Fidelity vs. Musicality...........Is there a tug of War?

Colours would be visible fundamental wavelengths/frequencies. Not harmonics of the fundamental.

We’re not talking about harmonics in the recorded music, but harmonics added where they did not exist at all. Adding harmonics to piano, that are different than piano overtones, is distorting piano sound (creating beats). You might like it, but it is distorted sound with reduced clarity. Trying to cover bright metal dome tweeter with warm sounding gear is adding further reduction in clarity. Now, we have both odd and even harmonics added, when replacing tweeter (or speakers) seems to be the better choice, at least to me.

@kijanki:  

"One might prefer to look at the paintings thru yellow glasses. There is nothing wrong with it, but he doesn't see what artist painted".

Yes... BUT    we are not robots with identical identical sound perception software installed!  We each hear sound differently and our brains interpret it differently. 

And there's a further difference. Whereas, perception of visual art is a direct process-- from canvas to eye to brain, in audio, the process has more intermediate steps (recording/mixing and conveyance of the music to our ears via circuits and speakers). 

Is it not true that these added steps color/distort the accuracy of the original "painting ?

You can have the more accurate system in the world and you are still hearing what pleased the ears of the engineer/producer in the studio-- your experience is ultimately subject to the coloring/distortion associated with their taste and this is associated with their preferences in mics, monitors, etc. 

Perhaps I'm missing something but I don't see how looking at a painting and listening to a recording are analogous. 

It seems to me that for the analogy to hold up, we'd have to compare viewing a painting in a gallery to hearing music in a concert hall.  

I prefer amplifier that does not add any distortion. My Benchmark AHB2 has THD=0.00011% (-119dB, inaudible). Any distortion is coloring sound (reducing clarity).

No, you actually prefer an amp that adds distortion, and your benchmark reduces clarity.

Our hearing evolved over millennia to interpret the fundamental frequency and even ordered harmonics as natural and clear sound. There is no natural sound in nature that is not accompanied by even ordered harmonics.

The 0.00011% THD is achieved by dialing in large amounts of NFB. NFB results in odd ordered harmonics. Even in minute amounts, odd ordered harmonics sound unnatural, sterile and not musical. Odd ordered harmonics do not occur naturally. You make the mistake in thinking 5% 2nd order harmonics is more disruptive than 0.00011 5th order harmonics. That’s true for an oscilloscope, it’s not true for human hearing.

The Benchmark AHB2 has pushed distortion and noise so low it is inaudible to humans. Kijanki is correct you might not like it but the AHB2 is as close to a straight wire with gain as we've gotten. All this blabbing about harmonics is nonsense with this amplifier they are inaudible , even and odd. 
High Fidelity means something. It isn't whatever you happen to prefer. 

Ideally, high-fidelity equipment has inaudible noise and distortion, and a flat (neutral, uncolored) frequency response within the human hearing range.

All this rhetoric about the order of Harmonics....

It's rubbish.