Score Generation in Voice-Leading and Chord Spaces
Michael Gogins · 2006
Common principles of voice-leading can be represented using an orbifold (i.e. a quotient space) in which each point is a chord, and the smoothness of voice-leadings corresponds to the closeness of their chords in the space (Tymoczko 2005). The set of such voice-leadings for the major and minor triads includes the Tonnetz, which leads to an understanding of how to use related geometries for all trichords, higher arities of chord, voice-leading solutions, and chord progressions. The present work demonstrates the use of such spaces for algo-rithmic composition. A Lindenmayer system takes an axiom and symbol replacement rules, and recursively rewrites the axiom by applying the rules. A turtle that represents a chord, which moves within either a voice-leading space or a chord progression space, then interprets the symbols in the final production of the Lindenmayer system as commands for writ-ing a score. This shows how score generators can work in mathematical spaces which have intrinsic musical structure. 1