Circle of fifths

In music theory, the circle of fifths (or circle of fourths) shows the relationships among the twelve tones of the chromatic scale, their corresponding key signatures, and the associated major and minor keys. More specifically, it is a geometrical representation of relationships among the 12 pitch classes of the chromatic scale in pitch class space. Musicians and composers use the circle of fifths to understand and describe those relationships.

At the top of the circle, the key of C has no sharps or flats. Starting from there and going clockwise by ascending fifths, the key of G has one sharp, the key of D has 2 sharps, and so on. Similarly, going counterclockwise from the top by descending fifths, the key of F has one flat, the key of B♭ has 2 flats, and so on. At the bottom of the circle, the sharp and flat keys overlap, showing pairs of enharmonic key signatures.

Starting at any pitch, ascending by the interval of an equal tempered perfect fifth, one passes all twelve tones, to return to the beginning pitch. (Ascending by justly tuned perfect fifths fails to close the circle by a small amount, the Pythagorean comma.) Reversing the direction, playing tones separated by a perfect fourth, gives the same result. (To the ear, the sequence of fourths gives an impression of settling, or resolution.