As a music teacher, if find this quite a bit insulting. I
Sorry, I didn't mean to insult. Obviously if there weren't music teachers I wouldn't be able to even think about any of this. The disagreement is not really because of my experience learning music, but because I have needed to program musical software. When I try to program musical logic I tend to think in terms of Occams razor, in which distances between pitch frequencies are counted from zero, like if you were to count 5 inches, the beginning of the distance would not be marked 1 inch.
You make a good point though. Whole numbers are crucial in musical philosophy. Whenever I think of Pythagoras applying ratios to discover the idea of musical scales and chords, I imagine him to be working with ratios formed of whole numbers. So although to me any resulting frequency relationship distances should, in my mind as a programmer, begin with a zero, notes on paper are obviously treated as things, not distances. These notes are played on instruments, usually, with fingers, which I guess emphasizes your point. Maybe a lot more guitarists are going to relate to your method than mine.
I guess in the back of my mind, in order to understand all this I have somehow formed the habit of converting these "things" to ratios. I.e. a ii-V-I progression is a statement of ratios, which are not pitch/key specific. In the same way, I in the back of my mind I have compared every scale to the chromatic scale, and every other tuning to the equal tempered tuning. On my guitar, to get a pure minor third, as blues players often do without realizing it, I bend about 14/100ths sharp, which sounds ecstatically more beautiful than the crummy equal tempered minor third. To think about what I'm doing, I need to think in terms of a ruler with 100 steps from the equal tempered minor third to the major third, and go up 0.14 of a half step (towards the major third).
If I bend up 14 cents (0.14 semitones) from the 15th fret, before playing an open E minor chord for example, I am rewarded with something that has nuance that I immediately recognize in players like Gary Moore, who always seem to "sing notes". So to me, ratios are formed of whole numbers, but measuring the frequency of pitches that form the ratios, as we do when we compare two cent positions in the equal tempered octave, is best likened to the use of a ruler, where one would start at zero.
The reason this was brought up is that in the harmonizer, -2, a diatonic M7, is one half step down from the root. This implies that the root is both +1 and -1. Or why would one jump to -2? When you start going up from the root and down from the root, and use the convention of negative numbers, to me this is unnecessarily confusing. I shouldn't tried to inject humor into my post. It was snide. It was really only this that was my intended point: that to a programmer it is difficult to inculcate music theory into GUI's.
Again, the abacus and modern calculator can peacefully coexist. Counting things (like diatonic scale steps) is as valid as measuring things, they both inform the brain.