The harmonic series (of which the first three intervals are octaves, fifths, fourths in pythagorean tuning) is not arbitrary. How you construct a more useful s

The harmonic series (of which the first three intervals are octaves, fifths, fourths in pythagorean tuning) is not arbitrary. How you construct a more useful set of notes from the harmonic series is arbitrary. The 1.5^12 ~= 2^7 coincidence I note above allows you to construct a scale using octaves and fifths. You can just as easily do it with other similar coincidences, use fifths and fourths instead, etc etc. Check the smoothness/roughness functions in my blog link - the reason you think e.g. a 3rd sounds as 'right' as a 7th is likely purely cultural. Other cultures have other scales. One of the Indian ragas has over 100 notes. (I'm aware OP claims it's ALL learned, including the octave, but even if true I don't think that means it's all cultural).