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Towards a topological fingerprint of music. (English) Zbl 1339.00005
Bac, Alexandra (ed.) et al., Computational topology in image context. 6th international workshop, CTIC 2016, Marseille, France, June 15–17, 2016. Proceedings. Cham: Springer (ISBN 978-3-319-39440-4/pbk; 978-3-319-39441-1/ebook). Lecture Notes in Computer Science 9667, 88-100 (2016).
Summary: 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 Tonnetz. The 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 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.
For the entire collection see [Zbl 1337.68003].

MSC:
00A65 Mathematics and music
Software:
dynamicTreeCut; EDA
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