Related
The circle of fifths is a diagram that arranges the twelve keys by perfect fifths. It deserves its own entry because half of the "just memorise it" conclusions in music theory can be derived from this one picture.
Two sequences on the circle
Start at C and step clockwise by a perfect fifth each time:
C → G → D → A → E → B → F♯ → (D♭) → A♭ → E♭ → B♭ → F → C
Two things hold at once:
| Direction | Each step | Result |
|---|---|---|
| clockwise | add a sharp (or remove a flat) | sharps appear in the order F C G D A E B |
| counter-clockwise | add a flat (or remove a sharp) | flats appear in the order B E A D G C F — exactly the reverse |
So the question "why is the order of sharps F–C–G–D–A–E–B?" is answered on the circle: that is the order you get by walking clockwise.
What it explains
| Question | Answer on the circle |
|---|---|
| how many sharps or flats? | count the steps from C to that key |
| which keys are close? | neighbouring keys, one signature apart — the smoothest modulations (see [[concept:modulation |
| where are tonic, dominant and subdominant? | one step either side of the tonic: clockwise is the dominant, counter-clockwise the subdominant (see [[concept:harmonic-function |
| what is F♯ to G♭? | two spellings of one position (see [[concept:enharmonic |
The second and third rows are especially useful: functional relations are literally neighbour relations on the circle — which explains why I–IV–V–I sounds so natural, and why the dominant pushes hardest back to the tonic.
Why fifths, and not thirds or fourths
Because the perfect fifth's ratio is 3:2 — the only non-octave member among the simplest ratios (see perfect intervals). Stack fifths twelve times and you arrive almost back where you started (the small discrepancy is the comma), so the chain closes into a circle. Stacking thirds or fourths does not do this.
Diagram: function lives among neighbours
Listen: click around the circle
Below is a clickable circle — click any segment to hear that key's tonic triad, with the key name and signature shown in the middle. Try C first, then the neighbouring G, then the opposite F♯/G♭, and compare how the three distances feel.
Common misconceptions
- "The circle is for memorising key signatures." That is its shallowest use. It also explains close relations, functional positions and enharmonic equivalence.
- "Clockwise always means adding a sharp." Strictly, clockwise means adding a sharp or removing a flat. After six sharps you enter the flat region.
- "Neighbouring keys sound alike." They make modulations smooth, because they share notes — which is not the same as sounding like one key.
- "F♯ major and G♭ major are two keys." Identical pitches, enharmonic keys, differing only in notation and habit (see enharmonic).
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Listen in the library
All tracks from midicn-lib — inline badge is the license tier (C1 commercial / C2 non-commercial / C3 study only).
Sources
- 五度圈按纯五度依次排列十二个调，升号与降号顺序由此得出，属乐理通则
- 近关系调（相差一个调号）与等音调在圈上的位置关系，为通行表述
Used for fact-checking only; all prose is original.