Acoustics & Music Theory
why it sounds like that
Concept

Interaural level difference — where it appears

The difference in sound level between the two ears, produced by the head's acoustic shadow on the far side of a source. It is the main cue to direction above about 1.5 kHz, and one decibel of it is roughly the smallest a listener detects, which fixes what a decibel is worth against a delay.

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

A source 45° off centre, and the path difference it makes. A head from above with a source to one side. The near ear is reached first; the far ear's path runs round the head, and the difference between the two is 13.1 centimetres, which at 343 metres a second is 381 microseconds. That number, and the level difference the head's shadow produces, are the whole of what the ear has to work with.

Two ears, and the whole of the difference is 655 microseconds

Direction is computed from two numbers — when a sound reaches each ear and how loud it is at each — and which of the two is usable is decided by the wavelength against the width of a head. The changeover frequency is not a design choice. It falls out of 343 metres a second and 17.5 centimetres, and it is why the mechanism of hearing where something is changes halfway up the piano.

perception · Localisation A listener whose ears differ by a decibel or two has a straight ahead that moves with the dynamic. Where the median plane sits for a listener whose two ears' thresholds differ, against the level of a 500 Hz tone, if the whole of the latency difference the published brainstem latency law gives reaches the comparator that reads interaural delay. 1 dB worse: 19.5° at 30 dB (172 µs), 12.0° at 60 dB (106 µs), 7.4° at 90 dB (65 µs); 2 dB worse: 40.6° at 30 dB (347 µs), 24.4° at 60 dB (214 µs), 14.9° at 90 dB (132 µs); 3 dB worse: 65.6° at 30 dB (524 µs), 37.7° at 60 dB (323 µs), 22.7° at 90 dB (200 µs). Every curve halves its offset every 43 dB and none reaches zero at any level a listener hears; the dashed line is one detectable step on the median plane, 1.68°.

A quiet bass is further off-centre than a loud violin

An ear whose threshold is a decibel worse than the other is a little later to report every sound, and the published brainstem latency law says how much later: a gap that halves every 43 decibels and grows toward the bass. Taken at full size, a one-decibel asymmetry would put straight ahead twelve degrees round at a moderate level — seven times what the ear's own two thresholds say a decibel is worth, so most of that latency cannot be reaching the comparator that reads direction. What survives any scaling is the shape. The displacement is not one number but a curve in level and in pitch, and it deforms an orchestra rather than moving it.

perception · Localisation

Named alongside it

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

Interaural time differenceLocalisationCalibrationCone of confusionDuplex theoryDynamicsHead shadowHearing thresholdJust-noticeable differencePinna

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