Editing Nomos Alpha

{{italic title}}
'''''Nomos Alpha''''' ({{langx|el|Νόμος α΄}}) is a piece for solo [[cello]] composed by [[Iannis Xenakis]] in [[1965 in music|1965]], commissioned by Radio [[Bremen]] for cellist [[Siegfried Palm]], and dedicated to mathematicians [[Aristoxenus|Aristoxenus of Tarentum]], [[Évariste Galois]], and [[Felix Klein]].<ref>DeLio, Thomas. "The Dialectics of Structure and Materials: Iannis Xenakis' ''Nomos Alpha''". Cited in DeLio (1985). p.xii</ref>  This piece is an example of a style of music  called, by Xenakis, symbolic music – a style of music which makes use of [[set theory]], [[abstract algebra]], and [[mathematical logic]] in order to create and analyze [[musical composition]]s.  Along with symbolic music, Xenakis  is known for  his development of [[stochastic music]].

During his lifetime, Xenakis was a vocal critic of [[Contemporary classical music|modern Western music]] since the development of [[polyphony]] for its diminished set of outside-time structures, especially when compared to [[Folk music|folk]] and the [[Byzantine music|Byzantine]] musical traditions.  This perceived incompleteness of Western music was the main impetus for the development of symbolic music and for composing Nomos Alpha, his most well-known example of the genre.

''Nomos Alpha'' consists of 24 sections divided into two layers.  The first layer consists of every section not divisible by four, while the second layer consists of every fourth section.<ref>DeLio, Thomas. "Iannis Xenakis' ''Nomos Alpha'': The Dialectics of Structure and Materials", ''Journal of Music Theory'', Vol. 24, No. 1 (Spring, 1980), pp. 63–95; Published by: Duke University Press on behalf of the Yale University Department of Music. Citation on p. 63.</ref>

==Layer 1==
Layer 1 of ''Nomos Alpha'' is determined by the 24-[[Element (mathematics)|element]] [[octahedral group]] [[isomorphism|isomorphic]] to the rotations of a [[cube]].  The elements of the set are [[permutations]] and the [[binary operator]] is [[Function composition|composition]].

==Layer 2==
Layer 2 of ''Nomos Alpha''—in contrast to Layer 1—is not determined by [[group theory]], but is instead, a "continuous motion of registral evolution".<ref>DeLio.  op. cit.  83</ref>

==References==
{{Reflist}}

==Sources==
*DeLio, Thomas, ed. (1985). ''Contiguous Lines: Issues and Ideas in the Music of the '60's and '70's''. {{ISBN|0-8191-4330-8}}.
*DeLio, Thomas. "The Dialectics of Structure and Materials: Iannis Xenakis' ''Nomos Alpha''". Cited in DeLio (1985).
*Xenakis, Iannis (1971). ''Formalized Music'', pp.&nbsp;219–236. Bloomington, Indiana: Indiana University Press.

==External links==
* [https://www.youtube.com/watch?v=TJHAgkjhjFM Nomos Alpha] performed by [[Moritz Müllenbach]]
{{Iannis Xenakis}}
{{Authority control}}

[[Category:Solo cello pieces]]
[[Category:Compositions by Iannis Xenakis]]
[[Category:1965 compositions]]
[[Category:Compositions that use extended techniques]]

{{classical-composition-stub}}