Structural properties of euclidean rhythms

Francisco Gómez-Martín, Perouz Taslakian, Godfried Toussaint

    Research output: Contribution to journalArticle

    Abstract

    In this paper we investigate the structure of Euclidean rhythms and show that a Euclidean rhythm is formed of a pattern, called the main pattern, repeated a certain number of times, followed possibly by one extra pattern, the tail pattern. We thoroughly study the recursive nature of Euclidean rhythms when generated by Bjorklund's algorithm, one of the many algorithms that generate Euclidean rhythms. We make connections between Euclidean rhythms and Bezout's theorem. We also prove that the decomposition obtained is minimal.

    Original languageEnglish (US)
    Pages (from-to)1-14
    Number of pages14
    JournalJournal of Mathematics and Music
    Volume3
    Issue number1
    DOIs
    StatePublished - Jan 1 2009

    Fingerprint

    Structural Properties
    Structural properties
    Euclidean
    Decomposition
    Bezout's Theorem
    Tail
    Rhythm
    Decompose

    Keywords

    • Euclidean rhythms
    • Maximally even

    ASJC Scopus subject areas

    • Modeling and Simulation
    • Music
    • Computational Mathematics
    • Applied Mathematics

    Cite this

    Structural properties of euclidean rhythms. / Gómez-Martín, Francisco; Taslakian, Perouz; Toussaint, Godfried.

    In: Journal of Mathematics and Music, Vol. 3, No. 1, 01.01.2009, p. 1-14.

    Research output: Contribution to journalArticle

    Gómez-Martín, F, Taslakian, P & Toussaint, G 2009, 'Structural properties of euclidean rhythms', Journal of Mathematics and Music, vol. 3, no. 1, pp. 1-14. https://doi.org/10.1080/17459730902819566
    Gómez-Martín, Francisco ; Taslakian, Perouz ; Toussaint, Godfried. / Structural properties of euclidean rhythms. In: Journal of Mathematics and Music. 2009 ; Vol. 3, No. 1. pp. 1-14.
    @article{978f682c8a474f58871d3bee7baec7e3,
    title = "Structural properties of euclidean rhythms",
    abstract = "In this paper we investigate the structure of Euclidean rhythms and show that a Euclidean rhythm is formed of a pattern, called the main pattern, repeated a certain number of times, followed possibly by one extra pattern, the tail pattern. We thoroughly study the recursive nature of Euclidean rhythms when generated by Bjorklund's algorithm, one of the many algorithms that generate Euclidean rhythms. We make connections between Euclidean rhythms and Bezout's theorem. We also prove that the decomposition obtained is minimal.",
    keywords = "Euclidean rhythms, Maximally even",
    author = "Francisco G{\'o}mez-Mart{\'i}n and Perouz Taslakian and Godfried Toussaint",
    year = "2009",
    month = "1",
    day = "1",
    doi = "10.1080/17459730902819566",
    language = "English (US)",
    volume = "3",
    pages = "1--14",
    journal = "Journal of Mathematics and Music",
    issn = "1745-9737",
    publisher = "Taylor and Francis Ltd.",
    number = "1",

    }

    TY - JOUR

    T1 - Structural properties of euclidean rhythms

    AU - Gómez-Martín, Francisco

    AU - Taslakian, Perouz

    AU - Toussaint, Godfried

    PY - 2009/1/1

    Y1 - 2009/1/1

    N2 - In this paper we investigate the structure of Euclidean rhythms and show that a Euclidean rhythm is formed of a pattern, called the main pattern, repeated a certain number of times, followed possibly by one extra pattern, the tail pattern. We thoroughly study the recursive nature of Euclidean rhythms when generated by Bjorklund's algorithm, one of the many algorithms that generate Euclidean rhythms. We make connections between Euclidean rhythms and Bezout's theorem. We also prove that the decomposition obtained is minimal.

    AB - In this paper we investigate the structure of Euclidean rhythms and show that a Euclidean rhythm is formed of a pattern, called the main pattern, repeated a certain number of times, followed possibly by one extra pattern, the tail pattern. We thoroughly study the recursive nature of Euclidean rhythms when generated by Bjorklund's algorithm, one of the many algorithms that generate Euclidean rhythms. We make connections between Euclidean rhythms and Bezout's theorem. We also prove that the decomposition obtained is minimal.

    KW - Euclidean rhythms

    KW - Maximally even

    UR - http://www.scopus.com/inward/record.url?scp=77950701208&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=77950701208&partnerID=8YFLogxK

    U2 - 10.1080/17459730902819566

    DO - 10.1080/17459730902819566

    M3 - Article

    VL - 3

    SP - 1

    EP - 14

    JO - Journal of Mathematics and Music

    JF - Journal of Mathematics and Music

    SN - 1745-9737

    IS - 1

    ER -