[kazinator]

In Western music theory, intervals are one based. No pitch change is "unison"; one diatonic step is a "major second" and so on. As a result of this silly state of affairs, an octave occurs every 7 notes, even though the root "oct" means eight. Furthermore, a "rule of nines" is needed to invert an interval: e.g. inversion of minor 3rd is a major 6th (exchange major/minor, subtract from 9).

[OscarCunningham]

And addition also gets broken. Like a third plus a fourth is a sixth.

[oh_my_goodness]

True, and it's a great example of how this whole drama is about a practical trade-off, not about a unique Right Answer. If you play piano, the second is the second finger; the fifth is the fifth finger, and it all makes sense. No problem. On the other hand trying to actually count that way (two thirds make a fifth and so forth) is maddening.

[qu4z-2]

Clearly the solution is we need to start numbering fingers from 0.

[kazinator]

No, just use subtraction for the intervals. Third finger minus first finger = 3 - 1 = 2.

The floors of a building might start at 1, but you go up 1 flight of stairs from the 5th to the 6th floor, not two.

[oh_my_goodness]

Maybe that would do it. The only problem is that I'd have four fingers on each hand.