Algorithms for computing geometric measures of melodic similarity

Greg Aloupis, Thomas Fevens, Stefan Langerman, Tomomi Matsui, Antonio Mesa, Yurai Nuñez, David Rappaport, Godfried Toussaint

    Research output: Contribution to journalArticle

    Abstract

    Two algorithms to find the minimum area between two given orthogonal melodies, Ma and Mb, of size n and m, respectively (n > m) are presented. Both algorithms can be used for cyclic melodies as well as in the context of retrieving short patterns from a database. The algorithms are described for the case where the melodies are cyclic. The first algorithm assumes that the Θ direction is fixed, and it runs in O(n) time. The second algorithm finds the minimum area when both the z and Θ relative positions can be varied. It is proved that it runs in O(nmlogn) time. In each case, it is assumed that the edges defining Ma and Mb are given in the order in which they appear in melodies. Finally, natural extensions are discussed both for the polygonal description of melodies and for different types of queries.

    Original languageEnglish (US)
    Pages (from-to)67-76
    Number of pages10
    JournalComputer Music Journal
    Volume30
    Issue number3
    DOIs
    StatePublished - Sep 1 2006

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    ASJC Scopus subject areas

    • Media Technology
    • Music
    • Computer Science Applications

    Cite this

    Aloupis, G., Fevens, T., Langerman, S., Matsui, T., Mesa, A., Nuñez, Y., ... Toussaint, G. (2006). Algorithms for computing geometric measures of melodic similarity. Computer Music Journal, 30(3), 67-76. https://doi.org/10.1162/comj.2006.30.3.67

    Algorithms for computing geometric measures of melodic similarity. / Aloupis, Greg; Fevens, Thomas; Langerman, Stefan; Matsui, Tomomi; Mesa, Antonio; Nuñez, Yurai; Rappaport, David; Toussaint, Godfried.

    In: Computer Music Journal, Vol. 30, No. 3, 01.09.2006, p. 67-76.

    Research output: Contribution to journalArticle

    Aloupis, G, Fevens, T, Langerman, S, Matsui, T, Mesa, A, Nuñez, Y, Rappaport, D & Toussaint, G 2006, 'Algorithms for computing geometric measures of melodic similarity', Computer Music Journal, vol. 30, no. 3, pp. 67-76. https://doi.org/10.1162/comj.2006.30.3.67
    Aloupis G, Fevens T, Langerman S, Matsui T, Mesa A, Nuñez Y et al. Algorithms for computing geometric measures of melodic similarity. Computer Music Journal. 2006 Sep 1;30(3):67-76. https://doi.org/10.1162/comj.2006.30.3.67
    Aloupis, Greg ; Fevens, Thomas ; Langerman, Stefan ; Matsui, Tomomi ; Mesa, Antonio ; Nuñez, Yurai ; Rappaport, David ; Toussaint, Godfried. / Algorithms for computing geometric measures of melodic similarity. In: Computer Music Journal. 2006 ; Vol. 30, No. 3. pp. 67-76.
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