The circle of fifths explained: keys, signatures and chords

The circle of fifths arranges all twelve major keys in a ring so that each step clockwise moves up a perfect fifth and adds one sharp to the key signature, while each step anticlockwise moves down a fifth and adds one flat. C major, with no sharps or flats, sits at the top; G, D, A, E, B and F♯ follow clockwise, and F, B♭, E♭, A♭ and D♭ run anticlockwise. Inside the ring sit the relative minors. The interactive circle of fifths shows any key's signature, scale and chords when you click it.

How the circle is built

A perfect fifth is seven semitones, the distance from C up to G. Keep going up in fifths, C, G, D, A, E, B, F♯ (G♭), D♭, A♭, E♭, B♭, F, and after twelve steps you are back at C, having visited every note once. That loop is the circle. Why does each step add exactly one sharp? The major scale starting a fifth higher shares six of its seven notes with the previous one; only the 4th of the old scale must be raised. G major is C major with F raised to F♯, D major is G major with C raised to C♯, and so on.

Reading key signatures

Sharps are always added in the order F, C, G, D, A, E, B, and flats in the reverse order, B, E, A, D, G, C, F. So a key with three sharps has F♯, C♯ and G♯ (A major), and a key with three flats has B♭, E♭ and A♭ (E♭ major). Two tricks read a signature on sheet music quickly:

• For sharp keys, the key is a semitone above the last sharp. Last sharp G♯, so A major.
• For flat keys, the key is the second-to-last flat. Flats B♭, E♭, A♭, so E♭ major. F major, with one flat, has to be memorised.

At the bottom of the circle, F♯ major (six sharps) and G♭ major (six flats) are the same keys on a piano, spelled differently; likewise B and C♭, and D♭ and C♯. Composers usually choose the spelling with fewer accidentals. On sheet music the signature sits just after the clef at the start of every line.

Relative minors

Each major key shares its key signature with a minor key three semitones lower: C major with A minor, G with E minor, D with B minor, F with D minor, B♭ with G minor. On the circle the relative minor sits inside its major, so the inner ring is itself a circle of fifths for minor keys. Two keys with the same signature have the same notes, so telling them apart means listening for the home note, as Major vs minor scales: what actually differs explains.

Finding the chords in a key

The circle also lays out the most useful chords of a key. Take any major key and look either side of it: in C, the neighbours are F and G. Those three are the major chords of the key, numbered I, IV and V. The three relative minors beside them, D minor, A minor and E minor, are the minor chords ii, vi and iii. The only chord left is the diminished chord on the 7th degree, B diminished. Together they are the seven diatonic chords:

• C major: C, Dm, Em, F, G, Am, B dim
• G major: G, Am, Bm, C, D, Em, F♯ dim
• F major: F, Gm, Am, B♭, C, Dm, E dim

That cluster of six neighbouring segments is why so many songs use just I, IV, V and vi. The chord progression generator builds common progressions from those chords in any key.

Neighbouring keys and modulation

Keys next to each other on the circle differ by only one note, so moving between them sounds smooth; these are called closely related keys. A piece in C major modulating to G major only needs an F♯. Keys on opposite sides, such as C and F♯, share very few notes, so a jump between them sounds dramatic. The circle also explains common chord movements: going anticlockwise means going down a fifth, which is how a dominant chord resolves, as G7 resolves to C.

Everyday uses

I use the circle for three practical jobs: reading a key signature, predicting which chords will fit a song, and choosing a new key. Transposing a song up a fifth means moving one step clockwise, and every chord moves with it; the chord transposer does that for a whole chord sheet, and How to transpose chords to another key explains the method. To see the full scale of any key on the circle, open it in the scale finder. The circle's honest limit is that it describes major and minor tonality; modal, blues and atonal music bend its rules, though the key signatures still apply.