Topological Analysis of Musical Works

Student: Anton Medvedev

Educational Programme: Data Science (Master)

Year of Graduation: 2024

Computational topology opens up scope for research in data analysis problems. In particular, topological data analysis is used to study stylistic features and trends in musical compositions. In this work, we describe a method for constructing a weighted directed graph of a finite metric space, applying to which standard algorithms for topological data analysis based on the concept of persistent homologies, we obtain a feature-based description of this data. We apply this method to weighted directed graphs that encode information about transitions between pitch classes characteristic of the musical piece in question. Finally, using this method we will explore the stylistic features of D. Shostakovich's string quartets.

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