PARSING CONTEXT-FREE GRAMMARS FOR MUSIC: A COMPUTATIONAL MODEL OF SCHENKERIAN ANALYSIS

We outline a formalization and computer implementation of Schenker’s theory of tonality. The theory of Context-Free Grammars and their parsing, which has been developed extensively by computer scientists and computational linguists, offers a natural framework to address our problem. We show how Schenker’s prototypes and transformations can be cast in the form of a ContextFree Grammar. This allows us to implement for the first time a parsing algorithm that automates the analytical process. We develop a computer program using Prolog’s Definite Clause Grammar formalism. The program parses a piece presented in a suitable encoded form, producing a tree that represents a Schenkerian analysis of that piece. If more than one syntactically correct parsing is possible, the program produces corresponding analyses in separate trees. We discuss our work’s implications for music theory and music psychology. BACKGROUND AND AIMS For over twenty five years, music theorists have been trying to implement Schenkerian theory and analysis on the computer; Kassler, 1 Smoliar,2 Snell,3 and others, have written programs based on Schenkerian principles. And with good reason. By explaining tonal relations in terms of prototypes and transformations, Schenker’s work is particularly well suited to implementation on the machine. In return, implementation on the computer allows music theorists to check the consistency and completeness of the theory, as well as to track the enormous number of transformations required to generate complex tonal surfaces.