Circle of Fifths, Explained

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The circle of fifths may be the most-photocopied diagram in music. It hangs on practice-room walls and fills the back pages of method books, and plenty of people who own a copy have never really heard it. Let’s fix that. Pick a key, and listen before you read.

Everything on the wheel can be played: every chord sits beside its name, its signature and its staff, in the register it actually sounds. Two relationships come up again and again, so meet them now. The relative minor shares the signature. The parallel minor shares the tonic. Keep those two straight and half the wheel is already yours.

How to use: choose a major key on the wheel. Enlarge wheel makes the small ring signatures readable; Download wheel saves your chosen key and markings as a printable PNG.

Keys: signatures and relationships

Think of the wheel as a neighbourhood map. Each major key lives on the outside; its relative minor lives just inside, sharing the same front door — the same key signature. C and Am share one; so do G and Em.

Walk clockwise and you collect sharps, one per step. Walk counter-clockwise and you collect flats. The sharps always arrive in the same order — F–C–G–D–A–E–B — and the flats arrive in exactly the reverse. Down at the bottom of the wheel the two meet at the enharmonic seam, where F♯ major and G♭ major are two names for one sound. In equal temperament your ear can’t tell them apart; the page can.

Your nearest neighbours are the five closely related keys: the relative minor, plus the major/minor pairs one step either side. For C, that’s Am, F, Dm, G and Em — the keys a piece in C can visit without packing a suitcase.

The parallel minor is the relative the map treats badly. Same tonic, different signature: C and Cm share a home note, yet the wheel puts Cm three steps away toward the flats. That’s one of the circle’s blind spots, and there’s more on those at the end.

How to use: the signatures have their own outer ring, and the selected one is shown larger beside the wheel. A soft tint marks the neighbours; the stronger mark shows your chosen major and its relative minor. The parallel minor is dashed on the minor ring. At the seam, the card keeps the parallel spelling even when the wheel uses an enharmonic name.

Try it

Choose the C example. Listen to C major, then Am, then Cm. The first pair shares a signature; the second shares a tonic. Which pair sounds more like family to you? (The buttons play tonic triads only — the front door, not the whole house.)

Go deeper

Book: Chapter 1.4, Scaling the Heights — scales and key signatures.

• Survey [5]: Hubert Mossburger, Kriterien der Tonartenverwandtschaft von Heinichen bis Schönberg (2022) — changing models of key relationships.
• Survey [17]: David Temperley, The Line of Fifths (2000) — why note spelling matters.

Scales & modes: an arc with a tonic

Here’s something the circle does that a scale chart can’t: any seven neighbouring wedges give you a complete mode. The wheel shows the notes as an arc of fifths; the staff puts the same notes in step order, the way you’d play them.

Start on C Lydian and slide the arc one wedge toward the flats. F♯ becomes F, 4̂ drops a semitone, and you’re in Ionian — plain major. Keep sliding: Mixolydian, Dorian, Aeolian, Phrygian, Locrian. Each move lowers exactly one note, and each one dims the lights a little. Lydian is the sunniest room in the house; Locrian is the basement.

Take only five neighbouring wedges and you get a pentatonic — the scale under countless guitar solos and folk tunes. C major pentatonic is C–D–E–G–A; C minor pentatonic is C–E♭–F–G–B♭. No semitones, no tritone, nothing to rub. That’s why it’s so hard to play a wrong note with it, and why it gets a bit boring if you never leave.

How to use: choose a tonic and a mode. The solid outline marks the tonic. Play scale goes up to the octave and back; Over tonic adds a held, sampled tonic an octave below. The dashed edge and the note-change reading show which note moved. Notes are spelled for the chosen tonic, double accidentals included. On narrow screens the staff scrolls at its printed size.

Try it

Choose C Lydian and play it over the tonic. Then choose Ionian and listen again. Find F♯ → F on both the wheel and the staff. Then compare C major and C minor pentatonic without changing the tonic.

Go deeper

Book: Chapter 1.4, Scaling the Heights.

Sources: [31] Carey & Clampitt, Aspects of Well-Formed Scales (1989); [75] Wen & Krumhansl, Perception of Pitch and Time… (2019).

Chords in a key: one arc, seven triads

Every major key holds seven chords, and on the wheel they sit side by side in one tidy arc. In C it runs F–C–G–Dm–Am–Em–B°: IV–I–V–ii–vi–iii–vii°. The majors huddle together, the minors follow, and the diminished chord hangs off the end as if it isn’t sure it was invited.

We start with three families: tonic (I, iii, vi), predominant (ii, IV) and dominant (V, vii°). It’s a teaching lens, not a law — a chord’s job is whatever the music makes it do — but it’s a lens that explains an enormous amount of music.

Play vi–ii–V–I and you’re hearing the engine room of a century of songwriting: every root falls by a fifth, straight toward home. Start on I instead — I–vi–ii–V — and you’ve got the opening of “Blue Moon” and the A section of Gershwin’s “I Got Rhythm”.

One thing to untangle: two different tritones live in this picture. The one across the wheel, C opposite F♯, is a measure of distance — F♯ is as far from C major as you can get. The tritone inside C major is F–B, the two ends of the arc. Those two notes are the restless heart of B° and of G7, and they’re a big part of why V wants to go home. (In this view, V is the plain G triad, without the seventh.)

How to use: choose a major key, then a chord on its coloured arc. Its Roman numeral, name, staff and piano controls belong together; the soft colour tints back up the names and numerals rather than replacing them. Listen plays the root-position triad; Arpeggio spreads its notes out. Seven chords plays them in scale-degree order. I–IV–V–I and vi–ii–V–I play short progressions, with the staff and sounding mark following along. Stop returns to your selection. Every chord uses the key’s signature and the pitches the house piano actually plays.

Try it

In C major, choose V and match G–B–D across the name, the staff and the sound. Compare ii (Dm) with IV (F), then play vi–ii–V–I. Now switch to C♯ major and look at vii°: B♯–D♯–F♯. Yes, B♯. It sounds like C, but in C♯ major it’s spelled B♯, and the spelling tells you what job it’s doing.

Go deeper

Book: Chapter 2.2, Harmony. For progressions that actually travel, see the Motion exercise.

[74] Butler, Describing the Perception of Tonality in Music (1989) — the survey’s rare-interval discussion.

Motion: hear the soprano through a circle

This is where the circle stops being a map and becomes a road. Drop a root by a fifth — G to C, D to G — and you get the strongest pull in tonal harmony. Chain those moves together and you have a circle progression. Bass players feel this in their hands before they can name it: down a fifth, down a fifth, down a fifth, with the harmony riding on top. It’s the spine of “Autumn Leaves” and “Fly Me to the Moon”, and it’s why jazz players practise ii–Vs in every key until they can play them in their sleep.

ii–V pairs. Each pair is a complete minor seventh followed by a dominant seventh: in C, Dm7–G7. Then the trick. Instead of landing on C, the implied tonic turns minor and becomes the ii7 of the next key: Cm7–F7, in B♭. Six pairs carry you through C, B♭, A♭, F♯, E and D, then back to Dm7. Set B starts a semitone higher, so between them the two sets visit all twelve key centres. These are linked ii–V pairs, not twelve finished ii–V–I cadences: the I keeps getting promised and postponed, which is half the fun.

Dominant sevenths. Here every chord is V7 of the next: C7–F7–B♭7 and on through all twelve roots. Each arrival is itself a new dominant, so the music never quite lands. It’s the same chain of dominants that drives “Sweet Georgia Brown”.

Listen to the top. The coloured top note is the soprano, the voice your ear naturally follows. Every chord keeps all four tones, connected smoothly from one to the next, so there’s a melody hiding inside the harmony. Follow it all the way round.

Somewhere along the way the spelling has to change. In the circle starting on C, E♭7 becomes D♯7 just before G♯m7 — same keys on the piano, new name, so the next connection reads cleanly. A small circled equals sign on the wheel marks the spot, and both names appear beside the matching marker below the wheel.

How to use: choose ii–V pairs or dominant sevenths above the wheel. ii–V pairs has two six-key sets (their keys are listed on the Set A and Set B buttons); switching sets transposes your pair, and switching back restores its original key and spelling. Click a chord on the wheel; for ii–V pairs, either member selects the whole pair, and both chords share the local key and Roman numerals shown beside the notation. Hear this pair (or Hear this chord) plays your selection. Play circle from this pair (or chord) starts there, goes all the way round, then repeats your starting choice; Stop brings you back to it. Both exercises move counter-clockwise on the wheel. During playback the sounding chord fills more strongly, its notes and labels light up on the staff, and one arrow shows the current root move (the first chord has none). ii7 and V7 share one continuous staff and clef. Each chord releases before the next one sounds, so no leftover notes blur the change, and accidentals and inversions match the piano.

Try it

In Set A, choose Cm7 on the wheel. See and hear the whole Cm7–F7 pair in B♭. Then Play circle from this pair: it starts with Cm7–F7 and comes back to it. Watch the wheel and staff as you go, then choose Set B. At the join, compare the two spellings while you hear the same chord.

Go deeper

Book: Chapter 2.2, Harmony. Sources: Open Music Theory — ii–V–I; Music Theory for the 21st-Century Classroom — circle progression.

Hidden cycles: equal divisions

Walk around the wheel in equal strides and it shows you some shapes it’s been hiding. Every second position gives a hexagon: the whole-tone scale, C–D–E–F♯–G♯–A♯. Every third position (counter-clockwise) gives a square: the diminished seventh, C–E♭–G♭–B𝄫. Every fourth position gives a triangle: the augmented triad, C–E–G♯. And six positions takes you straight across to the tritone, C–F♯, drawn as a single diameter.

Here’s the neat part: the numbers line up. Two, three, four or six steps around the wheel become sounds spaced two, three, four or six semitones apart. (The square goes counter-clockwise so that it spells rising minor thirds; the tritone’s clockwise spelling is an augmented fourth.)

Each of these shapes cuts the octave into equal slices, and that’s exactly why they feel unmoored. With no step bigger or smaller than any other, there’s no natural home: any member could be the tonic, so none of them is. The diminished seventh is the classic double agent — respell its four notes and it can act as the leading-tone seventh in four different keys, which is why silent-film pianists so often reached for it in moments of suspense.

How to use: choose a pattern, then a starting note. The solid outline keeps the start visible. Hear together plays all the members at once; Around the cycle plays them rising and returns to the start an octave higher. The wheel and staff follow each sound, and keyboard focus stays where you put it. The staff has no key signature: accidentals sit beside each note. Wheel choices use the ordinary starting-note spellings from the menu; re-selecting C♭ or C♯ keeps that spelling, and the accessible wheel label names both the member and the starting choice. Stop clears the sounding marks but keeps your choice. Enlarge and Download keep the chosen pattern.

Try it

Choose C diminished and predict what will happen to the square if you start on D. Change the start, then listen. The square and its minor-third spacing stay; the notes change. Compare that sound with the augmented triangle. Then try one collection on your own instrument, or sing it, before going back to the piano buttons.

Go deeper

Book: Chapter 4.6, Equal Division of the Octave.

Tuning

Here’s the circle’s dirty little secret: it doesn’t actually close. Stack twelve perfectly pure fifths and you overshoot your starting note by a sliver — about 23.5 cents, a little under a quarter of a semitone. That sliver is the Pythagorean comma, and musicians have been arguing about where to hide it for well over two thousand years.

Equal temperament hides it by shaving every fifth a hair narrow. The circle closes, and every key sounds equally good — and equally, very slightly, out. Quarter-comma meantone strikes a different bargain. It narrows the fifths further, so that four of them (minus two octaves) land on a pure major third: the sweet thirds that Renaissance and early Baroque keyboards loved. The price is that its chain of twelve fifths falls short of the start. Squeeze that onto a real twelve-note keyboard and one fifth has to absorb the whole difference, and it comes out so sour it has a name: the wolf.

All the labels measure in cents. A cent is one hundredth of an equal-tempered semitone.

How to use: choose equal temperament, pure fifths or quarter-comma meantone. Each wheel note shows its actual frequency in Hz and its distance in cents from the equal-tempered position. On a phone, pan the wheel to read every label; playback scrolls the sounding label into view. The sound here is synthesized on purpose — a fundamental plus its second and third harmonics — so you hear the tuning differences without piano samples being stretched. Nothing sounds until you press a playback button, and Stop or any change of choice ends it.

Try it

Start on C. Hear the pure fifth, then switch to equal temperament and hear it again. Then compare the return gap: the start, the note after twelve fifths, then both together. Listen for the slow wobble, or beating, when they sound at once — that’s the comma made audible. Play the whole chain and predict where it will end; afterwards it repeats the start and the twelve-step return, separately and together, so you can compare. Then do it all again in meantone.

Go deeper

Book: Chapter 4.6, Equal Division of the Octave, for the equal-division comparison. Scholtz (1998), Algorithms for Mapping Diatonic Keyboard Tunings and Temperaments, especially sections 3, 4 and 6; Huygens–Fokker, Logarithmic Interval Measures. The numbers describe the model; your ears get the final say.

Modernist: the same geometry, different musical arguments

Twentieth-century musicians looked at the same wheel and drew very different conclusions from it. The geometry stays put; the musical argument changes.

Bartók · Lendvai’s axes. Ernő Lendvai heard Bartók’s music as organized by axes: four roots a minor third apart, sharing one function. In the C model the tonic axis is C, E♭, F♯ and A — the diminished-seventh square from Hidden cycles, wearing a new hat. The subdominant and dominant axes work the same way, each made of two opposite pairs. Lendvai’s reading is brilliant and contested in about equal measure; treat it as one listener’s map, not a rule.

Petrushka pair. Stravinsky’s famous “Petrushka chord” stacks C major on F♯ major: two triads from opposite poles of the circle, as far apart as keys can be. Hear them separately, then together. Is it two keys at once, or one very spicy chord? Your ears get a vote. Then choose Two major triads and try other pairings.

Debussy · whole tone. Debussy’s Voiles floats on the whole-tone hexagon from Hidden cycles: no semitones, no leading tone, no gravity. Well, mostly — the middle of the piece swaps it for a pentatonic.

“Giant Steps” centres. Coltrane split the octave into three equal parts — B, G and E♭, a triangle of major thirds — and approached each one through its own V7. The result is one of the most feared chord charts in jazz. The model plays each V7–Imaj7 arrival and then returns to the first; Hear centres strips the dominants away so you can hear the bare triangle.

How to use: choose one comparison and transpose it on the wheel. The staff keeps each musical unit together; at phone width, scroll to read it. In the axis view, select an axis to move the marked diameters; T, S and D label tonic, subdominant and dominant, so colour is never the only cue. Compare the major triads or hear only the roots. In “Giant Steps”, use the B example; the dashed spokes point from each dominant root to its key centre. While a roots-only or centres-only comparison plays, its notes replace the full model on the staff; Stop, or letting it finish, restores the model. Enlarge and Download keep the example.

Try it

Hear the Petrushka triads separately before combining them. Then choose Two major triads and change the second root — predict the result before you listen. Compare the triangle of major-third centres with the whole-tone hexagon. In the axis view, switch between tonic, subdominant and dominant and follow the two marked diameters.

Go deeper

Book: Chapter 4.6, Equal Division of the Octave. Sources: Bodamer (2011), Lendvai’s axis system; LA Phil — Petrushka; Debussy — Voiles, 1910 score; Pellegrin (2020), Giant Steps.

History

The circle wasn’t handed down on a stone tablet. It grew over the better part of a century, as theorists tried to explain how keys relate to one another, and each version had a slightly different job to do.

1650 · Kircher. Musurgia universalis, a landmark of musical science and a useful starting post — though nobody is claiming Kircher invented the circle.

Late 1670s · Diletsky. An early circle, in his treatise on composition. (The NYPL source reproduces a 1679 manuscript copy, in a publication issued in 1979.)

Heinichen · 1711 / 1728. One timeline entry covers both editions. The 1711 treatise still leans partly on older modal notation; by 1728 Heinichen explains relative keys through the scale notes they share.

1737 · Kellner. His second edition is part of how we arrived at the layout you know: majors outside, relative minors inside.

How to use: choose a date to compare how the diagram’s arrangement and purpose developed. This view makes no sound and quotes no historical musical passage.

Try it

Compare Heinichen and Kellner. Find C and Am in each, then choose another reference key. The pair stays related while its place on the page moves.

Go deeper

Primary material is linked on every timeline card: ETH Library’s Kircher edition, NYPL’s Diletsky facsimile, the Bavarian State Library’s Heinichen editions, and the Kellner second edition on IMSLP. For the separate question of tuning, see Chapter 4.6, Equal Division of the Octave.

What the circle doesn’t show

Every map leaves things out, and the circle is no exception. It measures one kind of closeness: shared notes. By that measure C major and Cm are three steps apart — yet any songwriter who has borrowed a chord from the parallel minor knows they’re next-door neighbours.

The circle also folds enharmonic spellings together. F♯ and G♭ share a wedge, even though in real music those two names can do quite different jobs.

And it’s a still picture. It shows where chords and notes live, not which way the music is moving. The Keys view shows key relationships; the Scales view shows which notes belong; neither shows the direction of a progression. For that, go back to Motion.

Further reading: [5] and [17] above.