How we hear direction

We can tell where a sound comes from with only two ears. The brain uses several cues that work together, and each has its own frequency range.

Time differences (ITD)

A sound from the side reaches the nearer ear first. For a head about 17.5 cm across, the largest difference is about 0.65 ms, for a source at 90°.

• Works best for low frequencies, below about 1.5 kHz, where the waveform repeats slowly enough for the brain to compare the two ears.
• Above this, the wavelength becomes shorter than the head, and the time cue becomes ambiguous.

Level differences (ILD)

The head shadows the far ear. The shadow is larger for shorter wavelengths.

• Negligible below about 500 Hz, where sound diffracts around the head.
• Up to 20 dB or more at high frequencies (several kHz and above).

The interplay of the two cues is known as the duplex theory: time differences below about 1.5 kHz, level differences above.

Pinna cues (spectral cues)

The folds of the outer ear change the spectrum depending on the direction of incidence, especially above 2 kHz. They help with:

• telling front from back,
• telling up from down,
• placing sounds on the median plane, where both ears receive the same time and level.

The set of these effects, including head, torso and pinna, is described by the head-related transfer function (HRTF). Every person's is different.

The cone of confusion

A given time difference corresponds to a whole cone of directions around the interaural axis. Sources on that cone, such as front and back at the same angle, give the same time and level differences. Head movements, pinna cues and sound spectrum resolve the ambiguity. This is also the reason why front-back confusion is common in artificial headphone listening, see Headphones and lateralisation.

Directional bands

Experiments show that narrow bands of noise are heard as coming from a particular direction on the median plane almost independent of the real direction. Roughly:

The exact values vary between listeners and sources; take them as a rough guide.

Precision

• In front, a change of about 1 to 2° is audible, which is remarkably precise.
• To the sides, the resolution is much worse, often 10° or more, because small angles change the time difference little.

Why this matters for recording

Stereo recording uses the same cues: level differences and time differences between the loudspeakers, see Stereo localisation. The listener's own head and ears then do the rest.

Draft: written by an AI assistant, awaiting technical review.