Remember: you don't hear with your eyes....

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Cross-over distortion is related only to the threshold that bias the transistors, not harmonically as you state. If you have complex stimulus lying above the zero line for some time and then below, which harmonic of the complex signal would you relate the cross over distortion too. If I use a square wave there will be no harmonics in the crossover point as the rise time will exceed the dead band.

Switching amps generates a lot of harmonics but zero cross-over distortion as the dead time is zero because of the high slew of the pulse.

You cannot get cross-over distortion using a square wave unless you are doing a quasi sine where you create a dead time. The harmonics related to the PWM signal should be much higher than what the ear is supposed to detect.

However, if we are talking pure sine waves, few listen to sine waves, it is boring - music is much better.

If the problem of high harmonics content both in frequency and amplitude exist in a music playing system the listener will only detect this as distortion if he/she has an intimate knowledge of the instrument playing.

Carlos Santana's guitar work, should be disturbing as it is actually a serious harmonic generator, but only to the person who does not consider him an artist or his work as music.
 
Cross-over distortion is related only to the threshold that bias the transistors, not harmonically as you state.

Crossover is harmonic distortion.
This can easily be verified by looking at its spectrum: all distortion products are harmonically related to the fundamental.

Set aside crossover distorsion that would result of a badly
OPS biaising, "designing" an amp that display such gross non
linearities would be truly a performance if i can say so...

It is a caricature, obviously: I exagerated the distortion levels to make it immediately visible.

My point is that the eyes have a different interpretation of "a clean signal" than the ears:
For the eyes, what is required is a continuous function, in the mathematical sense of the term.

But the ear is much more demanding: in the examples above, the magenta waveform will sound almost as bad as the red one; yet it looks rather "smooth" visually.
If the proportion of the distorted signal were reduced by 20dB, the magenta signal would still sound unpleasant, but visually, the distortion would be undetectable.
 

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Answering the questions:
1. It is not obvious.
2. It is more or less pointless.
You have to be more specific.
For question 1-why do you care? Is it original source or distortions introduces by any kind of amplifier?
For question 2-if you don't want distortions to be noticed and want to compare 2 different transfer functions of something in your signal chain, your have to be more specific about your application.
 
Crossover is harmonic distortion.
This can easily be verified by looking at its spectrum: all distortion products are harmonically related to the fundamental.



It is a caricature, obviously: I exagerated the distortion levels to make it immediately visible.

My point is that the eyes have a different interpretation of "a clean signal" than the ears:
For the eyes, what is required is a continuous function, in the mathematical sense of the term.

But the ear is much more demanding: in the examples above, the magenta waveform will sound almost as bad as the red one; yet it looks rather "smooth" visually.
If the proportion of the distorted signal were reduced by 20dB, the magenta signal would still sound unpleasant, but visually, the distortion would be undetectable.

Considering this an amplifier distortions, what will happen to both of them if you will lower signal level by 20 dB, by 40 dB?
And visual interpretation and listening - yes they may be absolutely different.
 
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