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On group-theoretical methods applied to music: some compositional and implementational aspects

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text
 

Genre(s)

article
 

Forme(s)

document numérique
 

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Titre

On group-theoretical methods applied to music: some compositional and implementational aspects
 

Nom(s)

Andreatta, Moreno (auteur)
 

Publication

Osnabrück, Germany , Electronic Publishing Osnabrück, 2004
 

Description

Sujet(s)

groups   mathematics   music   computer-music
 

Résumé

This paper focuses on the group-theoretical approach to music theory and composition. In particular we concentrate on a family of groups which seem to be very interesting for a ›mathemusical‹ research: the non-Hajós groups. This family of groups will be considered in relationships with Anatol Vieru's »Theory of modes« as it has been formalised and generalised to the rhythmic domain by the Roumanian mathematician Dan Tudor Vuza. They represent the general framework where one can formalize the construction of a special family of tiling canons called the »Regular Unending Complementary Canons of Maximal Category« (RCMC-canons). This model has been implemented in Ircam's visual programming language OpenMusic. Canons which are constructible through the Vuza's algorithm are called Vuza Canons. The implementation of Vuza's model in OpenMusic enables to give the complete list of such canons and offers to composers an useful tool to manipulate complex global musical structures. The implementation shows many interesting mathematical properties of the compositional process which could be taken as a point of departure for a computational-oriented musicological discussion.
 

Note(s)

Article paru dans : Perspectives in Mathematical and Computational Music Theory
 

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Date de la notice

2014-10-31 01:00:00
 

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