Transformational harmony and voice-leading: Analytical applications and methodological extensions of Klumpenhouwer Network theory
Item
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Title
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Transformational harmony and voice-leading: Analytical applications and methodological extensions of Klumpenhouwer Network theory
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Identifier
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d_2009_2013:b04c93051f7b:12083
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Creator
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Shuster, Lawrence Beaumont,
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Contributor
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Philip Lambert
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Date
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2009
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Language
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English
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Publisher
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City University of New York.
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Subject
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Music
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Abstract
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This dissertation develops a theoretical framework suitable for the analysis of harmony and voice-leading in chromatic post-tonal music. Section (1.0) is an introduction that defines the various parameters of the study, develops a corresponding analytical methodology, and concludes with a brief survey of the origins and development of Klumpenhouwer Network theory.;Section (2.0) entitled "Well-Formedness Conditions for K-net Graph Configurations and Parsimonious Voice-Leading Spaces for Tetrachordal, Pentachordal and Hexachordal K-Families," establishes a collection of well-formedness conditions for Klumpenhouwer networks (hence, K-nets) in order to determine and classify the number of distinct K-net graph configurations possible for pitch-class sets of any cardinality. In order to accomplish to this, a graph coloring algorithm is developed which provides a means of sorting and classifying K-net graph configurations of varying cardinalities based on their unique coloring schemes.1 Once the number of possible well-formed K-net graph configurations has been determined, corresponding parsimonious voice-leading spaces for each K-net graph configuration will be developed as based on Michael Callahan's innovative work regarding parsimonious voice-leading spaces for trichordal K-families.;Section (3.0), "Transformational Harmony and Voice-Leading in Post-Tonal Canonic Writing," uses K-nets to create network models of pitch structure from two perspectives, the linear-motivic and the vertical-harmonic, and explores how these two dimensions of pitch structure are integrated to establish unified compositional spaces. Post-tonal canonic writing provides a controlled context in which to explore the meaningful issues of harmony and voice-leading as well as in which to demonstrate the analytical method. Analytical examples include canons by Dallapiccola, Webern, Stravinsky, Rochberg and Schoenberg.;Section (4.0) entitled "Groups of Symmetries for Trichordal and Tetrachordal K-classes," proposes a new form of harmonic correspondence predicated on the basis of algebraic subgroup relations among pitch-class sets within trichordal and tetrachordal K-families. These group theoretical structures are subsequently "translated" to define novel inversional-sum spaces useful for the analysis of harmony and voice-leading in chromatic wedge progressions and other analytical contexts. Analytical applications include the harmonic design of Stravinsky's four-part arrays from Threni, Requiem Canticles, and A Sermon, a Prayer and a Narrative in addition to the opening ritornello to Schnittke's String Quartet No. 4.;1 The coloring algorithm assigns to each node in a K-net graph configuration a binary value or "color". If two nodes share the same color, they are related by transposition. If two nodes contain opposing values, they are related by inversion.
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Type
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dissertation
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Source
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2009_2013.csv
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degree
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Ph.D.