An exploration of some non-tonal pitch-class spaces with implications for a theory of voice leading

This dissertation develops a theoretical framework suitable for the analysis of neo-tonal music. Neo-tonal music fuses techniques of traditional tonality with elements of atonality: some representative composers include Debussy, Messiaen, and Stravinsky. Chapter one presents a modular-space approach to transformational voice leading and argues for a reconsideration of conventional approaches to pitch-class space. Chapter 2 provides us with the building blocks for pitch-class spaces, using the notion of maximally even sets as a point of departure. Some of the most common scales and sonorities in music are maximally even, or they deviate from maximal evenness ever so slightly. The chapter looks at the construction of maximally even sets and examines why maximally even structures are privileged. Chapter 3 uses maximally even sets as the building blocks for hierarchical pitch-class spaces similar to those discussed in Lerdahl (2001). These pitch-class spaces permit us to discuss the perceived distances between chords as well as to account for non-harmonic tones and chromaticism. Chapter 4 tackles the problem of pieces that feature different pitch-class spaces either presented successively or concurrently. Chapter 5 contains several analytical essays designed to show the theory in practice.