The circle of fifths

Seven semitones up. Play the hops in order and watch the keys light: each one starts where the last landed, and every hop covers the same distance.

Every hop up a fifth costs exactly one new sharp. And the sharps arrive in a fixed order (F♯ first, then C♯, then G♯…). That's why "which key am I in?" and "how many sharps?" are the same question.

Hop down a fifth from C and the mirror image happens: F major needs one flat (B♭), B♭ major needs two. Sharps sit clockwise around the circle, flats counter-clockwise, and they meet at the bottom.

A major scale writes each of the seven letters exactly once. That rule picks a black key's name: F♯ in G major because G is taken, B♭ in F major because A is taken.

Now string the hops together. Twelve fifths visit every key once, then land back on C: up the sharp side, down the flat side. The run is folded into one octave so it stays on the keyboard; the key names still trace the circle.

The chromatic scale closed the twelve notes into one circle. This is the other way to arrange them. Neighbors here share almost all their notes, which is why they sound like family. Tap any key on the wheel to see what it costs in sharps or flats, then play its ladder through on the keyboard.