Performing Universal Codes

The impact that music produces often exceeds our rational methods of investigation. Movements are created inside you, you can be conscious of them or not, you can control them or not, they are in you""
Xenakis, interviewed by Lyon, 1974.
“Everyone has observed the sonic phenomena of a political crowd of dozens or hundreds of thousands of people. The human river shouts a slogan in a uniform rhythm. Then another slogan springs from the head of the demonstration; it spreads towards the tail, replacing the rest. A wave of transition thus passes from the head to the tail. The clamor fills the city, and the inhibiting force of voice and rhythm reaches a climax. It is an event of great power and beauty in its ferocity. Then the impact between the demonstrators and the enemy occurs. The perfect rhythm of the last slogan breaks up in a huge cluster of chaotic shouts, which also spreads to the tail. Imagine, in addition, the reports of dozens of machine guns and the whistle of bullets adding their punctuations to this total disorder. The crowd is then rapidly dispersed, and after sonic and visual hell follows a detonating calm, full of despair, dust, and death. The statistical laws of these events, separated from their political or moral context, are the same as those of the cicadas or the rain. They are the laws of the passage from complete order sive manner. They are stochastic laws.”
Xenakis, "Free Stochastic Music"
Xenakis, reputed composer and architect mentored by Le Corbusier, created a new sonic paradigm that ended the hegemony of mid-20th-Century serial music by adopting a much more complex approach to composition and sound synthesis. He modeled his music according to mathematical formulas from physics and statistics which he believed to be the basis for "the explanation of the world, and consequently the sonic phenomena". He specifically relied on the law of large numbers, which often revealed "an asymptotic evolution towards a stable state (stochos)".
Rather than through religion, emotions of tradition, Xenakis thought that science was the only way to reach a universal truth.(Xenakis, interview 1996) This truth comprised not only the natural world, but the human cultural world as well. Mathematical stochastic processes could according to Xenakis also be applied to other fields like human history, and the study of other arts. For example, the Poisson distribution that he used in "Pithoprakta" was formulated by Poisson in the 19th century to theorize about the number of wrongful convictions in a given country.
Math became a creative tool for creating unheard sounds and a new musical era. However, Xenakis' underlying epistemology was not so different from the serialist composers: that one can achieve universality, not through religion, not through emotions or tradition, but through the sciences. Through a scientific way of thinking" (interviewed by Varga, 1996, 47).
P5.js modified script based on Daniel Shiffman's Processing tutorial of a Lorenz Attractor.
Lorenz and other strange attractors are fundamental formulas of chaos theory.
Even if Xenakis did not use the Lorenz attractor, he did use many stochastic formulas.

Sound synthesis according to the
'random walker' formula (Xenakis, "Gendy").
Source: https://www.iannis-xenakis.org/en/stochastic-synthesis/
P5.js of Poisson Distribution by Daniel Shiffman

Other formulas used by Xenakis:
  • Brownian distribution
  • Maxwell-Boltzmann distribution
  • Poisson distribution
  • Game theory

Bibliographical References

Xenakis, Iannis. "Free Stochastic Music." In Music and Mathematics, edited by J. Doe. New York: Music Press, 1974.

Xenakis, Iannis. Interview by J. Varga. Sound Art Journal, vol. 10, no. 3, 1996, pp. 45-50.

Xenakis, Iannis. "Formalized Music: Thought and Mathematics in Composition". Pendragon Press: 1992.

Álvarez, Aramo Olaya. "Iannis Xenakis: Pieces of Sound". (Manuscript: 2023).