Generator

Where each room stops being a set of resonances

The Schroeder frequency of 6 rooms — a carpeted bedroom at 217 Hz, a domestic living room at 183 Hz, a rehearsal room at 120 Hz, a jazz club at 68 Hz, a shoebox concert hall at 21 Hz, a gothic cathedral at 36 Hz — marked on a logarithmic frequency axis with the ranges of 4 instruments underneath. Below the mark a room is a handful of separable modes and a note's loudness depends on where the listener is standing; above it the modes overlap and the room is described by one decay time.

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: A bass note under one mode, The same note a tone higher, where the mode is not.

Called by 3 essays

the blast radius of changing it

Where a room stops being a room

A small room has frequencies it supports and frequencies it will not, and a hall has a reverberation time. Those are two separate accounts and they are descriptions of the same building at different frequencies. The crossover is one formula, and in a bedroom it lands at about two hundred hertz — in the middle of the bass register, and above nothing at all in a concert hall.

timbre · Room acoustics

Direct and reverberant sound in a shoebox concert hall. The direct sound falls six decibels for every doubling of distance and the reverberant field does not fall at all, so they cross once — at 5.5 metres in a room of 18700 cubic metres with a 2-second decay. Both are drawn relative to their level at that crossing. Everything past the crossing is a seat at which the room is louder than the instrument.

How far away the room takes over

Direct sound falls six decibels every time the distance doubles and the reverberant field does not fall at all, so the two cross once. In a concert hall the crossing is at about five and a half metres, which is nearer than nearly every seat — so almost everybody in almost every hall is hearing the building more than the players, and the number that says so is built from two quantities already computed — a room's reverberation time and an instrument's directivity.

perception · 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

All figures · What can be heard