Why LTI is desirable for audio signals

The following applets selectively introduce a component to an audio signal that is generated by a nonlinear system. The slider on the left controls a constant a in the expression
x(t) + ax2(t)

When a is greater than zero, this introduces what audio engineers call second-harmonic distortion. The slider on the right controls a constant b in the expression

x(t) + bx3(t)
Audio engineers call this effect third-harmonic distortion. Note that moving the sliders only has an effect the next time you play the sound.

If you were able to run applets, you would have a Delay demo here.
If you were able to run applets, you would have a Delay demo here.

Second and third harmonic distortion are usually highly undesirable for audio signals (except for special effects). Because they are generated by nonlinear systems, the output contains frequencies that were not present in the input. Because of the way that humans hear musical notes and timbre, this can be very grating.