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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.
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 language | English |
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Publication date | 12 Apr 2014 |
Publication status | Published - 12 Apr 2014 |
Event | RMA Music and Mathematics Study Day: Music and Mathematics - University of Leeds, Leeds, United Kingdom Duration: 12 Apr 2014 → … http://rmamusicandmaths.wordpress.com/ |
Conference
Conference | RMA Music and Mathematics Study Day |
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Location | University of Leeds |
Country/Territory | United Kingdom |
City | Leeds |
Period | 12/04/2014 → … |
Internet address |
Keywords
- all-partition array
- Milton Babbitt
- twelve-tone music
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Dive into the research topics of 'Anatomy of the six-part all-partition array as used by Milton Babbitt: Preliminary efforts towards a computational method of automatic generation'. Together they form a unique fingerprint.Projects
- 1 Finished
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Lrn2Cre8: Learning to Create
EU Seventh Framework Programme (FP7)
01/10/2013 → 30/09/2016
Project: Research