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Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy (PhD)

Degree Program

Music

Year Degree Awarded

2017

Month Degree Awarded

February

First Advisor

Brent Auerbach

Second Advisor

Gary S. Karpinski

Third Advisor

Paul Siqueira

Subject Categories

Music Theory

Abstract

This dissertation focuses on a new method for examining harmony, identifying consonance and dissonance through differential tones, and describing voice leading for pieces using just intonation, in particular for Ben Johnston’s String Quartet No. 5 (1979). Johnston employs microtonality in nearly all of his works, which contain more than the typical twelve equal-tempered pitches in the octave. This particular quartet features a great number (over 100) of pitches within the octave as is the case with many of his pieces up to his composition of String Quartet No. 5. This complex tuning system for microtonality requires a meaningful method for analyzing the novel harmonic syntax in order to model an analysis. The purpose of this analysis is 1.) to establish a scale for measuring consonance and dissonance in the sonorities (particularly those in the homorhythmic sections), 2.) to illustrate and explain the mechanism of the smooth transitions between tuning areas, and 3.) to examine the continuity among sonorities at the phrase level.

The first level of analysis considers the consonant and dissonant qualities of the sonorities. This is measured by the resulting differential tones and is an extension of the theories of German physicist Hermann Helmholtz. The sonorities are then placed in context to their surrounding verticalities by observing the superparticular ratios of the melodic voice leading. These ratios yield a difference of one between the numerator and denominator, which signifies a common fundamental between the pitches.

The focus of this writing is to show the levels of consonance and dissonance at phrase endings and crucial sections in the quartet. Generally, more stable sonorities begin and conclude sections of repose that feature the recurring “Lonesome Valley” theme. Smooth voice leading and consonant intervals between tuning areas provide a sense of continuity in the more turbulent transitional sections between sections of harmonic stasis. This dissertation examines these phrases in the form of the quartet.

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