Author: Randall, Richard R.
Title: A General Theory of Comparative Music Analysis
Institution: University of Rochester, Eastman School of Music
Begun: October 2001
Completed: May 2006
This dissertation establishes a kind of comparative music analysis such that what we understand as musical features in a particular case are dependent on the music analytic systems that provide the framework by which we can contemplate (and communicate our thoughts about) music. I value how different analytic systems allow us to create different perceptions of a piece of music and argue that the identity of a musical work is in fact dependent on the combination of a work and an analytic system. Comparing musical works, then, necessarily compares such combinations. Therefore, I assert that comparing pieces ought to be reframed as comparing the interpretation of pieces under specific analytic systems.
Comparative analyses are carried out on local and global levels. Local music analytic systems map one set of musical events to another a set of musical events— the entirety of which comprises a piece of music. This is my description of what is normally thought of as analysis. Global music analytic systems analyze (or comment on) pieces of music determined by different types of local analyses.
The theory of comparative music analysis is divided into two parts. The first part defines a geometry of global music analytic systems. The geometric model covers all global systems. The second part defines a comparison of two local music analyticsystems. Specifically, these local systems are tonal models, one defined by Lerdahl and the other based on experimental data of Bharucha and Krumhansl. Comparing local systems requires the establishment of a contextual equivalence between the two systems. In the case presented below, the equivalence is the formal structure of the metric space. These two approaches (global and local) are not alternatives to each other. They are in fact comparisons of musical pieces on different, yet interrelated levels. Comparing local music analytic systems is complicated by arbitrary design choices inherent in each system. Like comparisons of local systems themselves, solutions to this “design choice problem” are contextual. One such solution is presented, as is a discussion of a meta-analytic ramification of comparing local systems.
Keywords: Analysis, metatheory, cognition, phenomenology, ontology, geometry, style analysis, comparative analysis, mathematics.
Richard R. Randall
Fine Arts Center
University of Massachusetts
Amherst, MA 01002