Constraint-Based Systems of Triads and Seventh Chords, and Parsimonious Voice-Leading

摘要

This paper presents a generalization of the neo-Riemannian PLR group to the set of triads with inversions (major, minor, diminished and augmented). A second generalization is proposed, using an extended system of seventh chords with inversions. Both the sets of triads and seventh chords are defined with constraints on semitone separation of voices. In the case of triads, the set of parsimonious transformations is shown to have the structure of a semi-direct product of groups of the form S_n × Z_(12)~(n-1), where n is the number of chord types in the set.