Abstract
This paper critiques Guerino Mazzola’s derivation of traditional counterpoint rules, arguing that those principles are not well-modeled by pitchclass intervals; that Mazzola’s differential treatment of fifths and octaves is not supported musically or by traditional counterpoint texts; that Mazzola’s specific calculations are not reproducible; that there are a number of intuitive considerations weighing against Mazzola’s explanation; that the fit between theory and evidence is not good; and that Mazzola’s statistical arguments are flawed. This leads to some general methodological reflections on different approaches to mathematical music theory, as well as to an alternative model of first-species counterpoint featuring the orbifold \(\mathbb{T}^2\)/\(\mathcal{S}_2\).
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References
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Tymoczko, D. (2011). Mazzola’s Model of Fuxian Counterpoint. In: Agon, C., Andreatta, M., Assayag, G., Amiot, E., Bresson, J., Mandereau, J. (eds) Mathematics and Computation in Music. MCM 2011. Lecture Notes in Computer Science(), vol 6726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21590-2_23
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DOI: https://doi.org/10.1007/978-3-642-21590-2_23
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