Pure Ratios
Build a whole-number ratio, hear it against a root, and see where it falls between the keys.
The ratio is exact — that is what just intonation means. The key is wherever the tuning you pick puts its nearest note, and every tuning in the list is a fixed set of twelve, which is why none of them can hold more than a handful of these ratios.
Only the root has a frequency of its own — type one, or tap a key to move it. Every other key is then priced from the root by the tuning you picked: take the cents that tuning gives the key, subtract the cents it gives the root, add 1200 for each octave between them. So an E above a 415 Hz A is 702¢ and 622.5 Hz in Pythagorean, but 696.6¢ and 620.6 Hz in Meantone 1/4 — same root, same key, different tuning.
That is why the keyboard is a ruler here and not an instrument, and why tapping a key sets the root instead of sounding it. The ratio never moves when you change tuning; the keys move under it. Where the ratio lands past the last drawn key the marker is pinned to the edge and dimmed.
Interval names follow the list of intervals compiled by the Huygens-Fokker Foundation, which covers every ratio these two grids can reach.