I’m also worried about how much of the harmonics in the music is LOST by the amp?

Can also be lost in the type of amp used, when phase shift happens to the 2nd 3rd 4th harmonic structure of the fundamental, mids and highs notes above in this case Class-D >1khz.
As can be seen (red trace) there is 75 degrees!!!!!!! of phase shift at 10khz cause by the switching noise "output filter" in this Class-D amp, and still 40degrees!!!! at 1.5khz. https://ibb.co/cCL1M8k

This is an older design that does not reflect modern class D amps. A good class D amp will have less than 1 degree of phase shift at 20KHz.

If the system has 20Hz to 20KHz bandwidth you're not losing any audible harmonics. So if it seems that you are, something else is afoot, and that something else is distortion. So yes.


For example a thinner, less 'fleshed out' sound might be because the amp has a coloration of brightness and harshness which is common with many solid state amps. This is caused by distortion- the ear assigns a tonality to all forms of distortion and the higher ordered harmonics get harshness and brightness.


Because the ear is sensing brightness, it will seem as if the sound is dry even though the bass is present. This is because the ear 'tilts' your perception depending on what spectrum is perceived as loudest.


When solid state amps exhibit this behavior its usually because they lack the feedback needed to clean up the distortion caused by the feedback itself, which is almost entirely higher ordered harmonics. This is literally why tube amps are still around after all these decades. They don't have enough feedback either, but they generate more 2nd and 3rd harmonic which masks the higher orders- and so sound smoother and often as a result more 'harmonically correct'. 

High end audio design is both science and art.

Yes. The trick is to design for the ear rather than the spec sheet. They are not the same :)

The spec sheet emphasizes low distortion, But it turns out that the ear will be less sensitive to distortion if the overall distortion has a certain signature: a predominate 2nd and/or 3rd harmonic in sufficient quantity to mask the higher orders. If this is the case then it will be very hard to tell the difference between 0.5%THD and 0.005THD.


If the lower orders are not in sufficient amplitudes, the higher orders (even if the amp has only 0.005% THD) will cause the amp to sound bright and harsh.


You have to know this simple fact when designing amps, if you want to make an amp that sounds like music rather than electronics.

I don’t want gross harmonic distortion, but don’t abuse or lose the precious harmonics in the virgin recording either. No way to measure that, though, right?

Sure you can.

The thing is, no amp is going to lose harmonic information in the audio range. They will all *add* harmonic information though and because distortion obscures detail, it will subjectively appear that some amps are better at getting the 'harmonic structure' (overtones) right than others.