Graph Theoretical Models of Abstract Musical Transformation: An Introduction and Compendium for Composers and Theorists

by Jeffrey Johnson

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.

Product Details

ISBN-13:	9780313301582
Publisher:	Bloomsbury Academic
Publication date:	08/21/1997
Series:	Music Reference Collection , #62
Pages:	216
Product dimensions:	6.00(w) x 9.00(h) x 0.62(d)

About the Author

JEFFREY JOHNSON is Associate Director of Artistic Education and Chair of the Music Theory Department at the renowned Boys Choir of Harlem. He has degrees in musical composition from Boston University, Eastman School of Music, and Ithaca College. He is an active composer, conductor, and theorist. His first book, Thesaurus of Abstract Musical Properties was published by Greenwood Press in 1995.

Table of Contents

Preface
Graphing
Introduction
Formalities
Enumeration: Degree Sequences
Comparisons and Structural Properties
Construction
Basic Techniques
Classification
K-Regular Graphs
Hierarchies
Realizations
Literal Spaces
Extended Possibilities
"Shock and the Ever-Extending Opposites": Pitch-Class Graphs and Broken Sequences
Exercises
Appendix I: Complementary Hexachordal Graphs
Appendix II: 12-Position Degree Sequences from 5-Regular
Appendix III: Selected 12-Position Degree Sequences by Edges Required
Bibliography

Editorial Reviews

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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