Automata and music contour functions

Abstract

There is a tradition in music theory which investigates contour functions. Schützenberger's Theorem [On the definition of a family of automata. Info Control. 1961;4(2–3):245–270] connects such functions to weighted automata. Hence, it should be of music-theoretical interest to study those automata. Precisely, the minimal weighted automata computing the ascending, descending, equalizing, semitone ascending, etc. contour functions are explicitly constructed. In this article, the general combinatorial form and compactness of a musical string (finite sequences of musical entities) are discussed and the minimal automata computing the corresponding functions are displayed. Finally contour situations arising from penalty systems, classical segmentation rules, and music identification are presented.