The circle of fifths

Arrange the twelve major keys going up fifth by fifth: C, G, D, A, E, B, F♯… At each step one more sharp joins the key signature. The other way, going down by fifths (or up by fourths): C, F, B♭, E♭… one more flat at each step. Laid out in a circle like the hours on a clock, they form the circle of fifths, the road map of tonality.

Click the keys to see their signatures. The inner circle shows the relative minor keys (same signature).

Why fifths?

Remember the major scale's two tetrachords: C-D-E-F + G-A-B-C. The upper tetrachord of C major becomes the lower tetrachord of G major; you just add D-E-F♯-G. Each new scale a fifth higher reuses half of the previous one and raises a single note: the new leading tone.

At the bottom of the circle: enharmonics

At the bottom the two paths meet: F♯ major (6 sharps) and G♭ major (6 flats) are the same key on the piano, spelled two ways. Likewise B/C♭ (5♯ / 7♭) and C♯/D♭ (7♯ / 5♭). Enharmonic equivalence "closes" the circle.

What is it for?

• Memorising key signatures and relative minors.
• Spotting closely related keys: neighbouring keys differ by only one note. Classical composers mostly modulate to the dominant (one step clockwise) or the subdominant (one step anticlockwise).
• Understanding chord progressions: moving down the circle (E → A → D → G → C) gives the most natural progression in tonal music, that of Baroque sequences and jazz standards.
• Organising practice: work through scales in circle order, one accidental at a time.

M:4/4
L:1/4
Q:1/4=80
K:C
"C"[CEG]2 "F"[CFA]2 | "Bdim"[B,DF]2 "Em"[B,EG]2 | "Am"[CEA]2 "Dm"[DFA]2 | "G"[B,DG]2 "C"[CEG]2 |]

Above, every root falls by a fifth (C, F, B, E, A, D, G, C) without leaving the C major scale: the "circle-of-fifths sequence" found in Vivaldi, Bach, Handel… and countless songs.