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@Article{          harasim.ea2021-exploring,
    author       = {Harasim, Daniel and Moss, Fabian C. and Ramirez, Matthias
                   and Rohrmeier, Martin},
    year         = {2021},
    title        = {Exploring the foundations of tonality: statistical
                   cognitive modeling of modes in the history of Western
                   classical music},
    abstract     = {Tonality is one of the most central theoretical concepts
                   for the analysis of Western classical music. This study
                   presents a novel approach for the study of its historical
                   development, exploring in particular the concept of mode.
                   Based on a large dataset of approximately 13,000 musical
                   pieces in MIDI format, we present two models to infer both
                   the number and characteristics of modes of different
                   historical periods from first principles: a geometric
                   model of modes as clusters of musical pieces in a
                   non-Euclidean space, and a cognitively plausible Bayesian
                   model of modes as Dirichlet distributions. We use the
                   geometric model to determine the optimal number of modes
                   for five historical epochs via unsupervised learning and
                   apply the probabilistic model to infer the characteristics
                   of the modes. Our results show that the inference of four
                   modes is most plausible in the Renaissance, that two
                   modes–corresponding to major and minor–are most
                   appropriate in the Baroque and Classical eras, whereas no
                   clear separation into distinct modes is found for the 19th
                   century.},
    doi          = {10.1057/s41599-020-00678-6},
    issn         = {26629992},
    journal      = {Humanities and Social Sciences Communications},
    keywords     = {computational musicology},
    mendeley-tags= {computational musicology},
    number       = {1},
    publisher    = {Springer US},
    url          = {http://dx.doi.org/10.1057/s41599-020-00678-6},
    volume       = {8}
}