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This paper presents a new method for sound synthesis based upon non-linear dynamics. The procedure is compact and can be interactively controlled in real-time. The sounds thus synthesized have dynamic characteristics and rich spectra. It is an economical method, for it uses only a cyclic buffer to control the audio output and a non-linear map to ge...
Context in source publication
Context 1
... analyze the non-linear maps one can use the phase space plot x k versus y k. On such plots, clusters of points mean that there is an attractor; cluster distribution regularity identifies quasi-periodic numerical behavior; irregularity typifies a chaotic one. Plots showing the phase space behaviour can be seen in Figs. 2 and 3. round returns the closest ...
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Citations
... Dobson and Fitch considered iterated complex quadratic maps [13] experimentally. Manzolli et al consider a set of two-variable iterations which are variations of the so-called standard map which in turn is related to the circle map [14]. Recently Valsamakis and Miranda consider a family of two variable coupled oscillator with sine waves in the feedback loop [15] The most widely cited reference of chaos theory is the computer music literature is [16]. ...
... Dobson and Fitch considered iterated complex quadratic maps [13] experimentally. Manzolli et al consider a set of two-variable iterations which are variations of the so-called standard map which in turn is related to the circle map [14] . Recently Valsamakis and Miranda consider a family of two variable coupled oscillator with sine waves in the feedback loop [15] The most widely cited reference of chaos theory is the computer music literature is [16]. ...
The circle map is a general non-linear iterated function that maps the circle onto itself. In its standard form it can be interpreted as a simple sinusoidal oscillator which is perturbed by a non-linear term. By varying the strength of the non-linear contribution a rich array of non-linear responses can be achieved, including wave-shaping, pitch-bending, period-doubling and highly irregular pat-terns. We describe a number of such examples and discuss their subjective auditory perception.
The circle map and its basic properties as non-linear oscilla-tor are discussed and related to other iterative mappings as proposed in the literature. The circle map is the simplest it-erative generator for sustained periodic and chaotic sounds and is easy to interpret as a basic sine oscillator with a non-linear perturbation.
