The step-class automorphism group in tonal analysis

Abstract

Until recently, researchers who have dealt formally with tonal hierarchy (prolongation) have considered only models in which the objects of the hierarchy are musical events (where a musical event might be a chord or a note in a particular voice). In contrast, (2006) proposes a concept called "dynamic prolongation" in which the objects of tonal hierarchy are motions between events rather than events themselves. The events in the model of (2006) are chords made up of harmonically related pitches from several voices. In the present study I develop a different approach to dynamic prolongation. Rather than expressing harmonic relations between notes by grouping them into chords, we can treat harmonic relations as intervals and mix them in a hierarchy with melodic motions. This creates a model that can posit long-range harmonic relationships and blur the boundaries between intervals of harmonic and melodic significance. © 2009 Springer-Verlag.