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Western musicians traditionally classify pitch sequences by disregarding the effects of five musical transformations: octave shift, permutation, transposition, inversion, and cardinality change. We model this process mathematically, showing that it produces 32 equivalence relations on chords, 243 equivalence relations on chord sequences, and 32 families of(More)
this possibility (Fig. 1, A to C, and movie S4). This central feature of Western counterpoint is made possible by composers_ interest in the harmonic property of acoustic consonance. A chord with duplicate pitch classes is permutationally symmetrical (P-symmetrical) because there is some nontrivial permutation of its notes that is a trivial voice leading.(More)
The practice of singing dates back to the beginnings of human history and represents the convergence of two similar systems: language and music. Within these two systems, the fields of linguistic prosody and musical meter each use the temporal domain to express their underlying structure. At times, these expressional requirements differ, necessitating(More)
Two approaches for characterising scales are presented and compared in this paper. The first one was proposed three years ago by the musician and composer Pierre Audétat, who developed a numerical and graphical representation of the 66 heptatonic scales and their 462 modes, a new cartography called the Diatonic Bell. It allows sorting and classifying the(More)
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