sandbox  /  exhibit 0005

The comma you can hear

Twelve pure fifths land a little above seven octaves. The gap is small, it has no solution, and every keyboard you have ever heard is somebody's opinion about where to hide it. Here are six of those opinions, out loud — and the page measures its own beating rather than asking you to take its word.

Twelve fifths drawn as a spiral, one turn of the circle each, stepping outward. Where the spiral ends relative to where it began is the amount by which the tuning fails to close, and each spoke is coloured by how far that fifth sits from pure.

Tap two or three notes. Every eight seconds of sound is computed here, sample by sample, and then read back to find the wobble.

Whether to believe it

A page about tuning is a claim — this is what those two notes do to each other — and the honest form of that claim is a number. Two harmonics a few hertz apart beat at their difference; that is not a convention, it is what a sum of two sines does. So below, the page renders sound, hands the samples to a measurement that is never told what to expect, and prints what came back next to what the arithmetic said it would be. Then it recovers the two commas themselves, and the tuning tables are checked against numbers published long before any of this ran.