I thought it might help some here if I posted a list of harmonic postions and their qualities.
I get confused with intervals above a 13th, so I broke them down to octaves + additional interval for simplicity.
The numbers are calculated fret positions above the fretted position rounded to one decimal place.
Code:
octave good 12.0
octave + perfect 5th okay 7.0 19.0
2 octaves good 5.0 ### 24.0
2 octaves + major 3rd flat 3.9 8.8 15.9 27.9
2 octaves + perfect 5th okay 3.2 ### ### ### 31.0
2 octaves + minor 7th v.flat 2.7 5.8 9.7 14.7 21.7 33.7
3 octaves good 2.3 ### 8.1 ### 17.0 ### 36.0
3 octaves + major 2nd okay 2.0 4.4 ### 10.2 14.0 19.0 26.0 38.0
3 octaves + major 3rd flat 1.8 ### 6.2 ### ### ### 20.8 ### 39.9
3 octaves + dim 5 v.flat 1.7 3.5 5.5 7.8 10.5 13.7 17.5 22.5 29.5 41.5
3 octaves + perfect 5th okay 1.5 ### ### ### 9.3 ### 15.2 ### ### ### 43.0
As a brief explanation, when you play a harmonic, you are subdividing the string length into equal parts. The twelfth fret harmonic is exactly half the length of the string, so when you touch that harmonic, you are dividing the string into two equal parts and sounds at a frequency twice the fundamental. The seventh and 19th fret harmonics divide the string into 3 equal parts and sounds at a frequency three times the fundamental. And so on.
