Abstract
A 20-note scale is revisited (from Balzano and Zweifel) and endowed with a version of Mazzola’s theory of modulation based on the symmetry group of the scale. Mazzola’s theory has been applied also by Muzzulini in the context of the usual 12-note equally tempered chromatic scale. A modulation for a 7 note exotic scale, based on this model, is presented in Sect. 4 to exemplify the algorithm by which the modulation quanta are computed, that is, the sets of notes that permit the calculation of the pivot progressions that lead from one scale to another. Then, the modulation model based on symmetries is applied to a 11 note diatonic scale, immersed within the 20 note scale, which shows the viability of the symmetry model for this microtonal case. This work is based on the premise that musical expression has an underlying mathematical structure.
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Gómez-Téllez, J.D., Lluis-Puebla, E., Montiel, M. (2017). A Symmetric Quantum Theory of Modulation in \(Z\!\!Z_{20}\) . In: Agustín-Aquino, O., Lluis-Puebla, E., Montiel, M. (eds) Mathematics and Computation in Music. MCM 2017. Lecture Notes in Computer Science(), vol 10527. Springer, Cham. https://doi.org/10.1007/978-3-319-71827-9_5
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DOI: https://doi.org/10.1007/978-3-319-71827-9_5
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