A pumping lemma for homometric rhythms

Joseph O'Rourke, Perouz Taslakian, Godfried Toussaint

Research output: Contribution to conferencePaper

Abstract

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.

Original languageEnglish (US)
Pages99-102
Number of pages4
StatePublished - Dec 1 2008
Event20th Annual Canadian Conference on Computational Geometry, CCCG 2008 - Montreal, QC, Canada
Duration: Aug 13 2008Aug 15 2008

Other

Other20th Annual Canadian Conference on Computational Geometry, CCCG 2008
CountryCanada
CityMontreal, QC
Period8/13/088/15/08

Fingerprint

Multiset
Threefolds
Chord or secant line
Histogram
Lemma
Interval

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

O'Rourke, J., Taslakian, P., & Toussaint, G. (2008). A pumping lemma for homometric rhythms. 99-102. Paper presented at 20th Annual Canadian Conference on Computational Geometry, CCCG 2008, Montreal, QC, Canada.

A pumping lemma for homometric rhythms. / O'Rourke, Joseph; Taslakian, Perouz; Toussaint, Godfried.

2008. 99-102 Paper presented at 20th Annual Canadian Conference on Computational Geometry, CCCG 2008, Montreal, QC, Canada.

Research output: Contribution to conferencePaper

O'Rourke, J, Taslakian, P & Toussaint, G 2008, 'A pumping lemma for homometric rhythms' Paper presented at 20th Annual Canadian Conference on Computational Geometry, CCCG 2008, Montreal, QC, Canada, 8/13/08 - 8/15/08, pp. 99-102.
O'Rourke J, Taslakian P, Toussaint G. A pumping lemma for homometric rhythms. 2008. Paper presented at 20th Annual Canadian Conference on Computational Geometry, CCCG 2008, Montreal, QC, Canada.
O'Rourke, Joseph ; Taslakian, Perouz ; Toussaint, Godfried. / A pumping lemma for homometric rhythms. Paper presented at 20th Annual Canadian Conference on Computational Geometry, CCCG 2008, Montreal, QC, Canada.4 p.
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