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 waveshaping, pitch-bending, period-doubling and highly irregular patterns. We describe a number of such examples and discuss their subjective auditory perception.

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