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gineers have accomplished rcmarkabic things with mulłiple microphoncs and speaker arrays. On thc othcr hand, scicntists have had to content them-sclvcs with a single stationary sound source and have even had to resort to the artifieiality of earphone listening. To datę no psycho-acoustic laboratory has developed the essential array of moving multiple sound sources in a large anechoic chamher nor devised the required servo systems and X-Y recorders to program and record the stimuli and the subjecfs response. One can only anticipate such reasearch for the ncxt decade or two.

Nevertheless. a unique and e\en ex-citing chapter in psycho-acoustics em-braces a number of interesting discov-eries regarding the directionality of human hearing, the relativc impor-tance of the several possible •‘cucs’* for directionality. the conditions under which directionally may be improved, and mathematical-statistical models of binaural hearing.

Two Ears Better fhan One?

The first question that must be re-solved is whether two ears are rcally better than one. The answer. for all practical purposes, is negatice for almost all aspects of hearing except

Fig. 2. Our ears »err* a* search radar. our eye* as lirę conlrol radar.

directionality. For contact detection or sensory discrimination any improvc-mcnt of the binaural combination over the monaural involves only a decibel or two—a negligible percentage. For loealization of sounds in space. how-ever. the monaural modę has almost nothing to recommend it. Whether one is judging distance to a sound source or angular direction. a second ear is almost indispensable. Probably the best confirmation for this statement in-volves tests madę with bats. While normal bats will be able to avoid wires strung around a room up to 76% of the time, bats with one ear cocered. however, have an avoidance record of 38-41%—35%, in this case, being due to chance alone.

One asks, then. how does this come about ? Both ears hear the same thing so how can the same information. being 100% redundant, fed into the scc-ond ear, add what amounts to neto information on the basis of which we can make further and remarkably precise judgments?

Fig. 1. We all lWe In an auditory world madę up ol concentric spheres.

The secret is that when one takes not a first but second look at the information reaching the two eardrums at any moment in time. the acoustic signals can usually bo shown to be markedly difTerent in their "hyperfine" details.

The temporal (or time determining) characteristics of the ear, its frequen-cy and intensity handling capacities, and the layout of its nervous system are admirably adapted to make a dis-tinction on the basis of just those hyperfine details by which the two acoustic signals differ. By "make a dis-tinction", we mean that the mechan-ical construction of the ear itself does not biur any of the features of the acoustic signal but passes them on. transformed, to the auditory nerve whcre they are again transformed (neural codingt, sent upward to the brain, and decoded, with surpassing exaetitude. into sensation.

Temporal Characteristics

Lot us first consider the temporal characteristics (time of arrival and phase) of the peripheral organ of hearing. If one presents a series of clicks to the ear. they do not merge into a continuous tonę until the repetition ratę reaches many hundreds per second. Contrast this phenomenon with the eye, where the critical flicker fre-quency is something under 50 per second—a relativcly slow-acting unit. But the ear is not a bioehemical system with slow time-constants like the eye —it is a mechano-hydro-electrical system with almost critical damping. (It is of course true that sevcral distin-gishable d.c. and a.c. components with-in the cochlea—or inner ear—are maintained by bio-chemical-metabolic equations. but the stimulation of thc auditory nerve fibers is true electrical stimulation. generatod by the hair cells within the inner ear.)

Only by keeping in mind the very fast-acting naturę of the peripheral organ of hearing can one believe the almost incredible performance revealed by laboratory tests. ]f one keeps all other physical parametcrs constant ex-cept the time of arrival at the eardrums of a short burst of noise, the subject can detect a difTercnce in arrival time of as little as 6 miUionths of <t seeontl. Evidently the end-organ and itsassociated nervous system carry and translorm time patterns with great fidclity—certainly with suflicient fidelity to provide an accurate sense of direction on the basis of time of arrival of the stimulus at the two ears.

Let us assume, for easy calculation, that sound travels one foot per milli-second. In .00001 second it will travcl .01 foot. In this case a sound source would havc to be ofT the mid linę by only a few degrees for one to sense, by the time-of-arrival cue alone. that the sound was not, in fact. in the median piane. (See Fig. 3.) This cue can apply. of course. only to discon-tinuous sounds.

Notę, however, that with a continuous pure (one another correlated cue is present. namely. time of arrival at the eardrums of a particular point in the phase. In this case the ears are sensitive to differences in phase at the eardrums at any moment in time. If om* varies the phase tor inserts a time delay. which is the same thingi in one arm of a pure tonę which is split and led to the two drums. one has the illusion of the sound moving back and forth betwecn the two ears. Judgments of the (illusory) "sidedncss". in degrees off the mid linę of the tonę, corres-pond surprisingly well to the actual geometry of a point source and an imaginary linę between the ears where the geometry would. under actual acoustic conditions. produce the phase difTercnce generated electronically. A lead or lag by 100 microseconds of a peak at one ear usually pcrmits a elear judgment of "olT mid linę”. (See Fig. 4.)

Phase relations as a loealization cue in naturę have. of course, a serious limitation where the distance between the two ears equals one wavelength. Herc the peak-to-peak times of arrival are idcntical and non-informative. This is morę apt to occur at high frequen-cies and with smali heads. This is why the bat has abandoned continuous tones and emits, instead, a series of heacily frequency-modulated and cx-tremely brief tones, thus utilizing fre-quency difTerences and times of arrival rather than phase for loealization pur-poses.

Intensity Capacities

Let us now consider the intensity handling capacities of the ear and the possible intensity cues to loealization.

Of course. if the head is tumed away from a sound source there will be a difTercnce in intensity depending on the sound dccay ovcr the distance. but the cue is not a simple one even with the immobile pinna (outer ear parts)

Fig. 3. Our ear* can tell time-ol-arrWal diłferencet brief-er than ten microtecond*.

8    B -A *.00001 SECOND

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