Computing Melodic Templates in Oral Music Traditions

TL;DR

This paper introduces a geometric optimization method to identify and analyze melodic templates in oral music traditions, capturing variations across performances without formal notation.

Contribution

It proposes the spanning tube problem to approximate melodic templates and quantify melodic variation in oral music performances.

Findings

Developed a new geometric optimization framework

Applied method to oral music performance data

Enabled quantitative assessment of melodic variation

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.