Date of Award

12-12-2024

Document Type

Thesis

Department

Music

First Advisor

Max Keller

Second Advisor

Anthony Bosman

Abstract

Beginning with Claude Debussy’s Berceuse Héroïque, I analyzed each triad using chord symbols along with their Roman numeral representation (where applicable).1 Next, I used integer notation and modular arithmetic, where each pitch name is given a number such that C is 0 and B is 11, creating a set, the integers (mod 12).

This leads to the development of pitch-class sets where the “mode” of a triad or arbitrary number of pitches is expressed in terms of interval spacings. In many cases, such as that of 12-tone or other serialized music, pitch class sets explain many of the composer’s artistic choices where the mode of said set is inconsequential. I used this analytical technique to assign each triad their numbers mod 12 and an arithmetic symbol, −=minor, +=major, ÷=diminished, and ×=augmented (eg. 6!= F minor). Julian Hook’s representation is similar to mine, where the pitch class number and mode are represented, but as an ordered pair (eg. (6,−) = F minor).

Upon completing the analysis of Berceuse Héroïque, by these techniques, I realized the piece did not include any augmented triads. I aimed to show the group structure of UTTs using the four basic tertian triads, namely major, minor, diminished, and augmented. Therefore, my research required my finding a piece by Debussy containing such triads.

Subject Area

Triads (Music); Triples, Theory of; Debussy, Claude, 1862-1918

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