Anatomy of the six-part all-partition array as used by Milton Babbitt: Preliminary efforts towards a computational method of automatic generation

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Abstract

For Milton Babbitt (1916–2011), twelve-tone techniques were indispensable forms of musical composition because they are fundamentally derived from mathematical constructs. Perhaps his most complex form of composition is the all-partition array. Its large-scale structure is formed by concatenated permutations of 12-tone rows under the common class of musical equivalence
relations, transposition, inversion, retrograde and retrograde inversion, and then organized into pairs of hexachordally combinatorial rows. The resultant pitch-class space is then partitioned into segment lengths of 12 integers or fewer distributed into a specified number of parts. Both its organization and number of parts are determined in part by the unique mathematical properties
of all-combinatorial hexachords. Through analyses of two works representative of two types of six-part arrays, initial ground work is established for the automatic generation of the all-partition array structure. Preliminary concerns in the computational process are also addressed.
Original languageEnglish
Publication date12 Apr 2014
Publication statusPublished - 12 Apr 2014
EventRMA Music and Mathematics Study Day: Music and Mathematics - University of Leeds, Leeds, United Kingdom
Duration: 12 Apr 2014 → …
http://rmamusicandmaths.wordpress.com/

Conference

ConferenceRMA Music and Mathematics Study Day
LocationUniversity of Leeds
Country/TerritoryUnited Kingdom
CityLeeds
Period12/04/2014 → …
Internet address

Keywords

  • all-partition array
  • Milton Babbitt
  • twelve-tone music

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