Generator

A wind instrument is a thermometer, and a string is not

Cents from the pitch at 20 degrees, against the temperature of the air inside a wind instrument and of a steel string, computed from the speed of sound as 343.2 metres a second times the square root of absolute temperature, and from a string's tension falling by Young's modulus times the expansion coefficient per degree. The wind slope is 2.95 cents a degree at 20 degrees, so 0.0 cents at 20, 11.7 cents at 24, 23.3 cents at 28, 34.7 cents at 32. The Pythagorean comma is reached at 28.1 degrees — 8.1 degrees of warming, which a wind instrument does from breath alone within a few minutes. The string goes the other way, 36 cents flat at 34 degrees, so the gap between the two sections opens at 5.4 cents a degree.

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. 9 of its 9 placements carry sound, built from the same numbers as the drawing, offering these buttons: A at 20°, Both at 32°, wind against string, Both at 40°, wind against string, The same fingering at 10° — -30 cents sharp, The same fingering at 24° — 12 cents sharp, The same fingering at 28° — 23 cents sharp, The same fingering at 30° — 29 cents sharp, Tuned at 20 degrees and played at 15: −15 cents, held against the pitch it was tuned to and 1 more.

Called by 2 essays

the blast radius of changing it

A wind instrument is a thermometer

Pitch goes as the square root of absolute temperature, so a warming clarinet sharpens by about three cents a degree and passes a Pythagorean comma after eight. The strings beside it go flat as they warm. Nobody chose either number, no temperament addresses either of them, and together they are twice the size of the discrepancy this whole field is named after.

tuning · Air column

Every pitch standard, given the width 8 degrees gives it. Each documented standard drawn not as a point but as the band an ensemble occupies while the room warms by 8 degrees: the air columns sharpen by 23.3 cents, the steel strings flatten by 20.1, and 13.8 cents of spread inside each wind instrument's own register cannot be pulled out because it is a gradient along the bore rather than an offset. The band is 57 cents wide, and 5 of the 6 adjacent steps in the whole record are narrower than it — which is to say that 5 of the distinctions four centuries of committees argued about are smaller than the pitch spread inside one orchestra on one evening.

A standard is a point, and a performance is a band

Nine earlier essays draw every pitch standard as a single number, because none of them has a temperature in it. An air column sharpens as the room warms and a steel string flattens, at 2.95 and 2.49 cents a degree; add the 13.8 cents of spread inside one wind instrument's own register and eight degrees makes an orchestra 57 cents wide. Five of the six steps in four hundred years of pitch standards are narrower than that.

tuning · Pitch standard

All figures · What can be heard