Transformational Music - Theoretical Applications Using GAP

Abstract

GAP (an acronym for Groups, Algorithms, and Programming) is a system of computational discrete algebra. The GAP software, which is free and downloadable via anonymous FTP, provides a programming language, a library of thousands of algorithms, and data libraries of commonly used algebraic objects. GAP has been used widely by mathematicians and other computational scientists since its first release in 1986. It has not, however, received attention in music-theoretical research. Nonetheless, GAP offers music theorists a powerful tool, particularly in the investigation of transformation theory and other mathematically oriented music theories. In particular, it includes applications which are not readily available elsewhere to music theorists, and which will assist them in experimentation with the increasingly sophisticated mathematical techniques being used in the discipline. Examples display how a music theorist may use GAP to build relatively complex algebraic structures efficiently. Once these structures are then formed, the theorist may explore them by using further GAP utilities. GAP is capable of building virtually any finite group-theoretical structure. Its usefulness and relevance to music-theoretic analysis is potentially vast, as it is adaptable to numerous musical applications.