Taking Music Seriously: on the Dynamics of `Mathemusical' Research with a Focus on Hexachordal Theorems

Moreno Andreatta ; Corentin Guichaoua ; Nicolas Juillet

Symmetry, integrability and geometry: methods and applications, Tome 20 (2024)

Résumé

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” and illustrate the new approach with original constructions and examples.

Détail

Keywords: mathemusical research, homometric sets, distance-sets, metric measure spaces, scalar curvature, Patterson function.
Mots-clés : ball volume

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