Counting set classes with Burnside's lemma

Abstract

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 $d$-note set classes exist in a $c$-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.