AP® Music Theory · Unit 1 · Topic 1.5
The Circle of Fifths
The circle of fifths arranges all twelve keys by stacking perfect fifths, so each clockwise step adds one sharp and each counterclockwise step adds one flat until the two sides meet.
Stack perfect fifths starting on C: C, G, D, A, E, B, F sharp, and so on. Because a perfect fifth is 7 semitones, stacking twelve of them lands you back on the pitch you started from, just spelled differently after a full loop. Arrange those twelve pitches in a circle and you get the circle of fifths, with C major at the top carrying zero sharps or flats.
Moving one step clockwise means moving up a perfect fifth, and each of those moves adds exactly one sharp to the key signature: G major has one sharp, D major has two, A major has three, and so on up to C sharp major with seven. Moving counterclockwise instead moves down a perfect fifth, and each step adds one flat: F major has one flat, B flat major has two, all the way to C flat major with seven. The sharp side and the flat side are built the same way, just in opposite directions, so they are guaranteed to meet.
They meet at the bottom of the circle, where six sharps and six flats describe the same sounding key: F sharp major and G flat major are enharmonic, same pitches, different spelling. Which name you use depends on the music around it, not on which has fewer accidentals. The circle also shows up in harmony: moving clockwise by fifths from a chord's root describes the falling-fifths motion that drives a circle progression, since each root sits a fifth above the next one, like C to F to B flat to E flat.
Key terms
- Circle of fifths
- A circular arrangement of all twelve keys ordered by perfect fifths, showing how many sharps or flats each carries.
- Perfect fifth
- An interval spanning 7 semitones, such as C up to G.
- Enharmonic
- Describes two different note or key names that sound identical, like F sharp and G flat.
- Circle progression
- A chord progression whose roots move by descending fifths, such as C to F to B flat.
Watch it explained
- How it worksHow does moving one step clockwise around the circle of fifths add exactly one sharp?
- How it worksWalk me through where the sharp keys and the flat keys meet at the bottom of the circle.
- Worked exampleFind how many sharps or flats B major, D flat major, and G major each carry using the circle.
- Going furtherWhat happens at the bottom of the circle where F sharp major and G flat major overlap?
- Ties togetherHow does moving clockwise around the circle of fifths predict the falling fifths root motion of a circle progression?
Check yourself
End of topic.