musicians use numbering systems that are actually far more confused than anything discussed here. how many notes in an OCTave? "do re mi fa so la ti do" is eight, but that last do is part of the next octave, so an OCTave is 7 notes. (if we count transitions, same thing, starting at the first zero do, re is 1, ... again 7.

the same and even more confusion is engendered when talking about "fifths" etc.

Musicians often use equal temperament, so they have their own numerical crimes to answer for.