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Counting set
classes with Burnside's lemma
Joshua Case, Lori Koban and Jordan LeGrand
Vol. 8 (2015), No. 2, 337–344
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Abstract |
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Mathematical tools from combinatorics and abstract algebra have been used to study a variety of musical structures. One question asked by mathematicians and musicians is: how many -note set classes exist in a -note chromatic universe? In the music theory literature, this question is answered with the use of Pólya’s enumeration theorem. We solve the problem using simpler techniques, including only Burnside’s lemma and basic results from combinatorics and abstract algebra. We use interval arrays that are associated with pitch class sets as a tool for counting. |
Keywords
set classes, pitch class sets, Burnside's lemma, group
actions
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Mathematical Subject Classification 2010
Primary: 00A65, 05E18
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Milestones
Received: 14 August 2013
Revised: 24 October 2013
Accepted: 23 December 2013
Published: 3 March 2015
Communicated by Kenneth S. Berenhaut
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Authors |
| Joshua Case | |
| Mathematics Department University of Maine at Farmington 228 South Street Farmington, ME 04938 United States |
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| Lori Koban | |
| Mathematics Department University of Maine at Farmington 228 South Street Farmington, ME 04938 United States |
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| Jordan LeGrand | |
| Mathematics Department University of Maine at Farmington 228 South Street Farmington, ME 04938 United States |
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