In this paper the author shows where concepts and mathematical models derived from the developing field of Chaos Science can be applied to electroacoustic and instrumental composition. Examples of non-linear dynamics include Lorenz’s model of fluid behaviour, Verhulst’s model of population growth, Hénon’s analysis of the multiple celestial body problem, Barry Martin’s Algorithm which produces quasi organic forms, and the ‘Baker’ mixing function. Besides broadening the numerical techniques available for electronic music generation, concepts such as fractal structure, feedback process and iterative function can be applied to ‘ordinary’ composition as well. For example, in designing melodic curve, defining meter, planning instrumentation, manipulating symbols, creating ornamentation and elaboration, etc. Some suggestions as to mapping are made, the critical boundary between science and art. Musical examples are used from the following works by the author: Harpsi-Kord for harpsichordist and tape, Fractal Piano for computer-guided pianola. The Five Seasons for 6 percussionists and tape, Brain-Wave for recorder-players, Modifications for marimba & tape, and Hyperion’s Tumble for tape.
300 years ago Newton formulated the laws of motion which laid the ground-work for a clockwork view of the universe. By the late 18th century the French astronomer Laplace optimistically stated that intelligent creatures could know any past or future state of the universe, if they only knew well enough its present state, what direction it was heading towards, and had powerful enough calculating methods. This deterministic world view has proved to need revision. Scientific and mathematical developments of the last 30 years have led to new insights into subjects, which because of their complexity, had previously been swept under the rug by the scientific establishment. Intractable problems in weather forecasting, the modeiling of wildlife populations, the geometry of nature, the understanding of turbulent flow and bio-rhythms gave startling new results when revolutionary methods of analysis were applied. As a result, words such as “chaos”, “order”, “simple” and “complex” have been redefined; and a new concept formed: “fractal”.
- David Clark Little. Born in the United States in 1952, he received a B.Sc in chemistry and then studied harpsichord with Gustav Leonhardt and composition with Ton de Leeuw in the Netherlands. Recipient of many prizes, grants and commissions, he has worked since 1988 on compositional methods using computers based on “chaos science” and “fractals”.
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