The Circle of Fifths, Drawn After the Journey

The circle of fifths is usually drawn as a clock face with twelve keys around the rim, and the first time most people meet it, it looks like something designed to frighten them. All those sharps and flats arranged in a ring, like a combination lock you have not been given the code to. I would like to take the fear out of it, because underneath the diagram is one of the friendliest ideas in music.

My old teacher Reuben, who taught me most of what I know about harmony, used to say that theory is a map somebody drew after the journey, not before it. The circle of fifths is the clearest example I know. Nobody invented it and then wrote music to fit. People made the music first, for centuries, and the circle is the map that turned out to describe where they had already been.

(I saw Reuben on Thursday, sharp as anything, and he corrected me on a chord voicing from memory, and was right. Forty years on, he is still the one drawing the map for me.)

What the circle actually shows

Put C at the top, where twelve would be. Move one step clockwise and you land on G. Another step, D. Then A, E, and so on around the ring. Each clockwise step moves you up a fifth, and (this is the useful part) each step adds exactly one sharp to the key. The keys nearest each other on the circle are near neighbours: they share almost all their notes. C major and G major differ by a single note. That is why a song can slip from one to the other and feel like stepping into the next room, not the next town.

Near neighbours and the long way round

Keys on opposite sides of the circle are the strangers. C major and F sharp major sit right across the ring from each other and share hardly a note between them. A move between them is the long way round, and the ear hears it as a real journey, sometimes a thrilling one. Near or far is not better or worse. It is just distance, and the circle lets you see the distance before you decide to travel it.

The relative minor, which is barely a step at all

Every major key has a minor key that shares its exact notes, its relative minor. C major and A minor use the same seven notes; only the centre of gravity moves. The move between them is so small the ear barely registers a change of key at all, only a change of light. It is the cheapest key change in music, and one of the loveliest. Have a listen: play a few bars centred on C major, then let those same notes settle around A minor instead. Same family, different weather.

This is the part I find most satisfying, and it reminds me of the cryptic crossword I lose to my wife most mornings. A good clue looks impossible, then resolves, and the instant it does you see it was scrupulously fair all along. A key change works on the ear the same way. It can surprise you and still feel completely right, because the circle was underneath it the whole time, making the surprise a fair one.

A key change can surprise you and still feel right, the way a good crossword clue does: the fairness was there all along.

Using it when a song wants to move

So: a song of yours feels like it wants to lift, or to darken, or to open out, and you suspect a key change. Reach for the circle. Step one place round for a near neighbour, a gentle, almost unnoticed shift; jump further round for something bolder. The chord that carries you there is usually the new key's V, its doorbell. If you would rather hear these neighbours than work them out on paper, the chord builder will give you the chords of any key in a click, so you can sit two neighbouring keys side by side and play the join. (And if you have not yet met the seven chords that live inside a single key, the diatonic family is the thing to read first.)

The circle of fifths is not a law and not a cage. It is a map, drawn after the journey, of which keys are near and which are far. Useful, beautiful, worth keeping in your pocket. Never the road itself.

Play two neighbours, and listen.