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Demonizing square waves is one of those things that may make intuitive sense, but doesn't stand up to technical analysis.
The salesman's patter goes on and on about all of the harmonics in sharp-edge square waves. Thing is that square waves can actually have lower harmonic content than some music!
Here's an example:
In this analysis, the upper signal is the same as the lower signal except that it is amplified by 1000 times but clipped at the same power level as the lower signal which is just below the clipping point.
The first surprise is that even though the amplifier was running just below clipping for the lower undistorted signal, , the energy in the distorted signal coming out of it was able to increase by an additional 22 dB. This is a more than 100 times increase in power, which is very significant to say the least!
If the amplifier had been rated at a high power level then the amount of power coming out of the more powerful amplifier would have been increased by 22 dB plus the difference in power rating between the two amplifiers. IOW the more powerful amplifier would have damaged the speaker even more severely.
The point that I want to make is that of course the clipped signal has far more energy in it at all frequencies, simply because it is louder. What some may find interesting is the fact that the amplifier was able to provide signficiantly more power to the speaker once it started clipping.
Yes, there is some shifting of energy towards the higher frequencies, but it pales in comparison to the energy that is added simply because the signal became louder.
The bottom line is that if you want to avoid damaging your speakers, listen to the music as you adjust its volume, and stop turning it up once it starts sounding distorted. This is the same common sense suggestion that was made above by FOH and Ivan, and all my colored pictures do is show a few more details about the process.