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.
Seed-turbulence-iteration
Abstract
Details
- Title: Subtitle
- Seed-turbulence-iteration
- Creators
- Joseph Norman - University of Iowa
- Contributors
- David K. Gompper (Advisor)Jean-Francois Charles (Committee Member)Zachary Stanton (Committee Member)Mathew Arndt (Committee Member)Nathan Platte (Committee Member)
- Resource Type
- Dissertation
- Degree Awarded
- Doctor of Philosophy (PhD), University of Iowa
- Degree in
- Music
- Date degree season
- Spring 2019
- DOI
- 10.17077/etd.5v65-pgdf
- Publisher
- University of Iowa
- Number of pages
- xv, 50 pages
- Copyright
- Copyright © 2019 Joseph Norman
- Language
- English
- Description illustrations
- color illustrations, music
- Public Abstract (ETD)
Seed-Turbulence-Iteration is a piece composed for chamber orchestration that involved a selective application of algorithmic processes which were coupled with human intuitive creative intervention over the course of its creation. The algorithms applied were Pierre Francois Verhulst's Logistic Map and Robert Devaney's Gingerbreadman Map. Verhulst's map demonstrate's chaotic behavior (in terms of chaos theory) and Devaney's Map demonstrates fractal geometric behavior. The plot points of these different systems formed an inspirational basis for the control of melodic contour and durational values within the confines of individual lines. Aesthetic selections and alterations of the algorithmically generated data caused me to assign lines to individual instruments and sometimes splitting those lines across groups of instruments, conceive of a form in which to frame material, and select the pitch material. The piece's title describes the mechanism of action for Verhulst's Logistic Map. Initial, or “seed” conditions are established, “turbulence” is applied in order to generate variable results, and the result of the algorithm is then fed into into its starting conditions, causing the process to iterate repeatedly. This sequence of actions is built into the structural fabric of the piece, as sequences of events are started and stopped in succession.
- Academic Unit
- School of Music
- Record Identifier
- 9983777027002771