Artikel,
On some properties of periodic sequences in Anatol Vieru's modal theory.
Tatra Mt. Math. Publ., (2001)
Zusammenfassung
Summary: 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to music in the second half of the twentieth-century (see M. Andreatta \/ Group-theoretical methods applied to music, unpublished dissertation, (1997), M. Chemilier \/ Structure et méthode algébraiques en informatique musicale.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. Basel: Birkhäuser (2002; Zbl 1104.00003) 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, Bucurest (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.
