Prolongation in equal and microtonal temperaments

Includes abstract and vita.This dissertation presents a compositional theory of prolongation in equal temperaments, some of which are microtonal. Part 1 is a discussion of problems associated with generalizing prolongation and an exposition of possible approaches to composing with prolongation. Using the work of Fred Lerdahl, John Rahn, and Joseph Straus as point of departure, a framework for discussing generalized theories of harmony and voice leading is advanced. Straus' four conditions for establishing prolongational systems serve as the primary constraints on the subsequent development of the theory. David Lewin's formal theory of generalized tonal functions is extended in order to meet the scale structure requirements of Straus's conditions. Building on the ideas from Part 1 and drawing from scale theory, the theory proper is developed in Part 2. Multiplicative operations on cyclic orderings form the basis for the construction of generalized diatonic systems, while Straus's conditions provide limits on the range of possibilities. Part 2 ends by generalizing some properties of generated, well-formed scales to show how generalized diatonic systems may be embedded in various equal temperaments. A "musical interlude" appears in each of the two parts in order to illustrate practical applications of the theory. The first interlude includes a compositional reconstruction of a canon from Bach's Goldberg Variations, employing prolongational synthesis. This is followed by an exploration of pitch-class transformations of the passage in order to discover how they do or do not preserve its prolongational structure. The second interlude introduces the "diatonic staff" concept to show that prolongational composition in a generalized diatonic system depends more on the structure of that system than the temperament it is embedded in. It also includes microtonal examples illustrating microtonal analogues to modal mixture and tonicization