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    %0 Book Section
    %A Andreatta, Moreno
    %T On group-theoretical methods applied to music: some compositional and implementational aspects
    %D 2004
    %E G. Mazzola, T. Noll and E. Lluis-Puebla
    %B Perspectives in Mathematical and Computational Music Theory
    %C Osnabrück
    %I Electronic Publishing Osnabrück
    %P 169-193
    %F Andreatta04c
    %K groups
    %K mathematics
    %K music
    %K computer-music
    %X 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.
    %1 4
    %2 3
    %U http://architexte.ircam.fr/textes/Andreatta04c/
    © Ircam - Centre Pompidou 2005.