Generalized continued fractions and equal temperament
It would be nice if we could divide an octave into equal notes and then be able to have an interval close to a perfect fifth (which raises the frequency by 3/2). That's how equal temperament works: it divides an octave into twelve equal notes and then it turns out that an interval of seven notes is close to a perfect fifth. That's actually why this particular scale was chosen and a reason it has been so successful.
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