The circle of fifths, explained
The circle of fifths is a map of all twelve keys. Start at C at the top. Move clockwise and each key is a perfect fifth higher than the last: C, G, D, A, E, B, then F♯ at the bottom, and back round through D♭, A♭, E♭, B♭ and F to C again.
The inner ring shows each major key's relative minor, and the middle shows the key signature.
Three facts that unlock the whole circle
- Clockwise adds a sharp, anticlockwise adds a flat. C has none. G has 1♯ (F♯), D has 2♯ (F♯ C♯), A has 3♯. Going the other way, F has 1♭ (B♭), B♭ has 2♭, E♭ has 3♭.
- Each step clockwise is up a fifth, each step anticlockwise is up a fourth. The neighbours of a key are its closest relatives: the dominant (V) on one side and the subdominant (IV) on the other.
- The relative minor is directly inside. A minor shares the signature of C major, E minor that of G major, and so on. It is always three half steps below the major key.
Reading a key signature from the circle
To name a key from its signature, count the sharps or flats and walk that many steps from the top. Four sharps? Four steps clockwise from C is E major (or its relative, C♯ minor). Three flats? Three steps anticlockwise is E♭ major (or C minor).
To go the other way, count the steps from C to your key. B♭ is two steps anticlockwise, so it has two flats, and they are B♭ and E♭.
The order of sharps and flats
Key signatures add accidentals in a fixed order. The sharps go F C G D A E B, and the flats go the other way, B E A D G C F. Notice that the order of sharps is itself a path round the circle of fifths. Each new sharp is the new leading tone, a half step below the new tonic.
Why it works
Moving up a fifth, say C major to G major, changes exactly one note: the 4th note of the new scale is the old 7th, F, raised to F♯. All the other notes stay the same. That is why neighbouring keys feel so close, and why composers modulate (change key) between them so easily.
Twelve fifths is almost exactly seven octaves, so after twelve steps the circle closes. The three keys at the bottom have two spellings: F♯/G♭, C♯/D♭ and B/C♭. They are the same pitches written differently, and usually you pick whichever has fewer accidentals.
Using the circle when you play
- Finding chords in a key. The I, IV and V chords are a key and its two neighbours. In C that is C, F and G. In A minor the i, iv and v are Am, Dm and Em.
- Transposing. Moving a song up a fifth is one step clockwise, up a fourth is one step anticlockwise. Use the chord transposer or the capo calculator to do it.
- Chord progressions. Many progressions move around the circle: ii-V-I in jazz is a path of fifths, and so is the "circle progression" Am-Dm-G-C.
- Modulating. To change key smoothly, move to a neighbour on the circle. Only one note changes.
How to practise with the trainer
- Warm-up: the circle is fully labelled. Tap the key a fifth or fourth away, and match a signature to its key. Watch how the sharps and flats change as you move.
- Working set: the minor ring is hidden and you take two steps at a time. Find relative minors and keys up to five sharps or flats.
- Heavy lift: a blank circle with only C marked. You tap any key, major or minor, from memory, with every signature up to seven sharps or flats.
- Go timed. A 1 or 2 minute set a day makes the circle automatic within a couple of weeks.
Every key has its own page in the keys library, the full signature tables are on the key signature chart, and relative key finder pairs any major with its minor. Learn the notes the circle is built on with the interval builder.
Frequently asked questions
What is the circle of fifths?
A diagram of the 12 keys arranged so that each step clockwise goes up a perfect fifth. It also shows each key's signature (it gains one sharp per step clockwise and one flat per step anticlockwise) and pairs each major key with its relative minor.
How do I use the circle of fifths to find a key signature?
Start at C at the top (no sharps or flats). Count steps clockwise for sharps: G has 1, D has 2, A has 3, and so on. Count anticlockwise for flats: F has 1, B♭ has 2, E♭ has 3.
Why does it go up in fifths and not in order?
Neighbouring keys on the circle share six of their seven notes, so they sound closely related and music modulates between them easily. Going up by fifth, each new key changes only one note: the new leading tone is sharpened.
What is the relative minor?
The minor key that shares a key signature with a major key, a minor third below it. A minor is the relative minor of C major. On the circle it sits on the inner ring directly below its major.
How do I remember the order of sharps and flats?
Sharps: Father Charles Goes Down And Ends Battle (F C G D A E B). Flats are the same list in reverse: Battle Ends Down And Goes Charles Father (B E A D G C F).
What is the difference between going up a fifth and up a fourth?
Up a fifth moves one step clockwise (adds a sharp). Up a fourth is the same as down a fifth: one step anticlockwise (adds a flat). That is why F, a fourth above C, has one flat.
Why do F♯ and G♭ share a spot at the bottom?
F♯ major (6 sharps) and G♭ major (6 flats) are the same pitches written differently. The same happens with B and C♭ and with D♭ and C♯. Going clockwise from C, the circle joins back up with itself after twelve steps.
How does the circle of fifths help with chords?
The I, IV and V chords of a key are neighbours on the circle: the IV is one step anticlockwise and the V one step clockwise. Many chord progressions, such as ii-V-I, also move around the circle by fifths.
Should I memorise the circle?
Yes, it pays off. The trainer starts with a labelled circle and removes the labels as you improve, so that by the Heavy lift level you can find any key, major or minor, from the blank circle.