Acoustics & Music Theory
why it sounds like that
Concept

Precedence effect — where it appears

The suppression of later arrivals as evidence of direction, which lets a listener in a reverberant room hear one source in one place. It operates over the first few tens of milliseconds and its limits depend on what the sound is.

Named by 8 essays across 2 fields — each of them below, with the objects they name alongside it.

How late a reflection has to be before it is an echo. What a single reflection does to the sound it follows, against its delay, on a logarithmic axis. Under a millisecond the two combine into one image that is pulled towards the earlier source. From there out to a few tens of milliseconds the reflection is not heard as a separate event at all and does not move the image — it only changes the timbre. Past the echo threshold it becomes a second sound, and the threshold is five times later for speech than for a click.

The first wavefront wins

A room sends a hundred copies of every note to a listener from a hundred directions, and the listener hears one note in one place. The mechanism that does it is brutal and simple: for the first few tens of milliseconds after a sound arrives, everything that follows is denied a vote on where it came from — even when it is louder than the original.

perception · Localisation 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 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 Where a room stops sending the two ears the same sound. The correlation between the two ears' signals against frequency, for a seat 15 metres from the source in a 15,000 cubic metre room with a 2 second reverberation time. The pale curve is the diffuse field alone — sin(kd)/(kd) for an ear separation of 17.5 centimetres, which first crosses zero at 980 hertz. The heavy curve adds the direct sound, which is coherent and lifts the whole thing by an amount the direct-to-reverberant ratio sets. At 125 hertz the coherence is 0.98 and at 1000 it is 0.16.

Where the two ears stop agreeing

A room sends both ears versions of the same sound, alike at low frequencies and increasingly unlike at high ones. Where they stop resembling each other is 980 hertz, and it is set by the 17.5 centimetres between the ears rather than by anything about the room — which is within a quarter of a frequency found earlier for a completely different reason. One minus that correlation is spaciousness, and it is computable from a room's own reverberation.

perception · Localisation Every arrival at one seat, against the delay at which it would be an echo. The echogram: each reflection at its delay after the direct sound and its level relative to it, in a 22 by 45 by 15 metre hall with 18 per cent absorption. The line is the published echo threshold for speech — 40 milliseconds at equal level and about 3.0 more for each decibel of attenuation — so anything to the RIGHT of it is late enough and loud enough to be heard separately. The once-reflected rear wall arrives at 210 milliseconds, 25 decibels down, against a threshold of 114 — well past it. Nothing here stands clear enough of its neighbours to be heard as an echo, and 181 arrivals are fused with the direct sound instead.

An echo is prevented by the crowd around it

The echogram says when every reflection arrives and how loud it is; the published echo threshold says when a reflection that late and that quiet is heard separately. Put one against the other and the rear wall of every hall anybody builds is past the threshold — a 45-metre hall puts it 210 milliseconds late and 25 decibels down against a threshold of 114. It is not heard as an echo, and what saves it is not the geometry. It is everything else arriving at the same time.

perception · Localisation Where the sound is, and how wide. An earlier essay sorted a hall's arrivals into echoes and everything else. Everything else is not nothing: a reflection too early to be heard as a separate event still moves the apparent source, widens it and colours it, and all three come out of the same list of times, levels and angles. At this seat the direct sound arrives from 26.6 degrees off the front and the image is heard 8.5 degrees left of it, pulled by the near side wall. The apparent width is 33 degrees, from a lateral energy fraction of 0.23. And the strongest early reflection arrives 0.6 milliseconds behind off 1× the floor, which is a comb filter with notches every 1608 hertz and 25 decibels deep. The trading ratio and the discount on late arrivals are stipulated rather than measured, so the degrees are ordinal: what the figure claims is the direction and the shape, not the number.

A position and a width

Sorting a hall's arrivals into echoes and everything else settled that fusion is not a yes or a no. Everything else is not nothing: a reflection too early to be heard separately still moves the apparent source, widens it and colours it. All three come out of the same list of times, levels and angles, and none of them needed a new input.

perception · Localisation The hall, as two numbers a listener has. Every reflection at this seat, placed by the interaural delay it produces rather than by the direction it came from. Time runs down; the dot's size is its energy. The direct sound is at 0 microseconds and the reverberation spreads over the whole available range, with a root-mean-square width of 322 against a geometric maximum of 656. That is the position and width computed earlier, in the units a listener has instead of the vectors used until now. 10 of the 56 reflections arrive from behind and carry 9 per cent of the energy — and they are drawn where they are because the interaural delay of a reflection from 120 degrees is identical to one from 60.

The hall through a head

Every direction computed so far is a vector from a seat to an image source, and a listener has no vectors. Run the echogram through the head computed six essays ago and two things happen: the position and width become microseconds, and a third of the room disappears — because both cues fold at ninety degrees and a reflection from behind is identical to one in front.

perception · Localisation A turn of 0.99 degrees tells front from back. A source 45 degrees off centre and its mirror image 135 degrees off, which produce the same interaural delay and are therefore the same signal to a listener who does not move. As the head turns the two predictions separate: the front source's delay falls and the rear source's rises, because the fold at ninety degrees puts them on opposite branches of the same curve. They differ by the 15-microsecond threshold after 0.99 degrees of turn — which is exactly half the 1.97 degrees a source would have to move for the same listener to notice it moving, and it is half for a reason: a turn displaces the two hypotheses from each other by twice what it displaces either of them from where it started.

The turn is half the angle

A stationary head cannot tell a sound in front from the same sound behind, and an earlier essay said so at length. The turn that breaks the confusion is 0.84 degrees — exactly half the angle a source would have to move for the same listener to notice it moving, and half for a reason. In a hall the same turn does something else: the source swings at 8.9 microseconds a degree and the room swings at 2.7, so a listener who moves is separating the soloist from the reverberation as well as the front from the back.

perception · Localisation

Named alongside it

The objects these essays reach for when they reach for this one.

LocalisationReverberationAbsorptionImage-sourceInteraural time differenceRoom acousticsDiffuse fieldHall designHead shadowReflectionSpaciousnessClarity

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