A pumping lemma for homometric rhythms

Joseph O'Rourke; Perouz Taslakian; Godfried Toussaint

A pumping lemma for homometric rhythms

Joseph O'Rourke, Perouz Taslakian, Godfried Toussaint

Computer Science

Research output: Contribution to conference › Paper › peer-review

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 language	English (US)
Pages	99-102
Number of pages	4
State	Published - 2008
Event	20th Annual Canadian Conference on Computational Geometry, CCCG 2008 - Montreal, QC, Canada Duration: Aug 13 2008 → Aug 15 2008

Other

Other	20th Annual Canadian Conference on Computational Geometry, CCCG 2008
Country/Territory	Canada
City	Montreal, QC
Period	8/13/08 → 8/15/08

ASJC Scopus subject areas

Geometry and Topology

Cite this

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title = "A pumping lemma for homometric rhythms",

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.",

author = "Joseph O'Rourke and Perouz Taslakian and Godfried Toussaint",

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note = "20th Annual Canadian Conference on Computational Geometry, CCCG 2008 ; Conference date: 13-08-2008 Through 15-08-2008",

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T1 - A pumping lemma for homometric rhythms

AU - O'Rourke, Joseph

AU - Taslakian, Perouz

AU - Toussaint, Godfried

PY - 2008

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N2 - 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.

AB - 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.

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M3 - Paper

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T2 - 20th Annual Canadian Conference on Computational Geometry, CCCG 2008

Y2 - 13 August 2008 through 15 August 2008

ER -

A pumping lemma for homometric rhythms

Abstract

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ASJC Scopus subject areas

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