Non-Commutative Homometry in the Dihedral Groups

Abstract

The paper deals with the question of homometry in the dihedral groups $D_n$ of order $2n$. These groups have the specificity to be non-commutative. It leads to a new approach as compared as the one used in the traditional framework of the commutative group ${\mathbb{Z}}_n$. We give here a musical interpretation of homometry in $D_{12}$ using the well-known neo-Riemannian groups, some computational results concerning enumeration of homometric sets for small values of $n$, and some properties disclosing important links between homometry in ${\mathbb{Z}}_n$ and homometry in $D_n$. Finally we propose an extension of musical applications for this non-commutative homometry.

19 pages, 4 figures, 2 tables

References in corpus (1)

• Generalized Inversions and the Construction of Musical Group and Groupoid Actions