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==Music== <!--[[Stochastic music]] redirects directly here.--> In [[music]], [[mathematical]] processes based on probability can generate stochastic elements. Stochastic processes may be used in music to compose a fixed piece or may be produced in performance. Stochastic music was pioneered by [[Iannis Xenakis]], who coined the term ''stochastic music''. 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 ''Analogiques'', [[game theory]] in ''Duel'' and ''Stratégie'', [[group theory]] in ''[[Nomos Alpha]]'' (for [[Siegfried Palm]]), [[set theory]] in ''Herma'' and ''[[Eonta]]'',<ref>Ilias Chrissochoidis, Stavros Houliaras, and Christos Mitsakis, [https://www.academia.edu/249265/Set_theory_in_Xenakis_EONTA "Set theory in Xenakis' ''EONTA''"], in ''International Symposium Iannis Xenakis'', ed. Anastasia Georgaki and [[Makis Solomos]] (Athens: The National and Kapodistrian University, 2005), 241–249.</ref> and [[Brownian motion]] in ''N'Shima''.{{citation needed|date=May 2013}} Xenakis frequently used [[computer music|computers]] to produce his scores, such as the ''ST'' series including ''Morsima-Amorsima'' and ''Atrées'', and founded [[CEMAMu]]. Earlier, [[John Cage]] and others had composed ''[[aleatoric music|aleatoric]]'' or [[indeterminate music]], which is created by chance processes but does not have the strict mathematical basis (Cage's ''[[Music of Changes]]'', for example, uses a system of charts based on the ''[[I-Ching]]''). [[Lejaren Hiller]] and [[Leonard Issacson]] used [[generative grammar]]s and [[Markov chain]]s in their 1957 ''[[Illiac Suite]]''. Modern electronic music production techniques make these processes relatively simple to implement, and many hardware devices such as synthesizers and drum machines incorporate randomization features. [[Generative music]] techniques are therefore readily accessible to composers, performers, and producers.
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