Titlebook: Mathematics and Computation in Music; 7th International Co Mariana Montiel,Francisco Gomez-Martin,Octavio A. Conference proceedings 2019 S

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Categories, Musical Instruments, and Drawings: A Unification Dream gestures) and music analysis. Mathematical formalism can also be used to connect music with other disciplines such as visual arts. In our analysis, we extend former studies on category theory applied to musical gestures, including musical instruments and playing techniques. Some basic concepts of c

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Tropical Generalized Interval Systemsk allows to broaden the GIS model introducing a new operation and consequently new musical and conceptual insights and applications, formalizing consistent relations between musical elements in an original unified structure. Some distinctive examples of extensions of well-known infinite GIS for latt

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From Schritte and Wechsel to Coxeter Groupsts are in a natural one-to-one correspondence with the triangles in the infinite Tonnetz. The left action of . on the Tonnetz gives rise to interesting chord sequences. We compare the system of transformations in . with the system of Schritte and Wechsel introduced by Hugo Riemann in 1880. Finally,

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Embedded Structural Modes: Unifying Scale Degrees and Harmonic Functionsleading between generic diatonic triads we study parsimonious function leading between embedded structural modes. A combinatorics of diatonic embeddings of structural modes is given. In four analytical examples we study the interaction of relative minor and major modes within an encompassing diatoni

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Distant Neighbors and Interscalar Contiguities a radical break from or a natural extension of the conventional diatonic system. We examine the connections between the local behavior of voice leading among diatonic triads and their generalizations on one hand, and the global properties of voice-leading spaces on the other. In particular, we aim