# Circle of fifths

In music theory, the **circle of fifths** is a sequence encompassing all of the notes in the equally tempered chromatic scale. Starting on any note and repeatedly ascending by the musical interval of a perfect fifth, one will eventually land on the same note, after reaching all of the other notes:

Descending by fifths, and ascending or descending by fourths also works, since motion in one direction by a fourth is equivalent to motion in the opposite direction by a fifth. For this reason the circle of fifths is also known as the **circle of fourths**.

The circle of fifths, or fourths, may be mapped from the chromatic scale by multiplication, and vice versus. To map between the circle of fifths and the chromatic scale (in integer notation) multiply by 7 (M7), for the circle of fourths M5.

Moving around the circle of fifths is a common way to modulate.

This was supposedly invented in the sixth century B.C. by Pythagoras. It is said that Pythagoras also had the idea of tuning an instrument by fifths and thus discovered the Pythagorean comma.

See also: enharmonic, cadence (music), sonata form