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Computing melodic templates in oral music traditions

Author

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  • Bereg, Sergey
  • Díaz-Báñez, José-Miguel
  • Kroher, Nadine
  • Ventura, Inmaculada

Abstract

The term melodic template or skeleton refers to a basic melody which is subject to variation during a music performance. In many oral music traditions, these templates are implicitly passed throughout generations without ever being formalized in a score. In this work, we introduce a new geometric optimization problem, the spanning tube problem, to approximate a melodic template for a set of labeled performance transcriptions corresponding to a specific style in oral music traditions. Given a set of n piecewise linear functions, we solve the problem of finding a continuous function, f*, and a minimum value, ε*, such that, the vertical segment of length 2ε* centered at (x, f*(x)) intersects at least p functions (p ≤ n). The method explored here also provide a novel tool for quantitatively assess the amount of melodic variation which occurs across performances.

Suggested Citation

  • Bereg, Sergey & Díaz-Báñez, José-Miguel & Kroher, Nadine & Ventura, Inmaculada, 2019. "Computing melodic templates in oral music traditions," Applied Mathematics and Computation, Elsevier, vol. 344, pages 219-229.
    • Handle: RePEc:eee:apmaco:v:344-345:y:2019:i::p:219-229
    DOI: 10.1016/j.amc.2018.09.071
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    References listed on IDEAS

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    1. Valian, Ehsan & Tavakoli, Saeed & Mohanna, Shahram, 2014. "An intelligent global harmony search approach to continuous optimization problems," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 670-684.
    2. Diaz-Banez, J. M. & Mesa, J. A., 2001. "Fitting rectilinear polygonal curves to a set of points in the plane," European Journal of Operational Research, Elsevier, vol. 130(1), pages 214-222, April.
    3. Barba, L. & Caraballo, L.E. & Díaz-Báñez, J.M. & Fabila-Monroy, R. & Pérez-Castillo, E., 2016. "Asymmetric polygons with maximum area," European Journal of Operational Research, Elsevier, vol. 248(3), pages 1123-1131.
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    Cited by:

    1. Caraballo, L.E. & Díaz-Báñez, J.M. & Rodríguez, F. & Sánchez-Canales, V. & Ventura, I., 2022. "Scaling and compressing melodies using geometric similarity measures," Applied Mathematics and Computation, Elsevier, vol. 426(C).

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