Acoustics paper

BINAURAL HEARING

BY G. W. STEWART

University of Iowa

Any adequate theory of hearing must explain all the perceptions of binaural audition. I shall speak of three important divisions in reference to these binaural effects, not because they are new to those present, but because they give certain facts which must be explained in any really satisfactory theory of hearing.

The first is the binaural intensity eect. Here there are two significant facts. By different intensities at the ears, the frequency and phase conditions being alike at the two ears, there will be caused different displacements of the phantom source of sound from the median plane, the angie of displacement being proportional to the logarithm of the ratio of the intensities at the two ears. I have tested this law quantitatively for several frequencies from 256 to 1000 cycles and have found it to hold admirably. I have also shown quantitatively that the intensity ratio required for a given angular displacement of the phantom source is many times greater than the difference of intensity that would be experienced at the ears were such a source actually placed at the given angular displacement from the median plane and not unusually close to the head. This statement refers to frequencies say less than 1200. Then, at these frequencies, the intensity effect cannot be the cause of localization. Later the cause will be assigned. But for the moment your attention is directed to the quantitative fact which has not been previously suggested, that this logarithmic law cannot have its origin in causes produced by the experiences of the individual, for, in the frequency region named, he has no correlation between intensity and localization as perceived. This logarithmic law is then only a part of something, I know not what, that is more significant. An adequate theory of hearing must then explain not only the cause for the logarithmic intensity effect, but also should state a more profound law.

The second important fact in the binaural intensity effect is that in many individuals there are certain large regions where this effect does not exist. For example, in my own case, for several hundred cycles on either side of 1000, I can increase the intensity at one ear until it is 100 times as great as at the other without at the same time having any

A paper on a special program of the Acoustical Society, December 1929.

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1930] G. W. STEWART 3[5

motion of the phantom source frc m the median plane. I have no suggestion in the direction of an explanation of the existence of these lapse regions. That too, must be the burden of an adequate theory of hearing.

The second effect is the binaural phase eect. The history of this is a long story. There have been many workers and at the present time there is not entire agreement. My remarks shall be confined to sustained sounds though a great deal has been done with impulsive sounds. The essential fact is that a difference of phase at the ears, the other factors being the same, will produce a localization of the phantom source at an angle from the median plane which is proportional to the phase difference if that is less than 180 . Second, the effect is essentially a difference-of-time effect. This is shown not only by direct experiment but indirectly by the fact that there is no confusion for complex sounds near the median plane. Third, computation shows that at least for frequencies less than approximately 1200 qualitatively the respon- sibility for localization near the median plane may be placed on the phase effect. The fourth significant point is that this effect can not be due to intensity either directly or indirectly because an individual can have a marked phase effect in precisely that frequency region where his intensity effect is actually absent. This discovery is, I fear, lost in the literature because no subsequent workers have referred either to it or to its importance. The evidence is sufficient, however, to cause the removal from psychological treatises of all expression of belief that the phase effect may be directly or indirectly an intensity effect. Regarding the above phase discussion as a whole, it is necessary to conclude that localization in the limited degree here stated depends upon the nature of the stimulus. Turning now to sounds that are not sustained we may remark that psychologists are particularly active in experiments with impulsive sounds. My own inclination would be to understand hearing first with sustained sounds and then extend observations to include

impulsive sounds. The latter would be more complicated physically and therefore more difficult to explain satisfactorily. On the other hand, the sustained sounds are more complicated psychologically because of the introduction of fatigue and doubtless other elements. But one is strongly influenced by the greater possibility of quantitative meas- urements to favor sustained sounds. This difference in views upon the part of psychologists and physicists gives good reason why physicists should be more active in this field. There should now be added to this


346 JOURNAL OF THE ACOUSTICAL SOCIETY [APRIL, brief account the statement that the phase effect, though commonly limited to frequencies less than about 1200, yet with exceptional individuals and some experience may have its limit raised to several thousand at least. The concluding remark concerning the phase effect is merely a reminder that this peculiar and important effect must be explained by any adequate theory of hearing. In this connection we should be reminded that by the perception called localization the ears can detect time differences of the order of Ill00,000 part of a second. The ears seem to be unique in this respect. Whether this remark is very significant or not, I do not know.

The third important binaural effect is that of binaural beats or beats occasioned by presenting the two sources one to each ear. These of course demand two tones differing slightly in frequency.

The chief early facts obtained may, with the intensities of the two sounds equal at the ears, be summarized as follows:

If binaural beats occur that are more rapid than one per second there appears one maximum and one minimum in one beat cycle. (According to Lane these binaural beats occur at less than 800 to 1000 cycles.)

When the beat frequency is about one in from one to five seconds, there appear three maxima in one beat cycle, two of them occurring on either side of a phase difference of 180 .

Lane found later an important additional fact: if the intensities are not nearly equal an optimum condition for beats also exists with one intensity 100,000 to 1,000,000 times the other. He explains these quite plausibly by cross conduction. Lane also found a lapse region of intensity ratio where beats do not occur.

All of these facts are not fully explained. I early attempted to explain the equal intensity beats by the excitation of skull sounds and the stimulation of the utricle and saccule. The argument seemed good; at least it showed unquestionably that no cross-conduction theory with two organs of hearing gave a satisfactory explanation. Later Lane set forth the theory that these beats produced by equal intensities were merely subjective, that they depended upon phase equality and the attention of the individual. I confess that both my explanation and Lane's leave me in grave doubt. Both are deficient in explaining the entire phenomena of these maxima both quantitatively and qualitatively. A theory of hearing will doubtless find, in all these facts of binaural beats a test for its adequacy.


1930] G. W. STEWART 3[7 I have cited three binaural effects in which there remains much to be

explained. In all of these quantitative research only should now be encouraged. Qualitative results are capable of misleading anyone searching for adequate theories. Some may think it is quite unfair to shoulder the desired explanations of these binaural effects upon him who would set up a theory of hearing. But I fear the task must include the biophysics and biochemistry of the entire act from the varying pressure at the drumskin to the perception of the individual. This is a long, long task. No present theory encompasses this range of phenomena. For the immediate future I anticipate that we must find some satisfaction in what are merely contributions to theories of hearing, without adopting any of them as satisfactory.


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