Music theory at this level is pretty rational despite the presence of an irrational number in the tempered piano semitone. The most basic harmonic interval (3/2 ratio, or the "fifth") when iterated, gives the notes in the melodic scale. With twelve iterations, you can get back to where you started although the intervals must be "tempered" instead of integer ratios so the interval of the fifth, for example is no longer 1.5 but about 1.498 This results in the typically plangent sound of piano chords.