Discrete phase retrieval in musical structures

John Mandereau (1, 2) , Daniele Ghisi (3) , Emmanuel Amiot (4) , Moreno Andreatta (1) , Carlos Agon (1)

1 STMS - Sciences et Technologies de la Musique et du Son
2 Dipartimento di Matematica [Pisa]
3 IRCAM - Institut de Recherche et Coordination Acoustique/Musique
4 CPGE Perpignan

This paper describes phase-retrieval approaches in music by focusing on the particular case of the cyclic groups (beltway problem). After presenting some old and new results on phase retrieval, we introduce the extended phase retrieval for a generalized musical Z-relation. This concept is accompanied by mathematical definitions and motivations from computer-aided composition. We assume from the reader basic knowledge of groups, topological groups, group algebras, group actions, Lebesgue integration, convolution products, and Fourier transform.

Mots clés: GIS (generalized interval systems); interval vector; Patterson function; Z-relation; homometry; phase retrieval; spectral units; k-deck

Domaines: Combinatoire [math.CO]; Musique, musicologie et arts de la scène

John Mandereau, Daniele Ghisi, Emmanuel Amiot, Moreno Andreatta, Carlos Agon. Discrete phase retrieval in musical structures. Journal of Mathematics and Music, 2011, 5 (2), pp.99-116. ⟨10.1080/17459737.2011.608820⟩. ⟨hal-00664787⟩