The music of Iannis Xenakis employs various mathematical theories, such as set theory and probability calculus, to give it a logical structure. Xenakis was both an architect and a composer, and his use of mathematics in music is analogous to its use in architecture in that it is used to “build” the music, although often this is not obvious to the listener.
Xenakis was born to Greek parents in Braïla, Romania, on May 29, 1922. His mother was an amateur pianist who died when the composer was only five years old. At age ten, Xenakis was sent to a boarding school on the Greek island of Spetzai, where he became interested in music, mathematics, and classical literature. In 1938, he went to Athens to the Polytechnic Institute to study engineering, but continued to study piano and music theory with Aristotle Kondurov. Xenakis’ studies were interrupted by World War II. During the occupation, he joined the resistance, becoming a member of the left-wing Army of Liberation and was repeatedly imprisoned.
After the war, violent resistance to the right-wing government continued, and Xenakis lost an eye and his jawbone was broken by shrapnel. Despite this, he managed to earn his engineering degree in 1945. By 1947, his continuing involvement in the nationalist movement had led to a death sentence. He was smuggled into Paris on a forged passport, where he found work with the architect Le Corbusier. Xenakis then settled in France and took French citizenship.
Xenakis took his scores to the Paris Conservatory and studied with Olivier MESSIAEN until 1962. However, Messiaen encouraged Xenakis to go his own way, and the composer remained an isolated figure experimenting with his sound structures. One of his first experiments was in the use of the Fibonacci series, which Le Corbusier used as a design principle in architecture. The sequence, in which each number is the sum of the two previous (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, etc.) gave Xenakis the form of his composition, Metastasis (1953), a memoir of the resistance, in which the durations of the sections were based on a Fibonacci series. It was performed at the Donaueschingen Festival of contemporary music in Germany in 1955. At about this time, Xenakis joined the Groupe de Recherche de Musique Concrète in Paris, and began to work with electronic tape. As a co-designer of the Philips Pavilion for the Brussels World Fair, he was able to broadcast his electronic music through 400 loudspeakers as an integral design element.
In 1954, Xenakis introduced the idea of stochastic music as a strategy to combat what he saw as the disconnectedness of contemporary music. He grouped his music into sound masses that he called clouds and galaxies, and then applied probability theory to chart the movement of the masses. The result was Pithoprakta (“actions through probability”). Stochastic elements were combined with game theory in Duel (1959) for two small orchestras, in which the two conductors have to respond to each other’s moves as in a game.
Another mathematical theory that Xenakis used was set theory, in Herma (1963). Set theory is another way of dealing with elements as groups (sets) that can include or exclude other sets. In Herma, the notes of the piano keyboard are organised into sets that can then be manipulated.
In 1961, Bruno Maderna conducted Xenakis’ Strategies the 1961 Venice Biennial, and in May 1965 there was a Xenakis Festival in Paris.
Xenakis continued to compose throughout the 1980s and 1990s, and taught at the School for Mathematical Music in Paris, which he had founded in 1966. Earlier, he had taught at Indiana University and also founded a centre for musical mathematics there.
Jane Prendergast
SEE ALSO:
ALEATORY MUSIC; BOULEZ, PIERRE; CHAMBER MUSIC; ELECTRONIC MUSIC; ORCHESTRAL MUSIC; VARESE, EDGARD.
Bois, Mario. Iannis Xenakis: The Man and His Music
(Westport, CT: Greenwood Press, 1980)
Xenakis, Iannis. Formalized Music
(Bloomington, IN: Indiana University Press, 1971).
Antikhthon; Metastasis; Nomos gamma;
Orient-Occident; Psappha.