Author: Turner, Mitchell M.
Title: Toward a General Theory of Pitch Structure: Unity Between Horizontal and Vertical Pitch-Class Sets
Institution: University of Georgia
Begun: January 1994
Completed: December 1999
Reductive analysis, one of the most powerful tools available in music theory, allows insight into the inner workings of a musical composition and yields detailed views into its pitch structure. By using reductive technique, pitches may be placed into a systematic, hierarchical position. Whereas some pitches may be considered of low significance, others can be elevated, as appropriate, to illuminate an underlying structure. This type of analysis was, of course, the invention and the focus of the theories of Heinrich Schenker. Later theorists have attempted methods of analysis similar to Schenker's in post-tonal music, but the attempts, as shown below, usually fall short of providing the degree of insight that Schenker's method achieved.
This dissertation proposes a new and more thorough method for the determination of structural pitch-class sets (pc sets) in post-tonal music. I establish criteria for assessing the structural importance of pc sets for non-tonal works. After determining structural pc sets, they are used to produce a graphic, reductive analysis. In so doing, I devise a consistent method for the determination of structural pc sets that may allow the use of reductive analysis in post-tonal music.
This dissertation avoids the pitfalls of the earlier prolongational models, devising a method for showing pitch structures that are primarily contingent upon pitch. Appeals to the ear are limited to the segmentation of pitches for analysis. The present study provides the foundation for a general theory of pitch structure analysis of post-tonal music by establishing a primary assumption regarding atonal stability conditions and showing a consistent methodology for the determination of pitch structure. Chapters 2 through 4 establish the primary assumption and details of my theory of pitch structure. Chapter 5 shows how this theory is used through analyses of short works from the early atonal pieces of Arnold Schoenberg and Alban Berg, including sections from Schoenberg's Op.11, No.1, Op.19, No.2, and No.6, and Berg's song Op.2, No.2. Chapters 6 and 7 present a detailed analysis of mm. 372-409, the "Cradle Song," from Act I, Scene 3 of Berg's Wozzeck and a section from Act I, Scene 2 of Berg's Lulu respectively. Chapter 8 draws conclusions and offers speculation as to the future use of this theory.
Keywords: Arnold Schoenberg, Alban Berg, Wozzeck, Lulu, Pitch-Class Set, Dyad, Voice Exchange, Music Theory, Linear Analysis, Prolongation, Horizontalization, Pitch Structure, Reductive Analysis, Graphic Analysis
List of Figures, vi
List of Tables, ix
Chapter 1: Introduction, 1
Chapter 2: Linear/Vertical Pitch-Class Sets, 13
Chapter 3: Dyadic Motions, 47
Chapter 4: Application of Pitch Structures, 71
Chapter 5: Preliminary Analyses 84
Chapter 6: Analysis of the "Cradle Song" from Wozzeck, 112
Chapter 7: Analysis of the Sonata Recapitulation from Lulu, 138
Chapter 8: Implications for Future Research, 176
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