zlacker

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.

>>fsckbo+(OP)
You can blame the Romans for that, as they practiced inclusive counting. Their market days occurring once every 8 days were called nundinae, because the next market day was the ninth day from the previous one. (And by the same logic, Jesus rose from the dead on the third day.)

>>fsckbo+(OP)
The 7 note scale you suggest (do re mi fa so la ti do) is comprised of different intervals (2 2 1 2 2 2 1) in the 12-fold equal tempered scale. There are infinite ways of exploring an octave in music, but unfortunately listener demand for such exploration is near infinitesimal.

>>waffle+ie
don't you mean 11-fold? ... oh wait, they aren't even consistent

>>fsckbo+2i
They sum to 12

>>waffle+DE
actually they multiply, 12th root of 2, to the 12th

>>fsckbo+2T
12th root of 2, to the 12th = 2 :D The collection of 7 intervals I provided, 2 2 1 2 2 2 1, which are a differential representation of "(do) re mi fa so la ti do", sum to 12. Those intervals are linear within the log2 scale you identified as having a 12th root of 2 basis, or in other words, are the major diatonic (7 note) scale which are a subset of the 12-tone equal tempered scale. The laws of logarithms can help explain why these intervals are additive, whereas the semitone basis (12th root of 2) is multiplicative.