Acoustics & Music Theory
why it sounds like that
Concept

Early reflections — where it appears

The first arrivals at a listener after the direct sound, within roughly eighty milliseconds, each bouncing off one or two surfaces. They are fused with the direct sound rather than heard as echoes, and how much of their energy arrives from the side is the best single predictor of how spacious a hall sounds.

Named by 2 essays across one field — 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 Why a concert hall is narrow. The lateral energy fraction at the middle seat as the same hall is widened, everything else held. It peaks at 12 metres across at 0.235 and falls to 0.000 at 44. A wide hall's side walls are further away, so their reflections arrive later, weaker and — this is the part Sabine's model cannot say — from nearer the front, where the sideways weighting discounts them. The shoebox halls the orchestral repertoire was written for are all between about eighteen and twenty-five metres wide, and this is the arithmetic they are the answer to.

A room with directions in it

Every room until now has been a reservoir of energy that drains at a rate. That model has no directions in it at all, so it cannot say the one thing every published measure of spaciousness is about: how much of what arrives comes from the side. Mirror the source in six walls and every reflection acquires an angle and a time — and the answer to why a concert hall is narrow falls out at eighteen metres.

perception · Localisation

Named alongside it

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

ClarityEcho thresholdHaas effectImage-sourceInteraural time differenceLocalisationPrecedence effectReinforcementReverberationRoom acousticsSpaciousnessSumming localisation

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