Persistent Homology and Discrete Fourier Transform An Application to Topological Musical Data Analysis /
This book proposes contributions to various problems in the field of topological analysis of musical data: the objects studied are scores represented symbolically by MIDI files, and the tools used are the discrete Fourier transform and persistent homology. The manuscript is divided into three parts:...
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| Format: | Électronique eBook |
| Langue: | anglais |
| Publié: |
Cham :
Springer Nature Switzerland : Imprint: Springer,
2025.
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| Édition: | 1st ed. 2025. |
| Collection: | Computational Music Science,
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| Accès en ligne: | https://doi.org/10.1007/978-3-031-82236-0 |
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Table des matières:
- 1 Introduction
- Part I The two-dimensional Discrete Fourier Transform
- 2 The DFT for modeling basic musical structures
- 3 Generalization of theoretical results
- Part II Persistent homology on musical bars
- 4 Mathematical background
- 5 Musical scores and filtration
- Part III Musical applications
- 6 The DFT as a metric on the set of notes and chord
- 7 Harmonization of Pop songs
- 8 Classification of musical style
- 9 A different approach: the Hausdorff distance
- 10 Conclusion and perspectives for future research.