Scales, Keys & Modes

Circle of Fifths

Definition

The circle of fifths arranges the twelve keys like a clock, each a perfect fifth from the next. Going clockwise from C adds one sharp per key; going counterclockwise adds one flat.

The circle of fifths is a diagram of the twelve major keys, usually with their relative minors, arranged in a circle so that each key is a perfect fifth above the one before it. It is one of the most useful maps in music theory: it shows the key signature of every key, which keys are close relatives, and how chords like to move.

Going around the circle

Start at the top with C major, which has no sharps or flats. Move clockwise and each step goes up a perfect fifth and adds one sharp:

C (none), G (1♯), D (2♯), A (3♯), E (4♯), B (5♯), F♯ (6♯)

Move counterclockwise from C and each step goes down a fifth (or up a fourth) and adds one flat:

C (none), F (1♭), B♭ (2♭), E♭ (3♭), A♭ (4♭), D♭ (5♭), G♭ (6♭)

At the bottom the two sides meet: F♯ major and G♭ major are the same key spelled two ways (enharmonic equivalent keys). Two more pairs overlap there: B major (five sharps) is the same as C♭ major (seven flats), and D♭ major (five flats) the same as C♯ major (seven sharps). That is why there are fifteen major key signatures but only twelve major keys.

Two treble-clef examples, four bars each, with a whole note per bar and a key name under it. Clockwise: C with no key signature, G with one sharp, D with two sharps, A with three sharps. Counterclockwise: C with no key signature, F with one flat, B-flat with two flats, E-flat with three flats. — Three steps each way from C, showing four keys in each direction. Clockwise, each key is a fifth higher and adds a sharp: C, G, D, A. Counterclockwise, each is a fifth lower and adds a flat: C, F, B♭, E♭. The whole note in each bar is that key's tonic.

The order of sharps and flats

The circle also gives you the order in which sharps and flats appear in a key signature. Each new sharp is a fifth above the last: F♯ C♯ G♯ D♯ A♯ E♯ B♯. The flats run the other way, each a fifth below the last: B♭ E♭ A♭ D♭ G♭ C♭ F♭. A popular memory aid for the sharps is "Father Charles Goes Down And Ends Battle"; read it backward for the flats.

Two shortcuts follow. In a sharp key, the tonic is a half step above the last sharp: two sharps, F♯ and C♯, means D major. In a flat key, the tonic is the second-to-last flat: three flats, B♭ E♭ A♭, means E♭ major. F major, with its single flat, is the one to memorize.

Relative minors

The inner ring of most circles shows the relative minor of each major key, which shares its key signature: A minor with C, E minor with G, D minor with F, and so on around. The minor keys follow the same order of fifths.

Neighbors on the circle

Keys next to each other on the circle differ by a single note. C major and G major share six notes and differ only in F versus F♯. That is why music most often modulates to a neighboring key, very often the dominant key one step clockwise. Keys on opposite sides, such as C and F♯, share the fewest notes and sound the most distant from each other.

Five steps clockwise around the circle as real pitches: C, G, D, A, E and B, each a perfect fifth above the last.

The circle also describes chord progressions. A bass line that moves counterclockwise by fifths, A, D, G, C, makes the strong progression vi–ii–V–I in C major, the root motion behind the ii–V–I progression and many other progressions.

Grand staff in 4/4, two bars of half-note chords: A minor, D minor, G major and C major, over bass notes A, D, G and C. Chord symbols above; vi, ii, V and I below the treble staff. — vi–ii–V–I in C major. The bass falls by fifths (or rises by fourths) from A to D to G to C: counterclockwise around the circle, one step at a time, until it reaches the tonic.

Common questions

How do you remember the order of sharps and flats?

Sharps: F C G D A E B, often remembered as "Father Charles Goes Down And Ends Battle". Flats are the same letters backward, B E A D G C F: "Battle Ends And Down Goes Charles's Father".

Why is it called the circle of fifths?

Because each key is a perfect fifth from its neighbors, and after twelve fifths you arrive back at the key you started from, so the keys close into a circle.