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
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