In the process of looking at how harmonics match notes I stumbled
on another big misconception I had.
The 5th harmonic does *not* correspond to a major 5th in an octave.
The 4th harmonic does *not* correspond to the 4th in an octave.
The 3rd harmonic does *not* correspond to a major 3rd in an octave.
etc...
In fact it goes like this:
7th Harmonic > 2 octaves + dominant 7th
6th Harmonic > 2 octaves + major 5th
5th Harmonic > 2 octaves + major 3rd
4th Harmonic > 2 octaves
3rd Harmonic > 1 octave + major 5th
2nd Harmonic > 1 octave
Seeing it this way makes it easy to see that the 2nd - 6th are
very consonant intervals. The 7th is nasty and also out of tune.
I'd make sure an amp had no trace of anything above the 6th.