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Persistent Homology on Musical Bars

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Mathematics and Computation in Music (MCM 2022)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13267))

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Abstract

This article presents a new way of building a filtered simplicial complex from a music piece and applying persistent homology in the context of musical analysis. Our approach consists of considering any musical score as the set of its musical bars, which we see as subsets of \(\mathbb {R}^3\). With this definition, we may consider the Hausdorff distance between two musical bars, which gives us a point cloud from any score, and that allows us to build the associated Vietoris-Rips complex. We will then use barcodes to visualize persistent homology and give an illustration of our construction on a famous movie music piece.

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Authors and Affiliations

  1. IRMA, UMR 7501, CNRS, Université de Strasbourg, Strasbourg, France

    Victoria Callet

Authors
  1. Victoria Callet
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Correspondence to Victoria Callet .

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Editors and Affiliations

  1. Georgia State University, Atlanta, GA, USA

    Mariana Montiel

  2. Technological University of the Mixteca, Huajuapan de León, Mexico

    Octavio A. Agustín-Aquino

  3. Universidad Politécnica de Madrid, Madrid, Spain

    Francisco Gómez

  4. Life University, Marietta, GA, USA

    Jeremy Kastine

  5. National Autonomous University of Mexico, Mexico City, Distrito Federal, Mexico

    Emilio Lluis-Puebla

  6. Georgia State University, Atlanta, GA, USA

    Brent Milam

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Callet, V. (2022). Persistent Homology on Musical Bars. In: Montiel, M., Agustín-Aquino, O.A., Gómez, F., Kastine, J., Lluis-Puebla, E., Milam, B. (eds) Mathematics and Computation in Music. MCM 2022. Lecture Notes in Computer Science(), vol 13267. Springer, Cham. https://doi.org/10.1007/978-3-031-07015-0_29

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  • DOI: https://doi.org/10.1007/978-3-031-07015-0_29

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-07014-3

  • Online ISBN: 978-3-031-07015-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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