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 Teyssčdre

 

 

 

 

 

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 Teyssčdre

 

 

 

 

 

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 Teyssčdre. 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 TEYSSČDRE

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 TEYSSČDRE

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 TEYSSČDRE

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 TEYSSČDRE

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 TEYSSČDRE

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 TEYSSČDRE

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 faēade 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 naļve. 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 Franēois-Bernard Māche. 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 TEYSSČDRE

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 Revķ 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 TEYSSČDRE

 

 

 

 

BERNARD TEYSSČDRE

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 TEYSSČDRE

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 TEYSSČDRE

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 TEYSSČDRE

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 TEYSSČDRE

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 TEYSSČDRE

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 TEYSSČDRE

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 TEYSSČDRE

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 TEYSSČDRE

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 TEYSSČDRE

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 TEYSSČDRE

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 TEYSSČDRE

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 TEYSSČDRE

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 TEYSSČDRE

You deal with them in order to dismiss them ...

 

 

IANNIS XENAKIS

No, not at all ...

 

BERNARD TEYSSČDRE

... 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 TEYSSČDRE

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 TEYSSČDRE

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 TEYSSČDRE

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 TEYSSČDRE

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 TEYSSČDRE 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 TEYSSČDRE

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 TEYSSČDRES

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 TEYSSČDRE

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 TEYSSČDRE

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 Teyssčdre

 

 

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 Teyssčdre

Collection «Synthčses contemporaines», dirigée par Michel Ragon

© Casterman 1979

ISBN 2-203-23170-X

Imprimé en Belgique par Casterman, s.a., Tournai, aoūt 1979. N° Impr. 4126. N°

Édit. 6112.

Dépōt 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 Teyssčdre

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 Teyssčdrega

 

 

 

 

 

 

 

 

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 Teyssčdre, 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 TEYSSČDRE

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 TEYSSČDRE

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 TEYSSČDRE

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 ˛est 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 TEYSSČDRE

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 passaa˛i, 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.