A GAP Tutorial for Transformational Music Theory

Abstract

GAP (an acronym for Groups, Algorithms, and Programming) is a system of computational discrete algebra that may function as an application for experimentation in transformational music theory. In particular, it offers tools to music theorists that are not readily available elsewhere. This tutorial will show how GAP may be used to generate algebraic group structures well known to music theorists. Furthermore, it will investigate how these structures may be applied to the study of transformation theory, using familiar concepts from Klumpenhouwer-network and neo-Riemannian theories.