Document Type


Date of Degree

Spring 2019

Degree Name

PhD (Doctor of Philosophy)

Degree In


First Advisor

Gompper, David K

First Committee Member

Charles, Jean-Francois

Second Committee Member

Stanton, Zachary

Third Committee Member

Arndt, Mathew

Fourth Committee Member

Platte, Nathan


Seed-Turbulence-Iteration explores the aesthetic application of chaos and fractal geometry onto the musical parameters of a work constructed for chamber orchestra. Verhulst's Logistic Map and Devaney's Gingerbreadman Map are the dynamic systems from which melodic contour and temporal duration are derived. These algorithms are used to produce heterophonic and polyphonic results that iterate for a set duration before restarting. Each new beginning involves a change in density (of individual lines, as well as points of articulation in time), orchestration, register, and the pitch reservoir. All pitches are derived from a quantized spectrum that interpolates from a state of harmonicity to inharmonicity across a series of changing fundamentals. Each stage of interpolation coincides with the reseting of algorithmic iterations. Self-similarity and self-affinity are represented vertically, in the family resemblances of the lines produced within each algorithm that occur inside of a given segment, as well as horizontally, in the reiterations that occur over time. Each algorithmic reiteration and each copy within a set of iterations has varied starting or “seed” conditions that produce differentiated results of greater or lesser degrees which are presented in non-linear, strategic arrangement. Turbulence is implemented in the form of probabilistic distortions inserted into algorithmic processes that are meant to vary to some degree the amount of unpredictability of an output parameter (pitch or duration) as well as in intuitive manipulations of algorithmically generated material.


Algorithmic, Chaos, Fractal, Spectral


xv, 50 pages


Copyright © 2019 Joseph Barnett Norman

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