Implementação computacional de uma gramática gerativa para música tonal

Abstract

This work deals with the computational implementation of a generative grammar aiming at the automatic analysis of musical samples. It is based on A Generative Theory of Tonal Music (Lerdahl, F. & Jackendoff, R., 1996, second ed., MIT Press, Cambridge, Massachusets), from now on named GTTM, which has as its main objective the analysis of musical samples from the point of view of an experienced listener perception. Following the original proposal of GTTM, the system implementation is built on four programs, one for each theory component, that run concurrently and are dependent, by means of a pooling system, of the other components results aiming the processing of their own. Obviously, there is a initial state in which from there on all the components are initialized. For the component Grouping Structure was employed a fuzzy system and tool for melodic pattern recognition based on a correlative matrix. In the Metrical Structure a multi-objective genetic algorithm was used whose task is to minimize the conflict between the component preferential rules. The Time-Span Reduction tries to find the best union between the results of the two former components aiming to build a time-span reduction tree. This component, besides its own autonomy, works also as a part of one of the Metrical Structure preferential rules, by means of a shared memory segment. Finally, the component Prolongational Reduction, scanning all the former results, aims at building a prolongational tree, that is to say, a tree that represents, at several levels, the states of tension/relaxation that exists in the tonal structure of the processed sample. As sample tests for the system Validation Tests were employed, for fragments of works, and Analysis, for complete pieces.