Computing Melodic Templates in Oral Music Traditions
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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, 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.
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