I'm not saying fa is half way, I'm saying you can take the scale in two sections which are just transposed versions of the same intervals. This is not helpful,

I'm not saying fa is half way, I'm saying you can take the scale in two sections which are just transposed versions of the same intervals. This is not helpful, but it is true. Pretty sure you can't get out of the fact that do appears twice by invoking multiplicative rather than additive logic: two octaves played together contains 3 dos, 3 octaves contains 4, etc.