Graph Theoretical Models Of Abstract Musical Transformation

Overview

An introduction to a new way of modeling musical surfaces for theorists and for generating precompositional relationships for composers, this unique music theory reference work introduces, classifies, and enumerates graph theoretical models for musical transformations in compositional and analytical applications. It also provides a practical application of musical applications for students of graph theory and could serve as an introduction to the further cross-integration of these two disciplines. Of interest to ...

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Overview

An introduction to a new way of modeling musical surfaces for theorists and for generating precompositional relationships for composers, this unique music theory reference work introduces, classifies, and enumerates graph theoretical models for musical transformations in compositional and analytical applications. It also provides a practical application of musical applications for students of graph theory and could serve as an introduction to the further cross-integration of these two disciplines. Of interest to scholars, advanced music theory students, and composers, this work endeavors to facilitate the expression and understanding of musical ideas by presenting an unexplored way of notating relationships between transformational objects that is not attached to specific compositional or analytical systems.

Graph theoretical models of abstract musical transformations supplement and refine the ability to articulate orderings with pitch structures in analytical environments. An extended analysis of the opening section of Form IV: Broken Sequences by Stefan Wolpe is used as a demonstration. The use of these diagrams to generate compositional surfaces differs slightly from their use in analysis: an analytical model relates to a single musical surface, whereas compositional applications can be used to generate any potential surface derived from construction of the graphs.

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Editorial Reviews

Booknews
An extension and intensification of graph-theoretical aspects of Lewin transformation networks. Part I introduces the musical-historical framework of the study and establishes terminology and techniques. Part II develops constructions of graphic figures, and Part III establishes a classification scheme to guide the selection of designs appropriate to various compositional plans. Part IV suggests types of musical parameters or passages that can be assigned to vertices of a transformation network, and analyzes pitch-class networks in a work by Stefan Wolpe. Includes tables of degree sequences, and exercises. Assumes prior training in basic notational practices of music- theoretical literature. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

  • ISBN-13: 9780313301582
  • Publisher: ABC-CLIO, Incorporated
  • Publication date: 8/30/1997
  • Series: Music Reference Collection Series
  • Pages: 214
  • Product dimensions: 6.00 (w) x 9.00 (h) x 0.63 (d)

Meet the Author

JEFFREY JOHNSON is Associate Director of Artistic Education and Chair of the Music Theory Department at the renowned Boys Choir of Harlem.

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Table of Contents

Preface
Pt. 1 Graphing
Introduction 3
Formalities 15
Enumeration: Degree Sequences 21
Comparisons and Structural Properties 27
Pt. 2 Construction
Basic Techniques 39
Pt. 3 Classification
K-Regular Graphs 51
Hierarchies 63
Pt. 4 Realizations
Literal Spaces 79
Extended Possibilities 89
"Shock and the Ever-Extending Opposites"; Pitch-Class Graphs and Broken Sequences 95
Exercises 121
App. I Complementary Hexachordal Graphs 127
App. II 12-Position Degree Sequences from Five-Regular 147
App. III Selected 12-Position Degree Sequences by Edges Required 159
Bibliography 179
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