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 us or and profited from the enl argemen t which may be created, necessitated of the principle of causality, the basis of wh i ch enlargement is fo r med by the law of large numbers. This law i mpl ies an asymptotic evolution towards a stable sta te , towards a kind of goal, of stochos, whence comes the adjective "stochastic. These laws operate on isolated states or on sets of elements with the o perati ons , the most primitive of which arc the union, notated u, the intersection, notated n, and the n egation. Equivalence, implication, and quantifications are elem en t ary relations from which all current science can be constructed. Music, then, may be defined as an organization of these elementary operations and rel at i ons between sonic entities or between functions of occupied by also for an alysis sonic entities.

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The full review can be accessed here: The following is a just a small portion of the complete review. As usual, I recommend reading the full thing. But the escalade is started and others will certainly enlarge and extend the new thesis. This book is addressed to a hybrid public, but interdisciplinary hybridization frequently produces superb specimens.

IMO, Xenakis has upped the ante for human intelligence so high that humanity shd be proud that he even existed. From Chapter 1: "Free Stochastic Music": "Art, and above all, music has a fundamental function, which is to catalyze the sublimation that it can bring about through all means of expression.

It must aim through fixations which are landmarks to draw towards a total exaltation 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 a single moment, it attains its goal.

This is why art can lead to realms that religion still occupies for some people. But, no, it only escalates.. All electro-acoustic music. Take the 1st paragraph of this caption for illustration B: "A ruled surface consisting of two conoids, a and d, is laid through the curve bounding the right half of the "stomach.

The straight directrix of a passes through a second peak and is joined by an arc to the directrix of d. Four hundred loudspeakers, lining the interior of the shell, were required to fill up the space with the sonic scintillations of Concret P-H and to effect a common emanation from architecture and music, conceived as an entity: the roughness of the concrete and its coefficient of internal friction was echoed in the timbre of the scintillations.

It is possible to produce ruled surfaces by drawing the glissandi as straight lines. I performed this experiment with Metastasis this work had its premier in at Donaueschingen. Thus I believe that on this occasion music and architecture found an intimate connection. I indicate the causal chain of ideas which led me to formulate the architecture of the Philips Pavilion from the score of Metastasis" p 10 Next up in the accompanying music to writing this review is "Kraanerg" , "S.

This will explain: "As a result of the impasse in serial music, as well as other causes, I originated in a music constructed from the principle of indeterminism; two years later I named it "Stochastic Music.

The music I love is all produced by strong personalities, driven by their own personal philosophy. They write scores in which certain combinations of sounds may be freely chosen by the interpreter. Two logical infirmities are apparent which deny them the right to speak of chance on the one hand and "composition" on the other composition in the broad sense, that is : "1.

The interpreter is a highly conditioned being, so that it is not possible to accept the thesis of unconditioned choice, of an interpreter acting like a roulette game. The martingale betting at Monte Carlo and the procession of suicides should convince anyone of this. We shall return to this. The composer commits an act of resignation when he admits several possible and equivalent circuits. In the name of a "scheme" the problem of choice is betrayed, and it is the interpreter who is promoted to the rank of composer by the composer himself.

There is thus a substitution of authors. The two infirmities mentioned above are terribly aggravated here. From the point of view of the composer there is no interest.

Why not? What wd the similarities be? As for serial composition becoming banal? Each of the conductors directs sonic operations against the operations of the other.

This value is written in a grid or matrix at the intersection of the row corresponding to move i of conductor A and the column corresponding to move j of conductor B. This is the partial score ij, representing the payment one conductor gives the other.

This game, a duel, is defined as a two-person zero-sum game. I stress the word "competitive" regarding the above - but not all games are competitive.

This is much more my approach. I was still able to remember all the particulars, above all - naturally - the fact that the two cellists were placed near the front of the platform on either side, with the percussion player between them as "umpire". The details of performance, with the types of sound, methods of articulation and gesticulation, and above all the markedly "sporting" character of the piece, remained in my mind with the utmost clarity.

At that time I was working on a composition for entirely different forces and with a totally different disposition of the material; I could see no relationship, as regards either content or form, between the sound world of the two concepts.

I did not want to give up work on the piece on which I was already engaged in order to bring a dream to realization. Nine nights later, however, the dream performance was repeated, with the same clarity of detail as before. I was perturbed, this time I made notes, and tried to define the elusive time element of the imaginary music in terms of concrete tempi.

On the following morning I realized that the dream had been repeated yet again. This time I laid everything aside, in the belief that fate had knocked three times, and that it was high time to do what was required of me.

The dream has never again been repeated, which is a pity, because I should like to compare it to the finished score.


Formalized Music: Thought and Mathematics in Composition (Harmonologia Series, #6)

Jump to navigation Jump to search edition 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.







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