Publication Date

2018-05-09

Availability

Open access

Embargo Period

2018-05-09

Degree Type

Dissertation

Degree Name

Doctor of Musical Arts (DMA)

Department

Studio Music and Jazz (Music)

Date of Defense

2018-04-03

First Committee Member

Gary Keller

Second Committee Member

Martin Bejerano

Third Committee Member

Dorothy Hindman

Fourth Committee Member

Kathryn Reid

Abstract

Musical tones consist of partial-tones which inform both timbre as well as unique acoustic signatures. Also known as overtones, these partial-tones can be the focal point in quantitative and qualitative comparisons of relative chord structures. The results of these comparisons can then inform evaluations and ranking of relative consonance and dissonance. The purpose of the study is to provide a framework toward the evaluation of the consonance and dissonance of chord voicings derived from the symmetric organization of the diatonic modes according to the cycle of fifths and the resulting bright/dark continuum. Presented here is an analysis of frequencies of overtones and undertones generated up to the 15th tier according to three statistical measures: Average Dissonance Value, Relative Dissonance Value, and Shannon Entropy. The diatonic modes could be considered to exist along a “bright” to “dark” continuum when their interval structures are organized according to the first seven notes of the cycle of fifths. Modes extending from the center exhibit increasingly sharped intervals (brighter) in one direction whereas modes in the opposing direction exhibit increasingly flattened intervals (darker). This organization places the palindromic Dorian mode as the nexus of the cycle, around which the other six modes present themselves as mirrored opposites.

Keywords

Jazz; Overtones; Undertones; Music; Modes; Harmonics

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