Abstract
Classification of scales began to take shape in the nineteenth century through the works of Camille Durutte, Hoëne Wronski, Anatole Loquin and some others, but it really took a new start in the twentieth century. The aim of this paper is to study a new classification of modes based on the plactic congruences. These congruences mimic a small perturbation from one mode to the other by the move of only one note. Two modes are in the same plactic class if they are related by a path of modes which are pairwise linked by plactic congruences. In this paper, a mode is an ordered series of musical intervals (or steps). A scale is an ascending or descending series of notes, representing a class of modes under circular permutations. In traditional Western music, the C major scale represents the circular permutations of the seven usual modern modes (Ionian, Dorian, Phrygian, etc.)
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© 2011 Springer-Verlag Berlin Heidelberg
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Jedrzejewski, F. (2011). Plactic Classification of Modes. 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_31
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DOI: https://doi.org/10.1007/978-3-642-21590-2_31
Publisher Name: Springer, Berlin, Heidelberg
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