Circle of fifths

How the circle is built

If you go clockwise from C, G, D, A, E, B and F♯ follow. Each step is a fifth upwards, and every new key gets exactly one more sharp. Anticlockwise the steps lead via F, B♭, E♭, A♭ and D♭ to G♭, and every key gets one more flat. After twelve steps you are back where you started, because twelve fifths and seven octaves close exactly in equal temperament.

Neighbouring keys share six of their seven notes, which is why modulations between them sound natural. C major and G major are one fifth apart and sound more familiar together than C major and F♯ major.

Reading key signatures

Sharps always appear in the key signature in the order F♯, C♯, G♯, D♯, A♯, E♯, B♯. Flats appear in exactly the opposite order: B♭, E♭, A♭, D♭, G♭, C♭, F♭. Two rules lead to the key: in sharp keys the tonic lies a semitone above the last sharp (last sharp F♯, so G major). In flat keys the tonic is the second-to-last flat. C major and F major are the two exceptions.

Every major key has a relative key in minor with the same key signature. It starts three semitones below the major key. The parallel key has the same tonic but three notes changed, such as C minor to C major.

Chords in the circle

The circle also shows the strongest chord movement: a fifth downwards, for example G → C or D → G. Tonic, subdominant and dominant, in C major C, F and G, lie next to each other in the circle. The progression I–V–vi–IV lies completely within one section of the circle, which is why these loops sound so familiar. More on the functions on the page Diatonic chords.

History and tuning

If you stack twelve pure fifths on top of each other, you miss seven octaves by the Pythagorean comma of about 23.46 cents. Only equal temperament lets the circle close. The first known drawing of a circle of fifths is in the treatise “Grammatika” by Nikolai Diletsky (late 1670s); Johann David Heinichen later and independently presented it in a figured-bass treatise of 1711. The source for this is the page Circle of fifths.

Common mistakes

• Mixing up fifth and fourth: Clockwise the circle goes up a fifth, counter-clockwise down a fifth (equal to a fourth up).
• Mixing up relative and parallel: Relative keys have the same key signature, parallel keys the same tonic.
• Enharmonic keys: F♯ major and G♭ major sound the same but are written differently. Composers usually choose the spelling with fewer sharps or flats, for example B major (five sharps) instead of C♭ major (seven flats); F♯ and G♭ major have equally many.