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Statistical characteristics of tonal harmony: A corpus study of Beethoven’s string quartets

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  • Fabian C Moss
  • Markus Neuwirth
  • Daniel Harasim
  • Martin Rohrmeier

Abstract

Tonal harmony is one of the central organization systems of Western music. This article characterizes the statistical foundations of tonal harmony based on the computational analysis of expert annotations in a large corpus. Using resampling methods, this study shows that 1) the rank-frequency distribution of chords resembles a power law, i.e. few chords govern a large proportion of the data; 2) chord transitions are referential and chord predictability is significantly affected by distinguished chord features; 3) tonal harmony conveys directedness in time; and 4) tonal harmony operates differently at the hierarchical levels of chords and keys. These results serve to characterize tonal harmony on empirical grounds and advance the methodological state-of-the-art in digital musicology.

Suggested Citation

  • 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.
    • Handle: RePEc:plo:pone00:0217242
    DOI: 10.1371/journal.pone.0217242
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    Cited by:

    1. 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.
    2. Daniel Harasim & Fabian C. Moss & Matthias Ramirez & Martin Rohrmeier, 2021. "Exploring the foundations of tonality: statistical cognitive modeling of modes in the history of Western classical music," Palgrave Communications, Palgrave Macmillan, vol. 8(1), pages 1-11, December.
    3. Fabian C. Moss & Robert Lieck & Martin Rohrmeier, 2024. "Computational modeling of interval distributions in tonal space reveals paradigmatic stylistic changes in Western music history," Palgrave Communications, Palgrave Macmillan, vol. 11(1), pages 1-11, December.
    4. Sabrina Laneve & Ludovica Schaerf & Gabriele Cecchetti & Johannes Hentschel & Martin Rohrmeier, 2023. "The diachronic development of Debussy’s musical style: a corpus study with Discrete Fourier Transform," Palgrave Communications, Palgrave Macmillan, vol. 10(1), pages 1-13, December.
    5. Ferreira, Paulo & Quintino, Derick & Wundervald, Bruna & Dionísio, Andreia & Aslam, Faheem & Cantarinha, Ana, 2021. "Is Brazilian music getting more predictable? A statistical physics approach for different music genres," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).

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