Chromatic circle

The chromatic circle is a geometrical space that shows relationships among the 12 equal-tempered pitch classes making up the familiar chromatic scale on a circle. If one starts on any equal-tempered pitch and repeatedly ascends by the musical interval of a semitone, one will eventually land on a pitch with the same pitch class as the initial one, passing through all the other equal-tempered chromatic pitch classes in between.

Since the space is circular, it is also possible to descend by semitone. The chromatic circle is useful because it represents melodic distance, which is often correlated with physical distance on musical instruments. For instance, to move from any C on a piano keyboard to the nearest E, one must move up four semitones, corresponding to four clockwise steps on the chromatic circle. One can also move down by eight semitones, corresponding to eight counterclockwise steps on the pitch class circle. Larger motions on the piano (or in pitch space) can be represented in pitch class space by paths that "wrap around" the chromatic circle one or more times.