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PROLONGATION, EXPANDING VARIATION, AND PITCH HIERARCHY: A STUDY OF FRED LERDAHL'S WAVES AND COFFIN HOLLOW

by Knoll, Jonathan Corey

Abstract (Summary)
This thesis consists of two independent yet interrelated portions. The theory portion explores connections between Fred Lerdahl’s theoretical and compositional output by examining his work Waves in relation to his theoretical writings, primarily A Generative Theory of Tonal Music and “Tonal Pitch Space.” The theories together form a generative theory of tonal music that strives to create a musical grammar. “Tonal Pitch Space” defines a hierarchy among pitches and chords within and across tonal regions. Lerdahl uses these ideas in Waves, which is in the key of D minor. All other pitch classes, and likewise all other chords and tonal regions, are elaborations of the tonic D. The initial D tonic statement, called a flag motive because it heralds each variation, is the fundamental construct in Waves. Just as all other pitches elaborate D, all other motives in Waves are elaborations of the flag motive. Thus rich hierarchies are established. Lerdahl also incorporates ideas from GTTM into his compositional process. GTTM focuses on four categories of event hierarchies: grouping and metrical structures and time-span and prolongational reductions. These four hierarchies and a set of stability conditions all interact with one another to form a comprehensive musical grammar. Grouping and metric structures in Waves are identified and analyzed in this thesis. These include the irregular grouping and metric structures elision, overlap, deletion, and compound grouping. Lerdahl, by fusing passing and neighbor diminutions, creates unstable harmonic cells that, due to their distance from the tonic, assume dominant and subdominant function in the context of Waves. These functional sonorities create both progressions and cadences. By using those same tonal diminutions to elaborate stable tonic chords and pitch classes, Lerdahl also creates prolongation. Both Lerdahl’s progressions and prolongations can be analyzed through the tree diagrams of prolongational reduction. Waves is shaped by a formal process called expanding variations. This is a procedure in which a single idea is expanded upon by interpolation in a series of variations. Each variation develops the previous one, creating a reduction in reverse. The expanding variations of Waves are governed by the Fibonacci series. Each number in the series corresponds to the number of tactus-level beats per variation. The composition portion of this thesis borrows aspects of Lerdahl’s music, most notably the expanding variations based upon the Fibonacci series, and incorporates them into an original composition for chamber ensemble (alto flute, clarinet, percussion, piano, violin, and violoncello). The piece, Coffin Hollow, is based upon a ghost story of the same name. The story, set in northern West Virginia during the Civil War, has two main characters, a Union soldier and Confederate soldier. Each is assigned his own series of variations. While the Confederate soldier’s variations expand, the Union soldier’s variations contract, giving the sense of the former consuming the latter, much like the ghost of the Confederate soldier hunts down and kills the Union soldier. The Union soldier’s theme is based upon the Union folk song “Just Before the Battle, Mother,” while the Confederate soldier’s theme is based upon the folk song, “I’m a Good Old Rebel.”
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Advisor:

School:Bowling Green State University

School Location:USA - Ohio

Source Type:Master's Thesis

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ISBN:

Date of Publication:01/01/2006

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