Sound Localization

Abstract

Sound localization, a form of auditory perception, is the auditory system's recovery, from a signal that carries no explicit spatial coordinate, of the direction a sound came from. This article follows the duplex theory, on which interaural time differences localize low frequencies and interaural level differences localize high ones, through the head geometry that sets those differences, to the cone of confusion, the set of directions sharing them that binaural cues alone cannot resolve. It then turns to the spectral cues imposed by the outer ear that fix elevation and front from back, the precedence effect that suppresses echoes in a reverberant room, and the brainstem circuits that compute the binaural differences, from the barn owl's coincidence-detecting map to the inhibition-based code of mammals. Three interactive demonstrations model the interaural cues, the cone of confusion, and the precedence effect.

Keywords: sound localization, interaural time difference, duplex theory, cone of confusion, precedence effect

A listener with closed eyes can point to a speaker across a room, follow a bird moving through the trees, or turn toward a voice that called their name, and can do so with a signal that contains no direct statement of where its source lies. The pressure wave at each eardrum is a one-dimensional record of amplitude over time; the direction of its source has to be reconstructed by the brain from the subtle ways the head and ears transform that wave before it arrives. Sound localization is that reconstruction, and it is the part of auditory perception that turns hearing into a sense of a surrounding space. The problem is genuinely one of inference, because the two ears sample the field at only two points, and the whole apparatus of binaural and spectral cues exists to recover three-dimensional direction from those two samples (Middlebrooks & Green, 1991).

What Sound Localization Is

Sound localization is the determination of the direction, and to a lesser extent the distance, of a sound source relative to the listener. Its natural coordinates are two angles: azimuth, the horizontal angle around the head, and elevation, the vertical angle above or below the ear-level plane. Human listeners are far more accurate in azimuth than in elevation, and most accurate of all for sources straight ahead, where the smallest change in direction that can be detected, the minimum audible angle, is about one to two degrees for sources in front and grows severalfold as the source moves to the side (Mills, 1958). Vertical resolution is coarser by a factor of several: the smallest detectable change in elevation for a broadband source in front is on the order of three to four degrees, and larger still for narrowband sounds or sources away from the midline, because elevation rests on the weaker spectral cue of the outer ear rather than on a difference between the ears (Middlebrooks & Green, 1991). That the frontal direction is the most finely resolved is the first clue that localization depends on differences between the ears, which change most steeply with angle when the source is near the midline.

The reason a spatial sense has to be computed rather than sensed is that the cochlea is a frequency analyser, not a spatial one: it maps frequency onto place along the basilar membrane and discards the direction of arrival entirely. Direction survives only in the relationship between the two ears' signals and in the way the head and outer ear filter the incoming wave, and the auditory system must reconstruct it from those traces (Middlebrooks & Green, 1991). The cues fall into two broad families: binaural cues, the differences in time and level between the two ears, which carry azimuth; and monaural spectral cues, the direction-dependent colouring of the sound by the outer ear, which carry elevation and resolve the ambiguities the binaural cues leave open.

Distance is judged far less precisely than direction, and from a different and weaker set of cues. Overall intensity falls with distance, but it is only a reliable cue for a familiar sound of known power, since a soft near source and a loud far one can reach the ear at the same level. More robust in a room is the ratio of direct to reverberant energy: a nearby source delivers most of its sound straight to the ear, whereas a distant one arrives mixed with a larger share of reflections, and the auditory system reads closeness from that ratio. Over long distances the air itself absorbs high frequencies more than low, dulling a far sound's spectrum, and within about a metre the interaural level difference grows even at low frequencies as the wavefront curves sharply across the head. None of these fixes distance as sharply as the binaural cues fix azimuth, which is why localization is, first and foremost, a sense of direction (Blauert, 1997).

The Duplex Theory: Interaural Time and Level Differences

The organising principle of horizontal localization is the duplex theory, set out by Lord Rayleigh, who reasoned that a source off to one side reaches the near ear both sooner and louder than the far ear, giving two cues rather than one (Rayleigh, 1907). The interaural time difference is the difference in arrival time at the two ears, produced by the extra distance the wave must travel around the head to reach the far ear. The interaural level difference is the difference in intensity, produced by the head casting an acoustic shadow over the far ear. Rayleigh's insight was that the two cues do not operate over the same range of frequencies, and that their division of labour is dictated by the wavelength of the sound relative to the size of the head.

At low frequencies the wavelength is long compared with the head, so the wave diffracts around it almost undiminished and the level difference is negligible; but the same long wavelength lets the auditory system read the ongoing phase difference between the ears unambiguously, so the time difference is usable. At high frequencies the situation reverses: the head casts a substantial shadow, giving a large and reliable level difference, as much as fifteen to twenty decibels for a source to the side at the highest frequencies (Middlebrooks & Green, 1991). The fine-timing cue, by contrast, fails at high frequencies for two reasons at once. The wavelength becomes shorter than the path around the head, so the ongoing phase difference no longer maps unambiguously onto a direction; and the auditory nerve stops phase locking, ceasing to fire at a fixed point in the waveform above roughly 1.5 kilohertz and losing the fine timing altogether by about four or five kilohertz, so the information is no longer even encoded for the brainstem to read (Grothe et al., 2010). The crossover falls near 1.5 kilohertz, where neither cue is strong, which is why localization is poorest for pure tones in that region. The size of the time difference follows from head geometry: Woodworth's spherical-head approximation gives the interaural time difference as the head radius divided by the speed of sound, multiplied by the sum of the azimuth in radians and its sine, so it grows from zero straight ahead to roughly 650 microseconds at the side (Kuhn, 1977). Modern work confirms that listeners do weight the two cues by frequency as the duplex theory predicts, while also showing that the story is not exhausted by pure tones: the time difference carried in the envelope of a high-frequency complex sound remains usable, so timing contributes even where the classical theory assigned everything to level (Macpherson & Middlebrooks, 2002). Figure 1 shows the geometry that sets the time difference, and the first demonstration lets the reader vary azimuth and read off both cues.

The Cone of Confusion

The binaural cues are powerful but fundamentally incomplete, because a given interaural time or level difference does not specify a single direction. The two ears lie on an axis running through the head, and every direction that makes the same angle with that axis produces the same difference in path length, and so the same interaural time difference. Those directions form a cone opening symmetrically around the interaural axis, and the whole surface of the cone is consistent with one value of the cue; it is called the cone of confusion (Blauert, 1997). A source directly in front and its mirror image directly behind, both at the same lateral angle, sit on the same cone and generate identical interaural differences, which is why front-back confusions are the characteristic error of localization: with the binaural cues alone, the auditory system cannot tell a sound in front from the same sound behind.

Two things rescue the listener from the cone. The first is that the outer ear filters sound differently depending on the direction it arrives from, adding a monaural spectral cue that breaks the symmetry, treated in the next section. The second is head movement: a small rotation of the head changes the interaural differences in opposite ways for a source in front and a source behind, so a listener who turns slightly can resolve the ambiguity from how the cues change, a dynamic cue that static listening cannot supply. The second demonstration makes the cone concrete, showing a front source and its rear mirror image sharing an interaural time difference to the microsecond, and letting the reader confirm that the binaural cue alone cannot separate them.

Spectral Cues and Elevation

Elevation and the front-back distinction cannot come from the binaural cues, because sources that differ only in elevation, or that are front-back mirror images, can share the same interaural differences. They come instead from the outer ear. The pinna, the visible folds of the ear, is a small, direction-sensitive acoustic filter: its ridges and cavities reflect and resonate so that the spectrum reaching the eardrum is shaped differently depending on the direction the sound arrives from, imposing peaks and notches whose frequencies shift with elevation. This direction-dependent filtering, summarised in the head-related transfer function, is a monaural cue, available at a single ear, and it is what allows a listener to hear whether a sound is above, below, in front, or behind (Wightman & Kistler, 1989).

That these spectral cues are genuinely used, and are learned rather than fixed, was shown by altering them. When the shape of the pinna is changed by fitting moulds into the ears, elevation judgements collapse at once, because the familiar mapping from spectral notch to elevation no longer holds; but over some weeks of continuous wear listeners relearn to localize with the new ears, and, tellingly, they retain the original mapping too, so that removing the moulds restores good localization immediately (Hofman et al., 1998). The spectral cue is thus a plastic, experience-dependent code, calibrated to the individual geometry of a listener's own ears. Table 1 sets out the full inventory of cues and the spatial dimension each one carries.

The Precedence Effect

Localization in an ordinary room is a harder problem than localization in the open, because every hard surface returns an echo: the direct sound is followed, within milliseconds, by a train of reflections arriving from many wrong directions, each a plausible source in its own right. That listeners nonetheless hear a single source in its true position is the work of the precedence effect, the auditory system's rule for handling closely spaced copies of a sound. When two versions of a transient arrive from different directions separated by a short delay, the perceived location is dominated by the one that arrives first, the direct sound, while the later copy is largely suppressed as a spatial cue (Wallach et al., 1949).

The effect is organised by the delay between the leading and lagging sound. At delays below about a millisecond the two fuse into one image whose location is a compromise between them, summing localization; over roughly one to five milliseconds for brief sounds the pair still fuses into a single event but its location is dictated by the leading sound, the precedence proper; and only when the delay exceeds the echo threshold, several milliseconds for clicks and longer for speech and music, is the lag heard as a separate echo (Litovsky et al., 1999). The functional point is that reflections in a room arrive within the precedence window, so the mechanism throws out the misleading directional information the echoes carry and preserves the true direction given by the first wavefront. The third demonstration steps a listener through these regimes, moving the lead-lag delay from fusion through precedence to the echo threshold.

Neural Mechanisms

The microsecond time differences that carry low-frequency azimuth are far finer than the duration of a nerve spike, so the brainstem needs a dedicated mechanism to measure them. Jeffress proposed one in a model of enduring influence: an array of coincidence-detector neurons, each firing only when inputs from the two ears arrive together, fed by axons of graded length acting as delay lines. A neuron whose delay lines exactly compensate the interaural time difference receives its two inputs simultaneously and fires, so the interaural time difference is read out as a place, the position of the most active neuron along the array (Jeffress, 1948). The model predicts a neural map of azimuth built by coincidence detection on delay lines.

In the barn owl, an auditory specialist, the Jeffress model is realised almost literally. Carr and Konishi traced axons from the cochlear nucleus that act as delay lines running into the nucleus laminaris, where neurons behave as coincidence detectors, producing an orderly map of interaural time difference and hence of azimuth (Carr & Konishi, 1990); this feeds a higher map in the midbrain, discovered when Knudsen and Konishi found neurons tuned to a specific direction in space, a true map of auditory space in the owl's tectum (Knudsen & Konishi, 1978). Mammals, however, turned out not to follow the owl. Recordings in the gerbil showed that the peak firing of many brainstem neurons falls outside the range of time differences the animal ever experiences, so azimuth is not read from which neuron peaks but from the relative activity of two broad populations, one in each hemisphere, an arrangement quite unlike a Jeffress place map (McAlpine et al., 2001). The mechanism underlying it is precisely timed synaptic inhibition that arrives slightly before the excitation and shifts each neuron's tuning, so that the mammalian code for interaural time difference is built from an interplay of excitation and inhibition rather than from delay lines alone (Grothe et al., 2010). The upshot is that auditory space is not inherited as a ready-made map but computed, and computed differently in different lineages, a plasticity of representation that runs throughout the system (King et al., 2001).

Worked Example

The demonstrations can be checked against the geometry that governs them. Woodworth's spherical-head model gives the interaural time difference as the head radius divided by the speed of sound, multiplied by the azimuth in radians plus the sine of that azimuth. Taking a head radius of 0.0875 metres and the speed of sound as 343 metres per second, the leading factor, the radius over the speed of sound, is 255 microseconds per radian. For a source straight ahead the azimuth is zero, its sine is zero, and the interaural time difference is zero, as it must be by symmetry. For a source at 30 degrees to the right, 0.524 radians, the bracket is 0.524 plus sin 30 degrees, which is 0.524 plus 0.500, or 1.024, and the interaural time difference is 255 times 1.024, about 261 microseconds. At 45 degrees it is 255 times (0.785 plus 0.707), about 381 microseconds; at 60 degrees, 255 times (1.047 plus 0.866), about 488 microseconds; and at 90 degrees, straight out to the side, 255 times (1.571 plus 1.000), about 656 microseconds, the maximum. These are the values the first demonstration reports as azimuth is varied, and the growth from zero to roughly two-thirds of a millisecond across the quarter-circle is the entire dynamic range the low-frequency system has to work with.

The second demonstration uses the same formula to make the cone of confusion exact. A source 30 degrees to the right and in front, and its mirror image 30 degrees to the right and behind, make the same angle with the interaural axis, so both yield an interaural time difference of about 261 microseconds; the demonstration displays the two locations and the single shared value, showing that the binaural cue cannot separate them. The third demonstration works in the time domain of the precedence effect: with the lead-lag delay set below about 1 millisecond the two copies fuse into one image located between them; raised into the 1-to-5-millisecond band the image stays single but snaps to the leading sound; and pushed past the echo threshold, about 5 milliseconds for a click and longer for speech and music, the lag emerges as a separate echo. Each regime boundary in the demonstration is a fixed delay, so the reader can confirm that the same physical delay always lands in the same perceptual regime.

Discussion

Sound localization is a model case of perception as inference: a direction in three dimensions is reconstructed from two one-dimensional pressure records by exploiting the lawful ways the head and ears transform an incoming wave. The duplex theory remains the backbone of the account, dividing horizontal localization between an interaural time difference that serves the low frequencies and an interaural level difference that serves the high, a division dictated by the wavelength of sound against the width of the head (Rayleigh, 1907; Macpherson & Middlebrooks, 2002). But the binaural cues are geometrically incomplete, degenerate along each cone of confusion, and the system closes the gap with the monaural spectral cues of the outer ear and with the dynamic cues of head movement, an arrangement in which no single cue is sufficient and the percept is the resolution of all of them together (Blauert, 1997; Wightman & Kistler, 1989).

Two themes give the field its shape. The first is calibration: the spectral cue is tied to the idiosyncratic geometry of an individual's ears and is relearned when that geometry is changed, so localization is a plastic achievement tuned to the listener's own body rather than a fixed reflex (Hofman et al., 1998). The second is robustness: the precedence effect lets the system localize in reverberant spaces by privileging the first wavefront and suppressing the echoes that would otherwise scatter the image (Litovsky et al., 1999). Underneath both sits a neural computation that the comparative work has made newly interesting, because the microsecond code that looks like a Jeffress place map in the barn owl is, in mammals, an inhibition-shaped balance between two hemispheric populations, so a single perceptual problem has more than one biological solution (Carr & Konishi, 1990; McAlpine et al., 2001; Grothe et al., 2010). The open questions concern how the separate cues are weighted and fused into one location, and how that fusion is learned and maintained (King et al., 2001); that localization is a computed inference from partial cues, rather than a direct readout of a spatial sense, is no longer in doubt.

Common Misconceptions

The ear directly senses the direction of a sound, the way it senses pitch or loudness.

It does not. The cochlea analyses frequency and discards direction; where a sound came from has to be reconstructed by the brain from differences between the ears and from the outer ear's filtering. Localization is a computed inference, not a primary sensation (Middlebrooks & Green, 1991).

Interaural time and level differences pin down a sound's direction on their own.

They cannot. Every direction on a cone around the interaural axis produces the same interaural difference, so a source in front and its mirror image behind are indistinguishable from the binaural cues alone. Front-back and elevation ambiguities are resolved only by the spectral cues of the outer ear and by head movement (Blauert, 1997).

An echo is heard as a second, separate sound coming from the wall.

Usually it is not. Within the precedence window the reflection is fused with the direct sound and suppressed as a directional cue, so a single source is heard in its true position; the reflection becomes an audible echo only when its delay exceeds the echo threshold. This is why rooms do not sound like a chaos of directions (Litovsky et al., 1999).

Glossary

Azimuth.

The horizontal angle of a sound source around the head, the dimension of direction carried chiefly by the binaural cues.

Binaural cue.

A cue to direction that depends on comparing the signals at the two ears, namely the interaural time difference and the interaural level difference.

Coincidence detector.

A neuron that fires only when its inputs from the two ears arrive together; in Jeffress's model, fed by delay lines, it reads out interaural time difference as a place.

Cone of confusion.

The cone of directions around the interaural axis that all share the same interaural time and level difference, and so cannot be told apart by the binaural cues alone.

Duplex theory.

Rayleigh's account on which interaural time differences localize low frequencies and interaural level differences localize high frequencies, the two dividing the range by wavelength.

Elevation.

The vertical angle of a sound source above or below the ear-level plane, carried mainly by the monaural spectral cue of the outer ear.

Front-back confusion.

The characteristic localization error of mistaking a source in front for its mirror image behind, or vice versa, because the two share the same binaural cues.

Head-related transfer function.

The direction-dependent filter describing how the head, torso, and outer ear transform a sound on its way to the eardrum; its spectral peaks and notches carry elevation.

Interaural level difference (ILD).

The difference in intensity between the two ears, produced by the head shadowing the far ear; the dominant azimuth cue at high frequencies.

Interaural time difference (ITD).

The difference in arrival time between the two ears, produced by the extra path to the far ear; the dominant azimuth cue at low frequencies.

Minimum audible angle.

The smallest change in the direction of a source that a listener can reliably detect; about one to two degrees straight ahead, growing toward the side.

Monaural cue.

A cue to direction available at a single ear, principally the spectral colouring imposed by the outer ear, which carries elevation and front-back information.

Phase locking.

The firing of auditory nerve fibres at a consistent phase of the waveform, which preserves the fine timing the brainstem needs to measure interaural time differences.

Pinna.

The visible outer ear, whose ridges and cavities filter incoming sound in a direction-dependent way, supplying the spectral cue to elevation.

Precedence effect.

The perceptual rule by which the location of a fused sound is set by the first-arriving wavefront and later reflections are suppressed as directional cues, enabling localization in reverberant spaces.

Woodworth's formula.

The spherical-head approximation giving the interaural time difference as r(θ + sin θ)/c, for head radius r, azimuth θ in radians, and the speed of sound c.

Key Researchers

Jens Blauert (1938-2026). Founder of the Institute of Communication Acoustics at Ruhr University Bochum and author of Spatial Hearing; he gave the standard psychophysical synthesis of human sound localization, drawing together the binaural cues, the cone of confusion, and the role of head movement. Faculty Page - Wikipedia - ORCID

Benedikt Grothe. Professor and Chair of Neurobiology at Ludwig-Maximilians-Universität München; his work on the mammalian brainstem showed that interaural time differences are computed through precisely timed inhibition, revising the classical delay-line picture of binaural coincidence detection. Faculty Page - Google Scholar - Wikipedia

David McAlpine. Professor and Academic Director of Macquarie University Hearing in Sydney; he proposed the two-channel population model of interaural time-difference coding, on which mammals read azimuth from the balance of activity between two broadly tuned hemispheric channels. Faculty Page - Google Scholar - ORCID

John C. Middlebrooks. Professor of Otolaryngology and Neurobiology at the University of California, Irvine; a leading experimentalist on human and cortical sound localization, he quantified listeners' accuracy in free field and virtual space and re-examined the duplex theory by measuring how listeners weight each cue. Faculty Page - ORCID

Lord Rayleigh (John William Strutt) (1842-1919). Cavendish Professor of Physics at Cambridge and Nobel laureate; he framed the duplex theory of sound localization, distinguishing interaural time differences at low frequencies from interaural level differences at high, which remains the organising principle of the field. Wikipedia

Frederic L. Wightman. Professor Emeritus of Psychology at the University of Wisconsin-Madison; he pioneered virtual auditory space, synthesising free-field listening over headphones from measured head-related transfer functions to isolate the spectral cues that resolve elevation and front-back confusions. Faculty Page

Frequently Asked Questions

What is sound localization?
It is the auditory system's determination of the direction, and to a lesser degree the distance, of a sound source; because the ear analyses frequency and not direction, the location has to be reconstructed from differences between the ears and from the outer ear's filtering (Middlebrooks & Green, 1991).

How do we tell which direction a sound comes from?
Mainly from two binaural cues: the sound reaches the near ear slightly sooner (the interaural time difference) and slightly louder (the interaural level difference), and the brain reads horizontal direction from these differences (Rayleigh, 1907).

What is the duplex theory of sound localization?
Rayleigh's principle that interaural time differences carry direction at low frequencies, where the head does not shadow the sound, while interaural level differences carry it at high frequencies, where the head casts an acoustic shadow (Rayleigh, 1907).

What is the cone of confusion?
It is the set of directions around the axis through the two ears that all produce the same interaural differences; a source in front and its mirror image behind lie on it, which is why the binaural cues alone cannot separate front from back (Blauert, 1997).

How do we tell whether a sound is in front or behind, or above or below?
From the outer ear. The pinna filters sound differently depending on the direction it arrives from, adding spectral peaks and notches that signal elevation and front-back, and small head movements provide a further, dynamic cue (Wightman & Kistler, 1989).

Why don't echoes in a room confuse us about where a sound is?
Because of the precedence effect: within a few milliseconds the reflections are fused with the direct sound and suppressed as directional cues, so the first-arriving wavefront sets the perceived location (Litovsky et al., 1999).

How does the brain measure differences of a few millionths of a second?
Jeffress proposed coincidence-detector neurons fed by delay lines, so that the interaural time difference is read out as the position of the most active neuron; the barn owl brainstem realises this scheme almost literally (Jeffress, 1948; Carr & Konishi, 1990).

Do all animals localize sound the same way?
No. The barn owl uses a Jeffress-style place map, but mammals read interaural time difference from the balance of activity between two broad populations, shaped by precisely timed inhibition rather than by delay lines (McAlpine et al., 2001; Grothe et al., 2010).

References