A Pumping Lemma for Homometric Rhythms

Homometric rhythms/chords (henceforth: rhythms) are those with the same histogram or multiset of intervals/distances. The purpose of this note is threefold. First to point out the potential importance of isospectral vertices in a pair of homometric rhythms. Second, to prove a "pumping lemma" that generates an infinite sequence of homometric rhythms that include isospectral vertices. And finally, to introduce the notion of polyphonic homometric rhythms, which apparently have not been previously explored.

• Type: Conference
• Year: 2008
• Where: CCCG
• Authors: Joseph O'Rourke, Perouz Taslakian, Godfried T. Toussaint
• Keywords: CCCG 2008, Computational Geometry, Homometric Rhythms, Isospectral Vertices, Polyphonic Homometric Rhythms