Circle of fifths

Starting at C major with no sharps or flats and moving up a fifth gives G major with one sharp, then D with two, A with three, and so on. Moving down a fifth instead gives F with one flat, B flat with two, and onward. The two directions meet at the bottom in the enharmonic keys, F sharp major and G flat major are the same pitches spelled differently.

Beyond memorising key signatures, the circle explains harmonic motion. Chord progressions overwhelmingly move by descending fifths, so a piece travelling from D minor to G to C is simply walking the circle. Relative minors sit inside the circle, a minor third below each major key, sharing its signature.