(back to SpatialLocalizationPaper)

Examining MonauralLocalization finds it more successful than many theorists expected. Our ability to locate objects in the median plane at all points to a well-developed monaural (or at least, non-interaural) ability, but what now concerns us is its relation to our entire system of auditory localization. The smallest detectable change in angle of a white-noise source is not appreciably reduced when one ear is plugged, especially when head movements are allowed. However, with pure tones the monaural case lags behind the performance of the binaural, indicating that some additional factors are at work (Moore, 159). Here we study two in depth:

Interaural intensity differences underlaid the first theories of localization, dating back to Rayleigh's binaural intensity ratio (Gulick, 318; Blauert, 155).* In any case, the underlying concept is rather elementary: as with the pinnae but on a larger scale, the head casts an acoustic shadow which obscures part of the signal from the ear more distant from a source. The apparent threshold frequency -- a wavelength corresponding to the dimensions of the head -- is about 1500 Hz, but detailed measurements show a detectable intensity difference (3 dB) as low as 250 Hz, and the maximum difference (20 dB) not until 10 KHz and higher. (To be sure, the largest shift in dI/dF is in fact around 1500Hz). When viewed as a function of azimuth, the curves are roughly parabolic with vertex at 90 degrees (Gulick, 324-5).**

Mathematics aside, it's clear that the brain gains a wealth of information from the purely physical interactions of air and mass, particularly with high-frequency waves. When a source moves laterally, the frequency-dependent intensity functions above serve to filter the sound in complex ways, not merely change its loudness. In this way, we can say that more distant (from 0 degrees azimuth) sounds will have attenuated highs at the more distant ear (Gulick, 326), which the brain can compare with the unequalized source heard at the other ear.

Reducing these effects to the case of lateralization, we unsurprisingly find that it takes about 15-20 dB of interaural intensity difference for subjects to report a sound as completely at one ear; between these extremes, the dependence is roughly linear, although as with any lateralization experiment the results represent rather subjective data. Below about 1.6 KHz, a signal may actually generate two distinct auditory events, suggesting that while we can obviously detect interaural intensity differences at these frequencies, we are not attuned to hear their effects as localizing (Blauert, 157-160).

The second major factor in binaural localization are the phase/time differences that result from the distance between the source and each ear. In short, due to the physical separation of the ears, a sound wave will reach the nearer one sooner (and at a "sooner" point in its compression/rarefaction pattern) than the other (Handel, 99). A rough geometric calculation with a spherical head corresponds rather well to experimental measurements: the time difference varies from 0 to 0.6 msec and back to 0 as the angle of incidence does from 0 to 180, with nearly linear dependence (Handel, 100; Gelfand, 299). As with the pinnae reflections discussed earlier, the absolute time difference is very small, although strictly detectable in this case. Unlike with the pinnae, however, the interference that results is a mental phenomenon. That is, our brain can sense that the two ears' signals are out of phase, even though the two waveforms are not physically interfering -- because in fact, they are (for our descriptive purposes) the same waveform.

A threshold of directionality again lies at the head's wavelength (1500 Hz). At and above this point, a phase difference becomes more and more ambiguous; is a tone perceived in phase offset by a complete cycle while nearer the left/right ear, or in absolute phase while equidistant? A particularly illustrative experiment follows:


This experiment is more or less the phase-based (and low-tech) equivalent of the cited lateralization experiment for intensity differences conducted with headphones. However, it is worth exploring the phase effect with headphones, as two important conclusions about the underlying psychoacoustics can be drawn. First, the use of electrical signal generators and headphones allows us to vary the phase and the intensity simultaneously, which quickly leads to the finding that one effect can be made to "cancel" the other, known as time-intensity trading. That is, introducing a phase difference that would lead to a leftward lateralization while "correcting" with a rightward-leaning intensity difference can produce an auditory event in the middle of the head. The precise relationship in the literature is marked by inconsistency, but it is clear that much more phase delay is required above 1500 Hz (Gelfand, 307). Indeed, near 1500 Hz the result is not centralized lateralization, merely confusion (Moore, 153).

The second phenomenon of note is that of binaural beats. If two frequencies are fed dichotically through headphones, a beating phenomenon similar to that of normal beats occurs at the difference frequency. However, we emphasize that this effect occurs entirely in the subject's mind, just like the phase effect. It continues to be audible with much larger frequency gaps than with physical beats, and even when one of the tones is below the threshold of hearing (Gelfand, 296). Oddly enough, men can perceive a greater range than women, except when the women reach the onset of menstrual flow (Moore, 154). Most interesting for our purposes, however, is the upper limit: although head diffraction is not a factor in these headphone-administered tests, subjects' ability to resolve binaural beats ends around 1500 Hz. This suggests that our neural system is equipped only to parse phase differences our ears would experience in the wild.

Thus, phase differences predominate in determining localization of lower frequencies (below 1500 Hz), and intensity differences the higher frequencies, though as we've seen this effect is not fully realized until 4 KHz or so. As such, we observe a total localization blur (including all factors) that from a baseline of 1-2 degrees increases between 1-3 KHz, peaking at around 3 degrees / 1.8 KHz. In the horizontal plane, blur is minimized in front and to a lesser extent in the rear, with maxima at the sides (Blauert, 40-41; Gelfand, 302-303). We also observe a dependence on sound pressure level: localization blur is high for low-level sounds but quickly decreases once a signal's intensity reaches 20dB and higher. Similarly, very transient sounds are localized with more statistical uncertainty than longer ones, only levelling out around 1000 msec (Blauert, 156). A final and unusual dependence is found between frequency and elevation: higher pitches are perceived up to 20 degrees higher (and vice versa) regardless of the source location -- even in subjects young enough not to know that high frequencies are called "high" -- with a directly frontal auditory event corresponding to about 1 KHz (Blauert, 106).

Unfortunately, these dependencies on geometry and signal characteristics do not exhaust the possibilities we wish to disambiguate. There is a locus of points extending from each ear for which all interaural differences would be equal given a spherical head, called the cone of confusion (Moore, 158; Gelfand, 303; Handel, 111). Luckily, a human head has some additional resources: the MonauralLocalization effects described previously can come into play, as can head movements. The latter come in two classes: reflexive movements, usually to face a source (placing it where localization blur is minimized in addition to the obvious visual benefits); and conscious searching motions, which examine the way sound changes with different orientations. The latter must be heterosensory actions, since to judge the effect a proper determination of motion must be made along with any aural calculation. In practice, rotating laterally, and rotating & tipping vertically seem to be the most common motions in response to both low- and high-frequency sounds; these correspond to the ability to determine front/rear and above/below position (Blauert, 178-185, which I note gives the mathematical derivation of these correspondences). For the complementary motion sensation, any of the following turns out to suffice: the position, tension, and posture receptors of the neck and vertebrae; the vestibular [inner ear's balance] organ; or the sense of vision (Blauert, 189).


*Helmholtz and followers went as far as specifically discounting phase differences as a factor.

**Interestingly enough, below about 1000Hz, the intensity difference has minima at 90 degrees, with peaks around 45 and 135 degrees. This is likely due to sound waves partially diffracting on the head and interfering with those that "bent" around it. See Handel, 103 and Gelfand, 300.


onward to BinauralMasking