How to count chords: A primer in hierarchical, functional tonal analysis for music psychology.

다국어 초록 (Multilingual Abstract)

Music psychology has made enormous strides in helping musicians to understand the cognitive processes that underlie thinking in and about music. Unfortunately, when psychologists talk about tonal harmony, they often use methodologies that are outdated, inelegant, and misrepresentative. For example, a frequently cited study by Helen Budge purports to tabulate the frequencies of occurrence of different chords in tonal music. Budge's tabulations are based on a theory of harmony that is essentially a 19th--century--based Stufentheorie--style chord classification; perhaps more problematically, her tabulation acknowledges chords solely on the surface of the music, without taking into account their hierarchical behavior. Music psychology has made enormous strides in helping musicians to understand the cognitive processes that underlie thinking in and about music. Unfortunately, when psychologists talk about tonal harmony, they often use methodologies that are outdated, inelegant, and misrepresentative. For example, a frequently cited study by Helen Budge purports to tabulate the frequencies of occurrence of different chords in tonal music. Budge's tabulations are based on a theory of harmony that is essentially a 19t h-century-based Stufentheorie-style chord classification; perhaps more problematically, her tabulation acknowledges chords solely on the surface of the music, without taking into account their hierarchical behavior.
This dissertation proposes a strategy for chordal tabulation, along the lines that Budge presents, that will be useful to psychologists of music, making two significant suggestions in the traditional harmonic approach of her study.
1. Stufentheorie classifies chords according to roots and inversions, but music theorists have learned from the function--theory of Hugo Riemann, and others, that this kind of classification is inefficient and often misleading. Here, chords are classified according to their functions (Tonic, Dominant, and Dominant Preparation) and to the scale degrees in their bass voices. This approach produces a much cleaner and more elegant way of thinking about harmony---with a much more manageable set of progressional possibilities, which might suggest stochastic developments beyond a mere tabulation of chords.
2. Music theorists have learned from the work of Heinrich Schenker that to speak of harmony without hierarchy is hardly to speak of harmony at all. Hence, a system is developed for representing chordal harmony on several different hierarchical levels, large-- and small--scale, simultaneously. Following the exploration of a quasi--musical notation for representing these levels, a strategy for counting chords on multiple levels is developed.
Several short tonal passages (and one entire selection, Song Without Words, by Mendelssohn) are analyzed within this function--bass, hierarchical system, and used for the collection of sample data, to illustrate how a large--scale tabulation project of this sort might be pursued. Some tentative results are drawn from these passages, and contrasted with the familiar tabulations of Budge.