Taking music seriously: on the dynamics of 'mathemusical' research with a focus on Hexachordal Theorems - Institut de Recherche et Coordination Acoustique/Musique Access content directly
Journal Articles Symmetry, Integrability and Geometry : Methods and Applications Year : 2024

Taking music seriously: on the dynamics of 'mathemusical' research with a focus on Hexachordal Theorems

Abstract

After presenting the general framework of 'mathemusical' dynamics, we focus on one music-theoretical problem concerning a special case of homometry theory applied to music composition, namely Milton Babbitt's Hexachordal Theorem. We briefly discuss some historical aspects of homometric structures and their ramifications in crystallography, spectral analysis and music composition via the construction of rhythmic canons tiling the integer line. We then present the probabilistic generalization of Babbitt's result we recently introduced in a paper entitled "New hexachordal theorems in metric spaces with probability measure" (published in the Rendiconti del Seminario Matematico della Università di Padova) and illustrate the new approach with original constructions and exemples.
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Dates and versions

hal-04306896 , version 1 (25-11-2023)
hal-04306896 , version 2 (29-01-2024)

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Moreno Andreatta, Corentin Guichaoua, Nicolas Juillet. Taking music seriously: on the dynamics of 'mathemusical' research with a focus on Hexachordal Theorems. Symmetry, Integrability and Geometry : Methods and Applications, 2024, 20 (009), ⟨10.3842/SIGMA.2024.009⟩. ⟨hal-04306896v2⟩
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