A GAP Tutorial for Transformational Music Theory

[1] About GAP [1.1] GAP (an acronym for Groups, Algorithms, and Programming) is a mathematical software package that has great potential as a tool for researchers and students of transformational music theory. Whereas many computer resources are available to music theorists in the investigation of pitch-class set theory and serial theory-pitch-class set calculators, matrix generators, and the like-few, if any, permit users to construct, analyze, and manipulate algebraic systems themselves. Such techniques, however, are an increasingly large part of the transformation theorist's methodologies. It is often necessary to consider concepts such as the subgroup structure of a group, or to determine a group's automorphisms. Whereas one can do such calculations by hand, the speed at which GAP performs them can dramatically increase efficiency of time for research. From a pedagogical point of view, GAP provides students of transformation theory a resourceful and effective environment for experimentation, and a means of providing preliminary empirical proofs for their results. [1.2] GAP was developed by and for mathematicians and other computational scientists. It began in 1986 as a project by four students at RWTH Aachen University, in Aachen, North Rhine-Westphalia, Germany: Johannes Meier, Alice Niemeyer, Werner Nickel, and Martin Schönert. Its first public release was in 1988, with version 2.4. Since that time, it has undergone a number of revisions, and has assumed worldwide recognition, (1) although it has not received much attention in musictheoretical research. http://www.mtosmt.org/issues/mto.11.17.1/mto.11.17.1.peck.php KEYWORDS: computer-assisted research, transformational music theory, group theory, Klumpenhouwer networks, neo-Riemannian 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