Tesla said the numbers 3, 6, and 9 are the secret to the Universe. If we apply those numbers to a tonality, we get a sequence of 4ths.
For the number correspondences, I'm using C as the tonic.
The cycle of fourths has been used as harmonic and melodic fodder by many greats, including George Russell and Walter Bishop, Jr. Actually, the whole harmonic palette of the American Songbook, traditional marches, and the jazz canon depend upon it.
Notice I've divided the circle into whole numbers and negative numbers. (Although the "negative" numbers are just flatted intervals in relation to the tonic.)