[goto11]

Yes, intervals are just ratios of numbers, corresponding to frequency ratios. 2:1 is an octave, 3:2 is a fifth, 4:3 a fourth and so on. I didn't even know this was controversial.

Of course a lot of other stuff in music and music theory is due to history and tradition. For example the names of the intervals (octave, fourth, fifth etc.) presumes a 7-note scale. Using 7 as reference is tradition, e.g. the pentatonic scale has 5 notes.

[kaoD]

> Using 7 as reference is tradition, e.g. the pentatonic scale has 5.

That's our point.

[goto11]

Ok, but that is kind of orthogonal to the point I was making. I was just stating that it follows from the math that the notes in a 7-note scale are not evenly spaced. The same is true for a pentatonic scale, for the same reason: The intervals corresponds to the simplest ratios (2:3, 3:4 etc.) but these do not in turn correspond to divide the octave evenly.