The circle of fifths
Drawn above with its standard settings, which is almost never how an essay draws it: an essay states the numbers it is arguing about, so the figure a reader meets there is about that argument rather than about the drawing in general. Every option a placement passes is checked against the ones this function actually reads, because an option it does not read is silently ignored and the figure quietly draws what is above instead.
It makes a noise. 10 of its 10 placements carry sound, built from the same numbers as the drawing, offering these buttons: Round the circle.
Called by 5 essays
the blast radius of changing it
Keys are neighbours, and the map is computed
Two keys a fifth apart share six of their seven notes. That single fact generates the circle of fifths, the key signatures, the shape of nearly every modulation, and the sense that some keys are far away.
As evenly as possible, which turns out to be a famous rhythm
Ask an algorithm to space five strikes over eight beats as evenly as it can. It produces the cinquillo. Ask for three over eight and it produces the tresillo. Nobody told it about Cuba.
Every interval a different number of times
Count the intervals inside a major scale and the six answers are 2, 5, 4, 3, 6 and 1 — six different numbers, no two alike. That is not decoration. It means the number of notes a key shares with a transposition of itself identifies the distance uniquely, so a listener who can only count common tones can still tell exactly how far a modulation went.
Parallel and relative are two different maps
Bring the seven modes to one tonic and order them by brightness, and each step lowers exactly one note by a semitone — and the notes it lowers, in order, are F♯, B, E, A, D, G, the chain of fifths read backwards. Do the same to harmonic minor's rotations and each step moves two, three or four notes at once. The famous chain belongs to the generator, not to rotation.
The circle is a circle, and the map is not
Among the twelve major keys, notes in common is a strict function of distance round the circle of fifths — one value for each step count, no exceptions — so there is nothing else to measure and the map really is one-dimensional. A second axis appears only when the minor keys are added, and it is a different kind of move: the relative shares all seven notes and the parallel is one semitone away.