[kian]

If you take the chromatic scale and then swap every other pair of notes on opposite sides of the circle, it yields the circle of fifths. You'll notice that on the circle of fifths notes that skip a step are a whole tone apart in the chromatic scale.

Although there have been some claims in these comments to the contrary, harmony is particularly mathematical. Symmetry and the breaking of within the integers mod 12 form the foundational principles of harmony.