Date of Degree


Document Type


Degree Name





Scott Burnham

Committee Members

William Rothstein

L. Poundie Burstein

Thomas Sauer

Subject Categories

Music Performance | Music Theory


Modulation, Chromaticism, harmonic shading, harmonic balance, culminations


This dissertation aims to develop an approach to analyzing common-practice repertoire based on the dynamic interplay of centripetal and centrifugal forces. It aims at interpreting various kinds of chromaticism and modulation in terms of the interaction of forces moving away from the tonic or principal key (centrifugal) and those returning to it (centripetal). Centripetal forces also correspond to the force of cadential substantiation of keys, not only the principal key, which I call temporal-centripetal force; temporal-centrifugal forces correspond to the phenomena of tonal instability, of motion through multiple regions.

The dynamic interplay and counterbalancing of these forces is a core concern of the dissertation. In chapter 1 I build upon Arnold Schoenberg's visionary metaphor for modulation as a struggle and a competition between the tonic and its regions, imagined as a sovereign ruler and his subjects. The tendencies of the regions generate centrifugal forces; the ruling tonic's desire to subjugate them correspond to centripetal forces. What I call temporal-centripetal forces correspond to the possibility for temporary centripetal forces to be generated by a region, which becomes the ruler of its own realm. The crucial application to analyzing harmonic motion is that centripetal and centrifugal forces are dynamically interdependent; each requires the other in order to stimulate a living tonal narrative.

In order to measure centrifugal forces, the tonal narrative approach draws on Gottfried Weber and Schoenberg's maps of tonal space and Weber's elucidation of degrees of relatedness between keys, which are explored in chapter 2. Centrifugal forces divide into sharp and flat sides or types, which correspond to very general character and coloristic shades: sharp-centrifugal forces associate with brightening and greater activity and flat-centrifugal forces with darkening and sometimes passivity. In chapter 3, I explore how the harmonic motion of entire movements can be divided into distinctive functions that define their overall shape, such as intensifications (accumulations of dissonance or centrifugal force or both), culminations, counterbalancing of sharp- and flat-CF forces, and the attainment a complete tour of keys or regions in the tonal spectrum. This chapter also offers a hierarchy of key-area substantiation, determining the structural significance of regions appearing in tonal narratives.

Chapter 4 interprets sonata form in terms of centripetal and centrifugal forces unfolding in broad stages, which often correspond with formal parts but sometimes cross their boundaries. It examines the expansion of centrifugal trajectories in piano sonata development sections by Mozart and Beethoven; the culmination of this expansion is the complete traversal of the enharmonic circle in the Waldstein sonata (first movement). I analyze this development section in terms of the number of fundamental steps travelled from the subordinate key to the point of furthest remove.

Chapter 5 develops a hermeneutic reading of Schubert's sonata D. 894/i; centrifugal and centripetal forces are matched to pastoral/epic expressive modes identified in this movement by Robert Hatten. This work also features an immense modulatory trajectory around the enharmonic circle, corresponding to an epic narrative journey into the tonal underworld. A remarkable aspect of the development section is the transient recurrences of passages returning to the pastoral mode and centripetal forces; these provide a welcome contrast and respite from the inexorable flatward trajectory. The conclusion of the dissertation briefly offers some applications of analyzing harmonic polarities to piano performance, drawing particularly on aspects of touch and technique discussed by Boris Berman.