The Circle of Fifths Explained at the Piano: Key Signatures, Relative Minors and the Chords That Fit

Put your right thumb on middle C and your little finger on the G above it, counting every letter name on the way: C, D, E, F, G. Five letter names, seven half steps. That interval is a perfect fifth, and it is the only building block the circle of fifths needs. Stack fifths one on top of another and you meet all twelve major keys, each one sharp or one flat away from its neighbors.

If the circle has been a poster on your wall that you never quite used, this lesson builds it from scratch at the keyboard and puts it to work: reading key signatures in seconds, finding relative minors, choosing chords that belong together and hearing why music so often travels to a next-door key.

Build the circle from one interval

Start on C and climb a fifth: G. Climb again and you reach D, then A, E and B. Each landing note is the home note of a new major key, and each key needs one more sharp than the last. G major has one sharp, F♯; D major has two, F♯ and C♯; A major has three. Past B come F♯ major, with six sharps, and C♯ major, with seven.

Now go the other way, down a fifth at a time from C: F, B♭, E♭, A♭, D♭, G♭ and C♭. Each step adds a flat. Bend both lines into a ring with C at 12 o'clock, sharp keys running clockwise and flat keys counterclockwise, and they meet at the bottom, where F♯ major and G♭ major turn out to use exactly the same piano keys. That ring is the circle of fifths, and our Circle of Fifths handout lays it out like a clock.

The circle of fifths. Outer ring: the twelve major keys, a fifth apart going clockwise. Middle ring: how many sharps or flats each key signature has. Inner ring: the relative minor that shares that signature. At the bottom, three positions have two names.

Clockwise is a fifth up: each step adds one sharp or takes away one flat. Counterclockwise is a fifth down, the same letter as a fourth up: each step adds one flat or takes away one sharp. Either way, next-door keys share six of their seven notes.

You can walk the whole circle on one piano. Start on the lowest C, the fourth key from the left, and play a fifth higher each time. Twelve fifths later you land on the very top C, seven octaves up, having touched each of the twelve notes once. The circle closes so neatly because pianos are tuned in equal temperament, with all twelve half steps exactly the same size. With acoustically pure fifths, twelve of them overshoot seven octaves by roughly a quarter of a half step, a gap called the Pythagorean comma (Circle of fifths).

Twelve fifths from C1 to C8 on an 88-key piano. The bold names are the notes you count up to; the gray names are the same keys as the circle spells them. The twelfth fifth is B♯, the key we call C.

Why fifths: one note changes at a time

The fifth note of a major scale is its dominant, second in importance only to the tonic, the home note (Tonic & dominant). So the key one step clockwise is the key of the dominant. Play the major scale recipe (whole, whole, half, whole, whole, whole, half) starting on G instead of C, and it forces you onto exactly one black key, F♯. Every other note is the same as in C major.

Look at where that new sharp lands. F♯ is the 7th degree of G major, its leading tone: the note a half step below home that pulls up into it (Scale Degree Names gives every degree its title). The same thing happens at each step clockwise. D major adds C♯, a half step below D; A major adds G♯, a half step below A.

The flat side mirrors this. Start the recipe on F and the only change from C major is B♭, the 4th degree of F major. Each step counterclockwise adds a flat on the new key's 4th degree: B♭ major adds E♭, and E♭ major adds A♭.

One step each way from C. G major changes F to F♯, its 7th degree; F major changes B to B♭, its 4th degree. The changed note is the only sharp or flat in its scale, and the numbers under the notes are scale degrees.

Read any key signature in two seconds

A key signature gathers a key's sharps or flats at the start of every line, so they don't have to be written on each note. Because each step away from C adds one more, they always enter in the same order. Sharps arrive as F, C, G, D, A, E, B, each a fifth above the last by letter, and the sentence "Father Charles Goes Down And Ends Battle" helps you remember them. Flats arrive in the reverse order, B, E, A, D, G, C, F (Key signatures). So a key with three sharps always has F♯, C♯ and G♯, and a key with four flats always has B♭, E♭, A♭ and D♭.

The seven sharps in signature order, written as notes in both clefs at their places in the signature. Under each: its name and the major key whose signature ends with it. Right of the double bar, all seven as the key signature of C♯ major.

On the staff, the signature zigzags up and down to stay compact, and in the bass clef the same pattern sits one line lower. The flats work the same way with the letters backward.

The seven flats in signature order, both clefs. Under each flat: its name and the major key whose signature ends with it; from the second flat on, that key is the flat just before. Right of the double bar, all seven as the key signature of C♭ major.

Two tricks follow straight from the last section, plus two keys to memorize:

• Sharps: the last sharp is the new key's leading tone, so the key is a half step above it. Three sharps end on G♯: A major.
• Flats: the last flat is the new key's 4th degree. Count down a fourth from it and you land on the flat before it, which names the key. Four flats end with A♭ and D♭: A♭ major.
• To memorize: one flat is F major, and no sharps or flats is C major.

Four rules cover every major key signature. Each signature also belongs to a minor key, which comes next.

The Key Signatures chart prints all fifteen signatures in both clefs, each with the minor key it also serves.

Relative minors: the inner ring

Every key signature serves two keys, a major key and its relative minor. The relative minor starts on the 6th degree of the major scale, three half steps below the major's home note: from C, count down B, B♭, A. C major and A minor both have no sharps or flats, G major and E minor share one sharp, and F major and D minor share one flat (Relative key). On the circle, each relative minor sits on the inner ring, right inside its major.

As you count the three half steps, count two letter names down as well, so the spelling comes out right: from E, the letters run E, D, C, which gives C♯ minor, not D♭ minor.

A minor uses the same seven notes as C major, but music in A minor often raises its 7th degree, G, to G♯, which gives it a leading tone that pulls into A. That G♯ is written as an accidental and the signature stays empty, so a piece with no sharps or flats that keeps showing G♯ is probably in A minor. The three minors shows the natural, harmonic and melodic forms, and Identify the minor scales gives you nine minor scales to name by form and key.

C major and A minor share a key signature. The natural minor uses exactly C major's notes; the harmonic minor raises G to G♯. Each scale begins and ends on its home note.

Don't confuse the relative minor with the parallel minor, which keeps the same home note. C minor is C major with its 3rd, 6th and 7th lowered, and its signature has three flats (Major & minor lets you hear the change). On the circle, a parallel minor always borrows the signature of the major key three steps counterclockwise: C minor uses E♭ major's three flats, and G minor uses B♭ major's two. Parallel vs Relative Minor sets C major, A minor and C minor side by side.

The bottom of the circle: one key, two names

Three pairs of keys at the bottom of the circle are played on exactly the same piano keys: B major (five sharps) and C♭ major (seven flats), F♯ major and G♭ major (six each), and D♭ major (five flats) and C♯ major (seven sharps). Pairs like these are enharmonic, the same sound written two ways (Enharmonic equivalence). Add the two numbers in any pair and you get 12, one for each step around the clock. It is the same idea as the black keys, each of which has a sharp name and a flat name.

The spellings follow one rule: a major scale uses each letter name once. So F♯ major calls the white key F "E♯", and G♭ major calls the white key B "C♭". Composers usually choose the spelling with fewer accidentals, B major rather than C♭ major and D♭ major rather than C♯ major (Key signature), while F♯ and G♭ tie at six. One more step would break the system: G♯ major would need eight sharps, including an F double sharp, so it is almost always written as A♭ major. Double sharps and double flats explains why the letters have to climb.

F♯ major and G♭ major: different letters, the same seven keys. E♯ and C♭ are the white keys F and B under a sharp or flat name.

On a modern piano, D♯ and E♭ are one key. Older tunings such as meantone made the two slightly different pitches, and some keyboards gave them separate keys by splitting the black keys in two (Split sharp).

The keyboard of the cembalo universale at the Organeum in Weener, Germany, built by Keith Hill in 1983 after a description by Michael Praetorius. Each black key is split in two, and extra keys sit between E and F and between B and C: 19 keys to the octave. Photo: Wikiwal, public domain, via Wikimedia Commons.

Where the circle came from

The oldest known circle of fifths was drawn in Russia. The composer and theorist Nikolai Diletsky (also spelled Mykola Dyletsky) included one in his Grammatika, a composition manual from the late 1670s that survives in versions from Smolensk (1677) and Moscow (1679 and 1681) (Mykola Dyletsky). In Germany, Johann David Heinichen drew his own "Musicalischer Circul" in 1711 and printed it again in his 1728 thoroughbass treatise, Der General-Bass in der Composition.

Two early circles of fifths. Left: Diletsky's, a five-line staff bent into a ring, in the 1679 Moscow version of his Grammatika (Russian State Library). Right: Heinichen's "Musicalischer Circul" from Der General-Bass in der Composition (Dresden, 1728). Images: public domain, via Wikimedia Commons.

Heinichen's ring runs through all 24 keys, each major key (dur) followed by its relative minor (moll): C dur, A moll, G dur, E moll and on around. Play the first six as chords, C, Am, G, Em, D, Bm, and you hear the pattern. Two reading tips: German calls B♭ "B" and B♮ "H", and Heinichen writes "Dis dur", D♯ major, for the key we call E♭ major. Because his minors sit between the majors, his neighbors are not a fifth apart. In the 1730s David Kellner put the majors on an outer ring and their relative minors on an inner one, the earliest surviving example of the layout in this article's diagram (David Kellner).

The chords the circle predicts

The circle is also a map of harmony. A key's three primary chords, I, IV and V, are built on its home note and the two notes beside it on the circle. In C major, C sits between F (IV, one step counterclockwise) and G (V, one step clockwise). In G major the trio is C, G and D; in F major it is B♭, F and C.

The primary chords of C, G and F major, each labeled I, IV or V. In each key, IV and V are built on the two neighbors of I on the circle.

All seven chords of a key are neighbors too. Build a triad on every note of C major, as The chords of a key does, and you get C, Dm, Em, F, G, Am and B°. Their roots, F, C, G, D, A, E and B, are seven positions in a row on the circle. Read the row from F: three major chords (F, C, G), then three minor chords (Dm, Am, Em), then the diminished B°. Name the chords of the key drills these chords in C, G, F and D major.

The seven chords of C major at their roots' places on the circle, colored by scale degree. The ii–V–I path, Dm to G to C, runs counterclockwise.

Chord progressions often move between chords whose roots are a fifth apart (Circle of fifths). The ii–V–I, a staple of jazz and popular music, does it twice, counterclockwise: Dm7, G7, Cmaj7 in C (ii–V–I progression). Put the vi chord, Am, in front and you take one more step: Am, Dm, G, C. The loops on Chords & Progressions in Every Key use I, IV, V7 and vi, all from the same patch of the circle.

Play the ii–V–I with the roots in your left hand and, in your right, the 3rd and 7th of each chord plus one note on top, as on our ii–V–I in Every Key sheet. Each chord's 7th slips down a half step to become the next chord's 3rd, while its 3rd holds and becomes the next 7th.

ii–V–I in C: left-hand roots D, G and C; right-hand 3rds and 7ths plus one note on top. C slips down to B, then F slips down to E.

To make a chord other than I sound like a brief home, borrow its own dominant, one step further clockwise. In C major, the chord on D is D minor. Raise its F to F♯ and add a C, and you get D7, the dominant 7th of G. Play C, D7, G, C: the F♯ rises a half step into G, and for a moment G sounds like home. Musicians call this D7 "V7 of V", a secondary dominant, and it is the one you will meet most often (Secondary chord).

I, V7/V, V, I in C. D7's F♯, the one note outside C major, rises to G, while its 7th, C, falls to B.

Modulation: a trip to the next-door key

When a piece changes key partway through, it usually goes to a closely related key, one whose signature differs from the home key's by no more than one sharp or flat (Closely related key). On the circle those are the two neighbors plus the relative minors of all three keys: from C major, G major, F major, A minor, E minor and D minor. A favorite trip from a major key is up to the dominant, one step clockwise, and Modulation shows how the new key's leading tone gives it away.

Christian Petzold's Minuet in G major, from the 1725 Notebook for Anna Magdalena Bach and long credited to J. S. Bach (Minuets in G major and G minor), makes exactly that trip in its second half. The clue is D major's leading tone, C♯: it appears in bar 20 and returns in each of the next three bars, and bar 24 comes to rest on D. Then the left hand plays a C♮, which turns D into D7, the dominant 7th of G, and the music heads home. Play bars 17–24 slowly and listen for the moment D starts to sound like home.

Petzold, Minuet in G major, bars 17–24. C♯, the leading tone of D major, appears in bars 20–23. The natural sign on the last C of bar 24 cancels it on the way back to G.

Practice: ten minutes a day around the circle

Ten minutes a day is plenty if you do four things in order, moving one step around the circle each day.

The daily routine. After twelve keys you are back at C.

1. Draw the circle from memory. Put C at the top, count five letter names up for each new key, then add the flat keys counterclockwise. Check yourself with Fill in the circle of fifths, which also asks for the relative minors, each key's neighbors and the keys with two names.
2. Name three key signatures. Begin with the quiz below, then work through Name the Key Signatures and write them yourself with Write the key signatures.
3. Play today's scale. Take one major key a day in circle order: C, G, D, A, E, B, then G♭, D♭, A♭, E♭, B♭ and F. Each step changes just one key on the piano. Scales in Every Key has all twelve on one chart in this order, with fingering for both hands.
4. Play its three main chords. Loop I–IV–V–I in the day's key with The Primary Chords in Every Key, then add the ii–V–I from The ii–V–I in Every Key.

Name the major key and its relative minor. Answers at the end of this section.

When the routine feels easy, move a short tune one step around the circle. Transposition shows two ways to work out the new notes, and Transpose the melody gives you a tune to move from C major to its two neighbors, G major and F major.

Quiz answers: 1. A major, F♯ minor. 2. A♭ major, F minor. 3. F♯ major, D♯ minor. 4. D♭ major, B♭ minor.

Free worksheets for this lesson

• The Circle of Fifths — the twelve major keys as a clock, with the order of sharps.
• Fill in the circle of fifths — build the clock yourself, with relative minors and neighbors.
• Key Signatures: Major & Minor — all fifteen signatures in both clefs.
• Name the Key Signatures — eight signatures to name, with answers.
• Write the key signatures — twelve keys to write out.
• The sharp: one half step up — the sharp name of every black key.
• The flat: one half step down — the flat name of every black key.
• Double sharps and double flats — why a scale's letters must climb.
• The major scale — the step recipe behind every key signature.
• Scales in Every Key — all 24 scales with fingering, plus charts of all twelve majors and minors.
• Tonic & dominant — home and away, a fifth apart, with audio.
• Scale Degree Names — tonic to leading tone.
• Major & minor — one home note, two moods, with audio.
• Parallel vs Relative Minor — C major, A minor and C minor side by side.
• The three minors — natural, harmonic and melodic, with audio.
• Identify the minor scales — nine scales to name.
• The chords of a key — the seven chords in four keys, with audio.
• Name the chords of the key — numerals and chord names to fill in.
• The Primary Chords in Every Key — I, IV and V in all 24 keys, with audio.
• Chords & Progressions in Every Key — four chords, three loops, with audio.
• The ii–V–I in Every Key — the progression with its guide tones, with audio.
• Secondary dominants — V7 of V and its relatives, with audio.
• Modulation — leading tones, pivot chords and close keys, with audio.
• Transposition — two ways to move a tune to a new key.
• Transpose the melody — a tune to move from C to G and F.

Keep the circle in your hands

Once you can draw the circle in a minute, C at the top, sharps clockwise, flats counterclockwise and relative minors inside, it tells you four things about any key before you play a note: its signature, its relative minor, its main chords and where its music is likely to travel. If you want a second pair of ears, a Tissimo piano teacher can check your key-signature reading, scales and chord voicings in a live lesson and help you choose the next key to learn.

Sources

• Circle of fifths — Wikipedia
• Key signature — Wikipedia
• Key signatures — Open Music Theory
• Relative key — Wikipedia
• Enharmonic equivalence — Wikipedia
• Split sharp — Wikipedia
• Mykola Pavlovych Dyletsky — Wikipedia
• David Kellner — Wikipedia
• ii–V–I progression — Wikipedia
• Secondary chord — Wikipedia
• Closely related key — Wikipedia
• Minuets in G major and G minor — Wikipedia