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


Of course, 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? Thats where the ears come in…
redwoodaudio
I mean, signal to noise ratio would seem to be the most relevant stat in common usage, right?
Even when it's below audible levels, I have always wondered if it can contaminate the sound.

A very strong SNR of 120dB is almost certainly beyond audible range, but could be important for the fragile harmonics.  I’m sure there are people here who know this scientifically.
Exactly! Where does the noise come from? It it mostly ripple on the DC supply? Is a massively over engineered supply helpful?

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Try not to worry so much.
Loads more is lost in other parts of the chain.

As you rightly say OP, 120dB below the signal is a looonnngggg way down.  You can demonstrate that to yourself if you have an amp with numbered volume settings at known dB intervals.  You won't hear it, but the full volume signal will blow your eardrums if you're silly enough.