Transformational harmony and voice-leading: Analytical applications and methodological extensions of Klumpenhouwer Network theory

Item

Title
Transformational harmony and voice-leading: Analytical applications and methodological extensions of Klumpenhouwer Network theory
Identifier
d_2009_2013:b04c93051f7b:12083
Creator
Shuster, Lawrence Beaumont,
Contributor
Philip Lambert
Date
2009
Language
English
Publisher
City University of New York.
Subject
Music
Abstract
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.
Type
dissertation
Source
2009_2013.csv
degree
Ph.D.