Some of his works have titles that refer to mathematical objects, such as Concret PH (short for "hyperbolic paraboloids") in 1958. Among other things, he drew on combinatorics, group theory, probability theory, and even the Fibonacci sequence, moving towards algorithmic music. One of his early works, Pithoprakta, composed in 1956, marked a transition from serial music to a more stochastic approach—that is, one involving chance.
His training as an architect led him to combine graphic forms with music. In 1958, while working with Le Corbusier, he designed the Philipps Pavilion for the Brussels World’s Fair, a striking work of sound architecture designed to house Edgard Varèse’s Poème électronique. In the 1970s, the UPIC (Unité polyagogique informatique du CEMAMu) emerged from a collaboration between Xenakis and the engineer Patrick Saint-Jean. CEMAMu was the Centre d’études de mathématiques et automatiques musicales, founded by Xenakis. One of the earliest graphical controllers for digital music, the UPIC underwent numerous improvements over time; it consisted of a graphics tablet connected to a computer, along with loudspeakers. When composing with the UPIC, Xenakis could draw and hear the musical transcription of his input in real time, then revise his drawing after listening to the sound it produced.
The idea was not so much to represent sounds through an abstract image as to "make drawings sound," with the sound parameters plotted along the x-axis (time) and y-axis (frequency) of a phase plane. Xenakis said: "This use of modern technology does not mark a break in the history of music. Music has always been, and continues to be, both sound and number, acoustics and mathematics—and therein lies its universality."
