Generator

Reverberation time, by two formulas

Sixty-decibel decay time against average absorption, divided by the room's volume-to-surface ratio so that every room sits on the same pair of curves. Sabine's equation, which is the one every textbook gives, and Eyring's correction to it. They agree in the reflective rooms Sabine measured and separate above ᾱ ≈ 0.18: at 0.6 Sabine reads 53% high, and at ᾱ = 1 — a room whose walls absorb everything, which is the outdoors — it still returns a positive time for a space with no reverberation at all. Marked: a concert hall 1.59 s, a stone church 3.37 s, a studio live room 0.45 s, a carpeted bedroom 0.13 s, an anechoic chamber 0.03 s.

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. 10 of its 10 placements carry sound, built from the same numbers as the drawing, offering these buttons: a bedroom at 4 kHz — 0.13 s, a carpeted bedroom — 0.13 s, a cathedral — 3.39 s, a concert hall — 1.52 s, a concert hall — 1.59 s, a concert hall — 1.95 s, a corridor — 1.01 s, a cube — 0.96 s and 12 more.

Called by 5 essays

the blast radius of changing it

How long a room rings, and where the formula stops

Sabine's reverberation time is one line of arithmetic — volume over absorption — and it built the modern concert hall. It also predicts that a room whose walls absorb everything still rings, which is a room with no reverberation at all, and the error is largest in exactly the rooms most music is now made in.

timbre · Room acoustics

Where each frequency goes, from a source 18 cm across. Polar response of a circular radiator of radius 9 cm at 200 Hz (ka = 0.3), 800 Hz (ka = 1.3), 2000 Hz (ka = 3.3), 5000 Hz (ka = 8.2). Zero degrees is straight ahead. The low frequency is a circle — it goes everywhere — and the high one is a narrow lobe with nulls either side of it, so a listener off to the side hears the same note with its top missing.

An instrument points

A source radiates evenly while it is small compared with the wavelength and beams once it is not, and the crossover is one number. So the same instrument is omnidirectional in its bottom octave and a searchlight in its top one — which means its spectrum depends on where the listener is standing, and a microphone position is a choice about what the instrument sounds like.

timbre · Room acoustics

6 chords in a gothic cathedral. Each chord's reverberant decay in a room with a 8 second reverberation time, at 1 chord a second. Decay is linear in decibels, so each line is straight with a slope of -7.5 dB a second. When a chord arrives, 2 earlier ones are still above 20 dB down.

The room chooses the harmonic rhythm

A chord in a cathedral is still sounding, seven decibels down, when the next one arrives — and the one after that, and the one after that. Reverberation is linear in decibels, so the number of chords audible at once is one number divided by another, and it puts a hard ceiling on how fast a composer writing for that building can change harmony. The ceiling is computable, and the music written for those rooms sits under it.

timbre · Room acoustics

Six reverberation times for one room. Sabine's arithmetic evaluated in each octave band from the published absorption coefficients of the surfaces. a large stone church runs from 6.3 seconds at 125 Hz to 2.4 at 4 kHz — a bass ratio of 1.38, where concert halls are specified between 1.1 and 1.25.

A room does not decay evenly

Sabine's arithmetic gives one number and absorption is a strong function of frequency, so a room has six reverberation times rather than one. A stone church rings for 6.3 seconds at 125 hertz and 2.4 at 4 kilohertz, which means a chord left in it does not fade — it changes shape, losing its top before it loses its bottom, and arriving at the listener as a different sonority from the one played.

timbre · Room acoustics

A general pause of a bar is worth 4.9 decibels in a hall and 8.1 in silence. What a rest is worth as a diminuendo, in rooms with different reverberation times. The upper curve is the earlier figure, which assumed the sound stops when the players do; each curve below it lets the hall go on sounding, falling sixty decibels in its own reverberation time until it reaches the background. At the bar of silence a general pause usually is — about 1.2 seconds — the dry value is 8.1 decibels, shoebox concert hall keeps 60 per cent of it and gothic cathedral keeps 22. At 3.5 seconds, where a gap stops being a pause and becomes an ending, the same hall keeps 86 per cent. A long silence outlives any hall's tail and a short one does not, which is why the room costs the device most at exactly the length a composer writes it.

A rest needs a dry room

The twenty-four decibels a general pause is worth assume the sound stops when the players do. Put a hall under it and a bar of silence keeps 60 per cent of its value in a shoebox concert hall and 22 per cent in a cathedral, while a three-and-a-half-second one keeps 86 and 45 — because a hall's tail has a length and a rest either outlives it or does not. A written bar of silence is worth half its dry value at 2.76 seconds of reverberation, which falls between the concert hall and the stone church.

form · Closure

All figures · What can be heard