A Preliminary Study of the Significance of Partial Tones in the Localization of Sound

James Rowland Angell

AN adequate theory of the localization of sound must take account of three general problems: (1) the physical conditions (extrinsic to the organism), upon which localization depends, must be determined; (2) the precise physiological processes involved in such localization must be discovered; and (3) the psychological activities, which are concerned, must be analyzed and described. Up to the present time no theory has dealt exhaustively with all of these considerations, and the psychological problem has often been practically disregarded.

The extensive experimentation of recent years has rendered it essentially certain that the most important precondition on the physical side of sound localization is found in the relative amplitude of the sound-waves distributed to the two ears.[1] It is also known that, in distinction from their amplitude, the composition of the sound-waves is sometimes of significance in localization. The evidence bearing on this point, however, is lacking both in definiteness and in detail.

The varying intensity in the stimulation of the two end organs with the resultant effects upon the cortex and other ganglionic centers has often been regarded as a sufficient and self-evident basis for an explanation of the physiological facts concerning localization. Wundt has advanced the idea that tactile nerves are stimulated by the movements of the tympanic membrane and thus contribute to the localization processes. He has made a similar suggestion with reference to stimulations of the tensor tympani muscle.[2] This type of view has been rigorously criticised by Stumpf, who emphasizes, among other difficulties, the undoubted fact that we can correctly localize two simultaneous sounds.[[3] E. Mach early suggested the theory that the external ears act as resonators modifying the quality of sounds heard from different directions, and affording thus a criterion of direction.[4] Theories like those of Preyer and Munsterberg have attempted (thus far with limited success) to make the semi-circular canals responsible for the physiological phenomena.[5] So far as these latter theories emphasize the release by sound stimulations of quasi-reflex movements of localization, they point to an important and genuine feature of such processes, whether their conception of the physiological mechanism involved be accepted or not.

On the psychological side various factors have been described as contributing to localization: e. g., (1) the immediate consciousness of position in an auditory space;

( 18) (2) the consciousness of positional relations gained by visual and other supplementary imagery; (3) the consciousness of tendencies to movement on the part of the head and eyes; and (4) apparently, at times, the consciousness of cutaneous sensations from the shell and membrane of the ear and possibly the tensor muscle.[6] Criticism has been much devoted to combating the frequent and careless assertion that we are conscious of the intensity of the sound heard by each ear and that we in this way localize the source of the sound upon the side most intensely stimulated. The fact is, of course, that we are conscious of one sound and one intensity only, and this is referred to some specific spatial position. But the details of the strictly psychological portion of our general problem have been, perhaps, most often honored by neglect. The recent paper by E. A. McC. Gamble is a notable exception.[7]

So long ago as 1875 Lord Rayleigh had made observations upon the localization of tuning-fork tones, which led him to surmise that differences in the quality and timbre of sounds, as heard by the two ears, were of quite as much significance for localization, as the mere differences in the intensity of the fundamental tone.[8] In 1879 S. P. Thompson, discussing experiments of his own with the pseudophone (cf. the similar observations of Weber, Berle/tie der Gesellscllaft der Wissenscltaften [Leipzig, 1851], p. 29 M. and P. Cl.), came to a like conclusion, which he formulated in a later article somewhat more explicitly.[9]

Despite the instructive character of these investigations, it must be admitted that the conditions which were employed are somewhat unnatural, and that in so far, therefore, they jeopardize the scope of the inferences which may be confidently based upon them. In certain of Lord Rayleigh's experiments, for example, two tuning-forks were struck on different sides of an observer, and then, one of them being stopped, the position of the other was estimated. Evidently the conditions produced by sounding two tones and then suddenly subtracting one are very different, both neurally and psychologically, from those arising when a tone is heard as it originates from some single source. In Thompson's interesting experiments an artificial pair of pinnae were used, enabling an exaggeration of the effects of reflection, etc., produced by the natural pinnae. That the localization of sounds could in this fashion be disturbed in certain definite ways is not surprising, nor is it remarkable that tuning-fork tones should show much less liability to modification in this manner than more complex sounds. But, in the nature of the case, such observations cannot furnish a complete chain of evidence as to the differences characterizing the localization of these various kinds of sounds under normal conditions. Notwithstanding the limitations upon the implication of these experiments, they certainly constitute presumptive evidence in favor of the belief that quality changes are

( 19) of genuine significance for sound localization, especially when taken in connection with such observations as Mach's,[10] and such mathematical deductions as Lord Rayleigh has made, showing that, save for a few positions, there is an extremely small difference in the intensity of the stimulation of the two ears by the fundamental tone of a sound.[11]

Pierce has demonstrated that localization in the median plane, which is notoriously uncertain and inaccurate, can be vastly improved, when complex sounds are used, by learning to note the modification in tone-color, or timbre, which is connected with different positions in this plane.[12] He has also made tests with organ pipes and tuning-forks, which suggest that auditory judgments of distance are affected by tonal complexity, the richer tones tending to be judged nearer than those more nearly pure.[13] In a paper published in 1865 Mach remarked a contrary fact and promised further communications upon the subject, which I have, however, been unable to find.[14] Bloch has made certain observations, which appear to agree with Pierce —the fuller, richer tones being judged nearer.[15] On the other hand, the computations of Grinwis, showing the relative intensity of the components of a complex sound for various distances, furnish a theoretical confirmation of Mach's view.[16] The issue is really somewhat ambiguous. Richer sounds may ordinarily be judged nearer than those more nearly pure. The upper partial tones of a complex sound may be relatively more prominent when the sound is heard from a distance, and still the total sound effect be poorer and less full, than when the same sound is heard near at hand.

The extended experiments recently carried out in the Psychological Laboratory of the University of Chicago showed conclusively that persons totally deaf in one ear could localize sounds of sufficient complexity with considerable accuracy, whereas approximately pure tones could not be localized at all.[17] The localizations were evidently based upon the modifications which the partial tones of complex sounds undergo, when the position of the sources of the sounds is changed relative to the ear. The introspective evidence offered by the observers in these tests confirmed perfectly the objective results in pointing to this explanation. It is interesting to note in passing, in connection with Pierce's observations upon median plane localization, to which reference has already been made, that in the Chicago experiments certain of the persons deaf in one ear distinguished front and back with distinctly greater accuracy than the normal subjects. It will be remembered that for normal persons the intensity criterion is for points in the median plane peculiarly ambiguous. But quality differences are relatively reliable, if one has learned to employ them.

The observations reported in this paper constitute an immediate outgrowth of these several previous discoveries and form an effort to begin the systematic investiga-

( 20) -tion of the part played by the partial tones in the localization of sound. The positive outcome of the work thus far is largely methodological in character and bears most immediately upon points (1) and (3) mentioned in the opening paragraph, and indirectly upon point (2). For reasons which will presently appear, the work is necessarily extremely slow, and the results already attained do not seem to warrant a more pretentious title than that I have chosen. The probability of unavoidable delay in the completion of the observations is the justification for publication at this time. Moreover, the implication of the experiments successfully executed seems altogether definite and distinctly significant for the theory of auditory localization.

angell_1903b.gif A solution of the problem in hand evidently involves certain indispensable conditions which the apparatus was designed to meet. There must be (1) a series of sounds of controllable intensity, including (2) at least one approximately pure tone. It must be possible (3) to produce these sounds at any position relative to the observer without his previous knowledge of their location. It must be possible (4) to have all the sounds given at equal distances from the observer. It is desirable also (5) that the distance should be capable of variation, although the present paper does not deal with experiments in which changes of this kind were employed. Not least in importance, as dearly bought experience has taught me, is (6) the absolute prevention of the reflection of the sounds. Working under expert assurance that reflection could be eliminated by properly arranged draperies, I wasted much valuable time indoors, with the result that often tuning-fork tones, when opposite one ear, would confidently be localized as opposite the other. My failure may have been wholly due to unskilful devices on my part, but I certainly question very seriously whether experiments with tuning-forks can be satisfactorily carried on save in the open air. With many kinds of sounds this consideration is of minor consequence. I may mention in connection with these indoor experiments the interesting effects of fatigue which were repeatedly apparent. If one ear were fatigued for a tone, and within a few moments both ears were permitted to receive the sound, the latter would often be confidently localized as opposite the unfatigued ear, or sometimes as in the median plane, depending on the degree of the previous fatigue. Thompson, in the paper already mentioned, remarks a similar phenomenon, but much less extreme than in my observations.[18]

( 21)


To meet the conditions named, work was carried on outdoors on windless nights —a deplorably infrequent circumstance in Chicago—rendering the observations very protracted. A narrow platform was erected upon which was mounted the apparatus shown in the accompanying diagrams (Figs. 1 and 2). The upright support (Fig. 1) carries a strong light semicircle of steel with a radius of four feet, which is so arranged as to permit a metal carriage mounted on soft rubber rollers (Fig. 2) to travel up and down upon it. The semicircle is marked off in degrees, so that the position of the carriage can at any time be determined. The carriage is held at any desired height by friction screws acting upon the rollers. The semicircle is very accurately hung and revolves noiselessly. The chair shown in the cut is adjustable in height, and when in use is put at such a point as will bring the line joining the observer's ears into the equatorial plane of the sphere determined by rotating the circle. The chair is mounted on heavy felt cushions which insulate it from any sound-waves which might be transmitted through the semi-circle. The platform under the chair is marked off like a compass, so that any position of the circle can be determined.

Upon the carriage are fastened the various instruments used for giving the sounds. These are so adjusted that at whatever position the sound is given a constant phase is presented to the observer.

angell_1903b1.gif FIG. 2 Carriage with tuning fork, resonator removed

The sounds employed were as follows: from (1) a tuning-fork of 1,000 vs.; (2) a stopped pipe of 768 vs.; (3) a reed pipe of 768 vs.; (4) a bell with a fundamental tone of approximately 2,048 vs.; and (5) a noise made by a telegraphic sounder. It would have been desirable to work with tones which were all of like pitch, but this was out of the question for the time being. It will be observed, however, that all the tones are within the middle range of the musical scale, and that they are quite close together in pitch, two of them being of identical vibration rate. The sounder and bell were operated by closing a noiseless electric contact. The two pipes were controlled by blowing through rubber tubing. The fork requires a somewhat more detailed description. It should be said that the intensity of all the sounds was kept as nearly constant as possible, and that the intensity aimed at was such as to render all of them perfectly distinct, without their becoming unpleasant.

The arrangement for the tuning-fork constituted the most elaborate and most troublesome technical part of the problem. To secure as nearly pure a tone as possible a carefully constructed resonator was made and mounted over the fork. The fork was supplied with a magnet between the tines, and this magnet was then connected with the circuit of an interrupting fork of just one-half its own fork's rate of vibration. This is the device employed by Helmholtz in his celebrated experiments

( 22) upon vowel sounds.[19] By bridging the spark in the driving fork one secures a tone in the second fork free from all accessory noises of interrupters, hammers, etc. In my experiments the driving fork was kept, where it could not be heard, in a house at a distance from the experimental platform. That I thus secured an absolutely pure tone is, perhaps, more than can be confidently asserted. Resonator analysis failed to detect any tone apart from the fundamental, and, so far as concerns my observers, it can be positively stated that they were utterly unable to discern any complexity in the tone. The tone of the stopped pipe was not to them noticeably complex, so that they could confidently detect the overtones, and yet it was not so perfectly pure as the fork. It had the muffled effect characteristic of such tones. All the other sounds were noticeably complex.

My observers sat in an erect position, with eyes closed, but without a head rest. Previous experiments had led me to fear the effect of such a rest, when working with tones of the present character. My subjects were instructed to eschew all tendency to head movements while making their localizations, and I watched them as closely as possible to detect any such movements. Light, open arm rests enabled them to retain an accurate sense of their general bodily orientation and, after a little practice, readily to assume and retain the correct position. They were trained in the nomenclature employed to designate the various positions on the sphere, and in cases of any doubt they were asked to open the eyes and point. Needless to say, on such occasions precautions were taken to move the semicircle and carriage first, so that their position during the experiment should not be thus discovered. The sounds were given for periods of three to four seconds. This time was hit upon as the result of actual experiments made to determine that duration of the stimulus which would permit clear perception, without any feeling of stress or haste, and at the same time avoid tedium and the confusion sometimes caused by wandering attention. The several tests with different sorts of sounds were made as nearly comparable as possible by using the same positions. This was, of course, not known to the subjects, who were given no indication of any sort as to the point from which they might expect the next sound. Moreover, the order was altered in which the various kinds of sound were given at the several positions employed.

Of the three men who served as reagents for me one had had no previous practice in such observations, one had had a moderate amount, and one was extensively drilled. The results gained from all of them agree thoroughly in their fundamental implications, although there is naturally some quantitative variation. I place most confidence in the results of the most experienced observer, and I shall devote myself mainly to his reactions. This is the more warranted by the relatively small number of experiments I have succeeded in making under reliable conditions some four hundred only. The accompanying table (Table I) exhibits compactly the results of this observer's localizations:


(Reagent, J. B. W.)

Average Error 
in Degrees
Sounder Reed Pipe Bell Stopped
Longitude 2 9.5 5 30.5 53
Latitude 7 4.5 11 13.5 41
Total 9 14 16 44 94


We may say at once, that under such conditions as these—i. e., entire freedom from reflection—there is never any confusion of points in one lateral hemisphere with points in the other, save when one approaches very near to the median plane. Even then this form of error is extremely rare and probably attributable to wandering attention, to accidental suggestion from some extraneous source, or to some similarly irrelevant circumstance. The case of pure tones formed no exception to this rule, and the theories, which make the intensity of the stimulation of the two ears fundamental in the explanation of localization, are at least correct so far as concerns the assignment of a sound to one of these hemispheres or the other. Sounds originating in the median vertical plane are also correctly referred to this plane.

When one scrutinizes the results further, however, it becomes clear that within the lateral hemispheres accuracy of localization appears to be a function of the complexity of the sound. The average error in localizing the tuning-fork tone is 94, which is more than a quadrant. With the stopped pipe the error is less than half as large, while with the bell and reed pipe it falls to less than a sixth, and with the noise is at its minimum with less than a tenth of the error with the fork. I lay no great stress on these precise figures, yet I have no question but that they indicate the intrinsic nature of the differences in the capacities of localizing these different forms of sound. Certainly the objective record was perfectly confirmed by the subjective assurance of the observers and their promptness of localization. Moreover, when, as in certain special experiments, the sounds were repeated two or three times in quick succession with a very brief duration for each stimulus, the accuracy of the localizations with the complex sounds was distinctly improved. This procedure seems to have the effect of making the quality differentia more noticeable than when the sounds are more continuous.

The comparison of the errors in latitude and longitude is not entirely free from ambiguity, because no points nearer than 45 to the poles were actually employed for giving the sounds. The observers did not know that this was to be so, but it makes comparison relatively unprofitable. In the case where localization is most accurate, the errors in latitude are notably larger than those in longitude, as one might anticipate from the standpoint of the intensity theory. In the tuning-fork case it would seem that mere chance might in the main be accountable for the results with a single exception to be mentioned in the next paragraph.


The longitudinal regions immediately opposite the ears show fewer errors, and errors of smaller amount, in the localization of the pure tones, than do the regions in front and behind this. Indeed, the most striking difference in the localization of complex and simple tones is to be found in the ascription of the exact location of sounds to the various points in these lunes diagonally in front and behind. This is in accord with Steinhauser's computations upon the effect of intensity.[20] In the vertical plane, in which lies the line joining the ears, the localizations of pure tones are apparently relatively accurate save as regards height. This constitutes the exception above mentioned and seems to agree with Lord Rayleigh's observations and mathematical calculations, showing that the objective differences in the intensity of the sounds reaching the two ears, which is always relatively small under normal conditions, becomes rapidly less, as we move away from the line joining the two ears. With the most experienced of my observers the average error of localization in latitude is nearly four times as large as that of longitude in this region.

angell_1903b2.gif  F, B, U, D, R, L indicate, respectively, front, back, up, down, right, left

Taken in their entirety the experiments seem to indicate that even with pure tones intensity differences alone are sufficient to enable our confident and correct assignment of such sounds (1) to the median vertical plane, (2) to the lateral hemisphere from which they may chance to come, and (3) the further less accurate and less up, down, right, and left    confident determination that certain sounds of this character belong to the vertical transverse plane of the head. But accuracy of localization as regards altitude in this transverse plane and accuracy in the several regions between this plane and the median plane—accuracy such as is commonly possessed, involving an average error of 10 to 25—is apparently dependent upon tonal complexity and the modifications in timbre, which complex sounds undergo through the change in the intensity of their partials, when heard from different directions. Localization in the vertical median plane is inaccurate with all sounds, but most inaccurate with pure tones.

The matter can be put diagrammatically as in the accompanying cut, which represents the sphere within which the observer sits (Fig. 3). Sounds in the planes FUBD and LURD can, as the intensity theory requires, be localized with considerable accuracy as regards the plane to which they belong. The exact point in the plane from which they originate is relatively uncertain, when intensity is the only available criterion. The experiments seem to show with some definiteness that, as we pass from one of these planes to the other, inaccuracy of localization rapidly increases, unless

( 25) there be definite qualitative differences in the successive sounds. Without such qualitative variations the lune UEDG is subject to persistent confusion with the lune UHDK and the several points in each lune respectively are subject to gross confusion with other points in the same lune. Whether the confusion of points in the upper with points in the lower hemisphere is in the case of pure tones notably different in quantity or other characteristics from the confusion of such points with others in the same hemisphere, it is not at present possible to say.

These statements concerning localization as a function of tonal complexity must not be understood as meaning that we are reflectively conscious of this local sign of direction involved in the changing quality, or timbre, of the tones. Sometimes this is noted, but it is not in any way necessary that it should be. Whether or not conscious experience teaches us in childhood to discriminate these varying sensations as having a varying spatial significance, is a question of genetic psychology with which it is not possible here to deal. Certainly as adults we make the localizations in an almost reflex manner. But the basis of the localizations is found in these symbols reported in consciousness as differences of quality, to which we have come to attach certain space values.

My subjects used much visual imagery in their judgments. My best trained observer seems in his localizations to be conscious of little else beyond such imagery and an occasional tendency to move the head in the direction of the sound. For him to localize a sound means chiefly to get a visual image of the sounding object in the position where he supposes it to be.

The work thus reported opens up the problem which I hope subsequently to work out in more detail. Much fuller observations along the line already pursued are required to permit more confident and inclusive conclusions. Differences in the localization of pure tones of widely varying pitch must be investigated, for the sound shadows involved with such tones and the diffraction experienced by them vary very considerably. It will be necessary to study more carefully the number and character of the partial tones concerned in the differences we have noted. This involves the whole question of relative intensity and pitch in the partials. All one can say at present is that with sounds of medium pitch such accuracy of auditory localization, as our common everyday experiences reveal, seems immediately connected with the presence of distinguishable (though not necessarily noticed) partial tones. When such partial tones are absent or very inconspicuous, gross inaccuracy of localization is at once apparent. Detailed information relative to the localization of very high and very low tones is still to be secured. The effect of the duration of the sound upon localizing deserves closer inspection. In connection with several of the points just mentioned the peculiarities of auditory judgments of distance, as distinct from direction, also require more exhaustive investigation than they have as yet received.

In conclusion I wish to express my sincere obligations to Mr. J. B. Watson and Dr. M. L. Ashley, who have given me unsparingly of their time and assistance. I am also indebted to Dr. Warner Fite for assistance in the construction of the apparatus, and to Professor E. W. Mahood for service as reagent.


  1. For discriminating criticism of the important views of modern scientists, see PIERCE, Studies in Space Perception.
  2. WUNDT, Grundzuge der physiologischen Psychologie, Vol. II (1893), pp. 93 ff.

  3. STUMPF, Tonpsychologie, Vol. II, pp. 53 ff.

  4. MACH, "Bemerkungen umber die Function der Ohrmuschel," Archiv fur Ohrenheilkunde, Vol. IX (1875), p. 72.
  5. Cf. PREYER in Pfluger's Archiv, Vol XL, p. 586; MUNSTERBERG, Beitrage zur Psychologie, Heft 2, p. 1S2.
  6. The general psychological question of the reality of an auditory space has been luminously discussed by Stumpf, and in some of its more empirical features is best treated by Pierce. Cf. STUMPF, loc. cit., and also Ueber den psychologischen Ursprungder Raumvorstellung, Leipzig (1873) ; PIERCE, loc. cit.
  7. GAMBLE, Psychological Review, Vol. 1X (1902), pp. 357-73.

  8. RAYLEIGH, Transactions of the Musical Association, (1876); also Philosophical Magazine (5), Vol. I11 (1877), p. 456.

  9. THOMPSON, Philosophical Magazine, January-June (1882), p. 415; ibid. (5), Vol. VIII (1879). pp. 385-90.

  10. Loc. cit.; also " Bemerkungen uber den Raumsinn des 0hres," Poggen. Annalen, Vol. CXXVI (1865), p. 331; Sitzungsberichtc der Wiener Akademie, Vol. L (1864), Leber einige der physiologischen Akustik angchorigen Erscheinungen."
  11. Loc. cit.
  12. Loc. cit., pp. 92 ff.
  13. Loc. el L. pp. 163 f.
  14. Poggen..Annalen. loc. cit.
  15. BLOCH, Das binaurale Horen, Wiesbaden, 1893.
  16. GRINWIS, "Ueber cylindrische Schallwellen," Pogg. Annalen. 1877, Beibl. 8, p. 443.
  17. ANGELL AND FITE. Psychological Review. Vol. VIII (1901). pp. 225, 449.
  18. Philosophical Magazine, Vol. (5) XII, p. 351.
  19. HELMHOLTZ, Sensations of Tone, translated by ELLIS, 3d ed., p. 399
  20. STEINHAUSER, "Theory of Binaural Audition," Philosophical Magazine (5), Vol. VII (1879), pp. 181, 261


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