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Solomon, Larry

Symmetry as a Compositional Determinant

Ph.D. West Virginia University, 1973

Symmetry is shown to be the major determining factor in composition. Some of the compositional parameters that are demonstrated to be symmetry 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, 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 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. These include Bartók's Music for Strings, Percussion, and Celesta 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, exchanging the dimensions of time and pitch. An essay on these also appeared in Perspectives of New Music, 1973, under the title "New Symmetric Transformations". A chapter is also devoted to the possible psychological effects of musical symmetry.

N.B.: This thesis may be downloaded from the following web site: