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arXiv · 2209.13598

Computing Melodic Templates in Oral Music Traditions

Sergey Bereg·José-Miguel Díaz-Báñez·Nadine Kroher·Inmaculada Ventura
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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 tradition, 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 an 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, $\varepsilon^*$, such that, the vertical segment of length $2\varepsilon^*$ centered at $(x,f^*(x))$ intersects at least $p$ functions ($p\leq n$). The method explored here also provide a novel tool for quantitatively assess the amount of melodic variation which occurs across performances.

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Sergey Bereg, José-Miguel Díaz-Báñez, Nadine Kroher, Inmaculada Ventura. 2022-09-27. Computing Melodic Templates in Oral Music Traditions. https://arxiv.org/abs/2209.13598

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