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DOI: 10.1080/17459737.2011.608819

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Journal of Mathematics and Music 5, 2 (2011) 83-98

Z-relation and homometry in musical distributions

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

(2011-09-23)

This paper defines homometry in the rather general case of locally-compact topological groups, and proposes new cases of its musical use. For several decades, homometry has raised interest in computational musicology and especially set-theoretical methods, and in an independent way and with different vocabulary in crystallography and other scientific areas. The link between these two approaches was only made recently, suggesting new interesting musical applications and opening new theoretical problems. We present some old and new results on homometry, and give perspective on future research assisted by computational methods. We assume from the reader's basic knowledge of groups, topological groups, group algebras, group actions, Lebesgue integration, convolution products, and Fourier transform.

1:	Sciences et Technologies de la Musique et du Son (STMS)
	IRCAM – CNRS : UMR9912 – Université Pierre et Marie Curie [UPMC] - Paris VI
2:	Dipartimento di Matematica [Pisa]
	Università di Pisa
3:	Institut de Recherche et Coordination Acoustique/Musique (IRCAM)
	IRCAM
4:	CPGE Perpignan
	Ministère de l'Education Nationale

Subject

:

Mathematics/Combinatorics Humanities and Social Sciences/Musicology and performing arts

Keyword(s): GIS (generalized interval systems) – interval vector – Patterson function – Z-relation – homometry – hexachord theorem

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From: John Mandereau <>

Submitted on: Tuesday, 31 January 2012 16:51:22

Updated on: Tuesday, 31 January 2012 16:54:32