Other Titles in the Harm onologia Series No. Portions of it appeared in Gravesaner Blatter, nos. Library of Congress Cataloging-Publication Data. Xenakis, Iannis, a Formalized music : thought and m thematics in composition 1 Iannis Xenakis. Includes bibliographical refer ISBN y and aesthetics. Musicth century-Philosoph.
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Other Titles in the Harm onologia Series No. Portions of it appeared in Gravesaner Blatter, nos. Library of Congress Cataloging-Publication Data. Xenakis, Iannis, a Formalized music : thought and m thematics in composition 1 Iannis Xenakis.
Includes bibliographical refer ISBN y and aesthetics. Musicth century-Philosoph. Music 3. Title cnucJsm. But the escalade is started and others will certainly enlarge and extend the new thesis. My musical, architectural, and visual works arc the chi ps of this mosaic.
T his table, in fact, sums up the true coherences of the successive. Only then will sound s y n th esis by computers digital-to-analogue converters find its. The English edition, a corrected and completed version, results from the initiative of Mr. Christopher Butchers, who translated the first six chapters. My thanks also go to Mr. Michael Aronson and Mr. Natalie Wrubel, who edited this difficult book with infinite patience,. This is why the arts are freer, and can therefore guide the sciences, which are entirely inferential and experimental.
This abstraction and formalization has found, as have so many other sciences, an unexpected and, I think, fertile support in certain areas of mathematics. It is no t so much the inevitable use of mathematics that characterizes the attitude of these experiments, as the overridin g n e e d to cons i der sound and music as a vast potential rese r voir in.
My compositions constitute the experimental dossier of this undertaking. In the beginning my compositions and research were. Scherchen and Olivier Messiaen in music, and Prof. Guilbaud in mathematics, who, through the virtuosity and liberality of his thought, has given me a clearer view of the algebras which constitute th e fabric of the chapter devoted to Symbolic Music.
The exploration of the co nc eptu al and sound world in which I have been involved necessitated an harmonious or even have presented always been. The artist man has the duty and the privilege to decide, radically alone, his choices and the value of the results.
By no mea n s should he choose Naturally, it. His interest lies in embracing the most vast horizon of knowledge and problematics, all p re sented above. It is on.
A sort of musical drawi ng board which, through the digitalization of a drawing, enables one to compose music, teach acoustics, engage in musical pedagogy at any age. This piece was written at the request. Will it eve r be found? When and by whom and. Art, and a bove all, music has a fundamental function, which is to catalyze the sublimation that it can bring about through al l means of expression.
It must aim thro ugh fixations which arc landmarks to draw towards a total e xalta ti on in which the individual mingles, losing his consciousness in a truth immediate, rare, enormous, and perfect.
If a work of art succeeds in this undertaking even for. This is why art can lead to realms that religion still occupies for some people. The music of antiquity, cau s al and deterministic, was already strongly influenced by the schools of Pythagoras and Plato. Plato insisted on the principle of c au sali ty , "for it is impossible for anything, to come into b e ing without cause" Timaeus. Strict causality lasted until the nineteenth century when it underwent a parallel between European.
It is only r ecen tly that knowledge has been able to penetrate chance and has discovered how to s epar a te its d egrees -in other words to ra t ion al ize it progressively, without, however, su cceed i n g in a definitive and total explanation of the problem of " pure chance.
It is therefore n ot surprising that the presence or absence of the principle of causality, first in philosophy and then in the sciences, might influence musical co mp os ition. The e xplanation of the world, and consequently of the sonic phenomena which surround.
This law i mpl ies an asymptotic evolution towards a stable sta te , towards. These laws. We understand the first-rate position which is set theory, not only for the construction of new works, but. In the same way a an investigation of history wi t h the help of carried thro ug h without the help of logi c-t he queen. For e verything that is said here on the subject. From t his very general, fundamental point of view, from which we wish to examine and make music, primary time appears as a wax or clay on which opera tio ns and relati ons can be inscribed and engraved, first for the purposes of work, and then for communication with a third person.
Commutative, metric time symmetrical is subjected to the same logical laws and can therefore also aid organizational speculations. What is remarkable is that these fundamental notions, which are necessary for construction, are found in m an from his tenderest age, and it is fa s ci n ating to follow their evolution as Jean Piaget1 has done. After this short preamble on generalities we shall enter into the details of an approach to musical composition which I have de v elo ped over several years.
I call it "stochastic," in honor ofprobabi1ity theory, which has served as a logi cal framework and as a method of resolving the conflicts and knots encountered. What, in fact, d oes a musical composition offer strictly on the cons t ru ction level? It o ffers a collection of sequences which it wishes to be causal. When, for simplification, the major scale implied its hierarchy of tonal functions-tonics, dominants, and subdominants-around which the other n ot es gravitated, it constructed, in a highly deterministic manner, linear processes, or melodies on the one hand, and simultaneous events, or chords, on the other.
What is paradoxical is that he did this in the modal field. He created a multimodal music which immediately found imitators in serial music. At the outset Messiaen's abstract systematization found its most justifiable embodiment in a multiserial music. I t is from here that the postwar nco-serialists have drawn their inspiration. They could now, following the Vienna school and Messiaen, with some occasional borrowing from Stravinsky and Debussy, walk on with ears shut and proclaim a truth greater than the others.
Other movements were growing stronger; chief among them was the systematic exploration of sonic entities, new instruments, and "noises. M u ltise ria l music, a fusion of the multimodality of Messiaen and the Viennese school, re ma i ned , nevertheless, at the heart of.
I described the. This is the fu nction of stochastic science. E v e ryon e has observed the soni c phenomena of a political crowd o f d oz e n s or hundreds of tho u s a n d s o f people.
The human riv e r shouts a sloga n i n a uniform rhythm. Then a no t he r slogan springs from the head of the demonstration ; it spreads tow a rd s the tail, re p l ac i n g the first.
A wave of transition thus passes from the head to the tail. The c l amo r fills t h e city, and the i nh ibiti n g force of voice and rhy t h m reaches a cl imax. It is an event of great power and beauty in its fe ro c i ty. Then the impact between th e demonstrators and th e enemy occurs. The perfect rhy t h m of t h e last s logan breaks up in a huge clu s t e r of ch aotic shouts, which also spr e a d s to the tail.
Imagine, in add i t i o n , the re p orts o f dozens of mach ine guns and the whistle of bullets a d d i r g their punctuations to this total disorder. T he crowd is t h e n rapidly dispe rsed, and after son i c and vi su al hell follows a detonating cal m , full of despair, dust, and death.
The statistical laws of t h e se events, separated from their p ol it i c al or moral context, are the same as t h os e of the cicadas or the rain. They are stochastic laws. Here we touch on one of the great p rob le ms that have haunted human intelligence since antiquity : continuous or d iscontinuous transformation. The sophisms of movement e. One may p rod u c e continu ity with either continuous or discontinuous elements.
A multitude of short glissandi on strings can gi ve the impression of continuity, and so can a multitude of p izzicat i. Passage s l arge mass. I f glissandi are long and sufficiently i n terl a c e d , obtain son i c s p aces of con t i n u ou s evolution. It is poss i b l e t o pr o d u c e r uled surfaces by drawing the gl issandi as straig h t l ines.
I- 1 -5 indicate the causal chain of ideas which led me t o formulate t h e arch i tect1. We s hal l examine one by one the in d e p e n den t components of an instrumental sound. Time metrical i s considered a s a straight line o n which the p o i nts correspond ing to the variations of the other components are marked.
Amon g a l l the sequences of poi n ts , which shall we choose? The comparison can be m ade with the aid of te sts , of which the most widely used is the x2 cri terion of Pearson.
It is known that if two populations are in a linear functional relationship, the correlation the amount of chance included in our. Among these let us consider glissandi. Of all the possible forms that a glissando sound can take, we shall choose the simplest-the uniformly continuous glissando. This We have been speakin g o f sou nd-points, or granular sounds, which.
Certain mathematical operations on the continuously variable sounds. It is for these reason s that I o ffer t h em as examples :. The absol u te value of sp ee d s ascending o r descending glissandi is uniformly ; i. There is isotropy ; that is, th e re is no privileged d ir e c t io n for the movements of mobile sounds in an y register. There is an equal number of sounds ascending and descending. From these th ree hypotheses of symmetry, we can define the fu n c t i on f v of the probability of the absolute s pee d v.
Formalized Music: Thought and Mathematics in Composition (Harmonologia Series, #6)
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Formalized Music: Thought and Mathematics in Composition is a book by Greek composer , architect , and engineer Iannis Xenakis in which he explains his motivation, philosophy, and technique for composing music with stochastic mathematical functions. It was published in Paris in as Musiques formelles: nouveaux principes formels de composition musicale as a special double issue of La Revue musicale and republished in an expanded edition in in Paris by Stock Musique. It was later translated into English with three added chapters and published in by Indiana University Press, republished in by Pendragon Press with a second edition published in , also by Pendragon. It has been described as a groundbreaking work. From Wikipedia, the free encyclopedia. McHard