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Not exactly, although I think I understand what you are getting at.

What I meant was that the interval between a major third and fourth in a 12-tone chromatic scale has to be a semitone due to math, not due to some historical accident or decision.

It might be an accident of history that we use a 12-step scale in the first place though, since you can have arbitrary many intervals in an octave - but you can't just divide the octave in arbitrarily places and get music out of it. The intervals still have to be ratios.

(Well I'm sure some avant-garde composer have tried making music with intervals that are not ratios just to be clever, but I hope you get my point!)