These pieces were produced as part of a research project sponsored by the Integrated Media section of the Canada Council. The computer programs incorporated certain techniques of the new science of Fractional Geometry developed by Dr Benoit Mandelbrot of the IBM Thomas J Watson Research Center to produce æsthetically pleasing musical objects. Specifically, the techniques employed in these three pieces are related to what Mandelbrot describes as the “monster curves”, the geometric monstrosities discovered early in this century by the mathematicians Helge von Koch and Giuseppe Peano. In the version of the program used for these pieces the process may be started with a freely chosen melodic “seed”, which grows geometrically in order to generate one of the musical elements necessary. The key concept in this process is “self-similarity”, whereby small scale features are related to larger scale and structural features within the object. “Fractal Study 1” is the earliest work given here; it uses strict self-similarity for all the musical elements, with the exception of the oboes introduced after the halfway point, which are randomly self-similar. The two other works are: “Fractal Jam” and “Duet”. All three works were recorded in the author's studio using the MIDIFORTH computer music system. BD
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