, it is an absolute thing too. The line, therefore, exists in nature. But, as a intellectual entity, it is the most attractive thing from the speed point of view, the direction point of view, and also from the continuity point of view. One cannot imagine something of simpler, the continuity point of view, than a line. Because, as soon as you have a curve for example, one supposes the forces which produce it, and there are all kinds of torsions, all kinds of rich curves, while the line is one, without forces repeating itself identically. Excuse me, I did not finish with regulated surfaces. It is the line, in three dimensions, which generates them (the glissando being a line in two dimensions). It makes it possible to imagine very complex forms with very simple, controllable elements. Michel SERRES. Minimum of technique, the maximum of achievements… Iannis XENAKIS. Results. Michel SERRES. Yes, of agreement… the final question will be as follows (I will finish on top): page 8 of your book [2], you have still mesh to leave with the data processing specialists, but it is necessary nevertheless to distinguish between data processing and the information theory. Iannis XENAKIS. Goods and the malicious ones! Michel SERRES. Finally, when one speaks about the disorder, it is about the thermodynamic disorder, but it is also about the background noise. Consequently, it is the same thing. Here the final question: there are at Xenakis two things which I do not manage to put together, initially a kind of fascination for the regulated invariants, i.e. regulated surfaces, then, for the syntactic invariants, and so on, invariance in general, in short, repetitive syntax, and in addition, a fascination which your thermodynamic concerns indicate, background noises, etc, and the glissandi which are elements, i.e. the opposite concern, the concern to slip irréversiblement towards a disorder, towards the background noise. How do you arrange this invariant fascination on syntax and this fascination towards the drift, towards the disorder? Perhaps is the music thus defined? JanDis XENAKIS. Not, because the disorder is a negation of the order which wants to say repetition here. The disorder thus, within the meaning of the periodicity, is reversible, of course (a periodic thing is reversible, but in its own definition). I want to say by there that it is what is not, essentially, temporal which is reversible. In this field, by definition except time, the beings can place themselves in any order. It is this constant concern of these two poles, the disorder or the order, personified by the periodicity (when periodicity is said, one says also invariant); it is all the range of the · possible degrees, from one pole to another, which constitutes a kind of mental category, in my opinion. It is it which is in all the history, as well of the philosophy as of the science, and which is one of the subjacent concerns of the music that I made. Michel SERRES. A last corollary question: can there be an order starting from the noise? Iannis XENAKIS. Yes. And then, which is interesting, it is that the noise which, physically, is a variation of the pressure which is not renewed identically (one can manufacture it either with cathode ray tubes, or with the calculating machine) can be simulated. However, the listener passes on the floor above, it does not remain in the event microscopically individual of the sample on the lower floor, and it perceives the noise like a whole macroscopically individual, therefore as something which has a regularity, an order! Michel SERRES. Alors the answer can now be done, it is perfectly general. You know that all the questions which currently arise pose around the problem: is there an order by the noise? However, it is your music which discovered that in first. Iannis XENAKIS. Thank you infinitely. DIALOGUE WITH BERNARD TEYSSÈDRE Bernard TEYSSÈDRE. Eh well, since the moment approach to conclude this defence and since the use (or protocol) leaves the last words to the president of the jury, allow him, expensive Iannis Xenakis, to tell you his joy, his emotion to see you presenting this thesis. This for personal reasons, initially. I o~blie not your surprise, and almost your skepticism, when I suggested you, here a few years, to present your candidature for a post of professor associated in U. E.R. of the Visual arts and Sciences of the Art, of which I was then the director. You gradually set up, within this new framework for you, a teaching which leads to your seminars of second and third cycle: “Formalization and programming in visual arts and in music”. I do not forget either, again, your surprise when, in agreement with our mutual friend Olivier Revault d' Allonnes, I committed you to present a thesis of doctorate of State, by gathering the partitions and the texts on which we discuss today. Here the personal reasons lead to questions of principle, those same as evoked Michel Serres presently. Like him, I am happy that researchers of high quality, but whose career and formation did not have anything “sorbonicole”, can from now on reach the doctorate of State. This situation is for a long time acquired in the foreign universities, in particular American; in France however, it is very new. I still remember incredulity that I met, in the years 1969-1970, by supporting the only idea that a musician or a sculptor could have his place in Sorbonne at the sides of a learned professor of history or philosophy. The University is not made for the artists, objected to me one. And why not? It seems to to me that, since, they automatically entered there. There does not exist only any more of trainings in musicology, fumology, history of art, but of the formations in music, cinema, in visual arts, where the practice and the theory, closely associated, go hand in hand. The artistic practice, as in a recent past, is not evacuated any more with the only profit of the reflexive speech, itself often subordinated to the hegemony of the history. In the interval of less than five years, complete university “courses” of artistic studies were set up, of the first cycle to the licence, the controls and the theses, of the IPES to the CAPES and aggregation. Personalities come from very diverse horizons, for example Michel Butor, Maurice Lemaître, George Charbonnier or Frank Popper, have their doctorate of State today, a fresquist like Jose Balmès or a man of theatre as Jacques Clancy teach their art under lecturers associated, and it is in this dynamics that present defence registers its full direction. Your thesis, expensive Iannis Xenakis, are a thesis, a true thesis, with the direction more devoted term - almost its medieval smell. It is it initially in this, that avoiding the pitfall of other defences “on file”, it is not equivalent by no means to a collection, a little randomly, disparate work; on the contrary, it is prevailed of a major unity, since texts presented, with the partitions which accompany them, convergent around the same fundamental topic, to which largely the debate related: the alloy (not “alliance”) between arts and sciences. Wouldn't it be rather about a certain design of art? And of a certain design of science? I acknowledge that I believe it. But it is by that precisely, that in a second direction, your thesis is really a thesis: not a research érudite on some point of detail, as it is very often the case, but an original, consequently debatable, and even contestable theory - again as in the Middle Ages, at time when the “doctors” clashed around Duns Scot or of Guillaume d' Occam. And it is with what I would like to attach me, not to briefly delay the exit of this already long meeting. I would like, by taking with witness only one works poured in the file, formal Musiques, to reveal it in-on this side, the latent assumptions which underlie the thesis, which melts its coherence and also its character of philosophical option: a very personal, valid option from this coherence even but, seems to me it, I am perhaps mistaken, Xenakis, valid among others which would be different, which of adventure could be contradictory for him, and neither more nor less valid than these other options. I will carry with what underlies, with what appears me to underlie, with this perhaps unperceived or unavowed whole of underground assumptions on which the building of the thesis would rest, a certain number of objections. I specify in advance that I do not assume them all (at least in their extreme form). It seems to to me however that “to play the devil's advocate”, afm to cause your reactions, your counterparts, in the hope to lead you to clarify the point of view which is clean for you, fact part of the rules of the game. And then, to go 3.lnSI to the extremes, for better apprecler or and Jusqu or your point of view is clean for you, that will help me to dissipate it Malayan that I have the weakness to feel in front of any aesthetic theory which would be presented in the form of universally valid, to evacuate the relents that I would suspect of a “cultural imperialism”. On this subject, I will say this: way in which I interpreted your work, formal Musiques, I found in him a major interest, comparable with that of axiomatic within the meaning of Hilbert or Peano, and who would be to base the music on a level of general information such as a certain number of musics (not all) of it would be deductible, as partial sets, by addition of restrictive constraints which would determine them. These constraints, which are called for example tonalities, or modes, or series, would come to particularize the sound universe, to cut out in him the field of possible musics. I say the universe well, not unplurivers. And I want to say that this book (but perhaps the thought of Xenakis it evolved/moved since) appears me to reason as if one could hope for an adding up theory, covering without gap the unit with the thinkable fields like if the old dream with Einstein with a theory unifying generalized relativity, quantum mechanics and thermodynamics was only on standby, as if the theorem of Godel could be overcome and not only circumvented by artifices of procedure. I believe to detect at Xenakis a choice in favour of the “system of the universe”; and in that its thesis appears all the more fundamental to me as it is really a thesis, in agreement with the conditions of production of a significant number of musical works, a thesis which however lets remain beside it of other theses, likely to found other musical works. Leaving this level of general information, I will pass to more precise questions, while trying to make appar~ître that the theory of Xenakis at the very least comprises two postulates and several options, the ones methodological, the others definitely subjective. The first postulate would be this one. In formal Musics, the history and the culture seem to me rejected in background, with the profit of a research of the invariants 10gico-mathematics. In this respect, perhaps the musical theory of Xenakis would find it equivalents in certain designs of the painting serial, or systematic, or programmed, for example in an inventory and combinative of the optical effects according to Vasarely. However I wonder whether the assumption of a stochastic distribution, with absolute equivalence of the probabilities in the starting points and the ways of passage, can be really constant. On the contrary, the anatomy and the embryology of the vertebrate superiors could indicate that the code of the genetic determinations so much “did not grow rich” (with the direction where “grows rich” a bank by information) during their evolution; that the development of the nervous system, particularly of the cortical centers, appeared rather by a proliferation of the neurons and a relative lability of their synaptic connections. In other words, by the most antiquated mammals to the man, the stock of the pre-established regulations would hardly have increased, it would have even strongly decreased if one brings it back to the multiplication possible connection networks. It would result from it a kind of random in the frayage of the ways, however random directed: not whole which it lacks determinations, but because it is governed by determinations other than genetic, i.e. because more and more the share of l’apprentissage s’étend aux dépens de la pure et simple maturation. However, this training is conditioned by a context which one could qualify, with the direction more general, of history, starting from the intra-uterine medium until the family life and school, until the sociocultural environment. You wonder where I want to come from there? With this. Account should be held, seems to to me it, of the interference between pre-established elements, which would include/understand invariants formalisables (these are those that formalizes Xenakis), and in addition a beam of cultural accidents or histories which would be inéliminables of the individual man. This interference constitutes, compared to genetic stock, a series of “chances”, with the most banal direction, that of Cournot, the intersection of independent causal chains. And what makes EC series of chances a continuous chain, directed, instead of an erratic dispersion, it is that it is fastened permanently with a relatively constant context, of a sociocultural nature. In these conditions, I wonder whether it is possible to maintain (as Xenakis on several occasions does it in its book) the fiction of amnesia: is it convenient to regard the man as “amnesic”, to locate it in the moment of its perceptions present by disregarding its individual past? Or, on the contrary, adme is not needed! is tre what a purely stochastic distribution almost excluded from the musical field, since it would have there equivalence of the probabilities neither in the starting points, nor in the ways of passage? In other words, is it possible to isolate the invariants logiço-mathematics, as if the musical experiment did not integrate determinations of a different nature, of a sociocultural, historical nature? Is my question clear, Xenakis? \ annis XENAKIS. Perhaps, I do not know. Bernard TEYSSÈDRE. I summarize my argument: Formal musics appears me to presuppose an equivalence of the probabilities at the same time as for the points starting and as for the ways of passage, whereas phylogenesis, the embryology and human physiology establish that such an equivalence is in theory excluded, if it is true that there is UJl numbers restricted genetic predeterminations, and that on the contrary the ways of nervous frayage are constituted mainly during the individual experiment in its social context. One would be obliged, to accept the theory of Xenakis, to suppose the “amnesic” man. I.e. the man who does not have history since the moment when the ovule was fertilized. Iannis XENAKIS. Je do not know if I said that. I do not believe it. Bernard TEYSSÈDRE. But the assumption of amnesia frequently intervenes. For example, page 35: “We will suppose that the points M higher defined can appear without any need other than that to obey a random law without memory.” Page 185: “We will start with us to abruptly consider amnesic so as to be able to go up with the sources of the mental operations of the composition and to release from the general principles valid for all the musics.” Iannis XENAKIS. Ah yes! But it is a provisional assumption of work, of reflexion and it is not) in the biological direction that I speak about amnesia. I speak! of amnesia in a mental effort to detach the major facts, to distinguish what is of what belongs to the current and conditioning that one receives, especially sociocultural fact. Bernard TEYSSÈDRE. What I want to say, it is that sociocultural conditioning would not be only one addition, something which would come to be added again to probabilities considered as at the beginning equiprobable, but would be on the contrary constitutive of the networks of connection themselves. So that one would never leave a kind of “No man' S absolute Land”, of a “close-cropped table”, but contrary to a ground highly laminated. Iannis XENAKIS. Yes, but this “highly laminated” is not proven at all. Precisely it is one of fundamental research in all the fields. For example, in biology and genetics, one knows very few things about the heredity of the mental structures, more or less elaborate and complex. It is a fact that heredity leads so that we are not plants or minerals. We are men who resemble each other besides, with eyes, bodies. But where one does not know at all what occurs, be in the constitution of our brain. Because one does not know which is the share of heredity in what one could call the categories. One does not know how the law of causality is born, why it is born. This principle, moreover, is equivalent to the reasoning reference frame. Then, the direction which one gives to time, with the temporal flow, which rests on the experiment but also on hard constructions of our brain which are made one does not know when: this is after the birth, or is this quite front, i.e. there is million or billion years. One cannot decide some. On the other hand, which one can possibly say, it is that, indeed, there is a part nongiven in our mental. Why can one say that? Eh well, because there are cultures so much, so much of approaches of reality, so much of reactions in front of an objective universe (if there exists)! This plurality makes that on higher levels, there is a greater freedom. Then, in this case could not one also change the things which appear immutable for the moment, and which seem universal? Let us consider the flow of time such as one conceives it and his structure of order which is subjacent so that we know, and who belongs to our everyday life, that of the atomic physicists, or that .du musician. This concept of the flow of time is it absolute or would be it modifiable? POlH” to sometimes happen to define these things and also to withdraw from them all slags of an education or a sociocultural tradition, it is necessary from time to time to suppose, make a little extreme assumptions, like amnesia for example. It is simply a working tool. Bernard TEYSSÈDRE. J' was very struck, Xenakis, when you have refers to the Greek music as with the feeder compost from which our Western tradition developed. I wonder whether it is not also the compost from which the theory of Xenakis is based on the universal music. And what Olivier Messiaen said on the possibilities of structures radically different from these undoubtedly does not contradict me. I point out my argument again: since genetic coding is extremely insufficient compared to the multiplicity of synaptic connections between neurons, the ways of passage are cleared in very great part during the individual development, development itself in very great part conditioned by the sociocultural context. Why did the agreement of third, which was perceived like “dissonant” with the Middle Ages, become at the time of Bach or Branch at this “consonant” point that a major or minor third defines “the triad” as major or minor? concluded from it that the postulate of an initial equivalence between the probable ones is perhaps not acceptable, and that the fact of rejecting the acculturation or the history of the music in the second plan to stick only to the invariants logico-mathematics, could be a ventured assumption. I am not even sure that one can eliminate the cultural one from the musical one, not on the level of sound perception. Iannis XENAKIS. Eh well, if one goes up on a stool and that one looks at the history of this stool, one sees that there are many things which occurred. More clearly, it would precisely be necessary to show this elimination of the sociocultural assets. If it is done, one can possibly find things which are independent of these assets and permanent, i.e. invariants as well in time in space. And therefore suddenly one finds, in the case of the scales ~u! change a little everywhere in the world, a personality which seems universal, it is the interval of quad. As by chance, it is by it which the musical theory of Aristoxène begins, it speaks about the quad-Juste. However it does not define it mathematically bus him rai~onne not as a pythagorician, though it knew mathematics and the pythagorism. But it regards the quad-Juste as the basic interval and it is by it that he begins his treaty. However, the quad-Juste, one meets it in all the cultures of the whole world. This corresponds to a kind of musical invariant, in a higher plan. But it is necessary, to realize it, to make close-cropped table of all epiphenomenes. • of all colourings which has such or such musical culture when it is said that it is a minor and sad mode or that it is a major mode. This example is very ~rivi~, obviously. In the same way on another plan, lorsqu one says that the music is melody, must be mélodiqu~, must be polyphonic, and that one cannot conceVOIr another music apart from this context. This, it is still a party taken which comes us from sociocultural designs. To release oneself from all that, i.e. to establish a fundamental thought, what does one have to make? The mathematicians and the logicians at the XIXe century, by removing mathematics from the verb and by creating the symbolic system, showed the way and it is well in this direction that I tried to see more clearly. Bernard TEYSSÈDRE. C' is what I said to the beginning, it is well a kind of axiomatic which is proposed to us there. Excuse me, I am obliged to go very quickly because it remains us little of time and I still have many questions to pose to you. I leave this debate to pass at another point. Another of your postulates, in my opinion. With that which one could call the principle “of made up dispersion”. By reading formal Musics, one can think that you admit an anteriority, at least methodological, elements, say sounds, or grains or clouds of grains, or classes logical, or of the boxes of flow chart, etc And this anteriority, I wonder (it is a question that I pose to you) up to what point it is compatible with the simplest data of perception, with those which founded, since nearly one century, Gestalttheorie. Generally, in your book, that is translated as follows: a certain number of components of the sound having been insulated and considered as basic elements, these fundamental elements are put in connection with musical hearing according to a model which would apply the law of Fechner, the feeling varying like the logarithm of the excitation. How that is it compatible with the already old reflexions of Von Ehrenfels on the very banal experiment of the transposition? Insofar as a musical sentence were heard in the tonality of major C, then heard, that I know, in minor F dièze, it may be in extreme cases that none the physical elements is common to both sets, and however both are perceived like “the same musical sentence”, only transposed into two tone different. How to explain that they are heard, if not like identical, at least like analogues? Couldn't one, instead of taking for starting points the elements (grains, or clouds of grains, or logical classes, etc), to consider that what is first, they are the relations and not the terms located at the two ends of these relations? Wouldn't this be what suggests, in your own music, the use of the glissandi? Your use of the glissandi would be equivalent almost contrary to what your theory exposes: it would not take any more for points of departure the elements, but their relation, their interval, and compared to this interval one could say that the grains of sounds would not play any more but one secondary part of stakes between the two extreme points of a glissando which would be, him, only perceived reality? Iannis XENAKIS. Yes, it is a good question, that one, because it is true that in the field of the music terms: composition, type-setter, indicate that which puts things together, therefore preexistent things, definite in a certain way. Bernard TEYSSÈDRE. Cela presupposes a primacy of the analysis compared to the synthesis. At least, the way in which “elements” are initially presented appears contradictory with the rather structural pace of the mode of presentation itself. Iannis XENAKIS. That does not presuppose that, necessarily, but that presupposes another thing, that presupposes a material universe in which the type-setter comes to put relations, structures, constructions, architectures. But this is true until certain point, because there is a whole part which is absolutely unknown, of the music and also of perception. Most of formal Musics is based indeed on this organization of sound objects given, but another part (it is the final chapter) share of a kind of total perception. If I say total perception, it is in the direction where there are not the molecules, objects that the type-setter comes to put together to constitute of the more or less advanced organizations, but a magma of possible states specific (discrete values of the pressure), in which it is able to manufacture forms following of the criteria that it must invent itself. The final chapter is another starting point completely contrary to what you have just said. If I baited myself with speaking here about discrete things, it is that, on the level of the samples of the pressure, they are discrete things well. It is because, fmalement, it is also the approach easiest and immediate to make and richest, with regard to the history of the music, as well of the past of today. One is more familiar, one is more at ease with discrete things as with continuous things, as well in the field of perception as on that of the judgement, but that does not exclude absolutely the things not défmies, the nondefinable things. Bernard TEYSSÈDRE. It is not at all of this indefinite that I spoke. I said that a melody is transposable without none of its physical elements remaining identical, and however it is recognized like “the same melody”. The point of view which starts from a sound form as a meaning totality is very other than that which starts from grains of sounds, then of clouds of grains, before establishing combinative between these clouds. To claim the opposite, it would be to confuse perception with its sensory stimuli. Iannis XENAKIS. Well, I do not see… Bernard TEYSSÈDRE. What none the sensory stimuli is the same one, and which however it is same perception? Iannis XENAKIS. Yes, but attention, you speak there about different levels. When you say that the notes are not any more the same ones, of agreement. In a melody there is not only that the notes, there are the relations between the notes, i.e. the intervals, etc Bernard TEYSSÈDRE. I said that precisely: that to a “molecular” point of view to some extent, one can oppose a “relational” point of view, according to which the famous molecules would be only the extreme points of the relations. Iannis XENAKIS. Naturally! That of which I treat in this book, they is relations of levels, in the plural, higher levels, above the elements! Bernard TEYSSÈDRE. Soit. Let us pass to another question. It is a little in connection with what one said, presently, on the concept of style. I wonder whether there would not be, in your work of theorist and type-setter, a privilege of saturation, i.e. a kind of option, subjective taste, for dense sound spaces, full, and not rarefied. It is striking of reading, page 74, this ergodic definition of the principle: “The capricious effect of an operation depending on the chance is regularized more and more by a sufficient repetition of this operation.” However, it may be precisely that the choice even of the principle ergodic is of stylistic nature. It may be that it is a subjective option, a personal taste which pushes Xenakis to choose saturated sound spaces, rather than rarefied, to choose great numbers rather that rare individuals, those whose, Leibniz would say, the definition would imply infinite analysis. It is undoubtedly by a principle of economy (but this principle of economy is also a claim of being able) which prevails the will to control the saturation of sound spaces. One can conceive very well the opposite option, which would be the taste for the rare individual, for the noncontrollable chance. In short, the choice of John Cage or Marietan, with the opposite pole of the choice of Xenakis. Iannis XENAKIS. I believe that you mixtures a little several things at the same time. Excuse me to say that to you. To return from there to the ergodism, the definition, there, is a definition of mathematics, it is not me which said it. Bernard TYESSÈDRE. I know it well. Iannis XENAKIS. I took it in the book of the very important French mathematician who wrote on the Markovian chains in the Forties, Maurice Fréchet. It has this definition of the processes ergodic, of ergodicity. But this is completely limited in this part of my work. On another side, when one speaks about chance, it is necessary to pay attention well. Bernard TEYSSÈDRE. It seems to to me rather than the choice repeated in favour of the great numbers, the simple fact of taking for principle the theory of probability, implies a preference for a plenitude to control, in opposition to the rare event which, would not be controllable for him. Iannis XENAKIS. But I made a whole work, with Achorripsis and other compositions, on the rare event and rarefaction. It is a question of density, and the density is a concept which is treated in formal Musiques, longitudinally and into broad. Bernard TEYSSÈDRE. Doesn't your music, for example, privilege the fortissimo and the pianissimo, rather than of impalpable nuances, the vast sound masses, rather than the vacuum or silence, the intense emotive load, rather than the destitution collected? Iannis XENAKIS. I did not do much rarefied music, it is sure. Bernard TEYSSÈDRE. Not, not much of rarefied music. Ni of music which would attempt to collect the individual one, within the meaning of Olivier Messiaen collecting a song of bird, within the meaning of John Cage collecting the fortuitous meeting of seven radio sets which transmit different emissions. There is place, in these musics, for the rare meetings, with the place that it seems me to find, in this book, an insistent search (even when would be to deviate some then) for highly probable meetings. Iannis XENAKIS. It is much more complex. Initially, the highly probable one has direction only in connection with probability distributions known a priori and relating to certain sets of well defined events. The notion of fortuitous, of unforeseeable, is fundamental for the probability. The highly probable one does not contradict the highly fortuitous one and it does not cease being fortuitous and becomes foreseeable only stochastically, with long and statistically. Consequently, to each occurrence of an event taken in a given unit, all occurs as if we are in front of a randomly which had phenomenon, unexpected, therefore rare in a strict sense of the periodicity. On the other hand, to make at the same time walk several stations, as of the moment when the stations are open, we are in front of a fact accomplished thus determined and vacuum of chance. In this case, the fortuitous one is born with the level from the unexpected meetings from chains of events suitable for each station, which, they, is more or less strongly given. Therefore, all occurs as if we were in front of an overall foreseeable phenomenon, but locally fortuitous, which would constitute the défmition of highly probable. The two approaches are, to some extent, equivalent. The appreciable difference is that, in my case, I try to create the chains of events but also the events, in a more faithful and homogeneous way with the basic idea which is the unpredictability, the fortuitous one. In addition, the concept of scarcity relates to a whole of possible states, and their recurrences. Many or little recurrences of a given event, in time, result in the concept of density (of scarcity). However, the second chapter of formal Musics starts with the rare events and their treatment. Bernard TEYSSÈDRE. It treats some for better eliminating them… Iannis XENAKIS. Non, at all… Bernard TEYSSÈDRE. … or to relegate them to the second plan… Iannis XENAKIS. Not, because from the technical point of view, it is with the formula of Poisson that I start, who precisely milked rare events that I integrate in my compositions. This known as, the rare events are rare only according to the temporal scale. And it happens that the rare states can be considered as being dense, frequent. Indeed, the events of a music can appear aggregate in a rarefied way, if the selected temporal unit is sufficiently small. While if the temporal unit is selected sufficiently large, the same events, laid out in the same way, with the same fortuitous meetings appear more brought closer, denser. Thus the phenomenon, qualitatively, remains the same one. It is like when one approaches a Geiger tube of a radioactive source or that one moves away it from there: it is the same probability distribution, independent of the distance (of the temporal unit). The phenomenon is the same one. It is the same law. Bernard TEYSSÈDRE. Yes, but forgives me if I return so that Michel Serres said a few moments ago, when it pos? it in problem: how to establish the order starting from the noise? This problem, it is that which you assume, it me ~mble, but one can just as easily conceive, I repeat it, a type different of musician, that of John Cage or Marietan, who would not propose to establish the order ~ to leave the noise, which on the contrary would endeavour to collect 1 ~vénement rare, the individual one as tel. not to make it emerge from the disorder, on the contrary to accept it as an individual whose exhaustive analysis would be impossible, because infinite. Iannis XENAKIS. C' is what I try to say. Bernard TEYSSÈDRE. But how this Xenakis-Ci, not another, could leave there? We find the problem of the personal style about which we spoke… Iannis XENAKIS. Considers rare events in a whole of other events, and applies the temporal report/ratio to obtain rarefaction. It is certain that you will find events rare isolated. But if you conceive the whole of the events, overall, the rare events will take shape on a bottom, in the middle of an environment which, is much more complex to him. To put a silence, around, on the left and on the right of an event, it is a completely possible question but which, logically, is not fundamental. It is a question of scale, which corresponds to the degree of attention that you carry on this event, therefore degree of relief that you wish to give him and who are an aesthetic decision of order. But in the nature or the thought of the man, there is nothing which is single in the universe and time. I.e., on the contrary, the periodicity (in the broad sense) of the event, its recurrence, in oneself or with its environment, is completely natural, and even unthinkable differently. Bernard TEYSSÈDRE. Certainly, but in the choice even of the elements that you are given at the beginning, it intervened already a certain restriction of the total field, i.e. the selected matrix does not comprise any more totality of the possible ones. Would be this only because it is agreed from the start that there will be, for example, an orchestra. These preliminary choices do not make it possible any more to incorporate among the possible sounds, which I know, the cough of a caught cold listener, nor noise of a fly which would fly in the room; and then, to integrate into the music the fly or cough, as John Cage would do it, that would concern another musical principle, different from the tien. Iannis XENAKIS. Well, I will say you why. Very simply because, in our life of the every day, we have all these fortuitous noises. They are full with banality and they annoy me. That does not interest me to reproduce banalities. Bernard TEYSSÈDRE. J' agree well; only, which I want to emphasize, it is that without your knowledge it is about an aesthetic choice… Olivier REVAULT Of ALLONNES. I believe nevertheless that there is in formal Musiques, page 142, in connection with the musical strategy and of Duel a brief reply which goes in the direction of what said Teyssèdre. When you give, page 141, the six events, it can do without a cloud grains, behaviours of cords, percussions, etc, and silence is nevertheless the sixth and last event. I do not draw any conclusion for the moment from it. However, on page 142, you speak only about the five events, the first five properly sound events, silence left, it appears only in bottom of the page. Why, then, this silence you have, if I dare statement, last under silence during more than one page, to reinject it in the second table? You say: “The introduction of the tactic of silence 6 modifies the preceding matrix.” And now I defer in bottom of page 141, whereas the various events can have mentions which are well, very well, etc, silence, is always “passable for him”. All in all, you do not like silence. Iannis XENAKIS. Silence is banal. Bernard TEYSSÈDRE. I do not want to lengthen this debate inordinately. It is clear that Revault d' Allonnes does not dispute of anything fruitfulness prospects opened by Xenakis. And, certainly, me either. What, for my part, I feared a little, they that these fertile prospects do not appear, is seen outside, like “imperialists”. I want to say that a very personal musical theory, underlying a very personal musical research, could not make null and void of other musical theories, different if they are not opposite. In the same way that the programming of serial tables for computers does not make obsolete the accidental painting, an “abstract” ink of Michaux, a “action painting” of Pollock, and that painting-painting within the meaning of Support/Surface did not reject into the limbs a not-painting with the direction dadaïste. I will almost come from there to say that if, as Heidegger claims it, any metaphysics is an experiment around an idea, then this doctrinal beam on which we discussed constitutes a metaphysics of the music more a musical science. Because it implies, in on this side its scientificity, a certain aiming towards science. The corpus presented has beautiful being as scientific as it is wanted it, the aiming subjacent with the corpus is not of the same order that the corpus itself, and it is perhaps there that this personal coefficient intervenes, this subjective question of style of which we discussed. It appears to me that on several occasions intervene of the selection criteria, of choices which underlie the thesis, and which consequently, this thesis even has as a secret base a certain number of principielles assumptions. I would consider readily the work of Xenakis the made-to-order of the treaty of Alberti, like a kind of “legitimate”, legitimate construction with the proviso of not becoming normative and of letting remain out of it, against it, other methods of constructions as legitimate as it. Of course, for being able to say that, other topics, I did not do it, time I would have been necessary to develop missed it. In a few words, I would have liked to discuss the problems arising from the report/ratio of in-time and of out-time, because it appears me to bring into play a certain philosophy of the time, a design which would oscillate between the idea aristotelician of time like numbers movement, on a side, and another side the concept, different undoubtedly, time like the fourth dimension of an event. It is by no means a question of taking again the old discrepancy bergsonienne: time versus lasted. What is in question, it is a time like dévidement ordered, linear, a time which belongs to the same system of thought as the monade of Leibniz (deployment of a mathematical function) or than the concept of Hegel (the sphere toujours-déjà-Ià of the en-soi spreading poursoi in cycle of the method). This time, it is that of the Occident, that of our mother Greece, where it drew one and the other of its two faces: logic and rhetoric. According to such a design, the music is thinkable, is thought like “speech”. To transpose a sentence of Barbaud, which affirmed being in search of “musics non-beethovéniennes”, I would say that Xenakis, in agreement with the Greek tradition then Western, proposes axiomatic music beethovénienne to us generalized. Be would the only possible one? I Barbaud, couldn't one evoked as evoke Japanese Gagaku, all-already-together, the irradiation of same around same - instead of the chain logic-rhetoric as is the musical “speech” of Occident, this passage of same to other-of-even? And since, ghost with my starting point, one would be maintained inside the “speech” of Occident, how to reconcile these two extreme points of its pendular oscillation, sometimes time like the “fourth dimension of the event”, sometimes time like “numbers movement”? In this second case, the movement would be the first, and time, far from being one of the co-ordinates in the series of the events, would hardly be but what counts it? Iannis XENAKIS. One spoke about that, I believe, a few moments ago, it is the metric one. It yale temporal flow, which are an immediate data, and it there with metric which is a construction that the man made over time. And one cannot escape from it, that one is a musician or that one is a physicist, one passes by the same bridge. I will answer you with another thing: I do not exclude at all from other approaches of the music, and I do not want at all but you me taxes of imperialist for what I did. Bernard TEYSSÈDRE. Not, not, Xenakis does not have anything a imperialist. It may be even that, behind its highly scientific tools, when Xenakis works with its music, Xenakis remains deeply humanistic: it lets show through a personal style, one Me of artist. Its choices are quite founded, since its music is of excellent music, but on what are based, if it is not, in addition to science, on an idiosyncrasy, the choices of a personality powerful and rich in initiatives? Under-Xenakis which would apply the science of Xenakis, without having personality of Xenakis, would never produce in music but under-Xenakis. Don't these choices so quite founded let remain a share of irrational, of not-founded? To take an example, which illustrates well the difference between two personalities, both of great scale, when Barbaud resorts to the computer, musical work, for him, it is the programming even. One can understand a quantity of sound versions resulting from the same program, without none of these versions being preferable with any other, since work is located in on this side its audible alternatives. With the place that with the ear of Xenakis, seems to me, all the versions will not be considered equivalent, it will be of it a certain number of “preferable”, and the partitions will retain those of which the sound effect “will have been preferred”; isn't this (Polytopes excluded) often the case? Iannis XENAKIS. But it is my privilege, it is my duty to prefer a thing with another. Bernard TEYSSÈDRE. Undoubtedly, since thus your personality decides some. Your maxim however does not have anything an obviousness: Barbaud, leaves to repeat me, does not prefer, it composes its programming and any hearing is equivalent to the different one. Xenakis, it is to him its right, has its preferences. Iannis XENAKIS. But it is natural, it is completely normal. Bernard TEYSSÈDRE. It will be your word of the end. The jury will withdraw itself to deliberate. (After a short deliberation, the jury returns and its president announces that the title of doctor ès-letters and social sciences is decreed with Iannis Xenakis with the “Very honourable” mention.) In the music of Xenakis, mathematics plays an essential part as a philosophical catalyst, like tool of working of the sound or visual buildings. Xenakis was also useful of the computer to compose some of its partitions. This musician who is a also architect, this man of science who is also philosophical, chose for topic of his arts doctorate and sciences the DC alloys” between arts and sciences. It is the defence of this doctorate, which took place in the Sorbonne, in 1976, that we publish, with the questions and the interventions of the members of the jury. We will not be astonished only that by Olivier Messiaen treats musical composition, that of Michel Ragon of architecture, celie of Michel Serres of mathematics and sciences. Summoned to be explained on its music, Xenakis shows that its culture is at the same time philosophical and scientific, which is, it is known, exceptional. Thus one will know better that by the way whose Antoine Goléa wrote: DC Xenakis, it is perhaps the most pathetic figure more attaching, and also more exasperating music of the xx& century. “Let us quote also Claude Lévi-Strauss who, questioned on Xenakis by the Literary Fortnight, on August 1, 1978, answered: DC I am very sensitive to his writings; I find that it is erudite, intelligent and subtle.”