The circle of fifths, explained by ear

This is the most looked-up diagram in music, and most explanations of it describe the picture rather than the thing the picture is of. The thing is simple: keep going up by a fifth and you eventually get back to where you started, having passed through every key on the way.

Loading the instrument… Touch the outer ring for a major chord, the inner one for its relative minor. The small print under each name is its key signature. Sound could not load. Try again

That is the diagram. Press a few of them before you read on, because the rest of this page is about what the picture means and it lands better once the sound is in your ear. There is a larger one on its own page if you would rather sit with it.

Walk it

Start at C. A fifth up is G. A fifth above G is D. Then A, E, B, and so on. Twelve steps and you are back at C, having visited all twelve notes without repeating one.

• C to G
• G to D
• D to A
• A to E

Nothing else does that. Go up in whole tones and you only hit six notes before repeating. The fifth is the interval that walks the whole set, and it is also the interval your ear finds most agreeable, which is a coincidence with enormous consequences.

Sharps clockwise, flats anticlockwise

Each step clockwise adds one sharp to the key signature. C has none, G has one, D has two, A has three. Each step anticlockwise adds a flat instead. F has one, B flat has two, E flat has three.

So the circle is a picture of every key signature, and the position of a key on it tells you how far from C it is in accidentals. That is genuinely all the diagram claims. Everything else people load onto it is interpretation.

The mechanics of why the sharps arrive in the order they do is on the key signatures page.

Reading a signature off it

A piece of music hands you four sharps and expects you to know where you are. This is the one job the circle does faster than counting.

Sharps: the last one sits a semitone below home. Four sharps are F sharp, C sharp, G sharp, D sharp. The last of them is D sharp. Go up a semitone and you are on E, so the key is E major. It works every time, because the sharps arrive in fifths as well, and the newest one is always the seventh degree of the key.

• E major
• D major, two sharps

Flats: the second from last one is the key. Four flats are B flat, E flat, A flat, D flat. Second from last is A flat, and that is the key. One flat leaves nothing to count, so that one has to be remembered on its own: F major.

• A flat major
• F major, one flat

Neither of these is a trick so much as the circle read sideways. If you can see the wheel in your head you do not need them, and if you cannot, they will get you through a page of sheet music this afternoon.

The two keys that are the same place

At the bottom of the circle the sharp side and the flat side meet. F sharp major has six sharps, G flat major has six flats, and they are the same notes on a piano. Same for B and C flat, C sharp and D flat.

Which name gets used depends on what is easier to read. Nobody writes twelve sharps when five flats will do. On a fretless instrument, or a voice, the two are not quite identical in practice, but on anything with fixed pitch they are one key wearing two hats.

What it is actually for

Three things, in the order I have found them useful.

Neighbours sound related. Keys next to each other on the circle share six of their seven notes. That is why moving a song up a fifth for the last chorus sounds like a lift rather than a derailment, and why a piece can wander to its neighbours without announcing it.

The chord to the left pulls home. Whatever key you are in, the key one step clockwise is your V chord, the one that leans hardest back to home. In C that is G. Play G7 then C and you can hear the pull.

The relative minor is inside it. Most printed circles have a second ring showing the minor key that shares each signature. A minor sits inside C, E minor inside G. Useful when you want the same notes to sound darker.

What it will not do

It will not teach you to hear. It is a map of relationships you can already hear, and a map is not the walk. I would spend twenty minutes with it and then go back to playing, rather than trying to memorise the diagram whole.

It also says nothing about rhythm, which is at least half of music and the half most listeners actually respond to. That lives over on time signatures.