Abstract
The paper deals with the question of homometry in the dihedral groups \(D_{n}\) of order 2n. These groups are non-commutative, leading to new and challenging definitions of homometry, as compared to the well-known case of homometry in the commutative group \( \mathbb {Z}_{n}\). We give here a musical interpretation of homometry in \(D_{12}\) using the well-known neo-Riemannian groups, some results on a complete enumeration of homometric sets for small values of n, and some properties disclosing the deep links between homometry in \(\mathbb {Z}_{n}\) and homometry in \(D_{n}\).
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Genuys, G., Popoff, A. (2017). Homometry in the Dihedral Groups: Lifting Sets from \( \mathbb {Z}_{n}\) to \( D_{n}\) . 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_4
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DOI: https://doi.org/10.1007/978-3-319-71827-9_4
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