Chromatic circle

The chromatic circle is a clock diagram for displaying relationships among the equal-tempered pitch classes making up a given equal temperament tuning's chromatic scale on a circle.

One can also move down by eight semitones, corresponding to eight counterclockwise steps on the pitch class circle.

For any positive integer N, one can represent all of the equal-tempered pitch classes of N-tone equal temperament by the cyclic group of order N, or equivalently, the residue classes modulo twelve, Z/NZ.

The semitonal generator gives rise to the chromatic circle, while the perfect fourth and perfect fifth give rise to the circle of fifths.

By contrast, the circle of fifths is fundamentally a discrete structure, and there is no obvious way to assign pitch classes to each of its points.