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Abstrakt
For Milton Babbitt (1916–2011), twelvetone techniques were indispensable forms of musical composition because they are fundamentally derived from mathematical constructs. Perhaps his most complex form of composition is the allpartition array. Its largescale structure is formed by concatenated permutations of 12tone 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 pitchclass 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 allcombinatorial hexachords. Through analyses of two works representative of two types of sixpart arrays, initial ground work is established for the automatic generation of the allpartition 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 pitchclass 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 allcombinatorial hexachords. Through analyses of two works representative of two types of sixpart arrays, initial ground work is established for the automatic generation of the allpartition array structure. Preliminary concerns in the computational process are also addressed.
Originalsprog  Engelsk 

Publikationsdato  12 apr. 2014 
Status  Udgivet  12 apr. 2014 
Begivenhed  RMA Study Day: Music and Mathematics  University of Leeds, Leeds, Storbritannien Varighed: 12 apr. 2014 → … http://rmamusicandmaths.wordpress.com/ 
Konference
Konference  RMA Study Day 

Lokation  University of Leeds 
Land  Storbritannien 
By  Leeds 
Periode  12/04/2014 → … 
Internetadresse 
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Projekter
 1 Afsluttet

Lrn2Cre8: Learning to Create
EU Seventh Framework Programme (FP7)
01/10/2013 → 30/09/2016
Projekter: Projekt › Forskning