Acoustics & Music Theory
why it sounds like that
Generator

3 against 2, from a rhythm to an interval

The same 3:2 pattern at 6 rates, an event rate from 1.5 to 300 per second, on a logarithmic axis. Below about 20 events a second the two streams are counted; above about 40 they are heard as two pitches a 3:2 apart, which for 3:2 is 702 cents. Nothing in the pattern changes across that boundary. The slowest rate drawn is a tempo of 90 events a minute; the fastest is a pitch of 300 Hz against 450 Hz.
3 against 2, from a rhythm to an interval. The same 3:2 pattern at 6 rates, an event rate from 1.5 to 300 per second, on a logarithmic axis. Below about 20 events a second the two streams are counted; above about 40 they are heard as two pitches a 3:2 apart, which for 3:2 is 702 cents. Nothing in the pattern changes across that boundary. The slowest rate drawn is a tempo of 90 events a minute; the fastest is a pitch of 300 Hz against 450 Hz.

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. 8 of its 8 placements carry sound, built from the same numbers as the drawing, offering these buttons: 1080 events a minute — counted, 120 events a minute — counted, 160 Hz against 320 Hz — heard, 180 Hz against 225 Hz — heard, 20 Hz against 25 Hz — heard, 240 events a minute — counted, 30 Hz against 45 Hz — heard, 300 Hz against 450 Hz — heard and 13 more.

Called by 3 essays

the blast radius of changing it

3 against 2, from a rhythm to an interval. The same 3:2 pattern at 6 rates, an event rate from 1.5 to 300 per second, on a logarithmic axis. Below about 20 events a second the two streams are counted; above about 40 they are heard as two pitches a 3:2 apart, which for 3:2 is 702 cents. Nothing in the pattern changes across that boundary. The slowest rate drawn is a tempo of 90 events a minute; the fastest is a pitch of 300 Hz against 450 Hz.

A rhythm fast enough to be a chord

Three against two is a polyrhythm. Speed the same pattern up until the events arrive faster than about twenty a second and it is a perfect fifth. The ratio never changed, the figure never changed, and the only thing that moved is the rate — which makes rhythm and pitch one continuum with a perceptual boundary across the middle of it.

rhythm · Polyrhythm The threshold before, during and after a burst. The level a brief probe needs in order to be heard, plotted against when it happens relative to a 70 dB burst that occupies the shaded band. To the right is forward masking, which decays over about 200 milliseconds. To the left is backward masking: the threshold is raised for a probe that has already finished before the masker begins.

A sound hides what came before it

Masking does not stop when the masker does. A loud sound raises the threshold for about a fifth of a second after it ends, which is unremarkable, and for several milliseconds before it begins, which is not. The auditory present is a window rather than an instant, and inside the window the order of events is not the order they arrived.

perception · Masking One pattern, four metres. The same 6-step onset pattern read under 3 candidate metres, each scored by a preference rule set: 3 for a strong position that carries an onset, -2 for one that does not, -1 for an onset that lands off every strong position. The scores are the 3 is the beat 8, the 2 is the beat 4, every step is a beat 8, so the 3 is the beat and every step is a beat tie and the model does not choose. Nothing about the sound differs between these readings; the bar line is supplied by the listener.

Which of the two is the beat

A polyrhythm is notated as a bar of two with three laid across it. Run the metre rules used here over the composite and they choose the three — at every ratio tried, without exception. Add the one other rule the rules have, and the answer changes hands at a bar of 1,013 milliseconds, which is 118 to the minute.

rhythm · Polyrhythm

All figures · What can be heard