Acoustics & Music Theory
why it sounds like that
Generator

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.
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.

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. 12 of its 12 placements carry sound, built from the same numbers as the drawing, offering these buttons: A chord as struck, A note at 220 Hz in a carpeted studio: 3.4 s at 125 Hz, 0.5 s at 4000, A note at 220 Hz in a hall with 1,400 m² of panelling: 3.1 s at 125 Hz, 1.5 s at 4000, A note at 220 Hz in a large stone church: 6.3 s at 125 Hz, 2.4 s at 4000, A note at 220 Hz in a shoebox concert hall: 3.1 s at 125 Hz, 1.5 s at 4000, A note at 220 Hz in an opera house: 2.9 s at 125 Hz, 1.4 s at 4000, A note at 220 Hz in an untreated room: 2.8 s at 125 Hz, 1.8 s at 4000, A note at 220 Hz in the full hall: 3.2 s at 125 Hz, 1.7 s at 4000 and 3 more.

Called by 6 essays

the blast radius of changing it

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 One decay, two verdicts, and the line is the listener's. The early-to-late energy ratio against reverberation time, for 50 millisecond and 80 millisecond windows. Nothing about the room differs between the curves; only where the line is drawn across its decay. Zero comes at 1.00 seconds for the 50 ms window and 1.59 seconds for the 80 ms window — which are, to two figures, the published rules of thumb for a room for speech and a room for music. The design targets were not put in; they came out.

The first eighty milliseconds are a different room

Draw a line across a room's decay and the energy on either side is two opposite verdicts about one building — clarity before it, reverberation after. The line is a property of the ear, not of the room, and putting it at 50 milliseconds and at 80 makes the two published design targets fall out — a room for speech at one second, a room for music at 1.6.

timbre · Room acoustics The same hall, empty and full. A hall of 18700 cubic metres with 900 square metres of audience, designed to 1.9 seconds occupied, with three kinds of seat under the audience. It is 2.76 s empty and 1.90 s full with hard wooden seats, a change of 31 per cent; 2.29 s empty and 1.90 s full with lightly padded, a change of 17 per cent; 1.96 s empty and 1.90 s full with heavily upholstered, a change of 3 per cent. The audience is 45 per cent of the total absorption when the hall is full, which is the largest single term in the equation — and how much the hall changes is decided entirely by what the seats were doing before anybody sat on them.

The model has nobody in it

Sabine's room is an empty box. The audience is 45 per cent of a full hall's absorption, a hall with hard seats goes from 2.76 seconds empty to 1.90 full, and because an audience absorbs far more treble than bass it does not shorten the decay so much as tilt it. And the players are inside the loop the model has no term for at all.

instruments · Room acoustics Long-term average spectra: an orchestra, playing forte against a trained operatic soloist. Each source's mean spectrum over a long passage, in decibels below its own strongest region, on a logarithmic frequency axis. An orchestra, playing forte peaks at 250 Hz and is 30 dB down by 3,150 Hz; a trained operatic soloist peaks at 250 Hz and is 11 dB down by 3,150 Hz. The shapes are the same until about 1 kHz and separate above it: at 3153 Hz the difference is 19.0 decibels, which is the largest anywhere in the range. Nothing here is about level. Both curves are drawn against their own peaks, so what is being compared is shape.

One voice over ninety players

A soloist heard over a full orchestra is not louder than it and could not be. What the trained voice does instead is put a peak of energy at three kilohertz, which is where the orchestra's spectrum has already fallen away and where the ear's own threshold happens to be lowest. Nineteen decibels of advantage, in a place nobody is competing for.

timbre · The voice A note gets duller as it dies. Each partial of a string note against time, with the loss rising as the partial number to the power 1 — so the fundamental takes 6 seconds to fall sixty decibels and the 8th takes 0.75. The heavy line is the power-weighted centroid, falling from partial 1.77 toward the fundamental; it is halfway there after 0.15 seconds. A single-rate envelope would draw all of these as parallel lines and the centroid as a horizontal one, and a struck string does neither: what is left at the end of a long note is very nearly a sine.

The note that gets duller as it dies

Every envelope drawn so far is one curve applied to a whole sound, and no struck string behaves that way. A string loses energy to air, to internal friction and to the bridge, and all three losses rise with frequency — so a note with a six-second fundamental has a sixteenth partial that is gone in under half a second, and the sound moving toward the listener is a spectrum collapsing toward its own fundamental. Which means an instrument is identified twice: once by the fifty milliseconds of its attack, which the earlier essays measured, and again by how fast its colour drains, which they did not.

timbre · Envelope From partial 3 the room is the slower of the two. Decay rates in nepers a second for each partial of a note on 130.8 hertz, in a concert hall. The rising curve is the string's own loss, which grows as the partial number to the power 1. The flat-ish curve is the room's, from its reverberation time at that partial's frequency. A reverberant field is the source convolved with the room, so a partial's tail falls at the SLOWER of the two — the heavy line — and the room keeps returning energy the string has stopped making. From partial 3, at 392 hertz, the room is in charge: 6 of the note's 8 partials are held up by the room rather than let go by the string. Those are exactly the partials the string was losing fastest, which is why the room does not merely lengthen the note.

The room is the slower of the two

A reverberant field is the source convolved with the room, so a partial's tail falls at the slower of the two rates rather than at their sum — and the room is slower for exactly the partials the string is losing fastest. Half a note's colour is gone in 0.163 seconds in no room at all, 0.313 in a concert hall and 1.441 in a stone church. The destination is identical in all three, because a room cannot hold a partial up above the fundamental it is also holding. What a hall takes away is the rate, and the rate was the whole of the identity cue.

timbre · Envelope

All figures · What can be heard