Towards a topological fingerprint of music
This work addresses the problem of music representation and classification for computational musicology, but it appears incremental as it builds on existing concepts like the Tonnetz and persistent homology.
The paper tackles the problem of representing music as a geometric and topological object by proposing a strategy to describe music features as a polyhedral surface using the Tonnetz and persistent homology, and it addresses automatic music style classification by computing hierarchical clustering of topological fingerprints, achieving results through analysis of paradigmatic compositional styles.
Can music be represented as a meaningful geometric and topological object? In this paper, we propose a strategy to describe some music features as a polyhedral surface obtained by a simplicial interpretation of the \textit{Tonnetz}. The \textit{Tonnetz} is a graph largely used in computational musicology to describe the harmonic relationships of notes in equal tuning. In particular, we use persistent homology in order to describe the \textit{persistent} properties of music encoded in the aforementioned model. Both the relevance and the characteristics of this approach are discussed by analyzing some paradigmatic compositional styles. Eventually, the task of automatic music style classification is addressed by computing the hierarchical clustering of the topological fingerprints associated with some collections of compositions.