La Musica Algoritmica e l'Offerta Musicale di J.S.Bach

Abstract

The object of this work is an algebraic – geometric analysis of the canons of the Musical Offering of J.S.Bach. We construct a simulation model, thanks to the logic of imitation and thanks to the classical techniques of the harmony, which are present in the Musical Offering. Many of these techniques give musical criteria to understand, compose and classify a canon, so we have translated them in the mathematical language, using the affinities of the euclidean bidimensional space. Such approach allows us to write each canon of each period in a suitable linear system. A treatment of this kind for a musical piece offers a new method to compose, giving different numerical values to the coefficients of the linear system.