Proceedings of the 20th Annual Canadian Conference on Computational Geometry, CCCG 2008
Homometric rhythms (chords) 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 establish a method ("pumping") for generating 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.
© the authors
O'Rourke, Joseph; Taslakian, Perouz; and Toussaint, Godfried, "A Pumping Lemma for Homometric Rhythms" (2008). Computer Science: Faculty Publications, Smith College, Northampton, MA.