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Formalized Music Formalized Music THOUGHT AND MATHEMATICS IN COMPOSITION Revised Edition Iannis Xenakis Additional material compiled and edited by Sharon Kanach HARMONOLOGIA SERIES No.No.6 6 PENDRAGON PRESS STUYVESANT NY Other Titles in the Harmonologia Series No.1 Heinrich Schenker: Index to analysis by Larry Laskowski (1978) ISBN 0-918728-06-1 No.2 Marpurg's Thoroughbass and Composition Contents Handbook: A narrative translation and critical study by David A. Sheldon (1989) ISBN 0-918728-55-x No.3 Between Modes and Keys: German Theory 1592-1802 by vii Joel Lester (1990) ISBN 0-918728-77-0 Preface No.4 Music Theory from Zarlino to Schenker: A Bibliography Preface to Musiques formelles ix and Guide by David Damschroder and David Russell xi Williams (1991) ISBN 0-918728-99-1 Preface to the Pendragon Edition 1 No.5 Musical Time: The Sense of Order by Barbara R. Barry I Free Stochastic Music (1990) ISBN 0-945193-01-7 II Markovian Stochastic Music-Theory 43 III Markovian Stochastic Music-Applications 79 Chapters I-VIII of this book were originally published in French. 110 Portions of it appeared in Gravesaner Blatter, nos. 1, 6, 9, 11/12, 18- IV Musical Strategy 22, and 29 (1955-65). V Free Stochastic Music by Computer 131 Chapters I-VI appeared originally as the book Musiques Formeiles, 155 copyright 1963, by Editions Richard-Masse, 7, place Saint-Sulpice, VI Symbolic Music 178 Paris. Chapter VII was first published in La NeJ, no. 29 (1967); the Conclusions and Extensions for Chapters I-VI English translation appeared in Tempo, no. 93 (1970). Chapter VII 180 VII Towards a Metamusic was originally published in Revue d'Esthtftique, Tome XXI (1968). 201 Chapters IX and Appendices I and II Were added for the VIn Towards a Philosophy of Music English-lan~ge edition by Indiana University Press, Bloomington IX New Proposals in Microsound Structure 242 1971. 255 Chapters X, XI, XII, XIV, and AppendiJC III were added for this X Concerning Time, Space and Music 268 edition, and all lists were updated to 1991. XI Sieves 277 XII Sieves: A User's Guide Library of Congress Cataloging-Publication Data 289 XIn Dynamic Stochastic Synthesis Xenakis, Iannis, 1922- 295 Formalized music: thought and mathematics in XIV More Thorough Stochastic Music composition / lannis Xenakis. p. c.m. __ (Harmonologia senes ; no. 6) Appendices 323,327 "New expanded edition"--PreE I & II Two Laws of Continuous Probability 329 Includes bibliographical references and index. III The New UPIC System ISBN 0-945193-24-6 335 1. o Bibliography Music--20th ccntury--Philos phy and aesthetics. 2. 365 Composl 'f.J.' on (MusiC) 3. Music--Theory--20th. century.. I 4. Discography Music __ 20thcentury--History and cntlClsm. I. TItle. 1. 371 Biography: Degrees and Honors Series. 373 ML3800.X4 1990 Notes 90-41022 383 781.3--dc20 RP Index L'P ~57(JlN v Preface The formalization that I attempted in trying to reconstruct part of the musical edifice ex nihilo has not used, for want of time or of capacity, the most advanced aspects of philosophical and scientific thought. But the escalade is started an d others will certainly enlarge and extend the new thesis. This book is addressed to a hybrid public, but interdisciplinary hybridiza­ tion frequently produces superb specimens. I could sum up twenty years of personal efforts by the progressive filling in of the following Table of Cohercnces. My musical, architectural, and visual works are the chips of this mosaic. It is like a net whose variable lattices capture fugitive virtualities and entwine them in a multitu~e of ways. This table, in fact, sums up the true coherences of the successive chronological chapters of this book. The chapters stemmed from mono­ graphs, which tried as much as possible to avoid overlapping. But the profound lesson of such a table of coherences is that any theory or solution given on one level can be assigned to the solution of problems on another level. Thus the solutions in macrocomposition on the Families level (programmed stochastic mechanisms) can engender simpler and more powerful new perspectives in the shaping of micro sounds than the usual trigonometric (periodic) functions can. Therefore, in considering clouds of points and their distribution over a pressure-time plane, we can bypass the heavy harmonic analyses and syntheses and create sounds that have never bc.:fore existed. Only then will sound synthesis by computers and digital-to-analogue converters find its true position, free of the rooted but ineffectual tradition of electronic, concrete, and instrumental music that makes use of Fourier synthesis despite the failure of this theory. Hence, in this book, questions having to do mainly with orchestral sounds (which are more diversified and more manageable) find a rich and immediate applica­ tion as soon as they are transferred to the Microsound level in the pressure­ time space. All music is thus automatically homogenized and unified. vii viii Preface to the Second Edition "Everything is everywhere'" IS h ' Coherences' Herakl 't Id t e word of thIs book and its Table of , el os wou say th t tl The French ed'( u' a le ways up and down are one, 1 IOn, ivmslques Fonnelles d d Richard director of La R Lf"' ' was pro uce thanks to Albert , evue iVluslcale The En r h d" completed version res It r h' .,.. g IS e HIOn, a corrected and , u s lrom t e InItIatIve of M CI' I who translated the fi t' hr.·lflStop ler Butchers, Preface to Musiques Formelles Hopkins and M ~sMsIX c apters, My thanks also go to Mr. G, W. and VIII respec:iv:~y' t rMs,JOMh~ Challifour, who translated Chapters VII .' ,0 r. Ichael Aro d M B IndIana University Pre } d' nson an r. ernard Perry of ss, w 10 eCIded t bl' h . Natalie Wrubel who d't d h' . 0 pu IS It; and finally to Mrs. , e 1 e t IS dIfficult bo k . h . fi . correcting and rephra . 0 WIt III Illite patience, SIng many obscure passages. 1970 1. X, This book is a collection of explorations in musical composition pursued in several directions. The effort to reduce certain sound sensations, to under­ TABLE (MOSAIC) OF COHERENCES stand their logical causes, to dominate them, and then to use them in wanted Philos(JphU (in the etymological sense) constructions; the effort to materialize movements of thought through sounds, Thrust towards truth, revelation Qu t' creativity. es In everything~ interrogation harsh c ·t' . then to test them in compositions; the effort to understand better the pieces elz . J rl IClsm, active knowledge through apltrs <,m th~ sense of the methods followed) of the past, by searching for an underlying unit which would be identical PartJaIly Inferential and experimental with that of the scientific thought of our time; the effort to make "art" Entire1y inferential and experimental Other methods ARTS (VISUAL, SONIC, MIXED ••• ) while" geometrizing," that is, by giving it a reasoned support less perishable SCIENCES (OF MAN, NATURAL) to con;e than the impulse of the moment, and hence more serious, more worthy of This is Why the arts are li d PHYSICS, MATHEMATICS, LOGIC • o ° feer, an can therefore guide the sciences hO o. the fierce fight which the human intelligence wages in all the other domains Categolles of Queslrons (fragmentation of th dO. 0 ,W lch are entirely mferential and experimental. e Irectlons leadIng to creativ k J -all these efforts have led to a sort of abstraction and formalization of the REALITY (EXISTENTlALJT'V)' CAU C now edge, to philosophy) AS A CONSEQUENCE OF ' SAUTY j INFERENCE: CONNEXITY j COMPACTNE • musical compositional act. This abstraction and formalization has found, NEW MENTAL STRUCTURES j INDETERMINISM SS..:...TE~PORAL AND SPATIAL UBIQUITY as have so many other sciences, an unexpected and, I think, fertile support FamUies of Solutions OT Proced:reJ (of th b . / ~ . bl-po!e ~ ••• DETERMINISM j •• e a OYe categones) ~ ... ~ in certain areas of mathematics. It is not so much the inevitable use of FREE STOCHASTIC MARKOVIAN GAMES mathematics that characterizes the attitude of these experiments, as the materialized by GROUPS a computer pro- overriding need to consider sound and music as a vast potential reservoir in ~. ~ ,eees (examples of particular realization) gram which a knowledge of the laws of thought and the structured creations of ACHORRIPSIS thought may find a completely new medium of materialization, i.e., of ANALOGlQUE A DUEL 'T/lO-I, 080262 AKRATA ANALOGIQ.UE B STRATEGIE NOMOS ALPHA communication, 'T/4B-l,240162 SYRMQS ATRBES NOMOS GAMMA For this purpose the qualification" beautiful" or "ugly" makes no Clas if" S . EI MORSIMA'AMDRSiMA sense for sound, nor for the music that derives from it; the quantity of us 0 onte ements (sounds that are heard and recog ° d O~CHESTRALJ ELECTRONIC (produced by analogue de:~~: as a whole, an~ classified with respect to their Sources intelligence carried by the sounds must be the true criterion of the validity o wIth computers and digital-to-analogue converters) S)J CONCRETE (microphone collected), DIGITAL (rt".:alize~ M rcrosounds J ••• of a particular music. Forms and structur . th . ° es In e pressure-time space recognition of h This does not prevent the utilization of sounds defined as pleasant or microstructures produce ,te classes to which microsounds belong h' M' ° orw Ich beautiful according to the fashion of the moment, nor even their study in Icrosound types result from questions and solutions that levels. were adopted at the CATEGORIES, FAMILIES, and PIEces their own right, which may enrich symbolization and algebration, Efficacy is in itself a sign of intelligence.
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