Author: Solomon, Larry Joseph
Title: Symmetry as a Determinant of Musical Composition
Institution: West Virginia University
Begun: February 1968
Completed: February 1973
Symmetry is shown to be the major determining operant in musical composition.Some of the compositional parameters that are demonstrated to be symmetrical operations are: all aspects of serialized composition, all contrapuntal operations (including imitation, canon, rounds, cancrizans, melodic inversion, invertible counterpoint augmentation and diminution, and cantus firmus composition), all musical forms (including all sectional, contrapuntal forms, and arch forms), isorhythm and isomelos, ostinati and passacaglia, mirror chords, planing and fauxbourdon, vibrato, scale formation, invertible counterpoint, meter and pulse, timbre, vibrato, trills and other ornaments, Alberti bass and other accompaniment figurations, antiphony, the circle of fifths, and pitch itself.
Definitions, descriptions, and mathematical formulations of the different types of musical symmetry are provided, and each of the major types is explored with examples. Parallels are shown in nature and other art forms. An analytical methodology is developed, and specific works are examined to demonstrate intensive applications of symmetry. These include detailed analyses of Bartok's Music for Srings, Percussion, and Celeste, and Webern's Variations for piano, Op 27.
Some new transformations are developed, called the Quadrate transformations, which are 90 degree rotations of a basic set (the author later wrote an article on these, which appeared in Perspectives of New Music, 1973). A chapter is also devoted to the possible psychological effects of musical symmetry.
Keywords: symmetry, composition, compositional theory, quadrate, rotation, translation, reflection, arch form
Chapter I: Introduction
Chapter II: Definitions and Principles
Chapter III: Reflection
Chapter IV: Translation and Rotation
Chapter V: Analytic Methods
Chapter VI: Analysis of Unspecialized Works
Chapter VII: Analysis of Works with Intensive Applications
Chapter VIII:New Transformations
Chapter IX: Some Psychological Considerations
Chapter X: Summary
Address: Center for the Arts, Pima College,
Tucson, AZ 85709, USA