Mathematical and computational modelling within a music analysis framework: motivic topologies as a case study

Abstract

This paper revisits a mathematical model of motivic analysis, together with its computational realization, from an interdisciplinary perspective, relating it to concepts and methods in the field of computational music analysis. Issues such as segmentation, motivic formation, knowledge representation, similarity and categorization, and interpretation of results are discussed. A further introspection on the approach, in the context of mathematics, computation, and music analysis as a large interdisciplinary field, reveals relations between the three: the mathematical model (motivic topologies), its computational counterpart (OM-Melos), and music analysis (Réti's and Nattiez’ methods). In doing so, we stress the importance of neutrality, objectivity, and scientific rigour in the modelling part while at the same time preserving the freedom of the music analyst in order to create musically interesting results.