Non-commutative homometric musical structures and chord distances in geometric pitch spaces

Abstract : We study two main topics: non-commutative homometry and the notion of distance between musical chords. Two melodies are homometric if they share the same set of intervals. We transpose this notion to a chord sequence and more generally to semi-direct products, which allows to build a framework for the general study of homometry in non-commutative groups, such as the dihedral group. In the second part we define a mesure of distance between musical chords of different cardinalities, from a distance based on the notion of voice-leading.
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Grégoire Genuys. Non-commutative homometric musical structures and chord distances in geometric pitch spaces. Category Theory [math.CT]. Université Pierre et Marie Curie - Paris VI, 2017. English. ⟨NNT : 2017PA066576⟩. ⟨tel-01912752⟩

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