Circle of Fifths

The Circle of Fifths is the twelve major keys arranged in a ring so that each key is a perfect fifth above the one before it. There are twelve notes, so after twelve fifths you are back where you started. That is what closes the ring.

C sits at the top with no sharps or flats. Every step clockwise is a fifth up and adds one sharp; every step counter-clockwise is a fifth down and adds one flat. At the bottom, six o'clock, the two directions meet at F# = Gb.

Listen to the ring as sound: a single note walking up by fifths (and down by fourths so it stays in one octave) visits all twelve notes and lands back on C.

Starting from C and moving clockwise, each new key is a fifth higher and needs exactly one more sharp than the key before it.

Why does this happen? The new key starts on degree 5 of the old one, so it inherits six of the old notes. The only note that has to change is the new key's degree 7, the leading tone, which must be a major seventh above the new tonic, sitting right under it. The old key only offers a minor seventh there. Raising it is the new sharp.

Play the scales in order. Each one sounds like the last with one note nudged up; that nudge is always the last note before the top.

Going the other way from C, each new key is a fifth lower (the same as a fourth higher) and needs exactly one more flat.

This time the new key starts on degree 4 of the old one. Again six notes are inherited; the one that must change is the new key's own degree 4, which has to be a perfect fourth above the new tonic. The old key only offers an augmented fourth there. Lowering it is the new flat.

Six steps clockwise from C is F# major (6 sharps). Six steps counter-clockwise is Gb major (6 flats). They are the same key on the piano: the same seven keys, with two different spellings. This is where the sharp side and the flat side join and the circle closes.

Two names for one sound are called enharmonic. E# is the white key F; Cb is the white key B. The same overlap exists one step further in each direction: C# major (7 sharps) is Db major (5 flats), and Cb major (7 flats) is B major (5 sharps). Musicians normally pick whichever spelling has fewer accidentals, so Db and B win, and only the bottom key is commonly written both ways.

With the join in place, here is the full loop of twelve. Starting from C and going clockwise, you pass through every sharp key, cross over at the bottom, and come home through every flat key:

Sharps never appear in a random mix: they are always added in one fixed order, and each key takes the first *n* of them.

Look at the list: in F# → C# → G# → D#… each sharp is a fifth above the previous one. That is not a coincidence. Each new key is a fifth higher than the last, and its new sharp is its leading tone, so the new sharps also climb by fifths. A key with 3 sharps has F# C# G#; a key with 5 has F# C# G# D# A#.

The best way to hear the order is to play the scale that introduces each sharp. Every button below adds exactly one new sharp to the one before it, and the new sharp is always the seventh note you hear.

Flats also arrive in one fixed order, and it is the order of sharps read backwards.

Each flat is a fourth above the previous one (Bb → Eb → Ab → Db…), exactly mirroring the sharps. A key with 2 flats has Bb Eb; a key with 4 has Bb Eb Ab Db. Notice the first four spell the word BEAD.

Again, hear each flat arrive inside the scale that introduces it. This time the new note is always the fourth note you hear.

You now know which sharps or flats a key has. Here is how to go the other way: look at a key signature on the staff and name the key instantly. There is one rule for sharps and one for flats.

Both rules come straight from sections 2 and 3. The last sharp is the leading tone (7), and 7 always sits directly under 1, a single semitone away. The last flat is degree 4 of the key, and the flat before it, a fifth up from that 4, is the tonic itself.

The rules also run backwards. Want the key signature of E major? Its leading tone is D#, so the sharps run F# C# G# D#, four of them. Want Eb major? It must be the second-to-last flat, so the flats run Bb Eb Ab, three of them.

Two keys that sit next to each other on the circle differ by one accidental, which means they share six of their seven notes. That single shared-note count is the reason the circle predicts what sounds close and what sounds far.

Every step you take around the circle swaps out one more note. Opposite keys, C and F#, keep only two notes in common and sound like different worlds. Play C major, then G major, and isolate the one note that changed; then jump to F# major and hear how little is left.

Every major key has a relative minor that uses exactly the same seven notes and therefore the same key signature. It lives on the inner ring of the circle, directly beneath its major.

Degree 6 is a major sixth above the tonic, which is the same note as a minor third below it. From C, a minor third down is A; from G it is E; from F it is D. Read the table top to bottom and the inner ring turns clockwise with the outer one.

Because the notes are identical, the inner ring is the outer ring rotated: A minor has no accidentals like C major, E minor has one sharp like G major, D minor has one flat like F major. Same neighbours, same distances, same rules. Everything else about minor keys, how they sound, why they feel different with the same notes, and the harmonic and melodic variants, is the next chapter.

The circle is drawn with keys, but you can read it with chord roots too, and then the three main chords of any key turn out to be three adjacent points.

V is one step clockwise from I (a fifth up), IV is one step counter-clockwise (a fifth down). That is why I IV V sounds so cohesive: the three roots are the closest possible neighbours. Pick any key on the circle and its IV and V are the two keys touching it.

The circle also shows the most common way chords move: counter-clockwise, root falling by a fifth. ii-V-I in C is D → G → C, three consecutive counter-clockwise steps. Each root is the 5 of the next chord, so every move is a dominant-style pull toward the next root. Extend it and you get vi-ii-V-I (A → D → G → C), still walking one way around the circle.

Modulation is changing key in the middle of a piece, and the circle tells you in advance how smooth or how startling that change will feel: count the steps between the two keys.

The smoothest tool for a near modulation is the pivot chord: a chord that belongs to both keys. Between C and G there are four: C, Em, G and Am. Take the C major chord: it is I in C but IV in G. Play it, then follow it with D7, the V7 of G, and the ear accepts G as the new home.

Almost every chapter of this course lives somewhere on the circle. Zoom out and you can see the whole subject on one ring.

• Major scales & key signatures: the outer ring and the count of sharps or flats at each point. Outer ring
• Relative minor (next chapter): the inner ring. C → Am
• Chord progressions: I IV V are three neighbours; ii V I is a counter-clockwise walk. I IV Vii V I
• Secondary (applied) dominants: borrowing the V of a neighbouring point for one chord.
• Modal interchange: reaching across to the parallel minor's chords on the far side.
• Modulation: moving your home point around the ring.

So when you are unsure which chord comes next, or which key a song could move to, look one step to either side of where you are. The circle, and the spiral, will almost always have the answer within reach.