Fokker periodicity blocks — the 5-limit lattice, folded

0\12

1/1

Just frequency

Just size

Tempered step

Tempered frequency

Deviation (just − tempered)

Beat rate

Deviation from the temperament

Every dot is a just interval 3^x·5^y. Its colour is how far that interval sits from the tempered step it collapses onto. The hollow ring is where the temperament puts it — the drift is small near 1/1 and grows with distance.

The block

Step	Ratio	x, y	Just ¢	Dev ¢

What am I looking at?

The short version

Axes are exponents: right = ×3 (fifths), up = ×5 (thirds). Octaves are free, so every point is folded into one octave.
Pick two intervals small enough to ignore — unison vectors, drawn as arrows. Declaring them zero glues the lattice to itself along both.
The determinant of that pair is how many pitch classes survive. It is the equal temperament — 12, 31 and 53 fall out of which commas you agreed to ignore, rather than being assumed.
The parallelogram is one block; its translates tile the plane. Hover any dot and every point that collapses onto the same tempered step lights up: different just intervals the temperament calls one note.

Controls

Drag to pan, scroll to zoom, arrow keys to walk the lattice, Enter to replay.
Both sounds the just interval against its tempered approximation — the wobble is the deviation, at the beat rate shown above. Try it on 12 vs 53.
The drone holds 1/1 so you hear an interval, not a lone pitch.