Yannis (or Iannis) Xenakis is best known to the general public as a composer. He was among the first to use computers in music, giving rise to what he called "stochastic music". He was also trained as an engineer and architect, notably working with Le Corbusier to create the Philips Pavilion for the 1958 Brussels World's Fair (see Mathématiques et Architecture, Bibliothèque Tangente 61). There he combined architectural and sonic structures to create an inseparable whole of sounds and volumes. Greek by origin, though born in Romania, he eventually opted for French nationality. The name Xenakis remains firmly associated with letters and the arts: his wife, Françoise Xenakis, a well-known woman of letters, and their daughter, the painter and sculptor Mâkhi Xenakis, have together contributed to the renown of the family name.
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Mathematical structures and composition
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What is revolutionary about Yannis Xenakis's approach to music is not so much his use of computers as the idea that a musical space could be created subject to a minimal number of constraints, and that this space could be generated in its entirety through mathematical modelling and, consequently, stochastic creation. Xenakis argues for the existence of wholly symbolic music whose structures could be derived directly from mathematical symbolism. To achieve this, the engineer-composer introduces what he calls "outside-time structures", which are independent of time and draw on what he calls an "algebra of intervals". His aim is to construct a "vector space" encompassing the pitches, intensities and durations of sounds. Temporal structures, which are essential to musical creation, are then expressed through an algebra of operators such as "before" and "after", acting as translation operators within what the composer calls "in-time structures".
Computers generate sequences of pseudorandom numbers. Computer-assisted composition therefore requires a two-way correspondence between the physical characteristics of sounds and the set of real numbers, so that sounds can be manipulated symbolically, like the numbers associated with them. With this in mind, Xenakis sets out to formalize the notion of a musical scale, drawing on a decidedly Pythagorean philosophy of music.
