On some properties of periodic sequences in Anatol Vieru's modal theory

Rok, strany: 2001, 1 - 15

Algebraic methods have been currently applied to music in the second half of the twentieth-century (see [M. Andreatta: Group-theoretical Methods applied to Music, unpublished dissertation, 1997], [M. Chemilier: Structure et Méthode algébraiques en informatique musicale:. Thèse de doctorat, L. I. T. P., Institut Blaise Pascal, 1990] and [G. Mazzola et al.: The Topos of Music—Geometric Logic of Concepts, Theory and Performance] for main references). By starting from Anatol Vieru's compositional technique based on finite difference calculus on periodic modal sequences, as it has been introduced in his book [ Cartea modurilor, 1 (Le livre des modes, 1). Ed. Muzicala, Bucarest, 1980. Revised ed. The book of modes, 1993], the present essay tries to generalize some properties by means of abstract group theory. Two main classes of periodic sequences are considered: reducible and reproducible sequences, replacing respectively Vieru's modal and irreducible sequences. It turns out that any periodic sequence can be decomposed in a unique way into a reducible and a reproducible component.

ISO 690:

Andreatta, M., Vuza, D. 2001. On some properties of periodic sequences in Anatol Vieru's modal theory. In Tatra Mountains Mathematical Publications, vol. 23, no.3, pp. 1-15. 1210-3195.

APA:

Andreatta, M., Vuza, D. (2001). On some properties of periodic sequences in Anatol Vieru's modal theory. Tatra Mountains Mathematical Publications, 23(3), 1-15. 1210-3195.