Abstract

Abstract

The theory of the combinatory potential of the scales is based on the operation with interval classes, being applicable to pitch and duration intervals. Interval classes offer an efficient synthesis for reducing and expanding information to a maximum. Interval classes turn out to be more efficient than the pitch classes, for, among other aspects, they reduce information of the intervallic groupings to a minimum number of cases. The notion of adjacent interval implies the notion of d1 minimal distance, which allows for the understanding of a scale as a continuum sequence of adjacent intervals. Music education by means of producing melodies, harmonies and counterpoints is among the essential applications of the d1 theory.

Bio

Doctor in Music and Musicology from the University of Strasbourg. Dr. Estrada is Visiting Professor of International Music Courses in Darmstadt, in the universities of Stanford, La Jolla, Albuquerque, Rostock and Sorbonne, where he holds the Chair Alfonso Reyes. Director of the Centre d’Etudes de Mathématiques et Automatique Musicales de Paris (2000-2001). He was granted the Order of Arts and Letters of France (1980, 1988) and National University Prize 2001. His training as a musical creator is enriched with the tradition of Orbón and Boulanger, Conservatoire de Paris, and the avant – Messiaen, Ligeti, Lachenmann, Stockhausen and Xenakis. He has been commissioned to create music for the festivals in Darmstadt, Donaueschingen, Bremen-Siemens, Musicadhoy, Rasegna di Nuova Musica, National Radio of Spain, Süd-West Rundfunk, International Contemporary Ensemble, etc. Among his works are “Memorias para Teclado”, “Los Cantos”, “Los yuunohui, ishini’ioni, eolo’oolin” and the multi-Opera “Murmullos del Páramo”. The Festivals Tage für Neue Musik (2001 Zurich), Music Factory (2002 Bergen) and Three Generations (2008 NY) are dedicated to his musical, theoretical and pedagogical work. Dr. Estrada is editor of “Musiv of Mexico” (1984), and author with Jorge Gil of “Music and finite group theory (1984). He postulates the D1 Theory of the combinatorial potential of scales (MUSiiC 2006). He is also author of “El sonido en Rulfo, el ruido ese” (2008 2nd ed.), and “Reality and continuous imagination”, “Philosophy, theory and methods of musical creation “(in press) and “Broken Chant: Silvestre Revueltas” (2012). He is Director of the journal “Perspectiva Interdisciplinaria de Música”.