Homometry in the Dihedral Groups: Lifting Sets from Z_n to D_n

摘要

The paper deals with the question of homometry in the dihedral groups D_n of order 2n. These groups are non-commutative, leading to new and challenging definitions of homometry, as compared to the well-known case of homometry in the commutative group Z_n. We give here a musical interpretation of homometry in D_(12) using the well-known neo-Riemannian groups, some results on a complete enumeration of homometric sets for small values of n, and some properties disclosing the deep links between homometry in Z_n and homometry in D_n.