Circle of Fifths

The circle of fifths is a map of all twelve keys arranged so that each adjacent pair is a perfect fifth apart. It's a reference tool, not a theory concept to memorize — once you know how to read it, it tells you key signatures, relative minors, and which keys are closely related (meaning they share most of the same notes).

The Circle

              C (0 sharps/flats)
         F               G
      (1♭)               (1#)
    B♭                       D
  (2♭)                       (2#)
    E♭                       A
      (3♭)               (3#)
         A♭           E
              D♭/C# (5-7 sharps/flats)
                   G♭/F#

Moving clockwise adds one sharp. Moving counter-clockwise adds one flat. The key at the bottom (around D♭/G♭) can be spelled with either sharps or flats — enharmonic equivalents.

Key Signatures — Sharps

G Major: F#
D Major: F#, C#
A Major: F#, C#, G#
E Major: F#, C#, G#, D#
B Major: F#, C#, G#, D#, A#
F# Major: F#, C#, G#, D#, A#, E#
C# Major: F#, C#, G#, D#, A#, E#, B#

Key Signatures — Flats

F Major: B♭
B♭ Major: B♭, E♭
E♭ Major: B♭, E♭, A♭
A♭ Major: B♭, E♭, A♭, D♭
D♭ Major: B♭, E♭, A♭, D♭, G♭
G♭ Major: B♭, E♭, A♭, D♭, G♭, C♭
C♭ Major: B♭, E♭, A♭, D♭, G♭, C♭, F♭

Relative Minor Keys

Every major key has a relative minor that shares its key signature. The relative minor starts a minor third (three semitones) below the major root — or equivalently, on the sixth degree of the major scale:

C Major ↔ A Minor
G Major ↔ E Minor
D Major ↔ B Minor
A Major ↔ F# Minor
E Major ↔ C# Minor
F Major ↔ D Minor
B♭ Major ↔ G Minor
E♭ Major ↔ C Minor
A♭ Major ↔ F Minor

What It's Good For

Closely related keys share most of the same notes and chords — modulating between them sounds smooth and natural. Keys that are adjacent on the circle (one accidental apart) are closely related. Keys on opposite sides of the circle (six apart, like C and F#) have nothing in common — a modulation there is jarring and dramatic.

The ii-V-I progression moves around the circle by fifths — that's why it's everywhere in jazz, and why it sounds like it's going somewhere. Every time you play a ii-V-I in C (Dm7 - G7 - Cmaj7), you're moving counter-clockwise three steps and landing on the destination key.

For chord substitutions, the tritone substitution swaps a dominant seventh chord for the one on the opposite side of the circle — same third and seventh, different root. G7 and D♭7 are tritone subs of each other.