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Computational modeling of interval distributions in tonal space reveals paradigmatic stylistic changes in Western music history

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  • Fabian C. Moss

    (Julius-Maximilians-Universität Würzburg)

  • Robert Lieck

    (Durham University)

  • Martin Rohrmeier

    (École Polytechnique Fédérale de Lausanne)

Abstract

Diachronic stylistic changes in music are to a large extent affected by composers’ different choices, for example regarding the usage of tones, intervals, and harmonies. Analyzing the tonal content of pieces of music and observing them over time is thus informative about large-scale historical changes. In this study, we employ a computational model that formalizes music-theoretic conceptualizations of tonal space, and use it to infer the most likely interval distributions for pieces in a large corpus of music, represented as so-called ‘bags of tonal pitch classes’. Our results show that tonal interval relations become increasingly complex, that the interval of the perfect fifth dominates compositions for centuries, and that one can observe a stark increase in the usage of major and minor thirds during the 19th century, which coincides with the emergence of extended tonality. In complementing prior research on the historical evolution of tonality, our study thus demonstrates how example-based music theory can be informed by quantitative analyses of large corpora and computational models.

Suggested Citation

  • 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.
  • Handle: RePEc:pal:palcom:v:11:y:2024:i:1:d:10.1057_s41599-024-03168-1
    DOI: 10.1057/s41599-024-03168-1
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    References listed on IDEAS

    as
    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. Rosenbaum, Paul R., 2010. "Design Sensitivity and Efficiency in Observational Studies," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 692-702.
    3. 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.
    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. Sally E. Street & Tuomas Eerola & Jeremy R. Kendal, 2022. "The role of population size in folk tune complexity," Palgrave Communications, Palgrave Macmillan, vol. 9(1), pages 1-12, December.
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