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Page 100 ï~~CHAOTIC NON-LINEAR SYSTEMS EXPLORATOL Barry Tn Dept. of Communication & Schoc Simon Fraser I Burnaby, B.C. CAN ABSTRA The study of classical dynamic systems has re in recognizing that even when such systems ar and chaotic behaviour. Such behaviour, whic system, has been observed in a wide variety of in acoustical systems one of the few applicati This paper presents examples of the applica synthesis for the purpose of timbral design, I.... 1..... _ _ 1.......t.......1 _? _ I 1... 1.., -
Page 101 ï~~oscillations appear as simple closed figures in such a for instance, a characteristic period doubling and tripl the delayed signal is usually only a few samples, this time digital synthesis with a stereo converter. The dire and y axes of an oscilloscope. The work in multiphonics suggests that other examp also be examined for chaotic behaviour. Generally, aspect of the processing of a signal such as by th difference tones) or by electroacoustic equipment C However, in digital synthesis, a variety of nonlinear tE frequency modulation (FM) and waveshaping, ha~ changing timbres (Dodge & Jerse, 1985). The time be chaotic in appearance, particularly at medium t j coincidental that route chaotic behaviour frequencies that occur as a ratio between the syster function corresnond to the Farev series. which has bq
Page 102 ï~~mapper more than in the source function. Thea notes, may be convinced there is more value or int used, but the half-life of such interest seems C sustained interest reflect a particular model of hov are a test of the validity of that model. If the mode value in sound synthesis, it must reflect certain tru as simply a model. The truth here would seem to I simple set of acoustical factors. It is relatively easy6to apply the one-dimensional lc simple oscillator, that is, to control its instantaneou scale at which the equation is re-iterated. When d the period of the waveform, values of r between 1 oscillation settles down to a fixed frequency. Beyon a frequency modulated signal, and in the chaoti calculation results in complex periodicitics rather tl
Page 103 ï~~in acoustics which can impact on digital synthesis whether all attempts to model chaos are artificial c the music of J.S. Bach is great because it is the aural can hardly deny that it arises from the same Zeitgeist of intellectual, cultural and aesthetic currents that i models will undoubtedly arise from the intellectual chaotic non-linear systems. But wil such music C geome onto conventional musical parameters contradiction of a marriage of unrelated partners? refocusing attention on micro-level audio domain be: References: Clark, T. 1989. "Coasts: On the creative edge with co Journal 13(1): 21-35. Degazio, B 1986. "Musical aspects of fractal geometz Computer Music Conference, San Francisco: