A cubic nonlinearity, as well as *any* odd distortion
law,^{10.2} generates only odd-numbered harmonics (like in a square
wave). For best results, and in particular for *tube distortion*
simulation [31,398], it has been argued that some
amount of even-numbered harmonics should also be present.
Breaking the odd symmetry in any way will add even-numbered harmonics
to the output as well. One simple way to accomplish this is to add an
*offset* to the input signal, obtaining

where is some small constant. (Signals in practice are typically constrained to be zero mean by one means or another.)

Another method for breaking the odd symmetry is to add some square-law nonlinearity to obtain

where controls the amount of square-law distortion in the more general third-order polynomial. The square-law is the most gentle nonlinear distortion in existence, adding only some second harmonic to a sinusoidal input signal. The constant can be set to zero the mean, on average; if the input signal is zero-mean with variance is 1, then will cancel the nonzero mean induced by the squaring term . Typically, the output of any audio effect is

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University