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.
    @conference{2a3d2be00cb64401868974bf2c27e172,
    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",
    year = "2008",
    month = "12",
    day = "1",
    language = "English (US)",
    pages = "99--102",
    note = "20th Annual Canadian Conference on Computational Geometry, CCCG 2008 ; Conference date: 13-08-2008 Through 15-08-2008",

    }

    TY - CONF

    T1 - A pumping lemma for homometric rhythms

    AU - O'Rourke, Joseph

    AU - Taslakian, Perouz

    AU - Toussaint, Godfried

    PY - 2008/12/1

    Y1 - 2008/12/1

    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.

    UR - http://www.scopus.com/inward/record.url?scp=67649893998&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=67649893998&partnerID=8YFLogxK

    M3 - Paper

    SP - 99

    EP - 102

    ER -