Slew rate distortion occurs when some part of the amplifier is asked to change voltage at a rate which is greater than its ability to do so and hence it enters a non-linear region. To avoid that without changing the design of the amplifier one of two things can occur besides the trivial case of keeping the level low enough using the volume control- either the input signal is deliberately band limited using a built in low pass filter to avoid any possibility of the signal exceeding the rate - which would be a good idea with say, synthesized music, OR the input power spectrum is such that the rate of change is naturally limited- i.e. that the input signals are pink noise-like (1/f) with a built in upper bound, which is most like natural music, or red noise-like (rap music (a joke!)). Interestingly enough some sources (such as some MC cartridges for example) with substantial peaking either in the high sonic or supersonic regions can induce distortion as a result of their changing the 1/f characteristic of music at HF.
(Occasionally cartridges are loaded with minimal capacitance and high resistance and this can create ultrasonic resonant peaks of 30dB or more which can cause this, and other effects- caveat emptor!)
When testing opamps, for example, the way slew rate limiting is evaluated is to set the amp in a known gain configuration then drive the input with a very small rise time square wave that is just large enough to create slew rate limiting. Square waves have a Fourier series in which the terms are purely odd harmonic and decay at a rate which is 1/f (i.e. the 3rd harmonic has amplitude 1/3 of the fundamental, the fifth is 1/5 etc.) so it approximates, if you will, infinite bandwidth music. If the square wave is low passed at say, 20kHz, then the rise time increases - although now overshoot exists due to the Gibbs Phenomenon. This is a reasonable proxy for a pink noise process with a built in, natural, bandwidth limitation.
If you test amps with this and not further overdrive the input then the slewing results can be different (more benign) than if the original wide bandwidth square wave is applied.