The Use of Stochastic Distributions in the Instrumental Works of Iannis Xenakis: Between Chance and Intuition

Abstract

Relying on various examples, some of which inspired by documents or sketches found in the composer’s archives, this presentation explores how Xenakis incorporates and deals with the results of his stochastic distributions in his instrumental works, discussing the degree of freedom implicit in his compositional choices. It focusses on examples taken from works where the stochastic distributions were calculated by different means: Achorripsis (1956-57) for chamber orchestra, Morsima-Amorsima (1962) for violin, violoncello double bass and piano, and Mists (1980) for solo piano. In Achorripsis, the stochastic distributions of durations and intervals were calculated by hand and expressed as tables of numbers. They appear as outside-time proportions. This is probably why Xenakis felt the need to represent them linearly, inside-time, as classes of durations and intervals as an intermediate stage in the compositional process. He then had to choose, intuitively, the intervals and durations in order to arrange them in lexicographic time. Later, at the beginning of the 60s, Xenakis designed a computer program (ST) that implemented the theories and ideas he had developed for Achorripsis. The ST program generates lists of data where each line corresponds to the definition of an individual note. The moment of occurrence and the pitch of each note are determined. But the program does not always take into account all the necessary parameters for the final results to be playable on the instruments. And the higher the density of the sound events, the more adjustments is needed. This is shown in Morsima-Amorsima by comparing the provisional results of the stochastic distributions with the final score. Finally, at the beginning of the 70s, Xenakis introduced probability theory in the field of sound synthesis when he suggested that the sound pressure be based on probability distributions. These new proposals also had an impact on his instrumental works. In Mists, he programmed a pocket calculator to obtain similar stochastic distributions where the occurrence and the pitch of each note were calculated separately. The input data were then modified to generate series of clouds of different densities. But the results were also altered by hand to fit different transpositions of the main sieve of the work. Whether he did his calculation by hand or resorted to technological means, Xenakis always seems to leave a gap between the output of his calculations and the traditional score. A gap that is filled manually. In the end, the composer decides, guided by his own intuition, which elements to assemble.