Analysis and compacting of musical texts

In this paper we examine the possibility of analyzing, according to a precise mathematic model, the structure of musical texts, and of describing them in a compact form. The approach that we have followed was to identify in the text, appropriately coded, some passages which can be obtained from preoeding passages by applying to them suitable operators. These passages can be coded synthetically with a referenoe to the preoeding passage and the operator applied to it. This approach may be used not only for musical texts, but in general, for any structure that can be considered constituted of various fundamental substructures which repeat themselves, unchanged or modified by suitable operators, inside the same structure. We give, in this general frame, a theoretical evaluation of the minimum and maximum "compacting value" which can be obtained considering repetitions only, and we also give an algorithm to calculate such a value for a given sequence. Then we specifically consider some classes of operators, selected on the basis of the analysis of some musical texts and of some considerations derived from composition practice, that are suitable for the analysis of sequences describing musical processes, Finally, we report some preliminary results of the analysis of a few pieoes of music