A framework for topological music analysis (TMA)
Por:
Alcalá-Alvarez A., Padilla-Longoria P.
Publicada:
1 ene 2024
Ahead of Print:
1 jun 2023
Resumen:
In the present article we describe and discuss a framework for applying different topological data analysis (TDA) techniques to a music fragment given as a score in traditional Western notation. We first consider different sets of points in Euclidean spaces of different dimensions that correspond to musical events in the score, and obtain their persistent homology features. Then we introduce two families of simplicial complexes that can be associated with chord sequences, and leverage homology to compute their salient features. Finally, we show the results of applying the described methods to the analysis and stylistic comparison of fragments from three Brandenburg Concertos by J.S. Bach and two pieces from the Graffiti series by Mexican composer Armando Luna. © 2023 Informa UK Limited, trading as Taylor & Francis Group.
Filiaciones:
Alcalá-Alvarez A.:
Institute for Applied Mathematics, Universidad Nacional Autonoma de Mexico, Ciudad de Mexico, Mexico
Padilla-Longoria P.:
Institute for Applied Mathematics, Universidad Nacional Autonoma de Mexico, Ciudad de Mexico, Mexico
Green Submitted, All Open Access; Green Open Access
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