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1/sin(x) would produce a squarewave because if the maximum of the medium is being used in the transmission, we would only get the maximas of the medium and the alternations. Put through a limiter, it sounds like square wave (odd-harmonics) with a 270-degree linear wave (even-harmonics) missing its base harmonic.

tan(x) put through a limiter sounds like a saw-wave (all-harmonics) missing it's base harmonic.

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