Computing melodic templates in oral music traditions

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

Applied Mathematics and Computation, 2019, vol. 344-345, 219-229

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.

Keywords: Melodic skeleton; Geometric algorithm; Oral music tradition (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:344-345:y:2019:i::p:219-229

DOI: 10.1016/j.amc.2018.09.071

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