Editing Iannis Xenakis (section)

== Works ==
{{See also|List of compositions by Iannis Xenakis}}
Specific examples of mathematics, statistics, and physics applied to music composition are the use of the [[statistical mechanics]] of gases in ''[[Pithoprakta]]'', [[statistical distribution]] of points on a plane in ''[[Diamorphoses]]'', minimal [[Constraint (mathematics)|constraints]] in ''Achorripsis'', the [[normal distribution]] in ''ST/10'' and ''Atrées'', [[Markov chain]]s in ''Analogique'', [[game theory]] in ''Duel'', ''Stratégie'', and ''Linaia-agon'', [[group theory]] in ''[[Nomos Alpha]]'' (for [[Siegfried Palm]]), [[set theory]] in ''Herma'' and ''[[Eonta]]'',<ref>Chrissochoidis, Ilias, Stavros Houliaras, and Christos Mitsakis. (2005). "Set theory in Xenakis' ''EONTA''". In ''International Symposium Iannis Xenakis'', edited by Anastasia Georgaki and [[Makis Solomos]], pp. 241–249. Athens: The National and Kapodistrian University.</ref> and [[Brownian motion]] in ''N'Shima''. ''Persephassa'', commissioned by the Shiraz Arts Festival, was performed by [[Les Percussions de Strasbourg]], receiving its world premiere in Persepolis in 1969. Subsequently, he was once again commissioned by the Shiraz Arts Festival and composed ''Persepolis'' for the occasion, a "polytope" composed specific to the historic site.<ref>{{Cite journal|last=Gluck|first=Robert|date=2007|title=The Shiraz Arts Festival: Western Avant-Garde Arts in 1970s Iran|journal=Leonardo|volume=40|pages=21–28|doi=10.1162/leon.2007.40.1.20|s2cid=57561105}}</ref>

Although [[Electroacoustic music|electroacoustic]] compositions represent only a small fraction of Xenakis's output, they are highly relevant to musical thinking in the late 20th century. Important works in this medium include ''[[Concret PH]]'' (1958), ''Analogique B'' (1958–59), ''[[Bohor (Xenakis)|Bohor]]'' (1962), ''La légende d'Eer'' (1977), ''Mycenae-Alpha'' (1978), ''Voyage absolu des Unari vers Andromède'' (1989), ''Gendy301'' (1991), and ''S709'' (1994).<ref>[[#DiScipio|Di Scipio]], 201.</ref>

By 1979, he had devised a computer system called [[UPIC]], which could translate graphical images into musical results.{{sfn|Hugill|2008|pp=95, 182}}<ref>{{Cite book |last=Gagné |first=Nicole V. |url=https://books.google.com/books?id=WxWbDwAAQBAJ&pg=PA397 |title=Historical Dictionary of Modern and Contemporary Classical Music |date=17 July 2019 |publisher=Rowman & Littlefield |isbn=978-1-5381-2298-3 |pages=397 |language=en}}</ref> "Xenakis had originally trained as an architect, so some of his drawings, which he called 'arborescences', resembled both organic forms and architectural structures." These drawings' various curves and lines that could be interpreted by UPIC as real time instructions for the sound synthesis process. The drawing is, thus, rendered into a composition. ''Mycenae-Alpha'' was the first of these pieces he created using UPIC as it was being perfected.<ref>[[#DiScipio|Di Scipio]], 220.</ref>

Xenakis also developed a stochastic synthesizer algorithm (used in GENDY), called ''dynamic stochastic synthesis'', where a polygonal waveform's sectional borders' amplitudes and distance between borders may be generated using a form of [[random walk]] to create both aleatoric timbres and musical forms.<ref name="Serra">[[#Serra|Serra]], 241.</ref> Further material may be generated by then refeeding the original waveform back into the function or wave forms may be superimposed. Elastic barriers or mirrors are used to keep the randomly generated values within a given finite interval, so as to not exceed limits such as the audible pitch range, avoid complete chaos (white noise), and to create a balance between stability and instability (unity and variety).<ref name="Serra"/>

Despite Xenakis's reputation as a "mathematical" composer, his works are known for their power and physicality. [[Alex Ross (music critic)|Alex Ross]] wrote that Xenakis "produced some of the rawest, wildest music in history—sounds that explode around the ears. Rarefied methods were employed to release primordial energies."<ref>{{cite magazine|url=https://www.newyorker.com/magazine/2010/03/01/waveforms|title=Waveforms: The singular Iannis Xenakis|last=Ross|first=Alex|author-link=Alex Ross (music critic)|date=22 February 2010|magazine=[[The New Yorker]]|access-date=23 October 2020}}</ref> [[Ben Watson (music writer)|Ben Watson]] expressed admiration for the "terrifying emotional impact of [Xenakis'] sonic objectivity", describing his music as possessing "truly majestic otherness. It is an alien shard, glimmering in the heart of the West."<ref>{{cite magazine |last=Watson |first=Ben |date=June 1995 |title=Iannis Xenakis: Primal Architect |magazine=The Wire |issue=136 }}</ref>

[[Tom Service]] praised Xenakis' music for its "shattering visceral power" and "sheer, scintillating physicality", noting its "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."<ref name="service" /> Service described Xenakis as 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 realise with arguably greater clarity, ferocity, intensity than any musician, before or since," and suggested that his music is "expressive: not in a conventionally emotional way, perhaps, but it has an ecstatic, cathartic power. Xenakis's music – and its preternaturally brilliant performers – allows its listeners to witness seismic events close at hand, to be at the middle of a musical happening of cosmic intensity."<ref name="service" /> Service concluded: "it took Xenakis for music to become nature. On holiday in Corsica, Xenakis would pilot his canoe into the teeth of the biggest storm he and his paddle could manage. When you're listening to his music, you also go out there into the eye of a musical storm that will invigorate, inspire, and awe. See you out there..."<ref name="service" />