Circle of fifths and key signatures

Picture a clock with C major at 12 o'clock. Each step clockwise goes up a perfect fifth, seven half steps on the piano: C to G, G to D, D to A. Each of those keys needs one more sharp than the last. Going counterclockwise from C goes down a fifth instead: C to F, F to B♭, B♭ to E♭, and each key needs one more flat.

After twelve steps you are back at C, which is why it is a circle. At the bottom, where the sharps and flats meet, three positions have two names for the same keys on the piano: B major is also C♭ major, F♯ major is also G♭ major, and D♭ major is also C♯ major. Musicians call these enharmonic keys. They sound the same and are only written differently.

The outer ring holds the major keys and the inner ring their relative minors. The small number outside each key is how many sharps (♯) or flats (♭) its key signature has. Every step around the circle adds or removes exactly one.

To find a key signature, count steps from C. D is two steps clockwise, so D major has two sharps. E♭ is three steps counterclockwise, so E♭ major has three flats. Which sharps or flats they are comes from the order below.

A key signature is the set of sharps or flats written right after the clef at the start of every line. They apply to that note in every octave for the whole piece, so a key signature with F♯ means every F is played as F♯ unless a natural sign says otherwise.

Sharps are always added in the same order, and flats in exactly the reverse order. A key with two sharps always has F♯ and C♯, never any other pair. A key with three flats always has B♭, E♭ and A♭.

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The first sentence gives the order of sharps: F C G D A E B. The second gives the order of flats: B E A D G C F. The order of sharps is itself a chain of fifths, the same letters you meet going clockwise around the circle from F.

Sharps: take the last sharp and go up one half step. With F♯ and C♯, the last sharp is C♯, one half step up is D, so the key is D major. With four sharps, F♯ C♯ G♯ D♯, the last is D♯ and the key is E major.

Flats: the second-to-last flat is the key. With B♭, E♭ and A♭, the second-to-last is E♭, so the key is E♭ major. One flat has no second-to-last, so learn it by heart: one flat, B♭, is F major.

No sharps or flats is C major or A minor.

Every signature also fits one minor key, its relative minor. To tell which one a piece is in, look at the last note in the bass and the last chord: music usually ends on its home note. A piece with one sharp that ends on E is in E minor, not G major. In minor keys you will also see the 7th note raised with an accidental, such as D♯ in E minor.

Each major key shares its key signature with one minor key, its relative minor. The relative minor starts on the 6th note of the major scale, which is three half steps below the major key's first note. C major and A minor both have no sharps or flats. G major and E minor both have F♯. F major and D minor both have B♭.

On the circle, each relative minor sits right inside its major key. The two keys use the same seven notes but start and finish in a different place, so the minor key sounds darker. Each scale page lists its relative key with the notes and fingering.

Find the chords that belong together. A key and its two neighbours on the outer ring are its three major chords, the I, IV and V. The three minor keys just inside them are its three minor chords. For C major that is C, F and G, plus Am, Dm and Em: six of the seven chords in the key, and the ones most songs in C use.

Follow chord progressions. Moving one step counterclockwise, down a fifth, is the strongest move between chords. That is why so many songs go Dm to G to C, the ii-V-I in C major, or Am to Dm to G to C, each chord one step counterclockwise from the last.

Learn scales in order. Go clockwise from C and each new major scale adds one sharp and keeps every other note: C, then G with F♯, then D with F♯ and C♯, then A with F♯, C♯ and G♯. The scales page lists every major scale in this order, so you only ever learn one new note at a time.

Change key. Moving a song to a neighbouring key on the circle changes just one note of its scale, which is why that is the easiest key change to play and to hear.