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Harmonic structures of Beethoven quartets: a complex network approach

Author

Listed:
  • Theo Frottier

    (Université de Toulouse,CNRS, UPS)

  • Bertrand Georgeot

    (Université de Toulouse,CNRS, UPS)

  • Olivier Giraud

    (Université Paris Saclay, CNRS, LPTMS)

Abstract

We propose a complex network approach to the harmonic structure underpinning western tonal music. From a database of Beethoven’s string quartets, we construct a directed network whose nodes are musical chords and edges connect chords following each other. We show that the network is scale-free and has specific properties when ranking algorithms are applied. We explore the community structure and its musical interpretation, and propose statistical measures stemming from network theory allowing to distinguish stylistically between periods of composition. Our work opens the way to a network approach of structural properties of tonal harmony. Graphicabstract

Suggested Citation

  • Theo Frottier & Bertrand Georgeot & Olivier Giraud, 2022. "Harmonic structures of Beethoven quartets: a complex network approach," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(7), pages 1-8, July.
    • Handle: RePEc:spr:eurphb:v:95:y:2022:i:7:d:10.1140_epjb_s10051-022-00368-z
    DOI: 10.1140/epjb/s10051-022-00368-z
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    References listed on IDEAS

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    1. Fabian C Moss & Markus Neuwirth & Daniel Harasim & Martin Rohrmeier, 2019. "Statistical characteristics of tonal harmony: A corpus study of Beethoven’s string quartets," PLOS ONE, Public Library of Science, vol. 14(6), pages 1-16, June.
    2. Antiqueira, L. & Nunes, M.G.V. & Oliveira Jr., O.N. & F. Costa, L. da, 2007. "Strong correlations between text quality and complex networks features," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 811-820.
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