Unifying tone system definitions

ordering chromas

Tobias Schlemmer

pp. 291-302

in: Tom Collins, David Mérédith, Anja Volk (eds), Mathematics and computation in music, Berlin, Springer, 2015

Abstract

This article suggests a tone system definition that uses abstract ordered groups as interval groups. The common operation of octave identification is replaced by a folding operation for ordered sets that is based on the factorisation of groups by normal subgroups. The resulting structure is used to provide a chroma system definition that can preserve a certain amount of the order relation. Additionally, a path is shown that allows the integration of the theory of Generalized Interval Systems into the extensional language that has been proposed by Rudolf Wille and Wilfried Neumaier.

Cited authors

Wille Rudolf