Circle of Fifths Explained: Keys, Sharps and Flats

How the circle is built

A perfect fifth is 7 semitones: C up to G, G up to D, D up to A. Start on C and keep stepping up a fifth. Because 7 and 12 have no common factor, you land on a new note every time until all twelve have appeared, and the thirteenth step brings you back to C. Twelve fifths are 84 semitones, exactly 7 octaves.

The third column is 7 × step, minus whole octaves of 12. Draw those twelve notes around a clock face, C at the top, and you have the circle. Going clockwise each note is a fifth above the last; going counterclockwise each is a fifth below, which is the same as a fourth above.

Key signatures around the circle

Each step clockwise from C adds one sharp to the key signature, and each step counterclockwise adds one flat. Sharps are added in a fixed order, F C G D A E B, and flats in the reverse order, B E A D G C F. The order of sharps is itself a chain of fifths, which is why the circle and the key signatures line up.

Two patterns in these tables let you read any key signature at a glance. With sharps, the key is one semitone above the last sharp: the last sharp in D major is C♯, and D is a semitone above it. With flats, the key is the second-to-last flat: B♭ E♭ A♭ is E♭ major. The one flat key without a second-to-last flat is F major, with B♭ alone, which you simply memorize.

At the bottom of the circle the two directions meet. F♯ major with six sharps and G♭ major with six flats use the same pitches in equal temperament, as do B and C♭, and C♯ and D♭. That overlap is what closes the ring.

Relative minors

Every major key shares its key signature with one minor key, its relative minor. The minor tonic is three semitones below the major tonic: C major and A minor have no sharps or flats, G major and E minor one sharp. On most circle diagrams the major keys sit on the outside in capitals and their relative minors on the inside in lowercase. The inner ring is itself a circle of fifths, starting from A.

The two keys use the same seven notes. What differs is the tonic, the note the music treats as home. Built on A, the white keys of a piano give the A minor scale; built on C, the C major scale. Three semitones down from any major tonic always lands on its relative minor: E♭ major gives C minor, A major gives F♯ minor.

The arithmetic of the fifth

A pure perfect fifth has a frequency ratio of 3:2. Play A at 440 Hz and the pure fifth above it, E, is 660 Hz. Equal temperament divides the octave into twelve equal semitones of the twelfth root of 2 each, so a fifth of 7 semitones is 2^7/12.

The tempered fifth is narrower by about 1.96 cents. That small shave is what makes the circle close. Twelve pure fifths multiply to (3/2)¹² = 129.746, while seven octaves are 2⁷ = 128. The pure stack overshoots by a factor of 1.01364, about 23.5 cents. Equal temperament spreads that gap evenly over the twelve fifths, so each one gives up about 1.96 cents and the ring lands exactly on C again. The guide to musical note frequencies lists the tempered frequency of every note. To hear the difference, play 660 Hz and 659.26 Hz one after the other on the tone generator.

Using the circle for chords

In any major key, the three major chords sit side by side on the circle: the key itself, its neighbor counterclockwise and its neighbor clockwise. In C major these are F, C and G, the IV, I and V chords. Their relative minors on the inner ring, D minor, A minor and E minor, are the ii, vi and iii chords. Together those six chords are the major and minor triads built only from the notes of C major.

• Chord families. To find the main chords of a song in E major, find E and read its neighbors: A and B major, plus C♯, F♯ and G♯ minor inside.
• Moving by fifths. The progression ii, V, I in C is D minor, G, C: each root a fifth below the last, which on the circle is one step counterclockwise at a time.
• Closely related keys. Neighboring keys differ by only one sharp or flat, so a modulation to a neighbor changes just one note. A move from C to F♯, on the far side of the circle, adds six sharps at once.

To practice progressions in time, set a slow tempo on the metronome and change chord on beat one of each bar.

Using the circle to transpose

Transposing moves every chord by the same interval. On the circle that means turning the whole song by the same number of steps. Move from C to D, two steps clockwise, and every chord moves two steps clockwise too: C, F, G, A minor becomes D, G, A, B minor. The key signature tells you how many sharps the new key has: D major has two, F♯ and C♯. The guide to transposing chords and using a capo covers the semitone method and capo positions in detail. Before you play the new key, check that your instrument is at pitch with the online tuner.

Frequently asked questions

Sources

• Schmidt-Jones, Understanding Basic Music Theory, 6.7 The Circle of Fifths (up a perfect fifth gives one more sharp or one less flat, down a fifth one more flat; the first sharp is always F sharp, the first flat B flat; major keys in capitals, minor in lowercase; used to find closely related keys)
• Open Music Theory (Wharton and Shaffer, eds.), 1.10 Key Signatures (the mnemonic read forward for sharps and backward for flats; the circle covers keys with up to seven sharps or flats; relative keys share a key signature, A minor is the relative minor of C major)
• The Open University, OpenLearn: An introduction to music theory, 6.5 (the relative minor tonic is three semitones below its major; major keys outside, relative minors inside the circle)
• NRICH (University of Cambridge), Equal Temperament (a pure fifth is 3:2; one equal-tempered semitone is the twelfth root of 2; a fifth of 7 semitones is 2^(7/12) = 1.498307)

Written by Tobias. Updated November 2, 2026.