Acoustics & Music Theory
why it sounds like that
Generator

Two tones in the ratio 3 to 2

Two sine tones whose frequencies are in the ratio 3 to 2, and their sum. The combined pattern repeats every time both waves return to the start together, which for a simple ratio is soon — here after 2 cycles of the lower tone and 3 of the upper.
Two tones in the ratio 3 to 2. Two sine tones whose frequencies are in the ratio 3 to 2, and their sum. The combined pattern repeats every time both waves return to the start together, which for a simple ratio is soon — here after 2 cycles of the lower tone and 3 of the upper.

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. 7 of its 7 placements carry sound, built from the same numbers as the drawing, offering these buttons: One at a time, Play 2:1, Play 3:2, Play 45:32, Play 5:4.

Called by 2 essays

the blast radius of changing it

Two tones in the ratio 3 to 2. Two sine tones whose frequencies are in the ratio 3 to 2, and their sum. The combined pattern repeats every time both waves return to the start together, which for a simple ratio is soon — here after 2 cycles of the lower tone and 3 of the upper.

Two notes and a ratio, which is the whole of consonance

Sound two tones together and the pair either settles or does not. What decides it is the ratio of their frequencies, and the rule is that simpler ratios settle — which is two and a half thousand years old and still not quite an explanation.

intervals · Consonance The comma is conserved; only the place it is paid is chosen. Every policy available to a continuous-pitch ensemble on one line: drift per circuit along the bottom, worst mistuned interval up the side. The line is straight and its intercepts are fixed, because the 4 moves of the pump have to absorb 21.51 cents between them however they are shared. Spreading it evenly puts 5.377 cents on each interval — the same narrowing quarter-comma meantone applies to every fifth.

Somebody has to pay the comma

A choir has no frets and no keys, so it can tune every chord exactly — and a common progression sung that way arrives a comma flat, every circuit. The freedom a keyboard lacks turns out to be a freedom about where the error goes rather than whether there is one, and the two costs always add to the same number.

harmony · The comma

All figures · What can be heard