How it is built
Arrange the twelve major keys a perfect fifth apart: C – G – D – A – E – B – F# (= Gb) – Db – Ab – Eb – Bb – F – C. Moving clockwise adds one sharp per step, counterclockwise one flat.
- Order of sharps: F# C# G# D# A# E# B#.
- Order of flats: Bb Eb Ab Db Gb Cb Fb (the same in reverse).
Each major key has its relative minor three semitones below: C/Am, G/Em, D/Bm, F/Dm, Bb/Gm…
Closely related keys
The keys closest to C major are those that differ by one accidental and their relatives: G, F, Am, Em, Dm. They correspond to the diatonic major and minor chords of C (V, IV, vi, iii, ii): for this reason modulations toward them sound natural and those toward Ab or E sound “distant.”
The circle as harmonic motion
Root motion by descending fifth (counterclockwise) is the strongest in the key. In C:
- Em7 – Am7 – Dm7 – G7 – Cmaj7 (iii vi ii V I)
In A minor the complete diatonic sequence: Am – Dm – G – C – F – Bm7b5 – E7 – Am (i iv VII III VI iiø V i). Note the F → Bm7b5 step: to stay in the scale the fifth F–B becomes an augmented fourth.
Practical uses
- Instantly finding the chords of a key and its secondary dominants (the dominant of each chord is its clockwise neighbor).
- Planning modulations: one step = gentle modulation; jumps of three or more steps = a sharp change of color.
- Understanding the ii–V–I: they are three consecutive steps of the circle.
Real example
“Fly Me to the Moon” (Bart Howard, made famous by Sinatra in 1964), in the fake-book version in A minor/C major: Am7 Dm7 G7 Cmaj7 Fmaj7 Bm7b5 E7 Am. It is the circle of fifths traveled almost in full.