The circle of fifths: how many sharps and flats in every key

One step, one sharp

Put C at the top of a clock face. Each step clockwise moves to the key a fifth higher and adds one sharp. Each step anticlockwise moves to the key a fifth lower and adds one flat. That single rule produces every major key signature.

A fifth is five letter names counted upwards, the first included: C, D, E, F, G. So one step clockwise from C is G, then D, then A. Twelve steps of a fifth pass through every key and come back round to C, which is why the keys close into a circle.

The sharp each step adds is always the new key’s 7th note, the one just below its name: G major gains F♯, D major gains C♯. Going the other way, the flat each step adds is always the new key’s 4th note: F major gains B♭, B♭ major gains E♭. Everything else in the scale stays as it was.

Every key signature

The sharps and flats in each signature are not a new set every time. Each key keeps all of the previous key’s accidentals and adds one more, which is why the lists above grow one name at a time.

The order of sharps and flats

Sharps are always added in the same order, F C G D A E B, and always written in that order on the staff. Flats come in exactly the reverse order, B E A D G C F.

There is no separate list to memorise. Read the circle clockwise starting from F, at 11 o’clock, and you have the order of sharps: F, C, G, D, A, E, B. Say it backwards and you have the order of flats. The order is the circle itself.

Four ways to read a key signature quickly

• ·Read it like a clock. For sharp keys, the hour is the count: E sits at 4 o’clock and has four sharps. For flat keys, count back from 12: D♭ sits at 7 o’clock and has 12 − 7 = five flats.
• ·Spell BEAD. Going anticlockwise from C, the first key is F with one flat; the next four spell B♭ E♭ A♭ D♭, then come G♭ and C♭.
• ·Last sharp, one below. In a sharp key, the last sharp is one semitone below the key’s name. A signature ending in G♯ is A major.
• ·Second-to-last flat. In a flat key, the second-to-last flat names the key: B♭ E♭ A♭ D♭ is A♭ major. One flat on its own is F major, which is worth simply knowing.

The relative minor

Every key signature belongs to two keys: a major key and the minor key that uses the same seven notes. The minor’s home note is the major scale’s 6th note, three semitones below the major’s name. A minor shares C major’s empty signature; B minor shares D major’s two sharps.

Nothing about the notes changes between the two. What changes is where home is: the note the music settles on, and the chord that sounds finished. Play a cadence in D major and then in B minor and the same seven notes lean towards a different resting place.

Three places with two names

At 5, 6 and 7 o’clock the circle overlaps itself. B major (five sharps) and C♭ major (seven flats) sound the same; so do F♯ and G♭ major (six each), and C♯ and D♭ major. That is why there are 15 key signatures but only 12 different-sounding major keys.

Which spelling to use is a reading choice: fewer accidentals usually wins, so D♭ major is far more common than C♯ major. The circle stops at seven because the next key, such as G♯ major, would need eight sharps including an F double-sharp; the same sounds are written as A♭ major with four flats instead.

Why each step changes exactly one note

A major scale is two identical four-note halves, each whole, whole, half, joined by a whole step. The top half of C major, G A B C, is exactly the bottom half of G major. So when you move up a fifth, half the scale carries over untouched, and only the new top half has to be built.

Building it with the same pattern of steps forces one note up: D E F♯ G rather than D E F G. That one raised note is the new sharp. Run the argument downwards and the bottom half changes instead, giving one new flat. The Why? view on the wheel walks through this for every step.

Tools for this

Common questions

How do you remember the order of sharps?

Sharps always arrive in the order F C G D A E B. A common mnemonic is “Father Charles Goes Down And Ends Battle”. You can also read it straight off the circle: start at F and go clockwise. Flats come in the reverse order, B E A D G C F.

How do you work out the key from a key signature?

With sharps, the last sharp is one semitone below the key’s name: a signature ending in C♯ is D major. With flats, the second-to-last flat is the key’s name: B♭ E♭ A♭ is E♭ major. One flat on its own is F major.

What is the relative minor of each major key?

The minor key three semitones below, which shares the same notes and key signature: C major and A minor, G and E minor, D and B minor, A and F♯ minor, F and D minor, B♭ and G minor, E♭ and C minor.

Why are F♯ major and G♭ major in the same place on the circle?

They sound identical and are written two ways: F♯ major with six sharps, G♭ major with six flats. B and C♭ major, and C♯ and D♭ major, are the other two pairs. That is why there are 15 key signatures but only 12 different-sounding major keys.

Why does the circle stop at seven sharps or flats?

The next key would need a double sharp or double flat. G♯ major would have eight sharps, F double-sharp among them, so musicians write the same sounds as A♭ major with four flats instead.

What is the circle of fifths used for?

Reading key signatures, and finding closely related keys: neighbours on the circle share six of their seven notes, so music modulates between them easily. Chord progressions also move round it, as in ii–V–I, where each chord’s root is a fifth above the next.