[BrianHV]

To be fair, it's not just the octave. The interval between a C and a C is a unison. The interval between a C and a D is a second. Two octaves are a fifteenth (not a sixteenth). The entire thing is one-indexed.

It's perhaps better to think of it as the number of notes you have to count before you reach the second note, starting with the first. If you start with C, you have to count one note before you get to that same C. You have to count 8 before you get to the second C, and 15 before you get to the third.

[tobr]

A related problem in music is how rhythm is counted, e.g. in recording software. Each new bar in 4/4 starts on beat 1, 5, 9, 13, rather than 0, 4, 8, 12, which makes it surprisingly difficult to figure out where you are.