The circle of fifths · Keys and key signatures · Music theory
If the major keys are arranged fifth by fifth upward, each one adds a sharp to the previous one: C, G, D, A, E, B, F♯ and C♯. Downward, each fifth adds a…
The circle of fifths
If the major keys are arranged fifth by fifth upward, each one adds a sharp to the previous one: C, G, D, A, E, B, F♯ and C♯. Downward, each fifth adds a flat: F, B♭, E♭, A♭, D♭, G♭ and C♭. This is the circle of fifths; the minor keys follow the same order, each with its relative.
At its ends the circle closes in three enharmonic pairs, which sound the same: B major and C♭ major, F♯ major and G♭ major, C♯ major and D♭ major. In all there are fifteen key signatures.
Who drew it and why it closes
The first known circle of fifths appears in the Grammatika of Nikolai Diletsky, from 1677. Johann David Heinichen published his in 1711, and later theorists placed the minor keys in an inner circle, as here.
That the circle closes is a convention of temperament. Twelve pure fifths do not return exactly to the starting note: they overshoot by about 23 cents, nearly a quarter of a half step, the so-called Pythagorean comma. Equal temperament shares that difference among the twelve fifths, each a little narrower, which is why F♯ and G♭ can be the same key.