The circle of fifths, explained without hand-waving

The circle of fifths is a map of key signatures arranged so that each clockwise step moves up a perfect fifth. Starting at C major with zero sharps and zero flats, one step clockwise gives G major (one sharp). Another step gives D major (two sharps). Another gives A major (three sharps). The rule is simple: clockwise adds a sharp, counter-clockwise adds a flat.

What “fifth” means here

A perfect fifth is the interval between two notes that are seven semitones apart. C to G is a perfect fifth. G to D is a perfect fifth. D to A is a perfect fifth. Stack twelve perfect fifths and you land back on C, seven octaves higher; the circle closes because equal-tempered tuning defines it that way.

How to read the circle

Major keys sit on the outer ring, relative minors on the inner ring. The relative minor of any major key sits three semitones below its tonic; A minor is the relative minor of C major, E minor of G major, B minor of D major.

Practise with the tool

Open the interactive circle of fifths to hear each scale and each I-IV-V-vi progression in every key.