The Circle of Fifths: How It Works and How Composers Actually Use It

What Is the Circle of Fifths?

The circle of fifths is a diagram that arranges all twelve major keys (and their relative minors) in a circle, so that each key is a perfect fifth above the one before it. Start at C at the top and move clockwise: G, D, A, E, B, F#/Gb, Db, Ab, Eb, Bb, F, and back to C. Twelve steps of a fifth bring you home.

That arrangement is not decorative. Two keys that sit next to each other on the circle differ by exactly one accidental, share six of their seven notes, and share three chords. Two keys on opposite sides of the circle have almost nothing in common. So the circle is a map of tonal distance: close on the circle means close in sound. Everything else the circle does, from key signatures to modulation to chord progressions, follows from that.

Read the other way, counterclockwise, each step is a perfect fourth, which is why the same diagram is sometimes called the circle of fourths. It is one circle; the name only says which direction you are looking.

How the Circle Is Built

Moving clockwise from C, every step adds one sharp:

• C major: no sharps or flats
• G major: 1 sharp (F#)
• D major: 2 sharps (F#, C#)
• A major: 3 sharps (F#, C#, G#)
• E major: 4 sharps (F#, C#, G#, D#)
• B major: 5 sharps (F#, C#, G#, D#, A#)
• F# major: 6 sharps (F#, C#, G#, D#, A#, E#)

Moving counterclockwise from C, every step adds one flat:

• F major: 1 flat (Bb)
• Bb major: 2 flats (Bb, Eb)
• Eb major: 3 flats (Bb, Eb, Ab)
• Ab major: 4 flats (Bb, Eb, Ab, Db)
• Db major: 5 flats (Bb, Eb, Ab, Db, Gb)
• Gb major: 6 flats (Bb, Eb, Ab, Db, Gb, Cb)

At the bottom of the circle the two sides meet: F# major and Gb major are the same key spelled two ways. (B major and Cb major, and Db and C# major, overlap in the same way; most charts show the simpler spelling.)

Notice the order in which sharps appear: F, C, G, D, A, E, B. That is itself a chain of fifths. The order of flats is the same list backwards: B, E, A, D, G, C, F. The circle is fifths all the way down.

Reading Key Signatures from the Circle

Because each step adds one accidental, the circle answers "how many sharps does this key have?" by counting steps from C. Two practical tricks make it faster than counting:

• Sharp keys: take the last sharp in the key signature and go up a half step. Four sharps end on D#; a half step up is E, so the key is E major.
• Flat keys: the second-to-last flat names the key. Three flats are Bb, Eb, Ab; the second-to-last is Eb, so the key is Eb major. (F major, with its single flat, is the exception you simply remember.)

Going the other way, from key to signature, you read the accidentals off the circle in order: a key with four sharps has the first four of F, C, G, D, A, E, B.

The Inner Circle: Relative Minors

Every major key shares its key signature with one minor key, its relative minor, whose tonic sits a minor third below. Charts usually show these as an inner ring: A minor inside C major, E minor inside G, D minor inside F, and so on around the circle. The inner ring is a second circle of fifths, offset by three semitones from the outer one.

Two terms are easy to confuse here. The relative minor shares the key signature (C major and A minor). The parallel minor shares the tonic (C major and C minor) and sits three steps counterclockwise on the circle, which is why moving between parallel keys feels like a real change of colour while moving between relative keys feels like a change of mood inside the same world. Both relationships are used constantly in film and game scoring, and the circle shows you at a glance which is which.

From Keys to Chords

So far the circle has been about keys. Its more useful face, for a composer, is as a map of chords.

Take C major and label the diatonic chords with Roman numerals. The three primary chords, I, IV and V, are C, F and G: the tonic and its two neighbours on the circle. Every key works the same way, which is one reason a chart is worth having on the wall. Pick any key, and the two chords either side of it are its subdominant and dominant.

The circle also predicts the strongest chord movements in tonal music. A root that falls by a fifth, G to C, D to G, A to D, produces the sense of resolution that harmony is built on; V to I is the most familiar case. Line several of these up and you get a chain of descending fifths, each chord resolving into the next. On the chart above, every link of that chain is one step counterclockwise. Lay the chain over the diatonic chords of a key and it reads: vii°, iii, vi, ii, V, I. If you want the wider picture of how progressions carry emotion, our guide to chord progressions covers the ground; here we stay with what the circle itself gives you.

Extending the ii–V–I

The ii–V–I is the most common cadence in tonal music, and it is nothing more than the last three links of that chain. Jazz musicians in the bebop era noticed that you can extend the chain backwards as far as you like: any ii–V–I can become vi–ii–V–I; that can become iii–vi–ii–V–I; and, more rarely, vii–iii–vi–ii–V–I. Following the circle gives a consistent result every time, and the longer chain builds momentum towards the cadence.

Japanese game and anime composers use this device constantly. A well-known example is the opening theme of Neon Genesis Evangelion: the progression starts on IV, runs iii–vi–ii–V, and then uses a secondary ii–V to land back on IV. That last move, a ii–V aimed at a chord other than the tonic, is the same logic applied one level down, and it is where circle-of-fifths thinking starts to feel like a technique rather than a diagram.

The Legend of Otoe: Levels 2 & 3 Circle-of-fifths gestures, tritone substitution and the harmony behind anime and JRPG music, with a full sketch written in every level. Explore the course

Circle-of-Fifths Gestures in Practice

In a score, the chain rarely appears as a textbook vii–iii–vi–ii–V–I. What composers use is what we call a circle-of-fifths gesture: a run of root movements by fifth that drives the music towards a target chord. Three habits make it work.

Work backwards from the target. Decide where you want to land, say a C major chord, then ask what its V is (G7), what could come before that (D), and keep stepping backwards. The chain can start wherever you happen to be, in whatever key or tonal centre you are in; it is a way in from anywhere. Once the chain rolls forward it has an inevitability that a sequence of unrelated chords never has.

Break the chain on purpose. A chain of fifths can go on for a very long time, and the further it goes, the further it drifts from the starting key. You can leave it whenever you want, but you need to be deliberate if you want to end up where you began. In a chase sketch from the third level of the Otoe course, the harmony lifts through the circle twice, C to F, then Eb to Ab, and then stops: a third lift would have been obvious and predictable, so the music holds on Ab and starts moving down instead, standing on the dominant before the next section. Two lifts and a break is a better gesture than three lifts.

Use it where it belongs. A circle-of-fifths gesture is functional, forward-moving harmony. It is exactly right for a chase, a build, or the approach to a cadence, and exactly wrong for a scene that is meant to sit in a mood. The same Otoe sketch planned circle-of-fifths gestures for its "doom" section and then cut them, because the story no longer had a chase in it. Knowing when not to use the device is part of using it well.

Planning Keys with the Circle

The circle scales up from chords to whole sections. In a sonata-style development, or any long cue that needs to wander and return, the question is which keys to pass through. One reliable approach is to fix the chord that brings the main theme back, typically the dominant seventh of the home key, and work backwards around the circle from there: precede the G7 with D, before that A, before that E, before that B. If the piece's secondary key is G major, you use the versions of those chords that belong to G major, and the whole development feels related to what came before.

The same plan works in the minor. Before the G7 you could have Ab, before that Eb, before that Bb, perhaps F minor before that, all drawn from C minor. Same skeleton, entirely different colour. The circle is not the only way to plan a development, and it should not be used every time, but it works reliably and it is a good place to start experimenting.

Transitions use the circle in miniature. If you know the chord you are leaving from and the V chord you need to arrive at, count the bars in between and fill them with a logical progression that gets you there: a chain through the circle of fifths is the classic choice, a series of rising thirds is another. The specific choice matters less than the fact that a harmonic sequence takes the listener through several harmonies in a way that is both comprehensible and interesting.

Pillars of Composition II Sonata form, key planning, transitions and reharmonization, taught by building a complete piece module by module. Explore the course

Using the Circle to Modulate

Because neighbouring keys share most of their notes and three of their chords, the circle tells you which modulations will feel smooth and which will feel dramatic. A move to the dominant or subdominant, one step, barely registers as a change of key. A move of two or three steps, to the relative or parallel minor for instance, is a clear shift of colour that still feels logical. A move to the opposite side of the circle, a tritone away, is a jolt, and is used precisely when a jolt is wanted.

A fifth relationship also makes a modulation easier to sell. In a transition between two major themes, moving into the minor side of the circle for a moment, C# minor to F# minor, then arriving on a suspended chord that resolves to the new dominant, makes the change of key feel like the natural next step rather than a cut. A sus4 resolving to a dominant seventh is one of the most dependable ways to land a modulation, and the circle tells you which dominant to aim for.

For Guitarists

Guitarists tend to meet the circle of fifths later than pianists, because open-position chord shapes make some keys feel like "guitar keys" and others feel foreign. The circle explains why: E, A, D and G sit next to each other, so songs in those keys share chords and shapes, while Eb or Ab are four or five steps away and need a capo or barre chords. Reading the circle as a chord map, with the I chord and its two neighbours, is the fastest way to work out the chords of any key, and the descending-fifths chain is the reason so many progressions move the way they do up and down the neck.

Common Mistakes

• Learning it as a list. The circle is a map, not a table. If you only memorize "G has one sharp", you miss the part that matters for composing: what sits next to what.
• Mixing up relative and parallel minor. Relative shares the key signature, parallel shares the tonic. They sound completely different and sit in different places on the circle.
• Running the chain too long. Every fifth is another step from home. Decide where the gesture ends before you start it.
• Using fifths harmony where the scene wants stillness. A circle-of-fifths gesture always moves. For a mood, a place, a texture, you want harmony that does not.
• Forgetting that the circle is symmetrical. Anything you can do with descending fifths you can do with descending fourths, which is the same chain read in reverse; and the tritone, directly opposite any key, is where the two directions meet.

For the wider harmonic context these moves live in, see our complete guide to chord progressions for composers and our look at the Royal Road progression, the anime progression whose standard form ends in exactly this kind of ii–V–I.