Iannis Xenakis: Musical Sorcery Using Mathematical Totems

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Iannis Xenakis, the Greek composer trained as an architect, created expressive works of mind-bending mathematical complexity that according to one critic, have “all the teeming unpredictable power of a glacier, the thrilling complexity of shape and movement of a mass animal migration.”

Xenakis, art, classical music, Wassily Kandinsky

At the convergence of art, mathematics, engineering, and modernist classical music, Iannis Xenakis’ compositions conjure an otherworldly sense of nature using probability, like when hearing a clap of thunder, like when looking into a bottomless abyss… Artwork by Wassily Kandinsky, Composition VII.

Destabilization of a Basic Rhythmic Pulse

Iannis Xenakis (May 29, 1922 – February 4, 2001) was a Greek composer-architect and musical theorist and a major figure in the postwar development of musical modernism worldwide. He was an important influence on the development of electronic music, particularly remembered for the pioneering use of stochastic mathematical techniques and computer means of handling large numbers of events in his compositions, including probability: Maxwell-Boltzmann kinetic theory of gases, aleatory distribution of points on a plane, minimal constraints, Gaussian distribution (ST/10, Atrées), Markov chains (Analogiques). He also based compositions on game theory (Duel, Stratégie), group theory, Boolean algebra and Brownian motion.

Xenakis was distinct from many of his contemporary “postwar avant-garde” composers, including Luciano Berio, Pierre Boulez, Gyorgy Ligeti, Krzysztof Penderecki, and Karlheinz Stockhausen, in that he worked assiduously to integrate into his music audible patterns and structures of a kind that others sought to avoid. Especially in his works from the late 1970s on, Xenakis frequently based his music on the establishment and subsequent destabilization and undermining of a basic rhythmic pulse. In the domain of pitch, he developed what he called “sieve theory” in order to construct new and elaborate scales for his music. Unlike traditional scales such as major and minor, Xenakis’ unique scales comprise intervallic patterns that span the entire range of available notes, instead of repeating with each octave.

Naturally, in the history of human ideas, progressions such as the golden number, magic squares, geometrical figures and all kinds of mathematical and astrological totems have played a very important part in the arsenal of sorcery. I don’t believe in them.”  —  Iannis Xenakis, Interview with Mario Bois, March 4th,1966.

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Metastasis, SWF Symphony Orchestra, Hans Rosbaud, conductor, October 1955

Dialectic Transformations Based on Le Corbusier’s Modernism

Metastasis or Metastaseis (“dialectic transformations,” 1954), is an orchestral work inspired by Einstein’s view of time (a function of matter & energy) and structured on mathematical ideas by Xenakis’s colleague Le Corbusier. The 1st and 3rd movements don’t have a melodic theme to hold them together, but rather depend on the strength of this conceptualization of time. The 2nd movement does have some sort of melodic element. A fragment of a 12-tone row is used, with durations based on the Fibonacci sequence (1,1,2,3,5,8,13,21,34…)

The preliminary sketch for Metastasis was in graphic notation looking more like a blueprint than a musical score, showing graphs of mass motion and glissandi like structural beams of the piece, with sound frequencies on one axis and time on the other. The video above tries to display this by presenting the frequency spectrum (0-20.000Hz) of the piece and how Xenakis actually “drew” music.


Synaphai, for piano and orchestra, Arturo Tamayo, Orchestra Philharmonique de Luxembourg

…a composer whose craggily, joyously elemental music turned collections of pitches and rhythms and instruments into a force of nature, releasing a power that previous composers had only suggested metaphorically but which he would realize with arguably greater clarity, ferocity, intensity than any musician, before or since. This is the music of Iannis Xenakis.  — Tom Service in The Guardian

An Anti-Fascist, Architect of Polytopes, Pioneer of Chaos

Xenakis was born on May 29, 1922 in Braîla (Romania) as a son of Clearchos Xenakis and Fotini Pavlou. Around the age of five, he settled, with his father, in Greece. From 1947 he started studying at the Polytechnical Institute in Athens, where he was also part of the anti-fascist and later anti-English underground movement. Shrapnel from a blast from a British tank causes a horrendous facial injury that meant the permanent loss of sight in one eye. Because of these activities he was sentenced to death in 1947. The same year he fled to France where he worked as an architect, an assistant of Le Corbusier. He continued working with Le Corbusier until 1960. In these years he realized among others the Couvent de La Tourette (1955) and the Philips Pavilion at the Expo in Brussels (1958).

Brussels World's Fair, Le Corbusier

Xenakis’ architectural output and its underlying mathematical construct offers ways into his music’s imaginative world. Take the Philips Pavilion he designed for the Brussels World’s Fair in 1958 and for which he and Edgard Varèse wrote electronic music to animate its still gorgeously futuristic-looking parabolas, swoops, curves.

Xenakis also designed what he called “polytopes”, high-art son-et-lumière installations that involved his lighting designs, his sets, his music, and his sound projection to create vivid multi-media experiences, in places from Canada to Iran to Greece. And he designed a system for the conversion of graphic stimuli into sound, a programme he called UPIC and which has now morphed into more sophisticated computer software like IanniX. (More than a decade before Boulez founded IRCAM, Xenakis had set up his own institute for music-technological research in Paris called EMAMu, which now exists as CCMIX.)

…a revelation of this music’s deep, primal rootedness in richer and older phenomena even than musical history: the physics and patterning of the natural world, of the stars, of gas molecules, and the proliferating possibilities of mathematical principles. Xenakis resisted the label of being a mere mathematician in music just as surely as he refused the idea of his music’s political or social message, and it was of course how he used those scientific principles (outlined in his book, Formalized Music) to create pieces of shattering visceral power.  — Tom Service

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His first musical studies were around 1948 with Arthur Honegger, Nadia Boulanger and Darius Milhaud. In 1949-50 he studied with Olivier Messiaen, who encouraged him to develop his musical ideas. When Xenakis first approached Messiaen in Paris for composition lessons, the latter turned him down, because, “I think one should study harmony and counterpoint. But this was a man so much out of the ordinary that I said… ‘No, you are almost 30, you have the good fortune of being Greek, of being an architect and having studied special mathematics. Take advantage of these things. Do them in your music’.” That, he did.

Updated 2 September 2016

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About Jack Eidt

Novelist, urban theorist, and environmental journalist, Jack Eidt careens down human-nature's all consuming one-way highway to its inevitable conclusion -- Wilder Utopia. He co-founded Wild Heritage Planners, based out of Los Angeles, California. He can be reached at jack (dot) eidt (at) wilderutopia (dot) com. Follow him on Twitter @WilderUtopia and @JackEidt