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Two Ears β ITD & ILD
Two ears pointing in opposite directions give the brain two independent measurements of every sound. The difference in arrival time and in level is enough to pinpoint any source in the horizontal plane.
π§
Use headphones for this page. ITD (the microsecond timing difference) collapses on speakers because each speaker reaches both ears. Headphones deliver a clean left-only and right-only signal.
Interaural Time Difference (ITD)
A source to your right reaches the right ear first. The extra distance sound must travel to reach the left ear β around the head β creates a delay of up to 650 Β΅s. The auditory system detects this with extraordinary precision: thresholds as small as 10 Β΅s have been measured.
Top-down view β path lengths to each ear
ITD
0 Β΅s
0 samples @ 44.1 kHz
Near ear
β
arrives first
The ITD is computed from the Woodworth formula for a spherical head of radius a = 8.5 cm:
ITD(ΞΈ) = (a/c) Β· (ΞΈ + sin ΞΈ)
// a = 0.085 m, c = 343 m/s
// ΞΈ = azimuth in radians
// valid for |ΞΈ| β€ 90Β°
At 90Β° azimuth: ITD = (0.085/343) Β· (Ο/2 + 1) β 636 Β΅s.
Phase limit: ITD works as a phase cue up to about 1 500 Hz. Above that, the interaural phase difference exceeds 180Β° and becomes ambiguous β the auditory system can't tell which cycle corresponds to which. Above ~1 500 Hz, the brain switches to using the envelope ITD of amplitude-modulated signals, and increasingly relies on ILD instead.
Interaural Level Difference (ILD)
Your head is an obstacle. At low frequencies (long wavelengths) sound diffracts freely around it β both ears receive nearly the same level. At high frequencies (short wavelengths) the head casts a real acoustic shadow, attenuating the far ear by up to 25 dB. The ILD grows steeply with frequency.
ILD (dB) vs azimuth β for four frequencies
ILD at current azimuth
0.0 dB
at selected frequency
Near / Far gain
1.00 / 1.00
linear amplitude ratio
Why does wavelength matter? At 250 Hz, Ξ» β 1.4 m β much larger than the head. The wave wraps around it with little attenuation. At 4 kHz, Ξ» β 8.6 cm β close to the head radius. The head is a significant obstacle and throws a strong shadow.
Duplex theory
Lord Rayleigh (1907) proposed that the auditory system uses two independent mechanisms: ITD for low frequencies and ILD for high frequencies. Modern research has confirmed this, with a handoff around 1 500 Hz where phase-based ITD becomes ambiguous.
Effective frequency range for each cue
Both cues reinforce each other. For a natural source, ITD and ILD point to the same direction, making localisation robust. If they conflict (one cue says left, the other says right), perception becomes uncertain β an effect used in audio research and exploited by some headphone virtualization tricks.
The cone of confusion
ITD and ILD are purely lateral cues β they encode the angle of a source around the interaural axis but carry no information about elevation or front/back. Every point on a cone centred on that axis produces identical ITD and ILD values.
Surfaces of equal ITD around the interaural axis
What resolves the cone? The shape of your outer ear (pinna) filters incoming sound differently depending on elevation and front/back angle β even when ITD and ILD are identical. That direction-dependent filter is the Head-Related Transfer Function (HRTF), the subject of the next page.