5 Aknowledgements

This paper is a condensed and updated version of my Independent Study Dissertation »Group Theorectical Methods in Music« (c.f. Andreatta, 1997). I would like to express my sincere acknowledgements to the editors, who gave me the possibility to revise and finally publish a study which seems to have progressively become a reference in the Minkowski/Hajós problem applied to the construction of tiling rhythmic canons. Many things happened since the period I was Visiting Student at the University of Sussex and the present article reflects the different ramifications of my present interests. Firstly the contact with the Music Representation Team at Ircam, expecially with Gérard Assayag and Carlos Agon, who trusted me in my algebraic approach to the formalisation of musical structures. The implementation of all these methods in OpenMusic is the most evident consequence of a very exciting collaboration between a mathematically-inclined musician, as I am, and a computer-music scientist, Carlos Agon, whose continuous encouragement and interest in this approach finally enabled to make the theory more suitable for compositional application. I would like to thank Thomas Noll and Guerino Mazzola for their great help in some mathematical aspects of Vuza Theory which has been progressively integrated in the more general framework of the MaMuTh-approach. Many thanks to Emmanuel Amiot and Harald Fripertinger for all the comments they provided on the mathematical strategies in the enumeration and construction of tiling rhythmic canons.

This paper is dedicated to Dan Tudor Vuza, with great respect and profound admiration.

References