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{"created":"2022-01-31T12:57:33.358951+00:00","id":"lit28738","links":{},"metadata":{"alternative":"Studies from the Yale Psychological Laboratory","contributors":[{"name":"Matsumoto, Matataro","role":"author"}],"detailsRefDisplay":"Studies from the Yale Psychological Laboratory 5: 1-75","fulltext":[{"file":"p0001.txt","language":"en","ocr_en":"RESEARCHES ON ACOUSTIC SPACE.1\nBY\nMatata ro Matsumoto.\nE. Weber2 seems to have been the first to call attention to the errors in localizing sounds. The particular problems involved seem to be two : i. the perception of the direction from which a sound comes; and 2. the perception of its distance. The investigations described in the following pages were made in the attempt to contribute data toward the solution of these two problems. The work was begun (1894) in the Psychological Laboratory of the Imperial University of Japan (Tokyo) at the suggestion of Professor Motora ; the greater part of the work, however, was done during the years 1896-1898 in the Psychological Laboratory of Yale University under the supervision of its director, E. W. Scripture. Many suggestions were also received from Professor Ladd.\nI. Preliminary investigations.\nThe first series of experiments was conducted according to Preyer\u2019s statistical method.3 Instead of Preyer\u2019s sound-helmet, a hollow spherical cage was devised as is shown in Figure 1. The imaginary surface of the sphere whose diameter is 1.35\u2019\" is divided into 8 equal parts by 4 vertical great circles. \u25a0 The surface is again divided horizontally by the equator and by two small circles parallel to the equator at a distance of 450 from poles. The intersecting points of these vertical and horizontal circles correspond to the 26 terminal points of 13 axes or diameters of the sphere. These 13 axes may be divided into three classes.\nI. Three primary axes which cut each other at right angles.\n(a) The frontal axis, or the diameter of the sphere from right to left in the plane of the equator. As this line corresponds to an imaginary line\n1\tSubmitted to the Tokyo Imperial University as a thesis for the degree of Hakusli (Ph.D. ).\n2\tEn. Weber, Ueber den Mechanismus des Geh\u00f6rorgans, Ber. d. kgl.-s\u00e2chs. Ges. derWiss., math.-phys. Classe, 1851, 29.\n3\tI\u2019rkykr, Die Wahrnehmung der Schallrichtung mittelst der Bogeng\u00e4nge, Archiv f. d. ges. Physiol. (Pfl\u00fcger), 1S87 XL 586.\nI\nI","page":1},{"file":"p0002.txt","language":"en","ocr_en":"2\nM. Malsumoto,\ndrawn through the external openings of the two ears of the subject seated in the cage, it may be called the auditory axis or the rl (right-left) axis.\n(/>) A vertical diameter which intersects the frontal axis at its middle point. This may be called the vertical or the ou (over-under) axis.\nThe plane determined by the two axes /-/and ou is called the frontal plane.\n(c) A horizontal diameter drawn perpendicular to the frontal plane, through the intersecting point of the frontal and the vertical axes. This may be called the sagittal or the fb (front-back) axis.\nThe plane determined by the sagittal and the vertical axes is called the the sagittal or median plane, while the plane determined by the sagittal","page":2},{"file":"p0003.txt","language":"en","ocr_en":"Researches on acoustic space.\n\u00f6\nand the frontal axes is called the horizontal plane. In the present essay no use will be made of median, frontal or horizontal planes except the primary ones, as just defined; the terms are always to be understood in this way.\nThe above three axes correspond to the X, Y, Z axes of the Cartesian system of coordinates, and represent the fundamental axes upon which our standard space is constructed with ourselves as the center.\nII.\tSix secondary axes, every two of which lie in the plane determined by the primary axes and cut each other at right angles.\n{(f) Two secondary frontal axes. These are the diameters lying in the frontal plane at the distance of 45\u00b0 from the frontal and from the vertical axis.\n(e) Two secondary sagittal axes. These are the diameters lying in the median plane at the distance of 450 from the sagittal and from the vertical axis.\n(/) Two secondary horizontal axes. These are the diameters lying in the horizontal plane at the distance of 450 from the sagittal and from the frontal axis.\nIII.\tFour tertiary axes. These are the diameters lying at 450 from the three neighboring secondary axes in each case.\nThese thirteen axes are illustrated in the model, Figure 2.\nThe 26 terminal points of the 13 axes are named in the following way :\nI.\tThe 6 terminal points of the 3 primary axes are /(front), b (back), o (over), u (under), r (right), / (left).\nII.\tThe 12 terminal points of the 6 secondary axes are :\n(a)\tfo (front-over), bu (back-under), fit (front-under), bo (back-over).\n(b)\tor (over-right), ul (under-left), nr (under-right), ol (over-left).\n(<r) fr (front-right), bl (back-left), fl (front-left), hr (back-right).\nIII.\tThe 8 terminal points of the 4 tertiary axes are :\n{a) for (front-over-right), bul (back-under-left).\n(b) fol (front-over-left), bur (back-under-right).\n{(') bor (back-over-right), ful (front-under-left).\n{(/) bol (back-over-left), fur (front-under-right).\nThe person to be experimented upon is seated in the inside of the cage ; his head is adjusted by means of a head-rest fixed to the back of the chair in such a way that his visual axis in the normal position of the body will lie in the median plane, and his auditory axis (an imaginary line drawn through the openings of the ears) with the frontal axis. Then the experimenter gives a short sound at one of the 26 terminal points, and the observer, with his eyes closed, is to judge the direction of the sound. In","page":3},{"file":"p0004.txt","language":"en","ocr_en":"4\n)/. Miitsumoto,\nmy experiments the sound was produced by means of a telephone or a small metallic hammer. Fifty experiments were made for each of the 26 points. The observer was Mr. T. Oku, a student of philosophy.\nIf we could not perceive the direction of sound at all, it would be, as Preyer1 noticed, theoretically possible that each of the 26 directions would be confused with each of the remaining 25 directions so that there would occur in all 26* \u2014 26 = 650 confusions. Therefore in 676experi-\n1 Preyer, Die Wahrnehmung tier Schallrichtnng mittelst tier Bogeng\u00e4nge, Archiv f. d. gcs. Physiol. (Plliiger), 1SS7 XI. 586.","page":4},{"file":"p0005.txt","language":"en","ocr_en":"Researches on acoustic space.\n5\nments the correct judgments would amount only to 26. Or in 1,000 experiments the correct judgments would not exceed 40. This was not the case, for in 1,300 experiments (780 telephone sounds and 520 metallic clicks) it was found that the correct judgments amounted to 768, namely, \u00a7\u25a0 of the total number instead of as theoretically required. Therefore, the perception of the direction of sound cannot be regarded as purely accidental.\nIt was noticed that in these experiments none of the 26 directions was actually confused with more than 8 directions. Of 650 possible kinds of errors only 113 kinds were actually observed in our 1,300 experiments and, indeed, many of these 113 kinds occurred only once or twice. What are the remaining kinds of errors which did not occur actually, though they were theoretically possible? This question leads to a very important principle in the perception of the direction of sound. In the experiments the following results were noticed.\n1.\tNo sound on the right side was perceived as being on the left side, and no sound on the left side was perceived as being on the right side. That is, none of the series, r,fr,for, or, bor, br, bur, nr, fur, was confused with any of /, fl,fol, ol, bol, bl, bul, ul, ful, and vice versa. As there are 9 ^-directions and 9 /-directions, then 162 (i. e., 2X9X9) kinds of errors must be subtracted from the total number of errors theoretically possible.\n2.\tNo sound on the right or the left side was localized in the median plane. That is, none of the above series was confused with the series in the median plane f,fo, 0, bo, b, bu, u, fu. Therefore we must subtract 144 (i. e., 2x9x8) kinds of errors from the total number theoretically possible.\n3.\tNo sound in the median plane was localized on the right or left side of the plane. That is, \u00bbone of the series f, fo, o, bo, b, bu, u, fu, was confused with /, fl, fol, ol, bol, bl, bul, ul, ful, r, fr, for, or, bor, br, bur, nr, fur. Here again 144 (i. e., 2 x 8 x 9) kinds must be subtracted from the total number.\nSubtracting these 450 kinds of errors from 650 theoretically possible kinds of errors we get 200 kinds of errors as actually occurring. These 200 kinds of errors are those which will be actually observed. They consist of 72 (i. e., 9 x 9 \u2014 9) confusions on the right side, 72 (i. e., 9 X 9 \u2014 9) confusions on the left side and 56 (i. e., 8 x 8 \u2014 8) confusions in the median plane.\nIn respect to these three fundamental facts the results of my own experiments perfectly agree with those of Preyer.\n1 hese facts lead us to believe that the possession of two ears gives us","page":5},{"file":"p0006.txt","language":"en","ocr_en":"6\nM. Matsu moto,\nan important means of perceiving the direction of a sound. When a sounding body is situated in the median plane, there is no difference between the intensities (and the other possible properties) with which vibratory movements arrive at the two ears. But when a sound is situated outside of the median plane the results will be different and the greater the angular distance from the median plane the greater will be the difference. The relative amount of this difference\u2014the binaural parallax\u2014may give us effective data by which we can judge the direction of the sound. If such a supposition be true, the direction of a sound will be best perceived when it is situated in or around the frontal or auditory axis, for here the difference will be greatest; we can also expect that the direction of a sound will be fairly well recognized when it is situated in the sagittal axis, for that axis is unique in its relation to the two cars. Moreover, it may be expected that the direction of a sound in the horizontal plane will be best perceived, for the shape of the pinna is most favorable for receiving a sound in the horizontal plane, especially in the case of binaural perception. Now let us examine the results of our experiments more closely to see whether they support these suppositions.\nFor each primary axis the ratio of the correct judgments to the total number was as follows : for rl axis, -fYy ; for fb axis, t7\u00ef\u00ef2\u00fc ; for ou axis, tYj. These results show that the sounds in the rl axis are best localized, while the sounds in fb axis are better localized than those in on axis. In Preyer\u2019s experiments the ratio of the correct judgments for ou axis was greater than that for fb axis.\nAgain the ratio of the correct judgments for the 8 directions in each primary plane was as follows : for the horizontal plane (/, fr, r, br, b, bl, l, fl), ; for the frontal plane (o, or, r, ur, it, ul, l, ol), -2r<A ; for the median plane (/,/<?, o, bo, b, bu, u,fu), fjjf. The results show that the sounds in the horizontal plane are localized best of all, while the sounds in the frontal plane are better localized than those in the median plane, these results agree with those of Preyer and Arnheim.1\nThe influence of the sounds from the right and left sides is so strong that even the ratio of all correct judgments for those 18 directions in which r and l take part has a greater value than the ratio of all correct judgments for either of the 18 directions in which / and b or o and u take part. In the last two groups r and / do not occur so often as in the first. The ratios of the correct judgments were as follows : for rl\n'ARNHEIM, Beitr\u00fcge zur Theorie von Schallempfindungen mittelst der Bogeng\u00e4nge, Diss., Jena 1887.","page":6},{"file":"p0007.txt","language":"en","ocr_en":"Researches on acoustic space.\n7\n18 directions, ; for fh 18 directions, ; for au iS directions, -\u00b1i\u00a3. Our supposition that the possession of two ears gives us by binaural parallax an important means for perceiving the direction of sound seems to be supported by these results. But this general principle is made more complex by various circumstances. For upon examining the number of the correct judgments in the three sets of hemispheres it was found that :\n1.\tThe direction of a sound in the right hemisphere was more correctly judged than that of a sound in the left hemisphere. The correct judgments for r,fr,for, or, l>or, hr, bur, ur, fur amounted to 278, while the correct judgments for /, fi,fol, ol, ho/, hi, bul, ul, ful amounted to 257. If the binaural parallax is an important means of localizing a sound, then it is highly probable that the localization will be more or less influenced by the difference in sensitiveness which exists between the two ears. Although the subject was not examined in this respect, it is probable that there was such a difference.\n2.\tThe direction of a sound in the front hemisphere was more correctly judged than that of a sound in the rear hemisphere. The correct judgments for f, fo, fu, fl, fol, ful, fr, for, fur amounted to 260, while those for ho, h, hu, hoi, bul, hi, bor, hr, bur amounted to 237. This difference probably finds its explanation in the function of the pinn\u00e6 whose shape is not favorable for receiving sounds in the rear hemisphere.\n3.\tLastly, a sound in the lower hemisphere was better localized than a sound in the upper hemisphere. The correct judgments for fu, u, hu, bul, ul,ful, bur, ur,fur amounted to 271, while those for fo, o, ho, hoi, ol, fol, bor, or, for amounted to 206. We cannot say that this will always be the case, for in Preyer\u2019s experiments the sounds were better localized in the upper hemisphere than in the lower hemisphere. The results of my experiments might have been more or less influenced by the probable reflection of sound from the lower parts of the apparatus and the floor, in consequence of which- the sound might have been peculiarly colored, as it were, according to its position, and better discriminated by the observer. Apart from such influences the results might have been influenced by the form of the pinn\u00e6.\nThe examination of these three groups of results enables us to say with great probability that the differences in the degrees of sensitiveness in the two ears and the action of the pinn\u00e6 are the factors which render our perception of the direction of sound more or less complex.\nlabi\u00e9 I. summarizes the results of these preliminary experiments. In this table the objective positions of sounds are indicated in the vertical column at the left, and the perceived directions arc given in the hori-","page":7},{"file":"p0008.txt","language":"en","ocr_en":"Table\n8\nM. Maisumoto,\nill\n\n\u2022s\n\ns\n\\D\trto M I^HM\u00ce\nN\\OON N \u2022-\u00bb\nTf\tX C H -t N H\nN N W m rj-\nM o\tf'i H M Cl\nt_l\t_\ntrj\u00c4 h\tu->\nC?\n'C iah N\nr^\u00ee\u00c2 \u00abh N ci\nr'I\u00c2CC Cl h i^fO\nCn fO\nrj- ci -* C m\n\u25baH --S3I *H\nM\tTj- X'-. O\nt-|\tM\nro rf m\nvO \u00c7IO\th ci\nS\u2019-^ - 4: \u2022\n\n\u25a0 ^\nTotal : 59 44 57 31 68 56 4S 37\t58 38 73 24 3S 48 67 30 74 40 34 65\t22 60 62 46 39 82\t1300","page":8},{"file":"p0009.txt","language":"en","ocr_en":"Jlesearehes on acoustic space.\n9\nzontal columns. The number of judgments of each kind is given by the figures which are found below each perceived direction.\nIn the same manner as the actual possibility of the confusion of the directions of sounds is limited to certain distinct regions, so the directions which are most liable to be confused with each other are also restricted to narrower limits than the regions of actual possibility.\nIn the following lists the frequency of the confusion between pairs of the 26 directions is shown by the figures. Here it is regarded as a matter of indifference whether\u2014for example\u2014^ is confused with for, or for with fr. and likewise for any other pairs of directions that may be confused.\nList I.\nConfusions in the Median Plane.\nConfusion between f and fo ( 15), fu ( 13), b ( I ).\n\u201c\t\u201c\tfo and 0 (17),/\u00ab\t(4), bo\t(3) ; 6 (l)\n\u201c\t\u201c\t0 and bo (23),/\u00ab\t(2), \u00ab\t(1).\n\u201c\t\u201c\tbo and b (18), bu\t(4),fu\t(1).\n\u201c\t\u201c\tb and bu (16),/\u00ab\t( 10), u\t(S).\n\u201c\t\u201c\tbu and u {27),fu{ I ).\n\u201c\t\u201c\t\u00ab vcaAfu (2).\nList II.\nConfusions in /he Left Hemisphere.\nConfusion between /and 0/(14), bol ( 6), \u00ab/( 5), /\u25a0/( 5 ), ff), ful(f), fol(2), bul{i). \u201c\t\u201c\t/and/o/(i4),/\u00ab/(i3), bol(z), \u00ab/(3), 0/(1).\n\u201c\t\u201c\t/\u00ab/and 0/(17), bol(3)fu/(2).\n\u201c\t\u201c\t0/andbol{22), fil(5), ul (2), bl(2).\n\u201c\t\u201c\t/\u00ab/and //( 13), /\u00ab/( 2 ), bu'( I ).\n\u201c\t\u201c\thi and <W( 9 ), \u00ab/ ( 5 ), fu/( 2 ).\n\u201c\t\u201c\t/w/and \u00bb/( 2y).\n\u201c\t\u201c\tul and ful(f).\nList 3.\nConfusions in the Right Hemisphere.\nConfusion between r and or(x6), ur (7), bor((>), f \u25a0((>), for{f), br(i), fur(l).\n\u201c\t\u201c fr and for( 13 ), fur ( 4 ), br( 4 ), o/-( I ).\nfor and or( 17 ) for (5), fur( 5 ).\n\u201c\tor and bor( 15), nr ( 3), br ( I ).\n\u201c\tbor and br( S ), fur ( 7 ), bur( 3 ), \u00ab/\u2022( 2 ).\nbr and bur(7), nr (5 ), fur( 3).\n\u201c bur and ur( 20), fus ( 2).\n\u201c\t7/r and fur{ 5 ).\n1 hese results show that the points which are most liable to be confused with each other are those which are situated nearest to each other in the region of actual possibility of confusion. This is in accordance with our view","page":9},{"file":"p0010.txt","language":"en","ocr_en":"10\nM. Matsu moto,\nthat the localization depends upon the binaural parallax, for the sounds at the points situated nearest to each other in the regions of actual possibility of confusion are those which are more nearly equal in their relations to the two ears than the sounds at other points. Moreover, we can notice a certain similarity in the three lists above. The errors that occur most frequently in the second list (first two columns) are of similar kinds with the most frequent errors (first two columns) in the third list. Moreover, if we disregard the question of right and left\u2014thereby cutting off /and r from the members in the second and third lists, then the most frequent errors (first column) will be the same in all three lists. In other words, the errors which occur most frequently in the median plane are repeated with almost the same regularity in the left and right hemispheres. The results are arranged in Table II.\nIn connection with the above three lists it is interesting to know the relation of the angular magnitude of the error to its frequency. In the median plane the possible frequencies of the errors out of a total of 64 are as follows : for 1800, S times, or 12 yic/o for 1350, 16 times, or 25% ; for 90\u00b0, 16 times, or 25^ ; for 450, 16 times, or 25% ; for o\u00b0, S times, or i2j4%.\nIn the actual experiments, however, 400 judgments were distributed as follows:\tfor 1800, 3 times, or ; for 1350, 13 times,\tor 3% ;\nfor 90\u00b0, 20\ttimes, or 5% ; for\t450,\t131 times, or 33%; for\to\u00b0, 233\ntimes, or 58%.\nComparing these two series it becomes evident that in reality the errors are not evenly distributed. The error of o\u00b0 magnitude (i. c., correct judgment) is by far the most frequent ; the error of 450 (next to the smallest magnitude) comes next to it, and the errors of greater magnitudes occur less frequently as the magnitude increases.\nThe same observation is to be made concerning the errors in separate hemispheres. If the errors were evenly distributed the frequencies for the right and left hemispheres would\tbe as\tfollows : for 1190, 2x4\ttimes, or\n5c/o of the\ttotal number; for\t9S0,\t2x8 times, or 10% ;\tfor 90\u00b0,\n2 x 12 times, or 15% ; for 85\u00b0, 2x8 times, or \\oc/0 5 for 6o\u00b0, 2x8 times, or 10% ; for 590, 2x8 times, or 10% ; for 450, 2 x 24 times, or 30r/(, ; for o\u00b0, 2X9 times, or nc/c-\nIn the actual experiments, however, 900 judgments were distributed as follows: for 1190, 9 times, or 1% of the total number; for 98\u00b0, 7 times, or Tsff% ; for 90\u00b0, 30 times, or 3\t; for 85\u00b0, 8 times, or\n; for 6o\u00b0, iS times, or 2% ; for 590, 23 times, or 2j\\% ; for 450, 270 times, or 30% ; for o\u00b0, 535 times, or 59%.\nJust as in the median plane, the errors of smaller magnitudes happen","page":10},{"file":"p0011.txt","language":"en","ocr_en":"Position of sound.\nResearches on acoustic space.\n'S\n'S\nS\nk\nS*\nS\nW fO N N\n\u00bb!? O rfC VO \u00ab\n_*\tSi\n55 ^\nf*> -i\nN\nN\nO fO\nTfCJ-fvO to m vo ro\nCN\nO CO\n'S\ns\n\n\n\u2022 ^ !\nI","page":11},{"file":"p0012.txt","language":"en","ocr_en":"12\nM. MatsU moto,\nalso in the both hemispheres more frequently than the errors of greater magnitudes. The exceptionally great percentage for 90 degrees arises from the familiar confusions between front and back and between above and below ; these will be considered in detail later.\nFrom these results it follows that the smaller the angular distance between the two points, the greater is their confusion with each other. Though this fact is a matter of common experience, the\" experimental determination of it is very important.\nThe frequencies of the errors relating to the magnitude, which we actually observed in our experiments, are shown in Table III.\nTadle III.\n\to\u00b0\t45\u00b0\t59\t6o\u00b0\t85\t90\u00b0\t98\t119\u00b0\t135\u00b0\t1S00\tis uni her ot experiments.\n/\t42\t7\ti\t\t\t\t\t\t\t5\u00b0\nr\t45\t5\t\t\t\t\t\t\t\t5\u00b0\nbl\t26\t19\t\t5\t\t\t\t\t\t5\u00b0\nfo-\t40\t7\t\t2\tI\t\t\t\t\t5\u00b0\nol\t3\u00b0\tJ9\t\t\t\ti\t\t\t\t5\u00b0\nor\t31\t17\t\t\t\t2\t\t\t\t5\u00b0\nfi\t35\t12\t\t3\t\t\t\t\t\t5\u00b0\nfi-\t31\t14\t\ti\t\t4\t\t\t\t5\u00b0\nni\t34\t12\t\t3\t\ti\t\t\t\t5\u00bb\nur\t27\t18\t\t4\t\ti\t\t\t\t5\u00b0\nbol\t12\t25\t6\t\t3\t4\t\t\t\t5\u00b0\nbor\t13\t21\t6\t\t\t5\t2\t3\t\t\t5\u00b0\nfol\t25\t22\ti\t\t\t2\t\t\t\t5\u00b0\nfor\t20\t24\t4\t\t\t2 '\t\t\t\t50\nbul\t29\t20\tI\t\t\t\t\t\t\t5\u00b0\nbur\t40\t9\t\t\t\ti\t\t\t\t5\u00b0\nful\t24\t14\t3\t\t2\t\t5\t2\t\t\t5\u00b0\nfur\t31\t5\ti\t\t2\t7\t4\t\t\t5\u00b0\nbo\t16\t30\t\t\t\t4\t\t\t\t50\n0\t32\t18\t\t\t\t\t\t\t\t5\u00b0\nf\u00b0\t27\t18\t\t\t\t4\t\ti\t\t5\u00b0\nf\t40\t10\t\t\t\t\t\t\t\t5\u00b0\n11\t3\u00b0\t12\t\t\t\t7\t\t\ti\t5\u00b0\nb\t32\t16\t\t\t\ti\t\t\ti\t5\u00b0\nbit\t29\t21\t\t\t\t\t\t\t\t50\nf\"\t27\t6\t\t\t\t4\t\t12\ti\t50\nTotal 768\t\t401\t23\tiS\t8\t5\u00b0\t7 9\t13\t3\t1300\nThe foregoing preliminary experiments have shown that the difference between the sensations with which a sound is heard in the two ears must be regarded as the fundamental datum for localizing the sound.\nThe next step must therefore be a closer examination of this datum of","page":12},{"file":"p0013.txt","language":"en","ocr_en":"Researches on acoustic space.\n\u00ab3\nlocalization. There are four characteristics of sound-waves by which one sound may be discriminated from another, namely, intensity, pitch, phase and complexity (or timber). The localization of a sound must be based upon a difference in one or more of these four characteristics.\nOf these four characteristics it was the question of intensity to which my chief attention was paid in the further experimental work, for from the nature of the subject the problem could be more definitely studied in reference to this characteristic than to the other ones.\nII. Dependence of the localization of a perceived sound upon\nTHE RELATIVE INTENSITIES OF THE SOUNDS HEARD BY THE\nTWO EARS.\nWe have seen in our preliminary experiments that a sound in the median plane is never localized on the right or the left side and a sound on the right or the left side is never localized in the median plane, and we have assumed that these facts depend upon the peculiar relation between the intensities with which the ears are excited by a sound in the median plane. Now the queston arises whether we do always localize the perceived sound in the median plane when both ears are excited with the same intensity. The following experiments were conducted to get an answer to this question.\ni. Dependence of the localization of a sound in the median plane upon the equal intensities of the impressions in the two ears.\nEach of the primary circles of the spherical cage was divided into degrees. In the horizontal circle the front (/) was taken as o\u00b0 and the degrees were counted on both sides of the circle from front to back, the back being i8o\u00b0. In the frontal circle the top was taken as o\u00b0 and the degrees were counted from the top downward, the point opposite to the top being i8o\u00b0 and that horizontally either right or left 90\u00b0. In the median circle the top was taken as o\u00b0, and the degrees were counted from the top downward, either front or back being yo\u00b0 and the point opposite to the top 1800.\nTwo telephones were placed at two symmetrical points of the same circle. The head of the observer was adjusted as in the preliminary experiments. The two telephones were sounded with equal intensities for two seconds. The observer was to judge the direction of the sound. The points at which the telephones were placed are given in Table IV.\nFor each pair of positions 4 to 8 experiments were made ; the total number of experiments was 125. To eliminate the effect of suggestion","page":13},{"file":"p0014.txt","language":"en","ocr_en":"14\nM. Matsu moto,\nand practice, the experiments were made in \u25a0 an irregular order, and not in the order given in the table. Mr. T. Nakashima, a well trained observer, was the subject of the experiments.\n\tAy horizontal.\t\tTable IV. B, frontal.\tCy median.\t\n\tright\tleft\tright\tleft\tfront\tback\nI\t22.5\u00b0\t22.50\t22.5\u00b0\t22.50\t22.5\u00b0\t22.5\u00b0\n2\t45\u00b0\t45\u00b0\t45\u00b0\t45\u00b0\t45\u00b0\t45\u00b0\n3\t67\u00b0\t67\u00b0\t67\u00b0\t67\u00b0\t67\u00b0\t67\u00b0\n4\t90\u00b0\t90\u00b0\t90\u00b0\t90\u00b0\t90\u00b0\t90\u00b0\ns\t112.50\t112.50\t112.5\u00b0 112.5\u00b0\t112.5\u00b0\t112.5\u00b0\n6\t135\u00b0\t135\u00b0\t0 ur> \u00ab\u201cO O >o \u00ab\u201cO\t135\u00b0\t135\u00b0\n7\t157-5\u00b0\t157-5\u00b0\t157-5\u00b0 157-5\u00b0\t157-5\u00b0\t157-5\u00b0\n8\t0\u00b0\t1S00\t0\u00b0\t180\u00b0\t0\u00b0\t180\u00b0\nThe fundamental phenomenon always observed in experiments of this kind is that the two similar impressions received by the two ears were combined into one sound.\nThe results of these experiments are given in Table V. The table is to be interpreted in the following manner. When the telephones were in the positions given in Table IV, the sound appeared to be in the directions given under similar headings in Table V ; thus Ai of the latter corresponds to A i of the former, etc. The expressions contained in the parentheses represents judgments of this character: \u201c front but a trifle upward,\u201d etc. The letter k means \u201cin the head;\u201d the other letters have the meanings given on p. 3.\nTABLE V.\nA\n1\t/. A\u00b0)> A\u00b0)> A\u00b01)\u2019 K\u00b0l)\n2\t/, /(\u00ab). /(<-)>\t''(*)> *(/)> A/)\n3\t6>\ti(i)> 'H\"). k(r)\n4\tf f b, b{k), b(k), <5(o), k, k(b)\n5\tb, b, b{k ), b(ko)\n6\tb, b, b, b, b(k)\n7\tb, b, b, b, b{k), b(ko)\n\u2022s iff /(<o. m\nB\nk, k{b), k(bu), k{o), k(/o), k(bo) k, f{o), k(t), k(b), k(b) k, k, k(u), /(o), /(o) f, /, b, b(k), b(k), b{o), k, k{b) b, b, k, k(b), bu b(u), b(k), b{u), b{ul), b it{rb), u(rb), u{f), \u00bb(>'), t'{rb)\n0, o(b), o(f)\nC\n< A\u00bb). A\u00bb), /(\u00bb), /(<>)> /(\u00ab)\n2\tA\u00b0),A\u00b0),Ao),/f\n3\tA\u00b0)> A\u00b0)> f f f\n4\t/, /, /, A*). A*)\n5\tt, *(\u00ab), f/ff\n6\tb(u), b(tt), b, b, b\n7\tu(b), u{b), \u00ab(\u00a3), b or f f or b\n8\t<\u2019(/), o(3)","page":14},{"file":"p0015.txt","language":"en","ocr_en":"Researches on acoustic space.\n'5\nTable V. shows that all the sounds were localized in the median plane. A slight deflection from the median plane, which is indicated by the letters in parentheses, seems to be the effect of slight deviations in the position of the head, in manner of placing the telephones and in occasional difference between the intensities of the two sounds, all of which we could not govern accurately.\nIn group A most sounds were perceived to be at b or h (b). But when the two ears were stimulated by sounds coming from 22.50 and\n22.50, or 450 and 450, or o\u00b0 and 1800, most of the perceived sounds were perceived to be at f.\nIn group B the sound was perceived to beat k (in the head) when the two ears were stimulated by sounds from above, whereas it was perceived to be at h or n when the two ears were stimulated by sounds from below. When the sounds were given at 0 and u the sound was perceived to be at o.\nIn group C most of the perceived sounds were localized at fo and f when the two ears were stimulated by sounds situated between o\u00b0 and\n112.50.\tBut the sounds were mostly perceived at b or u when the two ears were stimulated by sounds situated lower than 1350.\nThe conclusion seems to be justified by the results of this set of experiments that, in whichever of the three primary planes the objective sounds may be placed, the perceived sound is always localized (in so far as the sensitiveness of the two ears is the same and the two objective sounds are exactly equal) in the median plane if these sounds are placed in such a way that the distances between one ear and the sources of the sounds are equal to the distances between the other ear and the same sources respectively.\nSince equal distances have equal influences upon the intensity of a sound, the above conclusion can be expressed in terms of intensity, namely, when the two ears are stimulated simultaneously by sounds of equal intensity the perceived sound is always localized in the median plane. Conversely we can say that when a sound is localized in the median plane the intensities of the impressions in the two ears are equal.\nThere still remains the question concerning the component upon which depends the discrimination between front and back, above and below in the median plane. It is true that in the median plane the localization is very imperfect. Still the existence of some localizing power in this plane was proved by the results of the experiments conducted by v. Kries.1 Here the localization cannot be explained by the principle of relative\n1 v. Kries, Ueber das Erkennender Schallrichtung, Zt. f. Psych, u. Physiol, d. Sinn., 1S90 I 235.","page":15},{"file":"p0016.txt","language":"en","ocr_en":"i6\nM. Matsumoto,\nintensity, for the two ears are stimulated with the same intensity. The experiments of v. Kries and Rayleigh 1 show us that the possibility of the localization in the median plane depends to a great extent upon the constitution of the sound and upon practice. A pure tone, such as that produced by a tuning fork, is in general localized distinctly only with difficulty, but a noise or a tone mixed with overtones (such as the noise produced by striking small blocks against each other, or the human voice) seems to be better localized. The difference which exists between the two cases seems to arise\u2014though it it is not easy to make it definite by an experiment\u2014from the fact that the quality and pitch of a sound are more or less modified according to its position in the median plane, for the sound waves will be more or less influenced by the position of the sound with respect to the position of the pinn\u00e6. Not only the quality and the pitch, but also the absolute intensity of the sound will be different according to its position. These factors will be considered later.\n2. Dependence of the localization of a sound in the horizontal plane upon the unequal intensities of the impressions in the two ears.\nWhen a source of sound is situated not far from us, either on the left or on the right side, the intensities of the impressions produced in the two ears are not equal, for the intensity of a sound varies (according to the generally accepted law of propagation of sounds) inversely as the square of the distance. The difference between the distances becomes smaller as the source of sound approaches the median plane, while it grows greater as the source of sound moves more toward the side.\nThe question is whether or not we localize the perceived sound at different points according to the change in the relative difference between the intensities of the sensations received in the two ears. A definite answer was sought by the following set of experiments.\nIn the preceding experiments I noticed that the reflection of the sound from the surrounding walls had some influence upon the localization. It seemed desirable in further experiments to avoid this source of error, as far as possible. A small separate chamber 4 feet long, 4 feet wide and 4 feet high, with walls of felt, was arranged in a quiet spacious room on the top floor of the Yale Laboratory. Instead of a spherical cage as used in the foregoing experiments the following arrangement was made for determining the objective positions of the telephones.\nOn the floor of the chamber a circle was described, whose radius was 65'\u201c. This circle was divided into 12 equal parts by 12 radii at 30\n1 Rayleigh, Our perception of the direction of ci source of sound, Nature, 1876 XIV 32.","page":16},{"file":"p0017.txt","language":"en","ocr_en":"Researches on acoustic space.\n17\napart. The person experimented upon was seated in the center of the chamber. His head was adjusted by a support in such a way that the line connecting the openings of the two ears would intersect at its middle point an imaginary line drawn from the cent\u00e8r of the circle perpendicularly to the floor. In order to eliminate the influence of suggestion upon judgment, the eyes of the observer were blindfolded before he was allowed to enter the chamber. He consequently never knew anything of its construction or contents. Two telephone-stands of a T shape were prepared. Each stand could be erected on any of the 12 divisions in such away that the longer arm would be perpendicular to the floor and the shorter one would be parallel to the radius at that point. A telephone was hung on the shorter arm by means of strings. The height of the shorter arm was adjusted so that the telephone would lie in the same line with the openings of the ears.\nThe wires from one telephone were connected with the secondary coil of a sliding inductorium. The wires from the other telephone were connected with the two binding posts at one end of the primary coil, where the electric current coming through an electro-magnetic tuning fork in another room was to be divided into two circuits, one of which served for the primary circuit of the inductorium and the other for the circuit of the second telephone. The current for the latter telephone passed through a copper sulphate rheostat. By means of this rheostat the intensity of the current\u2014and consequently the intensity of the telephone sound\u2014could be regulated. The secondary coil, with which the wires of the first telephone were connected, carried a pointer which passed over the divisions of the millimeter-scale on the base of the inductorium. By changing the distance between the coil the intensity of the induced current\u2014and consequently the intensity of the telephone sound\u2014could be regulated.\nIn this set of experiments a self-interrupting electro-magnetic fork of 250 complete vibrations was placed as a shunt across the telephone circuit.\nI he current from a lamp battery1 passed through the fork during half its period of vibration, while during the other half of the period it passed to the telephone apparatus. Thus a tone of 250 vibrations could be produced in the telephones.\nThe standard intensity of the current could be regulated at pleasure by changing the lamps of the battery. When the telephone circuit was closed by the key each telephone produced a sound of definite pitch, with an intensity depending upon the amount of liquid resistance introduced or upon the distance of the secondary coil from the primary one.\n1 .Scripture. New apparatus ami methods, Stud. Yale I\u2019sych. Lab., 1S96 IV 76.\n2","page":17},{"file":"p0018.txt","language":"en","ocr_en":"i8\nM. Matsu moto,\nFirst group.\nIn the first group of experiments the telephones were placed directly opposite the openings of the ears at a distance of 40\"\". The current was turned on for a little more than a second, the two sounds being produced simultaneously. When the sounds ceased the observer was to announce the direction of the sound which he perceived. The experimenter was to take the record both of that direction and of the distance of the secondary coil from the primary, which represented the intensity of the current for one telephone. During the experiment the intensity of the current for the other telephone was kept constant.\nThe first subject was A. Fisher, the laboratory janitor, a well-trained observer without the slightest knowledge of the arrangements or interest in the results. He always perceived only one sound instead of two separate sounds and projected the sound in one of five directions in a horizontal plane about the same level as his eyes, i. e., at r,fr,f, fl, /, according to the difference between the intensities of the two sounds. If we call for the sake of convenience the relative intensities \u201cstrongest,\u201d \u201cstronger,\u201d \u201cequal,\u201d \u201cweaker\u201d and \u201cweakest,\u201d the results can be summarized as follows.\n1.\tWhen R, intensity of the component of the sound on the right side, was \u201cstrongest,\u201d and Z, intensity of the component of the sound on the left side, was \u201c weakest,\u201d the perceived sound was projected toward r.\n2.\tWhen R was \u201cstronger\u201d and Z \u201cweaker\u201d the perceived sound was projected toward fr.\n3.\tWhen R and Z were \u201cequal \u201d the perceived sound was projected toward /.\n4.\tWhen R was \u201cweaker\u201d and Z \u201cstronger\u201d the perceived sound was projected toward fl.\n5.\tWhen R was \u2018\u2018 weakest \u2019\u2019 and Z \u201cstrongest\u201d the perceived sound was projected toward /.\nThe next subject was Dr. C. E. Seashore, assistant in the laboratory. He knew where the two telephones were placed and how the intensities would be varied. The results were practically the same as those of the first observer. The only difference was that the second observer could distinguish finer differences of direction than the first, observer could. This suggested the possibility of having the results stated in a scale of degrees. This was tried with success on Mr. C. Wakamatsu, a young Japanese student of science, who was totally ignorant of the method of the experiment and the arrangement of the apparatus.","page":18},{"file":"p0019.txt","language":"en","ocr_en":"Researches on acoustic space.\n19\nBefore stating the results it must be made clear that the exact relation between the intensity of the electric current and the intensity of the telephone sound is not known, and that the rate of change in the intensity of the current which corresponds to the distance of the secondary coil from the primary can not be numerically stated. All we can say is that the intensity of the telephone sound increases with the increase of the induced current and that the intensity of the induced current becomes stronger as the secondary coil is moved nearer to the primary coil. The rate of change in the intensity is not constant ; in the particular instrument employed it is rather rapid between 2\u201c\u201c and 4cm, slow between 4\"\"' and 9cm and rapid again beyond <fm. It must also be noted that we cannot average directly the results for several days ; owing to the nature of the experiment we can not keep all the conditions perfectly constant during different days. Slight changes in the positions both of the telephones and the head of the observer and minor errors in apparatus were sufficient to produce somewhat varying results. I am, therefore, compelled in all succeeding experiments to take the average of the results of experiments conducted within a few hours on the same day, during which the above mentioned conditions could be kept tolerably constant. On the present occasion no attempt will be made to establish a numerical relation between the variation in the relative intensities of the two sounds and the variation in the localization of the perceived sound. We must be satisfied if the general dependence of the latter upon the former is proven.\nTaui.e V],\nDistance of the secondary coil\tCase I.\tNumber of\tCase IL Distance of the secondary coil\t\tNumber of\nfor the left telephone.\tLocalization.\texperiments.\tfor the right telephone.\tLocalization.\texperiments.\nIOcm\tfr S\u00b0\u00b0\t3\t10\u00ab\u201c\tJI 8o\u00b0\t2\n9\tfr 27.S\t2\t9\t\u00df 75\t2\n8\tfr 25\t2\t8\tfl 60\t2\n7\tfr 22.5\t2\t7\t\u00df 41-7\t3\n65\tfr 18\t2\t6-5\tbl 70\t2\n6\tfr 10\tI\t6\t/\t2\n5\t\u00df 0.5\t2\t5\tf or h\t2\n4\t\u00df \u00b0S\t2\t4\tfr 60\t2\n3\t\u00df 25\t2\t3\tfr 60 or hr 60\t2\n2\t\u00df 27-5\t2\t2\tfr 60\t2\ni\t\u00df 55\t2\tI\tfr 60\t2\n\u00b0-5\t\u00df 75\tI\to-5\tfr 82.5\t2\nI n Case I the probable error varies from 0 to \u00b1 30%.\t\t\tIn Case II the probable error varies from 0 to \u00b1 8%.\t\t","page":19},{"file":"p0020.txt","language":"en","ocr_en":"20\nM. Matsumoto,\nThe averages for the experiments are given in Table VI. Case I gives the results when the left sound was varied while the other was kept constant, and Case II gives the results when the right sound was varied and the other was kept constant. In these and subsequent similar experiments, the observer announced the direction of the perceived sound in a scale of degrees, taking/and l> aso\u00b0 and counting toward r and /. For example, fr 6o\u00b0 means that the sound is in the front 6o\u00b0 totvard r and br 6o\u00b0 means that the sound is in the rear 6o\u00b0 toward r.\nTo eliminate the effect of suggestion the experiments were made, as in the preceeding section, in an irregular order.\nThe general relations which were stated on page 18 are shown here more plainly. The transition of the perceived direction according to the change in the relative intensities of the two sounds is not only more gradual, but more minutely scaled. Figure 3 shows diagrammatically the\nresults of the experiments.1 This figure and the similar figures in the following pages represent the mental field of localization of sound. The median plane of the auditory field coincides with the real median plane of the head, but the mental right and left do not seem to lie exactly in the frontal plane of the head. The directions that appear to us a right and left, seem to lie slightly in front of the auditory axis. The apparent right and left seem to be determined by visual sensations and consequently to lie in a line tangent to both eyes. This seems to afford some explanation of the fact that we localize the preceived sound slightly in the back of the apparent right and left line when the two component sounds have the maximum relative difference in intensity.\nIn comparing the localizations of Case II with those of Case I we find that the latter is surer and finer than the former. In Case II we find not only a less careful angular scale, but sometimes a bewilderment of judgment as to whether the sound came from the front or from the rear. This difference seems to have its origin in the difference in sensitiveness between the two ears of the observer. The sensitiveness of each ear of the observer was examined by means of the audiometer2 and it was found\n1\tIn this and the next figures the full lines represent Case I and the dotted lines Case IT.\n2\tAccording to the method described by Scriiture, Threshold of intensity for sound Stud. Yale Psych. Lab., 1896 IV 103.","page":20},{"file":"p0021.txt","language":"en","ocr_en":"Researches on acoustic space\n21\nthat the ratio of the sensitiveness of the right ear to that of the left ear was as io to ii. It is probable that the discriminating ability for the change in the intensity of a sound depends upon the sensitiveness of the ear. As the right ear of the observer was less sharp than the left ear, the discriminating ability of the former would be less than that of the lat. ter. Accordingly, when the variable soundwas on the left side and the constant sound was on the right side the difference between the intensities of the two sounds would be more accurately perceived than when the sounds were given in the other way.\nMoreover, when the variable sound was on the right side and the constant sound on the left side the observer tended sometimes to localize the perceived sound in the rear hemisphere instead of the front, or sometimes he could not decide whether the sound was front or back, though he perceived the angular displacement of the sound from o\u00b0, for example, he could not decide whether the sound came from f or h, fr 6o\u00b0 or fir 6o\u00b0. The same uncertainty will be found again in later experiments. The cause of such confusion between front and back location, as we may call it, must be sought in the similarity of the relation between intensities with which the sounds situated in the two directions in question are received by the two ears respectively. This point will receive special consideration later.\nTabi.k VII.\n\tCask I.\t\t\tCase II.\t\nDistance of the\t\t\tDistance of the\t\t\nsecondary coil for the left\tLocalization.\tNumber of experiments.\tsecondary coil for the right\tLocalization.\tNumber of experiments.\ntelephone.\t\t\ttelephone.\t\t\n12cm\tbr 70\u00b0\tI\tI2cra\t/ 90\u00b0\tI\nII\t>\u00bb\u25a0 52-5\t2\t11\t\t\nIO\tbr 45\t3\t10\tbl 75\t3\n9\tbr 31\t4\t9\tbl 72\t3\n8\tbr 10\t3\t8\tbl 20\t3\n7\tb\ti\t7\tbr 5\t3\n6.5\tbl 5\t4\t6-5\tbr 13\t3\n6\tfit 25\t4\t6\tbr 40\t3\n5\tbl 30\t3\t5\tbr 66.7\t3\n4\tbl 57\t5\t4\tbr 23.3\t3\n3\tbl 50\t3\t3\tbr S3.3\t3\n2\t/ 90\t2\t2\tr 90\t3\ni\tl 90\t2\ti\tr 90\t3\nIn Case I the probable error varies from In Case II the probable error varies from \u00b0to\u00b1n%.\to to \u00b132%.\nM e must at any rate conclude that the dependence of the localization upon the relative difference between the intensities of the impressions","page":21},{"file":"p0022.txt","language":"en","ocr_en":"22\nM. Matsumoto,\nin the two ears does not necessitate that the perceived sound will, under the conditions of our experiments, always be localized forward. It is quite reasonable to suppose that the perceived sound will sometimes be localized backward under the same conditions, especially when the intensity of the perceived sound is weakened on account of physical, physiological or mental circumstances. In connection with this the results of experiments upon another person, Mr. W. S. Johnson (a student of psychology), are interesting. He localized all sounds backwards. The\naverage results of the experiments upon him are shown in Table VII. Case I gives the results when the sound of the left telephone was varied, and Case II the results when the sound of the right telephone was varied Figure 4 shows the results diagrammatically.\nThe preceding experiments were made without any previous practice, and the observers were required to tell only the direction of the perceived sound. It was found that after some practice an observer could tell not only the direction, but also the distance, of the perceived sound. So the experiments were repeated upon Mr. C. Wakamatsu to determine what would be the apparent distance of the sound. By this time the observer was somewhat practiced in the work, and the judgments were more definitely announced than in the previous experiments. The following table shows the average results. The Japanese unit \u2018 \u2018 sun \u2019 \u2019 was used by the observer in estimating the linear distances. One \u201csun \u201d\nis equal to 3.03 cm.\tnearly.\t\t\t\n\tTaiii.e VIII.\t\t\t\n\t\tCase I.\t\t\nDistance of the secondary coil for the left telephone.\tJudgment of direction.\tJudgment of distance.\t\tNumber of experiments.\n12cm\tA 76\u00b0\t7-38U\"\t( 22cm)\t3\n11\tA 6 7\t8.7\t(26)\t3\n10\tA 7\u00b0\t7\t(21)\t3\n9\tA 27\t10\t(3\u00b0)\t3\n8\tJ1 12\t9-3\t(28)\t3\n7\tfl 3\u00b0\t8.7\t(26)\t3\n6\tfl 47\t7-7\t(23)\t3\nS\tfl 70\t5\t(IS)\t3\n4\tA 77\t3-7\t(II)\t3\n3\t\u00df 80\t3-3\t(10)\t3\n2\tfl 83\t3\t( 9)\t3\nI\tfl 83\t3\t( 9)\t3\nI11 Case I the probable error for direction varies from o to varies from o to \u2014 3%.\n: 8% and that for distance","page":22},{"file":"p0023.txt","language":"en","ocr_en":"Researches on acoustic space.\t23\nCase II.\nDistance of the secondary coil for the right telephone. I 2cra\tJudgment of direction.\tgsuil\tJudgment of distance. (26e\"1)\tNumber of experiments. 2\nII\tbl S2.5\t7-7\t(23)\t3\nIO\tbl55 ; bl 30 or/30\t8\t(24)\t3\n9\tfl 60 ; bl 40 ; fl 20 or bl 20\t6 or\t8\t( 18 or 24)\t3\n8\t'borf\t8.7\t(26)\t3\n7\thr 50\t6-3\t(19)\t3\n6\tfr 65 ; hr 50\t5-5\t(17)\t3\n5\tfr 85 '; br 50\t4.5 or 5 (14 or 15)\t\t3\n4\tfr 80\t4-5\t(14)\t3\n3\t;* 90\t3-2\t(10)\t3\n2\tr 90\t3\t( 9)\t2\ni\t;* 90\t3\t( 9)\tj\nIn Case II the probable error for direction varies from o to \u00b1 3% and that for distance varies from o to \u00b1 11%.\nFigure 5 shows diagrammatically the results for Case I and Figure 6 the results for Case II.\nFig. 5.\nFig. 6.\nThe judgment of direction was surer in Case I than in Case II, as in the preceding experiments on the same person. In Case II the sound which was perceived under the same conditions was at one time projected at/ and another time at />, or the sounds which were at one time projected at fl 200 and fl 30\u00b0 were at another time projected at bl 20\u00b0 and bl 30\u00b0 respectively.\nAs to the perception of distance the intensity of the perceived sound seems to furnish the data for the judgments. In the above experiments the intensity of the variable sound was strongest when the secondary coil was at the distance of ic,n ; it grew less strong as the distance was greater, and became weakest at 12\"\". Accordingly the distance of the sound was perceived as least when the secondary coil was Tra distant","page":23},{"file":"p0024.txt","language":"en","ocr_en":"24\nM. Matsumoto,\nfrom the primary, and it was perceived to be greater as the coil was moved towards the other end of the scale. The gradual change in the distance according to the change in the intensity is clearly seen in the results.\nThe observer seemed to choose a certain intensity as a standard to which he ascribed a certain distance ; the distance of another sound seemed to be judged by comparing its intensity with this standard intensity. As a consequence the estimate of distance is different, at least so far as our experiment goes, in different individuals. This can be seen by comparing the above results with the following results which were obtained by making the same experiment on the observer, Mr. W. S. Johnson, in whose case all sounds were, as before, projected towards the\nback. He estimated the distance in i\t\tinches (\ti inch = 2}\t4 e\"1).\n\tTaiii.k\tIX.\t\t\n\tCase I.\t\t\t\nDistance of the secondary coil for the left telephone.\tJudgment of direction.\tJudgment of distance.\t\tNumber of experiments.\nncm\tr 90\u00b0\t4s1\u00bb\t( 120c,u )\t2\nto\tr 90\t57\t(143)\t4\n9\thr 52\t5i\t(\u00ab28)\t4\n8\tb\t36\t(90)\t4\n7\tM 7-5\t36\t(90)\t4\n6\tt'l 53\t28.5\t(71)\t4\n5\tM 75\t16.5\t(4\u00ab)\t4\n4\tl 90\t8\t(20)\t3\n3\tl 90\t6\t(\u00ab5)\ti\nIn Case I the probable error for direction varies from o to \u00b1 17$ and that for distance varies from o to \u00b1 10$.\nCase II.\nDistance of the secondary coil\tJudgment of\tJudgment of\t\tNumber /if PVt^trvi.\nfor the right telephone.\tdirection.\tdistance.\t\tCA11CI 1 nients.\ni Ie\"1\t1 90\u00b0\t6oin\t(150'\"')\t4\n10\tbl S2.5\t57\t(\u00ab43)\t4\n9\t/ 90\t60\t(150)\t4\n8\tb\t39\t(9S)\t4\n7\tbr 15\t31-5\t(79)\t4\n6\tbr 40\t33-3\t(83)\t4\n5\tbr 60\t26\t(65)\t4\n4\tbr S2.5\t6\t(\u00ab51\t4\n3\tr 90\t6\t(\u00ab5)\tI\nI11 Case II the probable error for direction varies from o to \u00b1 16% and that for distance varies from o to \u00b1 9 %.","page":24},{"file":"p0025.txt","language":"en","ocr_en":"Researches on acoustic space.\n2 5\nThus in Johnson\u2019s case the greatest distance was 60 inches (150\"\"), while in the case of Wakamatsu it was about 12 inches (30'\u201c) ; the shortest distance was 6 inches (150'\") in the case of the former and 3.7 inches (9\"\") in the case of the latter.\nIn the preceding experiments the intensity of the sound was not changed in regular succession, for it was desirable to eliminate the influence of suggestion from the results. It seemed, however, desirable to repeat the experiments by changing the intensity of sound, both descending and ascending in regular order. The average results of the experiments conducted in this way are given in Table X. Here the changes in the direction and the distance were perceived with greater regularity, but in other respects the results were not greatly different from those of the preceding experiments.\nFigures 7 and 8 show the results diagrammatically.\nIn closing the experiments of the first group I tried to see whether a curve of the localized points for the perceived sounds could be obtained if the two sounds were given continuously for a certain length of time during which the intensity of one of the two component sounds was varied in diminuendo or in crescendo. The experiments were made on the observer C. W.\na. When the intensity of the left sound was changed in diminuendo, by sliding the secondary coil from Tra to 15'\u201c, while keeping the intensity of the right sound constant, the sound was perceived as if travelling\nTa\u00fclk X.\nCase I.\n1 )istance of the\t\t\t\nsecondary coil\tJudgment of\tJudgment of\tNumber of\nfor the left\tdirection.\tdistance.\texperiments.\ntelephone.\t\t\t\nI3cm\t90\u00b0\t8.75,m (26e\"1)\t3\n12\tfr 76.7\t9\t(27)\t3\n11\tfr 76.7\t9\t(27)\t3\n10\t/>\u25a0 73-3\t9-3\t(28)\t3\n9\tfr 61.7\t10\t(30)\t3\n8\tJr 33-3\t10\t(30)\t3\n7\tfr 13-3\t9-3\t(28)\t3\n6\t/ or b\\\u00df 15\t8; 9 (24; 27)\t3\n5\tJt 26.7\t8\t(24)\t3\n4\tJl 40\t6.7\t(20)\t3\n3\t\u00df 43-3\t5-7\t(17)\t3\n2\t\u00df 7\u00b0\t4-5\t(13)\t3\ni\tfl 7\u00b0\t4-3\t(13)\t3\nIn Case I the probable error for direction varies from oto \u00b1 25% and that for the distance from o to \u00b1 5%.","page":25},{"file":"p0026.txt","language":"en","ocr_en":"1\tM. Matsumoto,\t\t\n\tCase\tII.\t\nDistance of the\t\t\t\nsecondary coil\tJudgment of\tJudgment of\tNumber of\nfor the right\tdirection.\tdistance.\texperiments.\ntelephone.\t\t\t\n13C.1\t\u00abSo0\t10s11\u201d (30\"\")\t3\n12\tbl 76.7\t10\t(30)\t3\nII\tbl 70 ; fl 85\t10\t(30)\t3\n10\tfl 73-3\t10\t(3\u00b0)\t3\n9\tn 43-3\t'O fO O \u00bb-\u00bb\t3\n8\tfl 3\u00b0 i bl 30\t10\t(3\u00b0)\t3\n7\tfr 35i/\t9i 8 (27; 24)\t3\n6\tfr 43-3\t8\t(24)\t3\n5\tfr 55 i \u00e0r So\t7! 5(2i; 15)\t3\n4\thr So\t4\t(12)\t3\n3\tfr So ; hr So\t4\t(12)\t3\n2\tr 90\t3-7 (11)\t3\nI\tbr 83.3\t3-7\t(11)\t3\nIn Case II (he probable error for direction varies from o to \u00b1 18% and that for distance from o to \u00b1 8%.\nFig. 8.\nfrom fl 8o\u00b0 or / 90\u00b0, 3\"\"' (9\u2122'), passing to the front at a distance of 6\u00e4\"\" (i8c\"\u2018) and stopping at fr 8o\u00b0, or R 90\u00b0, 12s1\"' (36\u2122'), so that the point of localization described a semi-oval ring with narrow end directed to the right of the observer.\nWhen the intensity of the left sound was varied in crescendo by sliding the secondary coil in the reverse way, the perceived sound started at fr 8o\u00b0, 10s'1\" (30e111), passed to the front at a distance of 7s\"\" (2icm) and stopped at / 90\u00b0, 4*\u201c\" (12'\"\u2019). Sometimes after the sound had reached about fl 60\u00b0 the observer became uncertain whether the sound travelled in front from that point to / 90\u00b0 or travelled in back from bl 6o\u00b0 to l 90\u00b0.\nb. When the intensity of the right sound was varied in diminuendo,","page":26},{"file":"p0027.txt","language":"en","ocr_en":"I\nResearches on acoustic space.\t27\nand that of the left sound was kept constant, the sound was perceived as if travelling from r 90\u00b0, 3'\"\"\u2019 (9\"\"), passing to the front and stopping at / 90\u00b0, 8\u2019\"\", 24e'\u201c. The sound seemed sometimes to travel in the rear, though at some points it was uncertain whether the sound was to the rear or the front.\nWhen the intensity of the right sound was varied in crescendo the sound seemed to start at blZo\u00b0, io,,m (30e\"') and travelling to the rear, to stop at hr 80\u00b0, 4sun (i2cm).\nThis completes the record of the first group. The results show conclusively the existence of a continuous functional relation between the relative difference in intensity (between the impressions in the two ears) and the localization in direction.\nMoreover, it can be considered as established that a perceived sound is located on the side from which the stronger sensation is received, the greater the relative difference between the two sensations, the greater being the angular magnitude of the side-localization.\nSecond group.\nWhen we perceive a sound as situated in the horizontal plane, the intensities of the sensations in the two ears are always different, except when the source of sound is situated in the sagittal, or fb, axis. The difference between the two intensities is greatest when the sound is situated nearly in the auditory, or rl, axis, for here the difference of distances between the source of the sound and the two ears is greatest.1 When the source of sound moves gradually from the auditory axis and at the same time approaches the sagittal axis this difference be comes smaller. It has also been shown in the first group of experiments that the localization depends upon the value of the difference between the intensities of the sensations in the two ears. From these two facts it is to be expected that when each ear is affected by two sounds coming from symmetrical points on the two sides respectively the limits within which the perceived sound is localized will be different according to the positions of the symmetrical points.\nWe have already studied the field of localization of the perceived\n1 It must be noticed here that even when the two ears are equally sharp the difference between the intensities of the sounds heard by the two ears cannot be determined simply by taking the inverse ratio between the squares of the distances from the sound to the ears. M hen an exact expression is wanted, we must take into account the effects of the refraction of the sound-waves around the head, the reflection of the sound from the surrounding walls, and of the conduction of the sound from one tympanum to the other through the head.","page":27},{"file":"p0028.txt","language":"en","ocr_en":"28\nM. Matsumo/o,\nsound when two objective components are placed at and /, that is, when the relative difference in intensity between the impressions in the two ears is greatest. In that case the field of localization covered almost an entire semicircle either in front or in back, and sometimes covered more than an entire semicircle. Our next task is to inquire whether this field of localization would be contracted if the relative differences were made smaller. To answer the question, experiments were made on the observer C. W. under the following conditions :\n1.\tTwo telephones were situated\tat fr 60\u00b0\tand fl 6o\u00b0 respectively.\n2.\tTwo\ttelephones were situated\tat fr 30\u00b0\tand fl 30\u00b0 respectively.\n3.\tTwo\ttelephones were situated\tat br 60\u00b0\tand hi 6o\u00b0 respectively.\n4.\tTwo\ttelephones were situated\tat br 30\u00b0\tand b/ 30\u00b0 respectively.\nThe average results of the experiments under condition 1. are shown\nin 'fable XI.\nTabi.e XI.\n\tCase I.\t\t\t\tCase II.\t\t\nDistance of secondary coil for icft telephone.\tJudgment of direction.\tJudgment of distance.\t\tDistance of secondary coil for right telephone.\tJudgment of direction.\tJudgment of distance.\t\nI2cra\tfr 46-7\u00b0\t10.351m\t(3icm)\tI2cm\tfl 36-6\u00b0\til5\u201c\t(33cm)\nII\tfr 40.8\tIO.\t(3\u00b0)\tII\t/317\t10.7\t(31)\nIO\tfr 18.3\tII. I\t(33)\tIO\tfl 23-3\tU\t(33)\n9\tfr IO\tII\t(33)\t9\t/ 0\tii\t(33)\n8\tfl 21-7\t9.1\t(27)\t8\tfr 15 7\t9.9\t(3\u00b0)\n7\t7746.7\t8.4\t(25)\t7\tfr 38-3\t8.4\t(25)\n6\t/50.8\t6.9\t(21)\t6\tfr 48.3\t6.9\t(21)\n5\t/S6.6\t5-9\t(18)\t5\tfr 45\t6-3\t(19)\n4\tfl 6O\t4-9\t(15)\t4\tA 48.3\t6.4\t(19)\n3\tfl 6O\t4-3\t( 13)\t3\tA 48.3\t4.6\t(14)\n2\tfl 62\t3-9\t(12)\t2\tA 51-7\t4-3\t(13)\ni\tfl 6O\t3-5\t(\u00ab)\ti\tA 4S.3\t3-8\t(11)\nThe number-of experiments on\t\t\teach\tIn Case II the probable error for direc\t\t\t\npoint is 6.\nIn Case I the probable error for direction varies from o to\u00b1 57%, and that for distance from \u00b1 3% to \u00b1 13%.\ntion varies from \u00b1 3% to \u00b1 17% and that for distance from I8\u00ab% to 8%.\nThe results are graphically represented in Figures 9 and 10.\nHere the relative difference between the intensities of the sensations in the two ears must, for external reasons, have been smaller than that in the preceding experiments. The field of localization of the perceived sound was accordingly much more contracted. When the sound of the left telephone was varied, the field covered a sector included between fl 62\u00b0 and/;-46.7\u00b0. When the sound of the right telephone was varied, the field was still more contracted, covering a sector included between fl 36.6\u00b0","page":28},{"file":"p0029.txt","language":"en","ocr_en":"Researches on acoustic space.\n29\nand fr 51.7 \u00b0. In both cases most of the perceived sounds were projected on the side on which the source of the variable component sound was situated. Again, in both cases no perceived sound was projected back-\nFig. 9.\nFjg. 10.\nward, and no doubt existed as to the position of the perceived sound, as was the case when two telephones were situated at right and left. The average results of the experiments under condition 2. are given in Table XII.\nTable XII.\n\tCase I.\t\t\t\tCase II.\t\nDistance of the\t\t\t\tDistance of the\t\t\nsecondary coil\tJudgment of\tJudgment of\t\tsecondary coil\tJudgment of Judgment 0\t\nfor the left\tdirection.\tdistance.\t\tfor the right\tdirection.\tdistance.\ntelephone.\t\t\t\ttelephone.\t\t\n12cm\tfr 36.7\u00b0\tU .Ml\"\t1 ( 34cnl\t') 12cm\t\u00df 5\u00b0\u00b0\t\u00c78tin ^ 2\"jcm\n11\tfr 35\t11-3\t(34)\t11\t\u00df 46.7\t10\t(3\u00b0)\n10\tfr 30\tii-3\t(34)\tIO\t\u00df 33-3\t9-3 (28)\n9\tfr 26.7\t11\t(33)\t9\t\u00df 36-7\tO O H\n8\tfr 20\t\u201d\u20223\t(34)\t8\t\u00df 23-3\t9-3 (28)\n7\tfr 7\t10\t(30)\t7-5\t/ 0\t10\t(30)\n6.S\t/ O\t10\t(30)\t7\tfr 3-3\t9-5 (28)\n6\t\u00df \u00ab6.7\t9-3\t(28)\t6\tfr 20\t9-3 (28)\n5\tfl 16.7\t9\t(27)\t5\tfr 36.7\t8-3 (25)\n4\t\u00df 3\u00b0\t6-5\t(\u00ab9)\t4\tfr 40\t6-3 (19)\n3\t\u00df 36.7\t5-7\t07)\t3\tfr 33-3\t6\t(18)\n2\t\u00df 40\t5\t(IS)\t2\tfr 40\t4-3 (13)\nI\tfl 40\t4-5\t(\u00ab3)\t1\tfr 36.6\t4.6 (14)\n1 he number of experiments on each point 1 In Case II the probable error for direc-ls 3-\ttion varies from o to \u00b1 19% and that for\nIn Case I the probable error for direction distance from o to \u00b1 10%. varies from o to \u00b1 31% and that for dis- I tance from o to 10%.\n!\u2022 igures 11 and 12 represent these results graphically.\nIn Case I the field of localization covered a sector included between fr 36.7\u00b0 andy? 40\u00b0 and in Case II it covered a sector included between","page":29},{"file":"p0030.txt","language":"en","ocr_en":"3\u00b0\nM. Matsu moto.\nfl 50\u00b0 and fr 40\u00b0. The observer was sure of his judgments and never projected the sound backward. The tendency to project the perceived sound more on the side on which the source of the variable sound was\nsituated was lessened here, and tributed.\nFig. h.\nlocalizations were more evenly dis-\nF10. 12.\nA similar contraction of the field of localization of the perceived sound was observed with the same subject when the sources of sound were situated behind the observer. Here we noticed that the perceived sounds were frequently located in front. Under condition 3., when the intensity of the sound on the side of the sharper ear (left) was varied, most of the perceived sounds were located in front, 62 of 72 perceived sounds being decidedly located in front. On the contrary, when the intensity of the sound on the side of the duller ear was varied most of the perceived sounds were located in back, though some of them were located in front. Table XIII gives the average results for the experiments.\nDistance of the secondary coil\nTable XIII. Case I.\nUsual localization.\nOccasional localization.\nthe left ephone.\tDirection.\tDistance.\t\tDirection.\tDistance.\t\n12\u00ab\tfr 64\u00b0\tiosun\t(3\u00b0cm)\thr 70\u00b0\t6.5sun\t( 19e\"1)\n11\tfr 56\t9-4\t(28)\t/>r 75\t7\t(21)\n10\tfr 44\t10\t(30)\thr 70\t6-5\t(19)\n9\tfr 40\t9.6\t(29)\thr 30\t7\t(21)\n8\tfl 8.5\t10\t(30)\thr 20\t6-5\t(19)\n7\tfl 31\t9\t(27)\t\t\t\n6\tfl 51-6\t6.9\t(21)\t\t\t\n5\tfl 60\t6.4\t(\u00ab9)\thi 40\t5\t(U)\n4\tfl 66.7\t4-5\t(H)\t\t\t\n3\tfl 7\u00b0\t3-8\t(\u00bb)\t\t\t\n2\tfl 72\t3\t( 9)\thi 80\t3\t( 9)\nI\tfl So\t3\t( 9)\thi 70\t3\t( 9)\nThe number ot experiments on each point is 6.\nIn Case I the probable error for direction varies from \u00b1 2% to 6% and that for distance from o to \u00b1 1%.","page":30},{"file":"p0031.txt","language":"en","ocr_en":"Researches on acoustic space.\n31\nI listance of the secondary coil\nCask II. Usual localization.\nOccasional localization.\nI n Case I ! the probable error for direction varies from o to from o to \u00b1 6%.\nor the right telephone.\tDirection.\tDistance.\t\tDirection.\tDistance.\t\n12cm\t0 0 i\".\t7-3s\u201c\"\t( 22cm)\t\t\t\nII\t/'/ 70\tS\t(24)\t\t\t\nIO\tfl 45\tIO\t(3\u00b0)\tbl 70\u00b0\tgsun\t(24cu'\n9\thi 35\t7-3\t(22)\tfl 20\tIO\t(30)\nS\tf or h\tIO\t(3\u00b0)\tfr or hr 20\t8\t(24)\n7\tfr or hr 30\tS.5\t(25)\t/ or h\tIO\t(30)\n6\thr 46.7\t6. i\t(I8)\t\t\t\n5\t^\u202246.7\t4-3\t(!3)\t\t\t\n4\thr 53-3\t3-6\t(IO\t\t\t\n3\thr 60\t3-3\t(IO)\t\t\t\n2\thr 63.3\t2.8\t( S)\t\t\t\ni\thr 66.7\t3-2\t(IO)\t\t\t\n: 12% and that for distance\nFigures 13 and 14 show these results diagrammatically.\n1 he results of the experiments under condition 4 are given in Table XIV.\nFigures 15 and 16 show the results graphically.\n1 hese results show that the field of localization of the perceived sound covered larger sectors in the experiments under condition 3. than in the experiments under condition 4. In the former it covered a sector included between fr 64\u00b0 and fl 8o\u00b0 in front and a sector included between /n 75 and bl 8o\u00b0 in back, while in the latter it covered a sector included between fr 55\u00b0 and fl 56.7\u00b0 in front and a sector included between hr 60\u00b0 and hi 6o\u00b0 in back.","page":31},{"file":"p0032.txt","language":"en","ocr_en":"32\nM. Matsumoto,\nTaule XIV.\nCase I.\nDistance of the second ary\tUsual\tlocalization.\tOccasional localization.\t\t\ncoil for the left telephone.\tDirection.\tDistance.\tDirection.\tDistance.\t\n12c,n\tbr 50\u00b0\t9\u2122\" (27e\u2019'*)\t\t\t\nII\tfr 35\t9\t(27)\thr 500\tS\u00bbuu\t(24cm)\nIO\thr 43-3\t8\t(24)\t\t\t\n9\tfr 35\t9\t(27)\tfr or hr 35\t9\t(27)\n8\tfr 30\t9\t(27)\thr 30\t8\t(24)\n7\t/or b\t8.7 (26)\t\t\t\n6\t\u00df 20\t9\t(27)\thi 3\u00b0\t7\t(21)\n5\tfl 43-3\t6.S (20)\t\t\t\n4\t\u00df 45\t5-5 (16)\thi 3\u00b0\t5\t(15)\n3\t\u00df 45\t5-5 (16)\tJl or bl 50\t5\t(15)\n2\t\u00df 43-3\t4-2 (13)\t\tm\t\nI\t\u00df 45\t4-5 (13)\t\u00df or bl 50\t3-5\t(IO)\nThe number of experiments\t\ton each point is 3.\t\t\t\nIn Case I the probable error for direction varies\t\t\tfrom 0 to rr 65% and that for distance\t\t\nfrom 0 to \u00b1 28%.\t\tCase II.\t\t\t\nDistanceof the secondary coil\tUsual localization.\t\tOccasional localization.\t\t\nfor the right telephone.\tDirection.\tDistance.\tDirection.\tDistance.\t\nI2cm\t/4\u00b0\u00b0\t8sun (24\"\")\tbl 6o\u00b0\tysun\t(2IC1\")\nII\tfl 53-3\t7-7 (23)\t\t\t\nIO\t7756.7\t7\t(21)\t\t\t\n9 8 7\tfl 5\u00b0 b or k f\t7.3 (22) 7\t(21) \u201d\t(33)\t7? 4\u00b0 ; hi 30\tr8 (24) \\ U (18) /\t\n6\tfr SS\t6.5 (19)\tbr 40\t5\t(15)\n5\tfr iS\t6\t(18)\thr 40\t6\t(IS)\n4\tfr iS\t6.5 (19)\thr 50\t4\t(12)\n3\tbr \\o\t4-5 (13)\tflr 30\t4\t(12)\n2\tfl' 45\t4\t(12)\tbr 40\t3\t( 9)\ni\tfr 40\t3-3 (10)\thr 50\t3\t( 9)\nIn Case II the probable error for direction varies from o to \u00b1 8% and that for distance from o to \u00b1 15%.\nOur expectation that the acoustic field would be contracted more as the two sources of sounds approached more to the median plane, and consequently the relative difference between the intensities of the sensations in the two ears would grow less, was realized by the second group of experiments. As to the forward and backward projection of the perceived sounds the above results resemble those of the first group of experiments,","page":32},{"file":"p0033.txt","language":"en","ocr_en":"Researches on acoustic space.\n33\nwhere it was asserted that the cause of such forward and backward localization must be sought in the equality of the relation between the intensities with which the sounds localized in the two directions in question are received by the two ears respectively. In a similar way we will say here that the forward and backward projection in the experiments under conditions 3. and 4. originates in the resemblance which exists between the relative differences in the intensities with which the two sounds at the\nback are heard by the two ears and the relative difference in the intensities with which the two sounds at the corresponding points in front are heard by the two ears, for otherwise the sounds would never be localized both in front and in back in such a confused way as shown in the above tables.\nj. Previous Investigations.\nIn going over a large number of monographs that treat of the localization of a sound as depending on the intensities with which the vibratory-movements affect the two ears we find several that are of special importance.\ne must first notice Seebeck\u2019s' computation of the intensities with which the air-vibrations from a sounding object reach the ears.\nLet us suppose that the right ear is turned to a sonorous body and the left toward a wall. Supposing the wave-length of the sound to be /., the equation of the vibratory movement will be\ny = a cos zr + vj,\nwhere e represents the velocity of the propagation of the sound, t the time, y the extent to which an air particle is displaced at the moment t,\n' Skkiseck, Die Zuriickwcrfung des Schalles, Annalen d. Physik u. Chemie (borgen. dorlT), 1S46 LVXIII 465.","page":33},{"file":"p0034.txt","language":"en","ocr_en":"34\nM. Matsu moto,\na the maximum value of y, and r a constant time-value indicating the phase. If the time be counted from the moment at which the value for the direct wave is greatest in the right ear, then the vibration will be ex-pressed by\nc t\ny = a COS 277 \u2014 .\nThe direct wave reaches the left ear in two ways. The first way is through the air whereby the sound-waves which have proceeded to the head are bent round to the ear. Let d represent the additional distance travelled by the sound-wave in reaching the left ear around the head after having arrived at the right ear. Then the vibration in the left ear will be expressed by\nct\u2014d\ny = \u2014 k a COS 2;r \u2014-\u2014,\nwhere the minus sign expresses the change in the phase and k is a positive number, which expresses the weakening of the sound due to the refraction around the head.\nIn addition to the refracted portion the ear receives vibrations transmitted from the right side to the left ear through the solid parts of the\nhead. If be the relation between this route and the wave-length\u2014the latter being referred not to the air but to the solid bony substance, then ? is a very small quantity for all usual tones. The second part of the wave\nin the left ear will be expressed by\n\u201e\t.\tct \u2014 e\ny \u2014 i cos 2- \u2014;\u2014\nwhere i indicates the weakening which the sound suffers on this second route. If we add together these two components for the left ear, we have\nct\u2014d\t.\tct\u2014 e ,\tct\u2014d\n/\" = \u2014 ka cos 2- \u2014 ------1- ta cos 2- \u2014\u2014 = Pa cos 2\" \u2014J\u2014>\n|~\t\u201c\t\u201c\td- c\nwhere\tf = .U'\u201c + * \u2014 2 ** cos 27r\nd .\t/\nk COS 2r ---t COS 2- \u2014\n(\u00ce\t/.\t/\u2022\nand\tcos 2~- =\t-\n>\u25a0\tP\nAs for the reflected wave, it will be expressed for the left ear by\nct - 1\nyv - \u2014 i/a cos 2-","page":34},{"file":"p0035.txt","language":"en","ocr_en":"Researches on acoustic space.\n35\nand for the right ear by\nct\u2014 l\u2014a y' \u2014 + qa cos 2-----------,\nwhere the factor \u2014q indicates the weakening of the sound and the change in the phase produced by the reflection, and l the distance from the median plane of the head to the wall.\nIf we now add the elements which proceed from the direct and reflected waves, we obtain for the right ear\nf = al cos 2 \"'(i+m)\nand for the left\ny = an cos 2\t+ vu|,\nwhere the phase differences -, and r,, do not concern us for the present purpose, but <7, and an are determined by the equations\n<r, = r? I I -f pq + 2pq cos 2  -^\u2014 I\naii =a' (/+<f+2/^cos2-21. \u00b0y\nThese quantities give the intensities of the two physical sounds in the two ears respectively, for the latter are to be measured by the squares of the amplitudes.\nIt should be in criticism that the direct transmission of the sound-waves through the skull is an utterly negligible quantity, but that the transmission from one tympanum to the other through the skull is a very important, though undeterminable, factor.\nWe must next consider Steinhauser\u2019s theory of binaural audition.1 He worked out on geometrical principles the laws which determine the relative intensities with which a sound will reach the two ears. According to him the pinna acts as a funnel to conduct into the ear those waves of sound which in consequence of their direction reach but could not otherwise enter it.\nThe regions of direct, indirect, and mixed hearing were distinguished according to the nature of the path by which the sound waves reach the\n'Steinh\u00e4user, The theory of binaural audition, Phil. Mag., 1879 (5) VII iSi, 261. (This is a translation of Steinh\u00e4user, Die Theoried, binauralen Horens, Wien JS77-)","page":35},{"file":"p0036.txt","language":"en","ocr_en":"36\nM. Matsumoto,\nears. In direct hearing the waves proceeding from the sonorous body reach the ear in a straight line and enter the auditory meatus directly. In indirect hearing the waves proceeding from the source of sound do not reach the ear in straight lines, but after undergoing reflection from external objects. In mixed hearing the waves reach the ear partly directly and partly indirectly.\nThe formula deduced by Steinh\u00e4user for direct hearing is as follows : Let\u00df be the angle between the plane of the pinna and the line of sight, and a the angle which the line of sight makes with the direction of the sound ; and let i\\ and t\\ represent the relative intensities with which the sound is heard in the two ears ; then\ntan \u00ab : tan \u00df : : i, \u2014 i.z :\t+ i.i.\nThe direction in which a source of sound is situated may, therefore, be,, according to Steinh\u00e4user, estimated by the different intensities with which a sound is perceived in the two ears. From the above formula the case can be deduced, in which /' = /,. We have then tan a = o and hence a \u2014 o . This is the case in which the sound is just in the direction of the line of sight.\nIf a source of sound is situated in the region of indirect hearing, no waves of sound can reach the surface of either of the pinn\u00e6 directly ; the sound produced by the sonorous body can evoke a sensation as the results of reflection, provided we neglect the possible conduction of sound through solid bodies and by refraction around the head and pinn\u00e6. Let a be the angle which the rays of sound make with the line of sight before reflection, a. the angle they make after reflection, and <f> be the complementary of the angle which the line of sight makes with the surface which reflects the rays of sound ; then by a geometrical operation\na =2 <2 \u2014 \u00ab. r\t\u2022\nThat which is heard, therefore, indirectly in the direction a makes the same impression as that heard directly in the direction in which case whose value is dependent on <?, may, without any change of the direction of the waves of sound, assume an indefinite number of different values, since the position of the reflecting surface may as well be any other than it is, or there may be many reflecting surfaces.\nIf a source of sound is situated in the region of mixed hearing, then the direct rays of sound can reach only one of the two pinn\u00e6, while both may be reached by the indirect rays. Accordingly let zj be the intensity with which the direct rays of sound affect one ear, and />, the increment of that intensity due to the effect of reflexion. Let /<, be the","page":36},{"file":"p0037.txt","language":"en","ocr_en":"Researches on acoustic space.\n37\nintensity of the sensation in the right ear, due to the reflexion alone. Then, on summing up the indirect and direct effects, the following equation is obtained :\ntan a =\tf>'--\u20142 tan \u00df.\n!i + /' 1 + i\u00b02\nHence, by calculation, we can find the angle within the region of direct hearing in which the source of sound is erroneously imagined to lie.\nSteinh\u00e4user devised an instrument called homophone, wherewith to test his theory. It consisted of a system of wooden tubes for bringing to the ears the sounds of two organ-pipes tuned to unison, whose respective intensities could be regulated by stop cocks. It was held by its inventor to confirm his theory.\nThe observation that by binaural audition the image of the perceived sound is localized apparently in the occipital region of the head was made first by Purkyn\u00e8.1 In his experiments it was shown that when a tone was conducted simultaneously to the two ears separately by means of rubber tubes the acoustic image was not perceived in the ears, but was perceived in the occipital region of the interior of the head.\nAn apparently similar localization of the sound in the occipital or frontal region was observed by several subsequent investigators, such as S. P. Thompson,2 Plumaudon,3 Urf.antschitsch,4 and Kessel.5\nPolitzer\u00ae emphasized the fact that for the perception of the direction of a sound the fact of binaural hearing was requisite. He made numerous experiments upon normal and abnormal persons and found that in monaural audition the sound was localized on the side of the open ear. When a watch was moved in the horizontal plane and heard with one ear closed, the tick-tick was localized on the side of the open ear even when the watch was moved some distance farther to the other side of the median plane. The perception of the position of the sound became more difficult when the sound was moved further toward the closed ear. In the case of persons who suffered from diseases of the cars a similar error was observed, a mistake of i8o\u00b0 for perceiving the direction of a sound being often made. The diminution of the localizing power was\n1 P\u00fcrkyn\u00e9, Prager Vierteljahresschrift, iS6o III 94.\n2Thomi'SON, On binaural audition, Phil. Mag., 1877 (5) IV 274; 1S77 (5) VI 2S3.\n3\tPlumaudon, The Telegraphic Journal, London, Sept. 1S79.\n4\tUrbantschitsch, Zur Lehre von der Sehallempfindung, Arch. f. d. ges. Physiol. (Pfl\u00fcger), 1881 XXIV 574.\n5\tKessel, Ueber die Function der Ohrmuschel bei den Raunnoahrnehmungen, Arch, f. Ohrenheilk., 18S2 XVIII 120.\ncPOLITZER, Studien \u00fcber die Paracusis loci. Arch. f. Ohrenheil., 1876 XI 231.","page":37},{"file":"p0038.txt","language":"en","ocr_en":"3\u00ab\nM. Matsu moto,\nobserved also in persons who suffered from hard hearing of one or both ears. With many persons the mistakes of localization were first noticed when they were subjected to a special test. He ascertained also that in binaural audition the localization was especially defective for a sound in the median plane, where the source of sound was equally distant from the two ears.\nThompson noticed, during his experiments on binaural hearing, an acoustic illusion due to the fatigue of the ear. One ear was fatigued by listening to a loud pure tone, and then the listener tried to estimate the direction of a sound of the same pitch. If his left ear were fatigued he would invariably imagine the source of the sound to be further to the right than it really was, and likewise the reverse. The illusory displacement in the direction of the sound was greater as the fatigue was more complete. But as the sounds of different pitch have to stimulate different fibres of the basilar membrane of the cochlea, it would be expected that the fatigue produced by a sound of a certain pitch would have no effect on the perception of a sound of another pitch. According to Thompson\u2019s experiments, when one ear was fatigued with a c\" fork no illusory displacement was perceived in an a\" fork.\nTarchanofk 1 found that when telephones were held opposite the ears and intermittent currents were sent through them, the perceived sound was localized in the median plane and that it was perceived outside the plane when there was the slightest difference between the intensities of of the two sounds.\nUrbantschitsch 2 found that when one and the same sound of a certain intensity was led into the two ears separately by means of a T tube, one group of his observers perceived the sounds as being in the right and left ears with equal intensities, whereas another group perceived the sounds in the right and the left temporal regions of the head. When the intensity increased, these two sounds seemed to expand and approached nearer to the middle of the head, being finally brought into fusion at a sufficient intensity. Sometimes besides the two sounds a third sound was observed in the center of the head ; the latter was perceived after repeated experiments or only when the observers paid special attention to it. A large proportion of the observers, when very attentive, perceived the sound\u2014not in the ears but in the interior of the head. Finally, there were some observers by whom the sound was not generally located in the head, but projected in front, to the back, or above.\n1\tTarchanoff, St. Petersburger med. Wochenschrift, 1S78, No. 43.\n2\tUrbantschitsch, Zur Lehre von der Schaltcmpfindung, Archiv f. d. ges. Physiol. (Pfl\u00fcger), 1SS1 XXIV 574.","page":38},{"file":"p0039.txt","language":"en","ocr_en":"Researches on acoustic space.\n39\nIn regard to the intercranial localization there were some individual differences as to the distinct position of the perceived sound. Some localized it in the occipital region of the head, others in the frontal region or in the forehead, while still others localized it in the nose or in the pharynx. Urbantschitsch asserted also that the degree of fatigue of the ear could possibly be determined by observing the position of an acoustic image. At first a very strong sound was conducted to one ear for a while ; then weaker sound of the same pitch was conducted to the two ears simultaneously. The acoustic image for the latter case was found at first in the ear which was not fatigued and remained there for a few seconds; then the image travelled gradually towards the median plane and at last was found at the centre of the head. Urbantschitsch explained the phenomenon in the following way. As one ear was very strongly stimulated in the beginning it was fatigued for some interval of time and the other ear, which was not stimulated, became relatively sharper. Consequently, when a weaker sound was conducted to the two ears simultaneously the sensation in the latter ear was evidently stronger and the perceived sound was located on the side of that ear. But the other ear began to recover gradually, and at the same time the sharper ear began to be fatigued. As a result, the perceived sound began to travel towards the median plane and at last reached the center of the head when the sharpness of the two ears became the same.\nKessel1 performed his experiments by inserting tubes from a funnel shaped sound-receiver into the ears, thus excluding the action of the pinnae. The sound of a tuning fork was conducted into the two ears by this apparatus. When the tubes were of the same length and were opened equally wide the ears were stimulated with the same strength and the resulting single sound was located in the median plane of the head. If one of the tubes was more or less pressed so that the two ears were stimulated differently, then the sound was perceived in the ear which was stimulated more strongly.\nKessel made another interesting experiment. According to him the principle of the localization of a sound on the side of a stronger excitation holds good even in the case when one ear is not directly stimulated by the waves of the sound, but stimulated by reflected waves. To prove this he hung a watch in the axis of a parabolic mirror ; the head of the observer was adjusted between the mirror and the watch so that the two ears were opposite them. Then the watch was so adjusted that the reflected rays, which were gathered at the focus, would stimulate the ear oppo-\nI Kessel, Ueber die Function der Ohrmuschel bei den Raumwahrnehmungen, Arch, f. Ohrenheilk., 18S2 XVIII 120.","page":39},{"file":"p0040.txt","language":"en","ocr_en":"40\nM. Matsumofo,\nsite the focus more strongly, in which case the sound was localized in the direction of the mirror. If the watch was brought nearer to the ear on its side, so that the direct rays of the sound would stimulate this ear more strongly, then the sound would be localized on the side of the watch.\nRogdestwensky1, one of Tarchanoff\u2019s pupils, produced sounds at symmetrical points, and observed that the perceived sounds were local\" ized in the head, breast and abdomen according to the difference in the height of the symmetrical points.\nTo exclude the function of one ear in perceiving the direction of a sound, Preyer- made experiments by using a telephone instead of the snapper sounder. The intensity of the telephone sound was weakened by reducing the intensity of the electric current so that by stopping the ears the sound could not be heard by the subject. 1 hen one ear was opened so that the sound was heard by that ear only. The result of the experiments showed that under such conditions errors occurred which were not observed in ordinary perception, and it was often very difficult, even with a strenuous attention, to get rid of these errors. These errors were localisations on the wrong side.\nSimilar experiments were afterwards made by Arnheim3. In his experiments the number of correct perceptions with one ear amounted to only 22<]o of the total, while with both ears it amounted to 39.7% (in Preyer\u2019s experiments 30%). He noticed also a decided tendency to locate the perceived sound on the side of the open ear.\nSchaefer,4 who had made elaborate experiments on the perception of the direction of sound in cooperation with Preyer, attacked a peculiar side of the problem at a later date, namely, the localization of beats and difference tones. His results may be summarized as follows.\nIf the relative intensity of the primary tones is equal, then the beats appear to proceed from the region between the points at which the two tones are situated whether they are on the same or different sides of the median plane. The localization of the beats in the median plane when the primary tones of equal intensity are situated on both sides of the plane, is a special case\u2019of this general fact. Schaefer thinks it clear that when the two forks are placed on the same side of the median plane the\n'Rogdestwensky, Ueber die Localisation der Geh\u00f6rsempfindungen, Diss. 18S7.\n2\tI\u2019rEYER, Die Wahrnehmung der Schallrichtung mittelst der Bogeng\u00e4nge, Archiv f. d. ges. Physiol. (Pfl\u00fcger), 18S7 XL 5SO.\n3\tArnheim, Beitr\u00e4ge zur Theorie von Schallempfindungcn nnttelest der Bogeng\u00e4nge, Diss., Jena 1SS7.\n4\tSchaefer, Ueber die Wahrnehmung und Localisation von Schwebungen und Differenzt\u00f6nen, Zt. f. Psych, u. Physiol., 1S90 I Si.","page":40},{"file":"p0041.txt","language":"en","ocr_en":"Researches on acoustic space.\n41\nbeats are perceived more strongly by the ear on that side ; and that the beats are perceived by the two ears with equal intensity when the sources of the tones are found in the median plane. For sounds located on different sides of the median plane it can be, according to Schaefer, mathematically proven that the intensity of the beats is equal on the two sides when the relative intensities of the primary tones are equal, but on the contrary the intensity of the beats is stronger on the side of the stronger primary tone when the relative intensities of the primary tones are not equal. Schaefer\u2019s conclusion is that the beats will be localized on the side of the ear which is more strongly excited by them, but in the median plane if the two ears are equally excited by them. Ihe further exact determination of the direction is dependent upon that of the relatively stronger primary tone. The localization of beats is, therefore, governed by the same principles as the localization of simpler sounds, i. e., the localization on the side of the ear which is excited more strongly, and the localization of sounds in the median plane when the two ears are excited with equal intensity.\nAs for the perception of difference tones, the localization is apparently contradicted by that of beats. For when two forks of unequal intensities are placed on the different sides of the median plane the difference tones are heard on the side of the weaker primary tone. This is not, however, really contradicted by the localization of the beats on the side of the stronger primary tone. l*or the localization of diflerence tones on the side of the weaker primary tone is based upon the fact that on this side the relation of intensity which is more favorable for the perception of the difference tones predominates, and the difference tones are heard louder on this side, for if the left sound, for example, is relatively stronger, the left ear is made \u201c physiologically deaf\u201d for the sound coming from the right side, and thereby the perception of the difference tone is made impossible. Difference tones are, therefore, localized after all on the side of the ear which is excited more strongly. As for the median localization of the difference tones, the result is similar to that of the beats, for when the two primary tones of equal intensity reach the ears from the two sides of the median plane either by air transmission or by cranial conduction, the difference tones are localized in the median plane.\nFinally, one more phenomenon which was emphasized by Schaefer 1 is to be mentioned. If a fork be placed on the top of the head the sound will be localized in the median plane, but it will shift to one ear if that ear be closed. Schaefer explained this phenomenon\n1 Sciiaefer, Kin Versuch \u00fcber die intrakranielle Leitungleiscs ter T\u00f6ne von Ohr zu Ohr, Zt. f. Psych, u. Physiol, cl. Sinn, 1S91 II in.","page":41},{"file":"p0042.txt","language":"en","ocr_en":"42\nM. Matsumoto,\nin the following way. The osseous parts of the auditory apparatus, the tympanum, and finally the air in the external auditory tube will be put into vibration by the waves which the sound produces in the labyrinth by means of cranial conduction. In this case, therefore, sound proceeds in just the opposite way to the usual one, where it passes from the air into the ear. Now, if we close the ear with the finger, the tympanum will be put into stronger vibration on account of the reflexion of the waves from the finger. Consequently the component sound is stronger in the closed ear and the perceived sound will appear to shift from the median plane toward the side of the closed ear. The same effect will be produced if we apply a resonator to the ear either by holding by fingers or by supporting on a stand. To this same class belongs another phenomenon which is noticed by many persons of normal hearing. When we sing loudly a low tone like the German \u201c u \u201d and stop one ear, but not very tightly, the tone will move from the initial position in the larynx to the stopped ear, but it will move again to the median plane in the interior of the head if the other ear is stopped in the same way.\nBloch1 investigated both binaural and monaural localization by measuring the least noticeable change in the position of sounding body. His conclusion runs as follows.\nThe most important function of binaural audition is the perception of the direction of a sound ; the perception of direction is more accurate in the horizontal and in the frontal planes than in the median plane ; in the former two planes the localization is based chiefly upon the relative difference between the intensities of the sounds heard by the two ears, and, secondarily, upon the change in the intensity of the perceived sound which arises from the influence of the pinn\u00e6 ; and in the median plane the action of the pinn\u00e6 which collect the sound-waves into the auditory meatus is the chief condition for the localization of sounds.\nThese investigations make it clear that the relation of intensity between the two components of a sound heard by the two ears is a fundamental\u2014 or the fundamental\u2014factor of localization in regard to direction. My own work, reported in this section, aimed to further define this factor and its effect.\nIII. Localization of the perceived sound at the middle point\nBETWEEN THE SOURCES OF TWO OBJECTIVE SOUNDS.\nIn the foregoing experiments the two telephones were restricted to the same primary plane at two points.\n\u2018Bl.ocil, Das binaurale H\u00f6ren, Zt. f. Olirenheilk., 1893 XXIV 25.","page":42},{"file":"p0043.txt","language":"en","ocr_en":"Researches on acoustic space.\n43\nIn the following experiments the telephones were placed at various points on the surface of the spherical cage (Fig. i).\n(a) One of two telephones was situated in the median plane and the other in the frontal plane. The two telephones were placed at a same level. The physical intensities of the two sounds were kept as far as possible equal and constant during the experiments. The positions of the two telephones were as follows :\nTable XV.\nNumber of position.\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n12\nPosition of the two telephones. fo and ro fo ** Io fit \u2018i ru fit \u201c lit bo \u2018 * ro bo 1 \u2018 Io bit * \u2018 ru bit \u201c lit\nf \u201c r f \u201c i\nb \u201c r b \u201c l\nOn the one hand, if a sound comes from the median plane only, the two ears will be stimulated equally, and consequently the perceived sound will be located in the median plane. On the other hand, if a sound comes from the frontal plane only, the two ears will be stimulated with the maximum relative difference in intensity, so far as the sounds at a same level are concerned, and consequently the perceived sound will be located nearly in the frontal plane. Now, if the two ears are stimulated simultaneously, as in our experiments by the two sounds situated in the above two planes, the relation between the intensities of the sounds heard by the two ears will be just like the relation between the intensities with which the two ears hear a sound coming from the plane which lies just between the above two planes. The perceived sound may accordingly be expected to be located in the plane between the median and frontal planes. Moreover, in our experiments, as the two telephones lie on the same level the perceived sound may be expected to be mostly localized on that level.\nThese expectations were fully realized by the actual results which are given in Table XVI. Mr. K. Matsumoto, a graduate student of psychology, and Mr. T. Nakashima were the subjects of the experiments.\nTo make the comparison between expectation and realization easier, I have arranged the results as in Table XVII. The symbols in","page":43},{"file":"p0044.txt","language":"en","ocr_en":"44\nM. Matsumoto,\nTable XVI.\nLocalization.\nObserver T. N.\tObserver K. M.\n1\n2\n3\n4\n5\n6\n7\n8\n9\n10\n11\n12\nfor, for, for, fo(r), o(r), fur.\nfol, fol, fol, 0, 0(1),\n6(0)1.\nfur, fur, fur, fur, (f)ur, lor (A).\nfui, fui, fui, fui, fui, ut, b(u)l.\nbor, bor,\nfor, for, fo(r), fur.\nbol, bol, b, o, fui, fui, (/)\u00ab/.\nfur, fur, fur, fur, ur.\nbilly bill\\\t(b) Illy lily\n(f)ul. fr, fr, fr,\nf(A), fo(r)(A), b(r).\n\u00df, \u00df, \u00df(>\u2018), bol, br, hr, br, bor, bor.\nb(A), b orf\nbl, /, b, bol(A), bol.\n\u00df.\nfor, ( f)or, o(r) o, o(b), bor (A).\nfol, ol, ol, ol, o(b),\no.\nfur, fur, bor, bor, b(u)r.\nfut, fui, bol, bo(l), bol.\nbor, bor (/\u00a3), bor (A), for, fo, o(A).\nbol, bo, bo, lo, o, bo, fol.\nbur, bur, bur, bur, (b)ur, h\u00f6r, h\u00f6r, ho, ur.\nbut, bul, (b)ul, ul, bol, bol.\nbor(A), bor(A), bor.\nTable XVII.\n\tA\t/>\u2019\tC\tD\n\tExpected\tUsual\tOccasional\tRare\n\tlocalization.\tlocalization\tlocalization.\tlocalization.\nI\tfor\tfor\tbor, bur\t\n2\tfol\tfol\tbol\t\n3\tfur\tfur\tbur, bor\t\n4\tful\tful\tbul, bol\t\nS\tbor\tbor\tfor\t\n6\tbol\tbol\tful\t\n7\tbur\tbur\tfur\t\n8\tbul\tbul\tbol\t\n9\tfr\tA\t\t\nIO\t\u00df\t\u00df\t\tfor, bor\nii\tbr\tbr\t\tbol\n12\tbl\tbl\t\u00df\tbor\ncolumn A show the directions in which the perceived sounds are theoretically expected to be localized; the symbols in column B the directions in which most of the perceived sounds were actually localized, and","page":44},{"file":"p0045.txt","language":"en","ocr_en":"Researches on acoustic space.\n45\nthe symbols in columns C and D the directions in which the perceived sounds were sometimes localized. The striking correspondence between A and B proves the correctness of our view. It is also very interesting to note that the perceived sounds were sometimes located in the directions in column C instead of the directions in column B. There is a reasonable justification for such localizations. When we are stimulated by a sound from the median plane the intensities of the sounds heard by the two ears are equal whether the sound is situated in front or in back. Subjective discrimination between front and back is, as we will see later, based chiefly upon the difference in absolute intensity, for the sound coming from the front is heard more strongly than the same sound from the back. So if the sound from the front in the median plane be weakened during the experiment by fluctuation of the electric current, while the ears are stimulated at the same time by the sound in the frontal plane, it will be quite possible that the relation of intensities will be like the relation of intensities with which the observer hears the sounds from the frontal plane and from the back part of the median plane. In such a case the observer may locate the sound to the rear instead of locating it to the front. This appears to be the reason why in the above experiments the perceived sounds were sometimes located at bor or bol instead of for or fo! ; at bur or bul instead of fur or fui For the similar reasons the perceived sounds were located at ful or fur instead of bul or bur ; and at fl instead of bl. These results agree with the confusion between front and back which we have frequently observed in our previous experiments.\nBesides the confusion between front and back we find here another kind of confusion ; above and below are sometimes confused with each other. In the above experiments the observer located the sound at fur when for was expected ; at bor or bol when bur or bul was expected. This kind of confusion can be explained by the function of the pinnte. It is found that on account of the peculiar shape of the pinnte a sound coming from ro or lo is perceived by the two ears with almost the same relative difference of intensity as a sound coming from ru or lit and a sound coming from fu is perceived with almost the same intensity as a sound coming from fo. So when we are stimulated simultaneously by sounds coming from fo and ro it is quite possible that the relation between the intensities of the sounds in the two ears will be like the relation between the intensities with which the sounds coming from fu and ru are heard by the two ears. In such a case the perceived sound may be located at fur instead of for. Moreover, the fluctuation in the electrical current will have some effect in producing the confusion. Such being the","page":45},{"file":"p0046.txt","language":"en","ocr_en":"46\nM. Matsu moto,\nfact, we have reasonable justification, under the above conditions, for occasionally localizing the perceived sounds in the directions in column C.\nAs for the localizations of the sounds in the directions in column D, they occurred very rarely and could be ascribed both to the inaccuracy of the experiment and inattention of the observer.\n(J>) The localization of the perceived sound at the middle point between the sources of the two component sounds is not restricted to the case in which the components sounds are put in the primary planes and at the same level. In the following experiments I placed two component sounds at different levels and one of them in a secondary plane, namely, one telephone was placed at the terminus of a secondary axis in the horizontal plane and the other telephone was placed at the terminus of a secondary axis in the frontal or median plane. The objective positions of the telephones were, therefore, as indicated in Table XVIII.\nTaule XVIII.\nNumber of\tPositions of the\tNumber of\tPositions of the\nposition.\ttwo telephones.\tposition.\ttwo telephones.\nI\tfr and ru\t9\tfr and ro\n2\tr \u201c fu\t10\tfr \u201c fo\n3\tfl \u201c lu\tii\tfl \u201c to\n4\ta \u201c /\u00ab\t12\tfl \u201c fl\nS\tbr \u201c ru\t13\tbr i i ro\n6\tbr 11 bu\t14\tbr \u201c bo\n7\tbl \u201c hi\tIS\tbl \u201c lo\n8\tbl \u201c bu\t16\tbl \u201c bo\nThe experiments were made upon T. N. and the results were as given in Table XIX.\nTable XIX.\nLocalization.\tLocalization.\n/'\u2022(\u00ab)> fr, fr, fr, fr, fr, fr.\t9\t/(\u00bb);-, f(o)r, f[o)r, fr, fr, fr, Jr.\nfr(ti), bur{k), fr, fr, fr, fr, fr.\t10\tMr), Mr), /{or), f(r), fr.\nfl\\u), fl.\tii\tf(u)l, f{\u201e)l, /(\u00ab), fl, fl, fl-\nfl\\\u00ab), fl(u),fl(a), fl, fl, fl-\t12\tf{u)l,fl{k), (/)/, \u201e(/\u2022), fl, fl-\nbr(tt), ru(b)t ru{b)t br, br, r(b).\t13\t(b)itr, (*)\u00abc, {t)ur, f{u)r, bur, br, br.\nbur, bur, (bXur, b(u)r, br(A), br.\t14\th{u)r, bn{k), b{uk), b{k), /\u2019, borf.\nbul, bul, bul, b(u)l, bl.\ti5\t(b)><l, (f)ul, lu, Ik,\nbul, bul, bul, bul, bul (A), b(l).\t16\tb(u)k, b\u201e, b{k), f,f{k),b{k),b{k).","page":46},{"file":"p0047.txt","language":"en","ocr_en":"Resta/rites on acoustic space.\n47\nAs the two telephones were situated at different levels, the localization of the perceived sound at the middle point between the sources of the two objective sounds was not so clear as in the preceding experiments. Still the results were in conformity with the preceding results, for the perceived sound was localized or tended to be localized at the middle point.\nI have already mentioned that a sound coming from ro, lo, fo or l>o is perceived by the two ears with almost the same intensity as a sound coming from ru,lit, fit or bit respectively. This is the reason why the perceived sound was sometimes located under the above conditions at a point on the same side at 90\u00b0 away from the middle point between the sources of the two component sounds, i. e., at the corresponding point in back instead of front, above instead of below and vice versa.\n(c) In the preceding two groups of experiments the two objective sources of sounds were kept unmoved during the experiment. If the perceived sound is located under such a statical condition at the middle point between the two objective sounds it may also be expected that if the two sounds are moved continuously during the experiment the perceived sound will move, too, in the direction resultant to the two directions along which the two sounds are moved.\nTable XX.\nDirections in which the two telephones were moved.\nDirections in which the two telephones were moved.\n10\n12\n11\n8\n5\n6\n7\n9\nb < hi \\hu","page":47},{"file":"p0048.txt","language":"en","ocr_en":"48\nM. Matsumoto.\nThis was the subject of the next experiments. As is show in Table XX the two telephones were started from one and the same point of the horizontal circle, and then one telephone was moved along the horizontal circle while the other was moved along one of the two vertical circles downward or upward. For example, the telephones were started at fl and one was moved toward ful while the other was moved toward/. The experiments were made upon T. N.\nTable XXI gives the results of the experiments. The expressions indicate the directions in which the sound appeared to move ; for example,\nfl-fu indicates that the sound appeared to move from fl to fu.\t\t\t\n\tTable\tXXI.\t\nDirection in which the perceived sound moved.\t\tDirection in which the perceived sound moved.\t\ni\tfl-fu, fl-fu, fl-fo, fl-f, fl-ful, fl-fu l.\t13\tfl-fo, fl-fu, f\u2019-f, fl-f fl-f, fl-fir.\n2\tfl-lu, fl-lu, fl-l( u ), fl-lo, fl-!-\tM\tfl-ro, fl-ro, fl-r(u), fl-r,fl-r, fl-r(b).\n3\tbi-blly bl-btiy bl-bUy bl-btt y bl-b.\tto\tbr-bity br-b y br-b ( /\u2022 ), br-b ( /\u2022 ), br-b ( k ).\n4\tl>l-hfy bl-ltly bl-ly bl-l, bl-l.\t16\tbr-nty br-u or br-r, br-r, br-r, br-r.\n5\tfl-fu, fl-fu, f'-fu, fl-f ur, fl-f ur, fl-fitr.\t17\tf-flr, f-fur, f-flr, f-fl,f-J>',f-flfl)-\n6\tfr-nty fr-nty fr-riiy fr-ruy fr-nt.\tiS\tf-fol, f-ful, f-fl,f-fl, o-/(l;), o-fo(fl).\n7\tbr-b/ty br-btty br-buy br-biiy br-bu.\t19\t\u00e0\u2014bur, b-bur, bo-bur, bo-bur, bo-b.\nS\tbr\u2014niy br-rity br-r tty br-nty br-r.\t20\tb-bl(ly b-buly b-b(u)ly b-b(u)l.\n9\tf-flr, /-/\"'\u2022> f-flr, f-Jur,f-Jr.\t21\tfl-fu, fl-lo, fl-lo, fl-lo, \u00df-fl\n10\tf-ful, f-fut, f-fll, f-f{u)l,ffl.\t22\tfl-lo, fl-lo(k),fl-fu, fl-l,fl-l.\n11\tb(u)\u2014bur, b-bltl'y b-blU\u2018y bu-br, b-br.\t23\tbi-bo, bl-bu, bl-bu, bl-b.\n12\tb-buly b-buly bu-bly b-bl.\t24\tbl-lu, bl-lu, bl\u2014lit, bl-l, bl-l, bl-l\nWhen one of the two telephones was moved along the horizontal circle\t\t\t\nand the other was moved downward (i. e., cases i to 12) the sound appeared to move in a direction resultant to those directions along which the two telephones were moved. The results can be explained by the relative and absolute differences in the intensities of the sounds in two the ears. If one telephone moving from fl, fr, bl or hr to f or b as in 1, 3, 5, 7 were to act alone the relative difference in the intensities of the sounds in the","page":48},{"file":"p0049.txt","language":"en","ocr_en":"Researches on acoustic space.\n49\ntwo ears would decrease gradually, and consequently the sound would be perceived to move from the secondary vertical plane towards the sagittal plane. On the other hand, if the other telephone moving downward were to act alone, not only the absolute intensity of the sound, but also the relative difference between the intensities of the sounds in the two ears would grow less and less, and consequently the sound would be perceived to move downward along the secondary vertical circle. Ihen, if these two sounds were to act at the same time, the relation of the intensities of the sounds in the two ears would be like the relation of intensities with which a sound moving in the resultant direction would be heard by the two ears. Therefore the sound appeared in i, 3, 5, 7 to move in the resultant direction. In 2, 4, 6, S, 9, 10, 11 and 12 the relative difference increased gradually, for one sound was moved along the horizontal circle more towards the auditory axis, while the other sound was moved downward. Accordingly the sound appeared to travel more towards the side and at the same time more downward, i. e., along the direction resultant to those directions along which the two sounds were moved.\nIn the cases 13 to 26 one telephone was moved along the hoiizontal circle and the other was moved upward. In these cases it would be expected that the perceived sound would travel as before along the resultant direction. The results were quite perplexing, for though the sounds were sometimes perceived to travel along the resultant direction most of them were perceived, as shown in the Figure 17, to move downward along the direction nearly vertical to the resultant direction. In the figure 01 and Oil are the directions along which the two telephones were moved ; OA is the direction nearly resultant to the above two directions ;\nOB is the direction along which the perceived sound sometimes appeared to move.\nThe explanation is not hard to find when we consider the fact that both the absolute intensity and the difference in the relative intensities become less and less when a sound is moved along the vertical circle upward. This decrease in intensity can be interpreted as the effect of the motion of the sound either upward or downward. If the former interpretation be taken the sound will be judged to move along the resultant direction, while if the latter be taken the sound will be judged to move along the direction nearly vertical to the resultant. Accordingly, the ob-\nI-'ig. i\n4","page":49},{"file":"p0050.txt","language":"en","ocr_en":"5\u00b0\nM. Matsumo/o,\nserver may perceive the sound to move sometimes in one direction and sometimes in the other. But we must note here that the confusion is not restricted to the case in which the sound moving upward is taken for a sound moving downward, for sometimes the opposite happened as in i and 2, though not frequently. We must conclude that the upward and downward directions, under the condition of our experiments, are liable to be confounded with each other, owing to the similarity of the relation in the stimulation of the two ears.\nThe results of the experiments in this section tend to show that : ( i ) two component sounds of equal intensity at the same or different levels will give in combination a localization at the middle point between the two points at which the components are placed; (2) two component sounds of equal intensity which start at one and the same point and move simultaneously in different directions will give in combination a localization in the direction nearly resultant to the two directions along which the components arc moved; (3) an occasional localization, under the above conditions, at the corresponding point in back instead of front, a*bove instead of below and vice versa, arises from the confusion between front and back, above and below. All these localizations can be explained by the principle of relative and absolute intensities.\nIV. Confusion between front and rack.\nWhen a source of sound is situated in the median plane the intensity of the sound heard by one ear is equal to that of the sound heard by the other ear. if the sensitiveness is the same for both ears; this is true whether the objective sound is situated to the front or to the rear. This is the cause of the confusion between front and back.\nAmbiguity of the judgment as to whether a sound which is not in the median plane is to be localized in front or in back can be explained in a similar way. To one side of the observer and probably nearly in the auditory line there must be, as was noticed by Rayleigh,1 one direction in which the ratio of the intensity of a sound as heard by one ear to the intensity of a sound as heard by the other ear has a maximum value which is greater than unity. For sounds situated in directions in front of this the ratio of the intensities has a less and less value, approaching unity as its limit when the sound is immediately in front. In like manner, for directions intermediate between the direction of maximum ratio and that immediately behind the observer, the ratio of intensities varies continuously between the same maximum value and unity. Accordingly, for\n1 Ravi.kicii, Acoustical observations, Phil. Mag., 1S77 (5) III 456.","page":50},{"file":"p0051.txt","language":"en","ocr_en":"Researches on acoustic space.\n51\nevery direction in front there must be a corresponding direction behind for which the ratio of intensities has the same value ; and these two directions are liable to be confounded with each other, lhe only directions as to which there is no ambiguity are the directions of maximum ratio itself, namely, right and left.\nThis view has been partly substantiated by the results of the foregoing experiments, but to make matter clearer I submitted it to the test of special experiments.\nTwo telephones were placed at fr 450 and hr 450 on the same side of the observer at a distance of 6o<\"'. A short sound was to be given by one of them and the observer (Mr. K. Miura), a student of law, was to localize the sound. The intensity of the sound could be changed, as before, by means of the sliding inductorium. When the sound was of moderate intensity the observer could generally distinguish whether it came from the front or the back. But when the sound from the front became very weak he was liable to perceive it in the back, and projected it backward more towards the median plane when it grew weaker. Even when the sound from the front was of considerable strength he was sometimes liable to project it in the back. As for the sounds coming from the back, they were mostly projected in that direction.\nA similar kind of experiment was made by using a watch instead of a telephone. The observer was seated, with his eyes closed, in the middle of a large room on a still evening. A watch was held at fr 450 or hr 450 at a certain distance, and the observer was to tell the direction of the sound. In this case the result was the reverse of that for the telephone experiment. For here we found that the sound coming from the front was never localized in the back, while the sound coming from the back was frequently liable to be localized in the front, especially when it was more distant. In respect to the latter point there were some individual differences. One person projected almost all the ticks of the watch in front. Another person projected the ticks in the back when the watch was held at the distance of 50'\"', while he projected them in front quadrant when the watch was held at the distance of ioo'\"\u2018. The general results of these experiments were, therefore, that when the sound coming from the back was situated near the ear, and was consequently stronger, the relative difference between the intensities of sensations in the two ears being also greater, it was generally localized in the back ; whereas it tended to be localized in front when the sound was more distant and was consequently weaker, the relative difference between the intensities being also smaller. In the latter case the perceived sound tended to be localized more towards the median plane, in front when the","page":51},{"file":"p0052.txt","language":"en","ocr_en":"52\nM. Matsumoto.\nobjective point of sound was more distant and consequently the relative difference between the intensities of the sensations in the two ears was smaller, and it tended to be localized more towards the side when the objective point of sound was less distant and consequently the relative difference was greater.\nRayleigh conducted an experiment of similar kind by using two 256 v. d. forks and resonators, the observer being placed between them. At a given signal both forks were struck, but only one of them was held over its resonator. The observer was required to keep his head perfectly still, a very slight motion being sufficient in many cases to give the information that was previously wanting. In these experiments the observer facing north made mistakes between forks bearing approximately north-east and south-east, though he could distinguish without a moment\u2019s hesitation forks bearing east and west.\nIn connection with the above I may mention another kind of experiment which I conducted. From the fact that the perceived sounds were located in the median plane when two sounds were placed at symmetrical points on two sides, one on each side, I thought it possible that the same results would be obtained if two sounds were placed at diagonal points of the horizontal circle, for the relation of intensities of sounds received in the two ears might be equal in the latter case to the relation of the intensities of sounds received in the two ears in the former case. So I placed two telephones in the horizontal plane in six combinations such as: (1) ,-22.5\u00b0 and / iS7-S\u00b0 (2) ^45\u00b0 and/1350; (3) r6 7.50 and /112-50 i (4) r 112.50 and '/6j.s\u00b0 ; (5) >'i35\u00b0 and ^45\u00b0 5 (6) r 157.50 and /22.5\u00b0. I found that under these conditions the localization of the perceived sound in the median plane was not so striking as was the case when the two sounds were placed at symmetrical points on the two sides of the median plane, one on each side, for though the observer located the perceived sounds at b or nearly at b for (2), (4) and (5) and at f or nearly at f and sometimes at b for (6), yet he located the sounds for (1) and (3) outside of the median plane. The results ran as follows: in case (1) the localizations were b or for, within the head (bor), within the head {for'), within the head (/') ; in case (2) they were within the head {b), within the head {/>), within the head (/>), b, or r ; in case (3) they were b or r, fo, r,fr 65\u00b0, fr 65\u00b0, r; in case (4) they were b, b, b, b, b (it) ; in case (5) they were b, b, within the head (/;), b (/), within the head (/-), //, Jl ; in case (6) they were/, /, f\nor b,/(/),/(/),/(/)-\nOn account of the comparative irregularity of these results I was doubtful whether the intensities of the sounds heard by the two ears under these","page":52},{"file":"p0053.txt","language":"en","ocr_en":"Researches on acoustic space.\n53\nconditions were equal as I had at first thought. At any rate it was evident from these results that there was a possibility of finding two points In diagonal quadrants (i. e., quadrants at opposite ends of the same axis), one in each quadrant, which in combination will give a localization in the median plane. I learned afterwards that this possibility had been realized in the experiments conducted by M\u00fcnsterberg and Pierce1 from which we can also conclude that the intensities of sounds heard in the two ears under the above conditions could not be regarded as exactly equal. From their experiments we learn that for any given point in either of the two quadrants upon one side of the median plane a point can be found in each of the two quadrants on the opposite side which in combination with the first will give a localization in the median plane at o\u00b0 or i8o\u00b0. For example, a sound at r 450 will give o\u00b0 or 180\u00b0 not only with its symmetrical / 45\u00b0, but also with a sound in the left back quadrant. Thus, for one of their observers B. r 450 gave o\u00b0 with / 105\u00b0, for another observer M. with / 1150, for W. with / 130\u00b0, for P. with / 140\u00b0, for N. r 450 gave o\u00b0 with 1450, but x8o\u00b0 with 1130\u00b0, and for R. with / 125\u00b0.\nM\u00fcnsterberg and Pierce regarded this as a special case of the more general principle : that for any given point in either of the two quadrants upon one side of the median plane a point can be found in each of the two quadrants on the opposite side which in combination with the first will give the same subjective localization. Thus their observer B. located r io\u00b0 -f /1 io\u00b0 and r io\u00b0 -)-/ 70\u00b0 at /20\u00b0; r 50\u00b0 + / io\u00b0 and 7-50\u00b0 -F l 130\u00b0 at 7-200; r ioo\u00b0 + \u00a350\u00b0 and rioo-F/1500 at 125\u00b0; 7-120\u00b0 + /400 and 7-120\u00b0 + / ioo\u00b0 at r 40\u00b0. The results were similar with other combinations. Again, according to them, very similar to this principle is the fact that different individuals at different times locate a given combination in two different quadrants. Thus B. locates o\u00b0 + /110\u00b0 at/6o\u00b0 and again at/1300; 7-30\u00b0+/no0 at /400 and /i6o\u00b0, etc. We may give the following as an illustration of the individual differences : sounds at o\u00b0 + r 1350 by B. 7-25\u00b0, by M. r 65\u00b0, by P. 7-160\u00b0; sounds at 0\u00b0 + 7-160\u00b0 by B. r 170\u00b0, by M. r 75\u00b0, by P. r 10\u00b0. The basis of these differences lies, they say, in the fact that not only 0\u00b0 and 180\u00b0, but also other points before and behind, are confused when they are sounding in a combination. In the example 0\u00b0 + r 1350, for instance, the judgment 7-65\u00b0 represents the middle ; 7-25\u00b0 represents the middle, if 7-135\u00b0 *s confused with the corresponding sound from the front at 45\u00b0; and 7-160\u00b0 represents the middle, if 0\u00b0 is confused with 180\u00b0. Just so\nM\u00fcnsterberg and Pierce, The localization 0/sound, Psychol. Rev., 1894 I 461.","page":53},{"file":"p0054.txt","language":"en","ocr_en":"J\n54\tM. Ma/su moto,\nwith o\u00b0 -f r i6o\u00b0, /-1700 results if o\u00b0 stands for i8o\u00b0 ; and rio\u00b0 ifr 2o\u00b0 stands for r i6o\u00b0.\nAll the foregoing results show that for a point given in the front quadrant a corresponding point can be found in the back quadrant on the same side of the median plane, which is liable to be confused with the first ; and that the ambiguity or uncertainty of the judgment as to front and back is based upon the similarity which exists between the relation of stimulation of the ears by a sound in one quadrant and the relation of stimulation of the ears by the same sound in the other quadrant.\nThe discrimination between front and back seems to be based upon the absolute intensity, pitch and duration of the sound, to which the tactual sensations of the pinnte and head may give some help, though the latter can not be made clear by experiment. The dependence of the discrimination upon the former was investigated by Bloch,1 as far as the discrimination between / and b is concerned. We can accept his results without further discussion, though they may not be applied to the discrimination between front and back in general. They are as follows.\nBloch gave sounds at/and b respectively and made his observer judge from which of these two directions the sounds came. The results show that the correctness of judgment depends upon the pitch, intensity, duration and distance of the sound. When he used a tuning fork of 220 v. d. it seemed clear in general that a loud and long sound at the distance of im was correctly judged as well in front as in back. A weak and short sound was not always localized correctly. A sound of greater intensity and duration\u2014i. e.,a sound of stronger acoustic excitation\u2014made the perception of the direction in the median plane easier. When Bloch made similar experiments with a pipe having a pitch of d% (1188 v. d. ) the sound at a greater distance was localized better. When the distance of the sound increased the sound at the back appeared considerably weakened and the discrimination between front and back became easier. In the median plane a higher tone was localized better than a lower one. Again when the click of a snapper sounder was given at a distance of 2.4'\" a weaker tone tended to be located more in back and a stronger tone more in front. With the increase of the intensity of tone the number of the /judgments increased and the number of the b judgments decreased, or with the decrease of the intensity of tone the number of the /judgments decreased and the number of the b judgments increased. We learn by experience, says Bloch, that a certain sound is perceived with less intensity when it comes from the back than when it comes from the front. Accordingly when the direction of the sound is not\n1 I\u00eelocii, Das binaurale H\u00f6ren, Zt. f\u00fcr Ohrenheilk., 1893 XXIV 25.","page":54},{"file":"p0055.txt","language":"en","ocr_en":"Researches on acoustic space.\n55\nclear we tend to locate a stronger sound in front and a weaker one in back.\nIn connection with the experiments on the confusion between front and back other experiments of somewhat similar kind may be mentioned. We have already seen that the value of the relative difference between the intensities with which a sound is heard by the two ears varies according to the direction of the sound. But the direction of the sound seems not to be the only condition upon which the change in the relative difference depends, for this difference seems also to depend upon the absolute intensity of the sound. In other words, this value seems to change, other things being equal, when the intensity of the sound changes. It has been a well-known fact since Fechner\u2019s 1 experiments that when two unison forks are held before the two ears respectively and one of them is more strongly sounded than the other, the single resulting sound appears to the subject to be heard entirely by the ear on the side of the stronger component. The ear which receives the weaker sound is said to become more or less \u201cphysiologically deaf.\u201d It seems to me that this \u201cphysiological deafness\u201d of one ear becomes relatively greater when the sound received in the other ear grows stronger, and thereby the perceived sound tends to be projected much more towards the side on which the source of stronger sound is situated than when a sound of weaker intensity is used. The following experiments were designed to make this point clearer.\nTable XXII.\nDistance of the secondary coil for the back Judgment of direction.\tJudgment of distance,\ntelephone.\nIOcm\tfr 8o\u00b0\t8.5 s\"\u201d (25e\"')\t\n9\tfr So\t9\t(27)\n8\tfr 85\t8-5\t(25)\n7\t;\u2022 90\t8-5\t(25)\n6\t/* 90\t8-3\t(25)\n5\thr 82.5\t7\t\t(21)\n4\thr So\t6-5\t(19)\n3\thr 80\t5-3\t(16)\n-\u25a0\u00bb\tbr So\t5\t(15)\nI\tbr So\t4-3\t(13)\no.6\tbr So\t4\t(12)\nThe number\tof experiments on each\ttion varies from o to\t\u00b1 1 To%\npoint is 4. The\tprobable error for direc-\tfor distance from o to j\t1 0/ \u00ef\u00ef r /o*\n1 Fechnkr, Ueber einige Verh\u00e4ltnisse des binocular en Sehens, Ges. d. Wiss., math.-phys. CI., i860 VII 339.\t\t\tAblil. d.","page":55},{"file":"p0056.txt","language":"en","ocr_en":"56\tM. Ma/su mo/o,\nTwo telephones were situated on the right side of the observer. One at 6o\u00b0 to the front and the other at 6o\u00b0 to the rear. The wires for the latter were connected with the secondary coil and the wires for the former with the primary coil of the sliding inductorium. In each experiment the intensity of the sound in front was kept constant, while that of the sound to the rear was varied. The subject of the experiments was C. W. Table XXII gives the results.\nFigure 18 shows the results graphically. The perceived sound was gradually placed more towards the back as the sound to the rear grew stronger and consequently the relative difference became greater. The gradual change of the angular magnitude of the localized position of the perceived sound corresponding to the gradual change in the intensity of the sound to the rear is shown in Table XXII. An interesting point is that when the sound to the rear reached its maximum intensity\u2014and consequently according to our view the relative difference between the intensities of the sensations in the two ears became greatest\u2014the perceived sound was located at hr 8o\u00b0. Experimentally it seems to be the fact that when the relative difference is greatest the perceived sound is in general located somewhat to the rear of the visual right and left line.\nSimilar results were obtained when the experiment was conducted by placing telephones on the right side of the observer at 300 both in front and to the rear. Table XXIII gives the average results.\n\tTable XXIII.\t\t\nDistance of the secon-\t\t\t\ndary coil for the back\tJudgment of direction.\tJudgment of distance.\t\ntelephone.\t\t\t\niocm\tfr 45\u00b0\tIOs\"\u00b0\t( 3\u00b0c\"* )\n9\t/'\" 55\t10\t(3\u00b0)\n8\t/>\u25a0 57-5\t9-5\t(28)\n7\tfr 65\t9-3\t(28)\n6\tfrt 7-5\t9-5\t(28)\n5\tfr 66.7, hr 70 or fr 70\t7-7\t(23), 10 (30)\n4\thr 7\u00b0>fr 75\t71\t(21), 7-5(22)\n3\tfr 73. hr 70\t6\t(iS), 5 (15)\n2\thr 72.5\t5\t( *5 )\ni\thr 70\t4-5\t(13)\nThe number of experiments on each\ttion varies from O to\u00b15r0% a,K' that for\npoint is 4. The probable error for direc-\tdistance from O to rfc f\u00e2.","page":56},{"file":"p0057.txt","language":"en","ocr_en":"Researches on acoustic space.\n57\nFigure 19 shows the results graphically. As the sound heard by the right ear grew stronger the perceived sound was located more towards the side. But as the value of the relative difference between the intensities of the sensations perceived by the two ears was smaller in this case than in the last experiment, the perceived sound was never /ocated so near to the auditory axis.\nV. Perception of distance.\nThe dependence of the perception of the distance of a sound upon its intensity has already been observed in foregoing experiments, though attention has been paid chiefly to the perception of the direction. In this section particular consideration will be given to the perception of distance with a view to determining under various conditions the relation between the intensity and distance of a perceived sound.\nFit;. 19.\ni. Dependence of the change in the distance of a perceived sound upon the change in the intensity of the component sounds.\nTwo telephones were situated on both sides at r 90\u00b0 and l 90\u00b0. The wires from both telephones were connected with the secondary coil of the sliding inductorium. In this experiment it was requisite to make the intensities of the two component sounds equal in every respect at each distance of the secondary coil. This was done with a fair approximation to correctness. The subject of the experiment was C. W. In this subject the left ear was sharper than the right ear. Taking this fact into consideration we could not expect that the subject would locate all sounds\nTaule XXIV.\nDistance of the sec-\tJudgment\tJudgment\nondary coil for\tof\tof\nboth telephones.\tdirection.\tdistance.\n9'\u201c\t/\ti2suu (36c,n)\n8\t/(/ 6-7\u00b0)\tii-5 (35)\n7\tf f 3-3)\tii-3 (34)\n6\t/(' 5)\t10.7 (32)\n5\t/(/6)\t9\t(27)\n4\t/\t6.7 (20)\n3\t/\t8.7 (26)\n2\t/\t7-7 (23)\ni\t/\t6\t(18)\nThe probable error for distance varies from o to 71V % -","page":57},{"file":"p0058.txt","language":"en","ocr_en":"5\u00bb\nM. Matsu moto t\nwhich he perceived strictly in the median plane. It would be more probable that when the intensities of sounds were weakened the observer would project the perceived sound a little towards the left of the median plane.\nA current of i'/> amp\u00e8res was used in the primary circuit and the sounds were given in an arbitrary order. The average results of three experiments on each point were as given in Table XXIV. Figure 20 shows the results graphically. pIG ,0\tWhen the same experiment was repeated with a cur-\nrent of 2 amp\u00e8res the average results of three experiments on each point were as given in Table XXV.\nTable XXV.\nI listance of the sec-\tJudgment\tJudgment\nondary coil for\tof\tof\nboth telephones.\tdirection.\tdistance.\ngem\t/('3-3\u00b0)\t14s11\u201c (42\"\u201c\nS\t/('3-3)\t12\t(36)\n7\t/\t10.7 (32)\n6\t/\t93 (28)\n5\t/\t9'3 (28)\n4\t/\t7\t(21)\n3\t/\t6\t(18)\n2\t/\t4-3 (\u00ab3)\nI\t/\t4 (12)\nThe probable error for distance varies from o to 4JC 'fc \u25a0\nFigure 21 shows the results graphically. In both experiments the perceived sounds were located in the median plane, though when the sounds grew weaker the effect of the left sound became relatively stronger and the perceived sound tended to be localized a little towards the left of the exact median plane. The distance of the perceived sound gradually increased as the intensity of the component sounds grew gradually weaker.\nWhen the same experiments were repeated and the sounds were given in ascending or descending order the results were more regular, but not much different.\t2I\nThe results show that in the case of a familiar sound the judgment of its distance is based upon the difference in intensity.\nA fact analogous to the results of these experiments is found in optics where the difference in distance is judged by the apparent magnitude of objects familiar to the sight and of known size.","page":58},{"file":"p0059.txt","language":"en","ocr_en":"Researches on acoustic space.\n59'\n2. Relation between the perception of distance of a sound ana its intensity.\nIn the preceding experiments we have considered the change in the distance of the perceived sound which depends upon the change in the intensity of the telephone sounds owing to the change in the intensity of the electric current. By this method the quantitative relation between the distance of a perceived sound and the physical intensity of the sound cannot be found, for it is very difficult to measure the change in the intensity of a sound, either absolutely or relatively, as depending on the change in the intensity of the electric current. To obtain a quantitative relation I was, therefore, compelled to change the intensity of a sound by changing the distance of the sounding body. By that method the relation between the change in the perception of distance and the change in the intensity of a sound could be more easily established, for the intensity of sound-waves diminishes according to the law of inverse square of distance. I could not perform the experiment for a greater distance than 8 feet, for the cloth chamber within which I was compelled to execute the experiment to avoid reflection of the sound was a cube of 6 feet, the diagonal being about 8.5 feet long. The subject was seated in a chair in one corner of the chamber. A tape measure was stretched from that corner to the opposite corner on a level with the top of the head of the subject ; the head was adjusted by a support in such a way that the tape measure would run in the median plane of the head. The point of the measure at which it was intersected by a perpendicular drawn from the middle point of the imaginary line connecting the openings of the ears was regarded as the zero point. I used a telephone sound which was connected with an electro-magnetic fork of 250 vibrations per second. Between the fork and the telephone a short circuit key was inserted, by means of which the duration of the telephone sound could be regulated. The telephone was to be moved below the tape measure and parallel to it, so that it was situated in the median plane at the level of the openings of the ears.\nThe first step of the experiment was to find the point at which the subject judged the sound to be distant just one foot. Let this point be called A. The next step was to give two short sounds with a brief interval between them, the first at the point A and the second at a different point. The subject was to judge, with his eyes closed, whether the second sound was twice as far distant as the first sound. If the subject thought that the second sound was nearer or farther than twice the distance of the first sound then the experiment was to be repeated by giving the second sound at a farther or a nearer point. After many experiments a point would be found at which the second sound appeared to be just twice","page":59},{"file":"p0060.txt","language":"en","ocr_en":"6o\nM. Matsumoto.\nas far as the first one. In a similar way the points were found, at which the second sound was judged to be three times, four times and five times as distant as the first sounds. In this way the relation between the distances in the mental and physical scales was established. During the experiment the intensity of the telephone sound was kept constant, so that the change in the intensity of the perceived sound would arise only from the change in the distance of the sound, and could be expressed by the accepted law of the propagation of sound.\nI made the experiments on the two subjects I. M. and K. M. More than ioo experiments were tried for each point of the scale of distance, care being taken to avoid the effect both of practice and fatigue.\nBoth subjects judged the sound to be about one foot (3.1e1\") distant when the sound was given at the point 40''\" distant from the o point of the tape measure. For the subject I. M. the relative mental scale of the distances 1, 2, 3, 4, 5 corresponded to the physical scale of the distances 40, 80.9, 112.4, 159.3, 185.9 cm., and for the subject K. M. the relative mental scale of the distances 1, 2, 3, 4, 5 corresponded to the physical scale of the distances 40, 79.2, 117, 152, 193.5 cm. . Now as these physical distances are the distances between the middle point of the auditory axis (connecting the ears) and the telephone, and as the distance between this point and the opening of the ear is about 8\"\", we have for the square of the distance between the ear and the telephone the sum of the squares of the above two distances, i. e., the distance between the telephone and the middle point of the auditory axis and the distance between the middle point and the opening of the ear, for these three distances correspond to the three sides as a right-angled triangle. Finding the squares of the distances between the ear and the telephone, which correspond to the distances in the mental scale, we have for I. M., 1664, 6609, 1298, 25440, 34623. Dividing these figures by 1664 (to get the relative distances) we have the ratios 1, 3.3, 7.5, 15.4, 20.8. The squares of the distances for K. M. are 1664, 6337, 13753, 23168, 37506. Finding the ratios we have 1, 3.8, 8.3, 13.9, 22.3.\nThe ratios in the above two cases are nearly equal to the squares of the distances of the sounds in the mental scale, namely, 1, 2, 3, 4, 5. As the reciprocals of these ratios represent the relative intensities of the sounds, the conclusion appears justified that when the intensity of a sound diminishes in geometrical progression the perceived distance of the sound increases in arithmetical progression.\n3. Continual change in the distance of a perceived sound due to the movement of the two component sounds.\nIn connection with the question of distance I conducted other sets of","page":60},{"file":"p0061.txt","language":"en","ocr_en":"Researches on acoustic space.\n61\nexperiments in which the objective positions of the two component sounds were simultaneously changed, while their intensities were kept constant, and obtained results which showed again the dependence of the perception of distance upon the change in the intensity of the perceived sound. In these experiments the spherical cage (Figure i) was used.\n\u0430.\tThe two telephones were moved along the radii of the horizontal circle of the cage. The directions in which the two telephones were moved are as given below. The arrows indicate the directions, and the letters indicate the points of the spherical cage as explained on p. 3 ; thus the expression for Number 1 means that the two telephones were placed at first very near to the ears and they were then moved simultaneously to the points r and l; Number 3 means that they were started at the front and the back very near to the head and were moved to / and l> ; Number 5 means that one of the two telephones was started at r and moved to the ear, while the other telephone was started at the left ear and moved to l; etc.\ni. /-\u00ab-sear, ears-\u00bb- r; 2. As-\u00bb-ear ear-\u00ab-ew'/\n3. /-\u00ab-\u00bbheads:-\u00bb- b ; 4. /\u00ab-*- head -\u00ab\u2014=-/ ;\n5. /-\u00ab-~;ear ear-\u00ab\u2014\u201c/\u2022/ 6. /s-\u00bb-ear ears-\u00bb-r.\nFive or eight experiments were made for each case and the judgments of the observer T. N. in regard to the directions of the perceived sounds under the conditions were as given below ; n means the nose, x means doubtful, k means within the head.\n1.\tk-f, k-x, k-b(x), k-b(x), k, iff), k-f and /-<\u2014rate-w, k-f and / -<\u2014*-r ;\n2.\tf b-k, b-k, b-k, b-k, b-k, f-n, k(f) ;\n3.\tk-f, n-f n-f /\u25a0(/)-/, n-f ;\n4- f~n, f-n, f-n, f-n, f-n, f-n ;\n5. l-r, l\u2014r, l-r, l-r ;\n\u0431.\tr-l, r-I, r-l, r-l, r\u2014l.\nIn Number 1 the two ears of the observer were stimulated at first by strong sounds and he felt the sound in the interior of his head. As the telephones were moved along the auditory axis farther and farther from the ears the intensities of two sounds grew weaker and the perceived sound emerged from the head and receded along the median plane more and more towards f. But it receded occasionally towards b. This result shows that the continual change in the distance of the preceived sound arises from the continual change in the intensity of the sound. In this experiment the observer perceived sometimes two sounds separately, though at the same time he perceived a third sound in in the median plane. Number 2 is just the reverse of Number 1. The sound was","page":61},{"file":"p0062.txt","language":"en","ocr_en":"\u00d62\nM. Matsumoto.\nperceived at first in front or back at a certain distance and then it gradually approached towards the head and at last entered the head.\nIt is interesting to note here that in Number 2 the sound seemed to start generally at b while in Number 1 it seemed to stop generally at f, though the intensity of the stimulation of the ears at the instant of starting in Number 2 was just like the intensity of the stimulation of the ears at the instant of stopping in Number 1. In Number 1 the observer was sure that the sound was in front, for in the first half of the experiment the perceived sound was very strong, and therefore he continued to think that the sound was still moving in the same direction even when its intensity grew weaker and weaker. He thought only occasionally that the sound moved towards the back, but he was very doubtful of his judgment.\nIn Number 2 the case is a little different. In this case the sound was heard with less intensity at the first moment than in the succeeding mo- ! ments, and the observer was in doubt at first whether it was in front or in back. It was his usual experience that when a sound was at the back he was generally in a state of doubt. So in this case he judged that the sound started from the back, and consequently he continued to think that the sonnd was still moving from back even when the sound grew stronger. Thus i and 2 show that the perception at a certain instant is influenced by the perception of the preceding instant.\nIn Number 3 the sound in front was heard with greater intensity than the sound at the back at the same distance. Moreover the sound was heard at first with great intensity. The observer could not, therefore', doubt that the sound was in the front very near to the head. As the intensity became less the distance of the perceived sound increased. Number 4 is the reverse of Number 3 and needs no explanation.\nMost interesting results were given by Number 5 and Number 6, in which we found striking examples of the dependence of the perception of distance upon intensity. In these cases the two telephones were moved in the same direction and not in the opposite direction as in the previous four cases. Here the observer perceived the sound to be travelling in a direction reverse to the direction of the movement of the telephones. In Number 5 one telephone was moved from r to the right ear, while the other telephone moved from the left ear to /, so that the direction of movement of the two telephones was from right to left. The observer perceived the sound to be travelling from left to right. The explanation is simple and clear. At first the sensation of the left ear was relatively stronger, and gradually grew weaker, whereas the sensation of the right car was at first relatively weaker and gradually grew stronger.\nAt a certain point the intensities of the two sensations became equal. Con-","page":62},{"file":"p0063.txt","language":"en","ocr_en":"Researches ou acoustic space.\n63\nsequently the sound was at first perceived on the left side near to the ear, then it was perceived in the median plane, and at last it was perceived on the right side near to the ear. The intermediate points were passed in succession. As a whole the sound seemed to have travelled from left to right. Number 6 is just the reverse of Number 5.\nAll the six cases show that the distance of the perceived sound depends upon the intensity of the sound. The change in the former is continuous when the change in the latter is continuous. Continuous change in the intensity of a sound is always perceived as a change in the distance of the sound, i. e., as a motion of the sound, whether that change in intensity is caused by actual motion or not.\nl>. The two telephones were moved along the circumference of the horizontal or frontal circle of the spherical cage. The objective path along which the two telephones were moved were as indicated below. The expression for Number 1 means that the two telephones were started at the front and were moved around simultaneously to the left and right ; Number 3 means that they were started at the left and right and were moved simultaneously toward the front, etc.\n1.\t; 2,\t3,\t4, /ss+b+\u00e6r; 5,\n6, l-*-vsu ; 7, As-vo-e-ss/-; 8, /\u00ab-\u25ba\nThe number of experiments for each case was from 4 to 6. The judgments of the observer T. N. in regard to the directions of the perceived sounds under these conditions were as follows :\n1 \u2022\t/-\u00bb, /, f-fo-o.\n2.\tb\u2014k, b\u2014k, />-/, b\u2014bo\u2014 0 or/-\u00ab.\n3.\tk-f,f k(b) or /\u25a0(/)-/ b\u2014x\u2014f.\n4.\tk-b, k-b, k\u2014b, 11-b.\n5.\to-k, o-k, 0 or/, o-b.\n6.\tu-u, u-k, 11-11/-/, u\u2014u/\u2014k.\n7- \u00ab-/ f-b,/-o,/-o, k-o{b'),/-/o-o.\n8. n-u, n-u, n-u, k\u2014u.\nIn all cases the intensities of the sounds for the two ears were equal and the perceived sound was always located somewhere in the median plane. Special results were observed as follows.\nNumber 1. When the telephones were moved from / to r and /, the \u2022sound was perceived to travel in the median plane from some distant point in front inward to the nose or the head of the observer. This decrease of distance presumably arose from the increase of the intensity of <he perceived sound, for under these conditions the perceived sound is stronger on account of the action of the pinn\u00e6, when the objective sounds are situated more towards the auditory axis than when they are situated","page":63},{"file":"p0064.txt","language":"en","ocr_en":"64\nAT. ATatsumoto,\nmore towards front. But as the tragus has some influence upon the intensity of the perceived sound, the observer was sometimes in doubt about the direction of motion of the sound as the telephones were passing about the points fl and fr.\nNumber 2. When the telephones were moved from b to r and l the sound was perceived to be travelling from b to k or from b to f This needs no explanation, for it is analogous to Number 1.\nNumber 3 and Number 4 are just the reverse of Number 1 and Number 2 and the sounds were perceived to pass from k to f and from k to b respectively.\nNumber 5 and Number 6 can be explained in a similar way. On account of the pinn\u00e6 and the direction of the external meatus, sounds coming from above or below are heard with less intensity than sounds coming from the direction of auditory axis. Accordingly the intensity of the perceived sound increases gradually as the telephones are moved from above or below toward the auditory axis, and the distance of the perceived sound seems to decrease.\nNumber 7 and Number 8 are the reverse of Number 5 and Number 6.\nIt is interesting to note that in Number 7 the sound was sometimes perceived to have travelled from / to b, or f to o, or n to / instead of travelling from k to 0. From this we can see that in discriminating directions in the median plane much depends upon the interpretation of the observer. In number 7 the stimulation of the ears was strongest in the beginning ; then grew less and less as the telephones were mo \u2019ed gradually upward. This decrease of the intensity can be interpreted by the observer as the effect of motion of sound from / to b, or /to 0, or n to /\nFinally in connection with the question of distance we must call attention to the endocephalic localization which we have already noticed. When the intensity of the two sounds opposite the ears becomes very great the perceived sound, which is localized at first in the median plane, approaches the head and at last enters it. This endocephalic localization is sometimes so strong .that the subject cannot get rid of the illusion, though he knows perfectly well that the objective sounds are outside the head. This illusion occurs more strikingly when the telephones are placed against the ears or when conducting tubes are put into the ears. Under such conditions the sound is heard in the head even if the intensity is not very great. An experiment of Schaefer1 is interesting in this connection. In his experiments a telephone was\n1 Schaefer, Zur intcraurealen Localisation diolischer Wahrnehmungen, '/X. (. Psychol, u. Physiol. <1. Sinn., 1890 I 300.","page":64},{"file":"p0065.txt","language":"en","ocr_en":"Researches on acoustic space.\n65\nbrought near to a funnel receiver, which communicated with the two ears by means of a forked tube with arms of equal length. The telephone was connected with the secondary coil of a sliding indue-torium. At the start the secondary coil was put at a great distance from the primary coil of the inductorium and then the secondary coil was gradually brought nearer to the primary, during which the change in localization was observed. It was found that the apparent sound approached the head according to the decrease of the distance between the primary and secondary coils, so that the sound finally crept into the head and occupied a position between the ears. If one of the arms was closed the sound would shift to the auditory canal of the opposite ear. If the secondary coil were then moved farther from the primary coil the sound would go out from the auditory canal to the space on the side of that ear. If the pressed tube were then opened, the sound would move to the median plane at some distance from the head. With many persons the sound entered or emerged from the head at the root of the nose according to the increase or decrease of the intensity of the telephone sound.\nAT. The least perceptible change in the direction of a sound.\nIn our previous experiments we found that when two telephones were placed on opposite sides just in the line of two ears and the intensity of one component of the perceived sound was changed while that of the other was kept constant, the perceived sound was located more toward the side on which the objective sound was stronger, and more toward the median plane when the intensities of the two component sounds became more nearly equal. While conducting these experiments I noticed occasionally that, when the relative intensities of the two sounds were in such a relation that the perceived sound was located at r 90\u00b0 or l 90\u00b0, a small change ( i to i cm. for the secondary coil) in the difference between the relative intensities of two sounds was not usually perceived as a change in the direction of the perceived sound and, in fact, was not perceived at all. But when the intensities of the two component sounds were in such a relation that the perceived sound was located just in front, the change in the difference between the relative intensities corresponding to 0.5\u2122 or iera was usually perceived as a change in direction.\nThe explanation of the difference in the above two cases seems to me to lie in the fundamental fact of sensation as expressed by Weber\u2019s law. For the initial difference between the relative intensities of the sounds heard by the two ears was greater in our experiments when the perceived 5","page":65},{"file":"p0066.txt","language":"en","ocr_en":"66\nM. Mafsumoto,\nsound was located more toward the side, and it was smaller when the perceived sound was located more toward front. Consequently a large change would be necessary in the former case if the change is to be perceived.\nThe object of the next experiment was to make this relation clear. As in my previous experiments, two telephones were placed on opposite sides. The distance between the ear and telephone was 45 cm. The intensity of one component sound was kept constant, while that of the other component sound was varied by means of the secondary coil ; the observer localized the perceived sound at a certain point as before when the two components were given simultaneously. This point was to be regarded as the initial direction. Then, while the two sounds were given, one of them was to be moved from its original position slowly along the auditory axis till the point was reached where the observer just noticed a change in the initial direction of the perceived sound. The distance traversed by this component sound was measured by a millimeter scale which was fixed along the path of the telephone. This distance is called an increment distance (J), for it is a distance which is required for producing the least change in the initial direction of the perceived sound.\nThe results of the experiments on the relation between the change in the initial direction and the corresponding increment distance were as given in Table XXVI.\nTaule XXVI.\n\tThe right component sound\t\tconstant. Observer :\tc. w.\t\nM\tD\t/\tJ\tE\tn\n27\t0.6 \u2122\t/\t13.1\tr\t15\n\t2\t\u00c4 3\u00b0\u00b0\t15.6\tr\t15\n\t3\tA 70\t21.7\tr\t\u00ab5\n\t4\tr 90\t26.1\tr{h)\t\u00ab5\n\t5\tr 90 (b)\t27-5\t,\\b)\t7\n.1/, date in March, 1S97.\t\t\tE, direction toward which\t\tthe sound\nD, distance of the secondary coil for j appeared to change, the left telephone.\tI \", number of experiments.\n/, direction of the perceived sound , The probable error of J varies from \u00b1 for the position D.\tI fa% to \u00b1 Iyo%-\nJ, change in the distance of the left | telephone.\nIn this experiment the intensity of the sound produced by the right telephone (connected with the primary coil of the inductorium) was kept constant while the intensity of the sound produced by the left telephone","page":66},{"file":"p0067.txt","language":"en","ocr_en":"Researches on acoustic space.\n67\n(connected with the secondary coil) was varied. When the secondary coil was moved away from the primary to the point o.6cra and sounds were given from both telephones at the same time the observer located the single resultant sound at /. The resultant sound was localized at fr 30\u00b0, fr 70\u00b0, r 90\u00b0, r 90\u00b0 (h) respectively as the coils were separated\noc \u00abcm \u00abcm -cm -cm\nas 2 >3 >4 > 5 \u2022\nWhen the observer located the sound at one of above directions the intensity of the left component was decreased again by moving, not the secondary coil, but the left telephone itself from the ear along the auditory axis, till the point was reached at which the sound was just noticed to shift from its initial position.\nAs we find in the table the increment distance was least when the perceived sound was initially located at /, it increased gradually till it reached its maximum when the perceived sound was initially located at r\tWhen the initial difference between the intensities of com-\nponents heard by the two ears was much greater the increment distance became greater than 35\"\u201d. In our small room we could not make an arrangement to move the telephone farther than 35\u00b0\u201c. The reason why the perceived sound shifted its position always toward the right in this experiment is easy to find, for the intensity of the right component became relatively greater as the intensity of the left component decreased. We must notice here the fact that the perceived sound was located at r 90\u00b0, but a little backward than just at r 90\u00b0, when the relative difference between the intensities of sounds in the two ears was very great. A similar case has been already observed in our previous experiments. I have said that it is probable that what we call commonly right and left lies in the line drawn tangent to the front surfaces of the two eyeballs. So when the maximum difference in the intensities of the components in the two ears is obtained, the perceived sound is not located just at visual right or left, but, being referred to the common standard of direction, it is located at right or left, a little toward back. Or we may say that the difference in the relative intensities with which a sound is heard by the two ears is greatest, not when the sound is situated in the visual rl line, but when it is situated a little behind it. On this basis the fact that the sound seemed to shift a trifle backwards from r 90\u00b0 when the intensity of the right component became relatively very strong does not disprove the dependence of the least perceptible change in the direction of a sound upon the change in the relative difference between the intensities of the components in the two ears. From similar experiments conducted on a different day, results were obtained in which the above relation can be seen still more clearly (Table XXVII).","page":67},{"file":"p0068.txt","language":"en","ocr_en":"68\nM. Matsumoto,\nOwing to the slight changes in the position of the telephones and the head of the observer and minute changes in the intensity of the sound arising from the fluctuaton of the electric current, there were some deviations in conditions for different days ; and consequently the results of the experiments must be considered for each day separately.\nTable XXVII.\n\tThe right component sound constant. Observer :\t\t\tC. W.\t\nM\tD\t/\tA\t\u00a3\t>1\n24\t1 CIU\tl 90\u00b0\t24.9 cm\tf\tiS\n\t2\tbl 70\t17.9\tb\t15\n\t4\t/\t12.5\tr\t15\n\t4-5\tb\t15-7\tr\t15\n\t6\tfr 60\t14.2\tr\t15\n\t7\tr 90\t25-7\tr{b)\t15\nNotation same as in Table XXVI.\nThe probable error of A varies from \u00b1irVX.to = 2 %.\nSome experiments made upon Dr. Scripture gave similar results which are given in Table XXVIII.\n\t\tTable XXVIII.\t\n\tThe right component sound constant. Observer, Dr. Scripture.\t\t\nM\tD\tI\tA\t\u00a3\t11\n27\t0.6 cm.\tfl io\u00b0\t23.3 cm.\t/\t9\n\t3\t/\t20.7\tr\t10\n\t5\tfr 60\t22.7\tr\t10\nNotation same as in Table XXVI.\nThe probable error of A varies from \u00b1 2f,% to \u00b1 3is%-\nIn these experiments the perceived sounds were sometimes located to the rear. In such cases the least change in direction was also made toward b. Again, when the initial direction was on the left side the least perceptible change was made toward the median plane. The shifting of of the left sound toward the median plane is really a shifting toward the right side, and can be explained by the relative increase of the intensity of the right component sound.\nSimilar experiments were made upon C. W. on different days, by varying the intensity of the right component sound while keeping that of the left component sound constant, and similar results were obtained, which are given in Table XXIX and need no special explanation.","page":68},{"file":"p0069.txt","language":"en","ocr_en":"Researches on acoustic space.\t69\nTable XXIX.\n\tThe left component sound constant.\t\t\tObserver : C. \\V.\t\nM\tD\t/\tJ\tE\tn\n18\t3\u2122\u2019\tr 90\t29.1e1\u201c\tl\t14\n\t5\tfr 70\t26.4\t/\t18\n\t1\t8.25\t/\tI3I\tl\t15\n\tr 10\t/ 90\t24.6\t1(b)\t20\nJ9\t7\t/70\t22.4\tl\t20\n\t6\t/\t20.5\tl\t19\n\tr 2\tbr 80\t34-7\tb\t5\n20\t4\tfr 20\t24.4\tf\t12\n\t7\tl 90\t33-2\t1(b)\t4\n\tii\tfl 80\t33-6\t1(b)\t15\n\t10\tfl 20\t21.4\t1\t17\n31\t9\tf\t17.6\tl\tIS\n\t7\tfr 10\t25.6\tl\t13\n\t5\tfr 20\t31-7\tl\t15\nD, distance of the secondary coil for\t\t\tOther notations same as in\t\tTable XXVI.\ne right telephone.\t\t\tThe\tprobable error of\tJ varies from\n\t\t\t= TV/o to \u00b1 2rV/0.\t\t\nAs the intensity of sound is inversely proportional to the square of distance, the intensity of the variable component sound in the foregoing\nexperiments is proportional, other things being equal, to \u201e 1 \u2022 where\n(C+J)\nC represents the initial distance (45'\"') between the telephone and the ear and J represents the increment distance. As C is constant in our experiments, the value of the fraction depends upon J. The greater the change in the increment distance, the greater is the change in the intensity of the component. But the change in the increment distance which is required for producing the least noticeable change in the initial direction would be expected according to Weber\u2019s law to depend upon the value of the initial difference between the intensities of the two components. This expectation was realized in the actual results of the foregoing experiments. For in these experiments the increment distance was smallest when the sound was initially located in front or behind, that is, when the initial difference between the intensities of the component sounds in the two ears had the smallest value possible (namely, zero). The increment distance increased gradually as the initial difference between the intensities of the component sounds in the two ears became greater, and consequently as the perceived sound was initially located more towards the right or left side.\nVII. Theoretical conclusions.\nSounds are located both as to direction and distance from ourselves as the center. In the foregoing experiments we have found that the judgment","page":69},{"file":"p0070.txt","language":"en","ocr_en":"70\nAI. Matsu moto.\nof the direction of a sound depends chiefly on the relative difference between the intensities of the component sounds heard by the two ears, while the absolute intensity of the perceived sound is supplementary to this fundamental factor. The judgment of the distance of a sound depends, on the contrary, chiefly on the absolute intensity. To these factors in the localization of a sound we may add other cooperating factors, such as relative and absolute pitch, timber and phase.1 With these data at hand it becomes necessary to inquire how they bring about the localization of a sound. There are several theories of the way in which this is done ; these will be briefly discussed.\ni. Theory of a direct acoustic space.\nThis theory assumes that a sound heard by the right ear is distinguishable from that heard by the left ear ; that the right and left components of a sound heard with both ears produce an effect in consciousness which varies with the relative intensity of the components ; that this effect is an experience analogous to that from simultaneous but not identical sensations of sight or touch ; that it should be considered to be one of the kinds of space analogous to visual space or tactual space ; and that this acoustic space is brought into relation to and modified by visual, tactual and muscular experiences.\nThis might be called a direct theory of acoustic space. Although no positive objection can be made, it seems somewhat artificial and not well adapted to explain the methods by which we localize sounds.\n2. Tactual theory.\nSome psychologists have sought the ultimate origin of acoustic space in the tactual sensations of the tympanic membrane.\nOne form of this theory assumes : i, that special sensations of touch are received from different parts of the tympanum; 2, that the soundwave arouses the sensations from the tympanum ; and 3, that different\n1 URBANTSCHITSCH, Zur Lehre von der Schallempfindung, Archiv f. d. ges. Physiol. (Pfl\u00fcger), iSSl XXIV 574.\nRAYLEIGH, Our perception of the direction of a source of sound, Nature, 1S76 XIV 32. RAYLEIGH, Acoustical observations, Phil. Mag., 1877 (5) III 456.\nMach, Bemerkung \u00fcber die Function der Ohrmuschel, Arch. f. Ohrenheilk., 1875 n. F. Ill 72.\nThompson, On binaural audition, Phil. Mag., 1877 (5) IV 274; 1878 VI 3S3 ; 1881 XII 351. THOMPSON, On the function of the two ears in the perception of space, Phil. Mag., 1882 (5) XIII 406.\nBloch, Das binaurale H\u00f6ren, Zt. f. Ohrenheilk., 1S93 XXIV 25.","page":70},{"file":"p0071.txt","language":"en","ocr_en":"Researches on acoustic space.\t7 x\nparts of the tympanum are affected according as the direction of the sound is different.1\nThe first assumption is in all probability justified ; the tympanum is undoubtedly sensitive and the stimuli applied to different portions can be presumably distinguished.\nThe second assumption is not so readily to be accepted in view of the fact that the energy of the air-vibrations is extremely small, in fact so small that a most complicated apparatus, the internal ear, has been specially adapted to transform the air-vibrations into nerve-currents. There is no conclusive experimental evidence to support the view that soundwaves can be directly felt by the end organs or the nerves of touch. In the perception of sounds the tympanum is not the true receptive organ, but only a part of a mechanical device by which the vibrations are gathered and conveyed to the internal ear.2\nThe third assumption is quite untenable. The diameter of the auditory canal is too small to permit of different degrees of pressure at different points of the tympanum at the same moment ; we can without hesitation consider the pressure as equal over all parts of the tympanum.3\nA second form of this theory to the effect that the touch organs of the tympanic membranes in the two ears are affected differently by sounds coming from different directions would be consistent with observations of cases in which the ability to localize sounds was lost, together with the sensitiveness of the tympanum.4 In spi \u2014 of some minor observations that may be interpreted in favor of this theory it is difficult to agree with Wundt5 6 in accepting it even partially ; at any rate such an extremely remarkable sensitiveness of the tympanum should be most thoroughly established before a final decision could be given in favor of it.\n3. Theory of a special space organ.\nAccording to Preyer the semicircular canals are the organs for the perception of the direction of a sound.0 By means of a specific energy of the\n1 K\u00fcpper, Ueber die Bedeutung der Ohrmuschel des Menschen, Archiv f. Ohrenheilk., 1874 n. F. II (3) 158.\n\u00abThompson, On the function of two ears in the perception of space, Phil. Mag., 1882 (5) XIII 406.\n\u00ab Helmholtz, Die Mechanik der Geh\u00f6rkn\u00f6chelchen und des Trommelfells, Archiv, f. <1. ges. Physiol. (Pfl\u00fcger), 1868 I I.\n4Gei.i.\u00c9, R\u00f4le de la sensibilit\u00e9 du tympan dans l'orientation au bruit, Soc. de Biol., 1886 III 448.\n5Wundt, Physiol. Psychol., II 94, Leipzig, 1S93.\n6 Preyer, Die Wahrnehmung der Schallrichtung mittelst der Bogeng\u00e4nge, Archiv, f. d. ges. Physiol. (Pfl\u00fcger), 1S87 XI, 5S6.","page":71},{"file":"p0072.txt","language":"en","ocr_en":"72\nM. Matsumoto,\nampullae of the semicircular canals a particular kind of sensation is produced when they are excited by a sound from a particular direction. The sensation is different according to the direction from which the sound comes, because a sound must stimulate more strongly one canal or pair of canals in a way depending on its direction. As the six canals are excited with different relations of intensities by sounds from different directions, the sensations which are produced by the specific energy of the ampullae are different corresponding to the different directions of the sounds. These differences of sensations give us the ideas of the directions of sounds. \u201cIf we consider,\u201d says Preyer, \u201c that by the stimulation of an ampulla with the vibration of the liquid of the canal belonging to that ampulla a sensation of sound is produced which is different from the sensation produced by the stimulation of another ampulla, though the two are exactly alike in respect to intensity, pitch and timbre, and if the difference between the two arises simply because the different nerve-fibers are stimulated, we cannot but regard this difference as spatial.\u201d\nPreyer\u2019s assumption that a canal is most strongly stimulated by a sound lying in the plane in which the canal lies is irreconcilable with the elementary facts of the physics of sound. The sound-waves which are transmitted through the air reach the membrana tympani and then move the chain of ossicles, and at last the lymphatic liquid of the inner ear. During this conduction the sound-wave is changed into a movement of a membrane, a movement of a set of bones, a movement of a liquid, etc. There is no possibility of any change of direction of these movements for changes in the direction of the sounding body, and consequently no possibility of a varied action on the semicircular canals.\nPreyer may have thought that the sound-waves are conducted directly from the air through the skull bones into the head and thus to the semicircular canals ; at least, this seems the only possible construction of his view. The conduction of sound-waves by the cranial bones comes into play when a sonorous solid body is either in immediate contact with the skull, or is connected with it by a chain of solid or fluid bodies, or when the medium immediately surrounding the head is not gaseous as, for instance, when the head is immersed in water. With aquatic vertebrates we can not deny the cranial conduction of sounds, out for most sounds it is certain that in the case of human beings the cranial conduction plays no part. The sound waves are mostly reflected from the surface of the head, and the conduction directly through the cranial bones and tissues is infinitesimal.\nPreyer\u2019s theory next involves the assumption that the sound-waves","page":72},{"file":"p0073.txt","language":"en","ocr_en":"Researches on acoustic space.\n73\naffect the canals differently, according to the direction of the sound. He evidently viewed the sound as a force entering the head and being resolved into three components with intensities depending upon the angles made by the direction of the force with the planes ; he had probably in mind the familiar method of resolving a movement or a velocity into three components in planes at right angles to each other. The absurdity of such a position is at once evident to any one acquainted with the elementary ideas of wave-motion. A sound-wave passing through the air consists of alternate condensations and rarefactions\u2014not of a line or of a plane\u2014but of a more or less spherical surface. The soundwave passing through the head is of a similar sort. There is not the remotest reason for believing that the molecules of a liquid in a curved tubular bone will vibrate differently according as the sound-wave approaches from different directions in the mass in which the bone is imbedded.\nThis theory of Preyer\u2019s was accepted by M\u00fcnsterberg1 as the starting point of a reflex-muscular theory of acoustic space. \u201cThe different movements of the head, which can be aroused by stimulation of the semicircular canals, arouses\u2014by means of the muscle sense\u2014that threefold system of sensations of movement which forms the basis of our acoustic space.\u201d \u201cTo localize a sound means to assign to its place in the whole system of sensations of head-movements the sensation of that reflex head-movement which is necessary in order to turn toward the source of the sound. \u2019 \u2019\nConcerning the possibility of the direct stimulation of the semicircular canals nothing further needs be said.\nAs for the results of M\u00fcnsterberg\u2019s experiments on the least perceptible change in the direction of a sound, they cannot be regarded as a proof of his theory. It has been made clear by the experiments of Bloch2 and by mine that the curve of the least perceptible change can be explained by the principles of relative and absolute intensities.\n4. Motor theory.\nThe essential factor in the motor theory seems to be this : A sound perceived by the ear brings with it an impulse\u2014conscious or unconscious\u2014to move toward it ; this motor impulse and its results are what appear to us as the localization of the sound. This theory assumes that these motor impulses are aroused in definite relations by the factors men-\n\u2022M\u00fcnsterberg, Raumsinn des Ohres, Beitr\u00e4ge z. exper. Psychol., 1S89 II 182.\n2 Bloch, Das binaurale H\u00f6ren, Zt. f. Ohrenheilk., 1S93 XXIV 25.","page":73},{"file":"p0074.txt","language":"en","ocr_en":"74\nM. Matsu moto,\ntioned at the beginning of this section (p. 70), namely, absolute intensity of the sound, relative intensity for the two ears, etc. The form of the motor space is derived from past experience under influence of the visual space ; in fact, the space in which the sound is localized is our usual visual-tactual-motor space with which the sound is connected by the motor impulses. In this compound space the visual sensation is the most important element. The tactual sensation seems rather to be of secondary importance except in the case of the blind. Speaking genetically we can recognize the position of a sound only when acoustic and visual sensations are connected with each other in a definite relation. It is unthinkable that we can recognize the position of a sound without connecting the former directly or indirectly with the latter. A definite connection between these two can be accomplished through the medium of a definite muscular action. These three elements have occurred in connection with each other, and have been firmly associated in the course of time, so that when one of them is present the others will be necessarily called forth. When the visual sensation fails, as in the case of a blind person, then tactual sensation takes its place.\nFrom a biological point of view this theory seems quite natural. In the course of natural selection the survivors have obtained the power of reacting suitably to the different acoustic sensations which they receive from the surrounding world.\nTo react suitably upon an acoustic sensation we must first of all recognize the direction from which the sound comes. To recognize the direction it is necessary that the auditory sense should be assisted by other senses. But as the auditory sense has to do with more or less distant object, it must be chiefly the visual sensation which is combined with the auditory sensation to assist it in perceiving the direction of the sonorous object. To perceive an object in a certain direction the head must be moved so that the object will be brought in the line of visual fixation or in the median plane. In the beginning this will not be easily done, but after practice it will be found that the instant at which the sound is equally loud in both ears is the instant at which the source of sound is found in the median plane. Again we have already seen that a sound situated in the median plane will be best heard when it is in the line of sight. Thus after the source of sound has been brought into the median plane, the next process will be to bring it into the line of sight.\nAgain we must notice the fact that by practice it has been found that the instant at which the sound is perceived with greatest intensity by one ear and with smallest intensity by the other ear is the instant at which the source of sound is situated nearly in the auditory axis or little","page":74},{"file":"p0075.txt","language":"en","ocr_en":"Researches on acoustic space.\n75\nbehind it. Accordingly, we sometimes try, by the movement of the head, to bring a source of sound into this axis when we find it more convenient, as for a sound of small intensity.\nThese movements of the head, which we perform in order to connect visual and acoustic sensations, affect our sense of equilibrium, by means of which we become conscious how much we have turned our head. By means of this sense of equilibrium we are enabled to estimate the position of a source of sound in reference to the position of our body.\nAgain, though a source of sound is usually brought into the line of fixation of sight by the motion of the head, we can effect this within a certain limit not by moving the head but by moving the eyeballs alone. In such a case the acoustic sensation is connected with the oculo-motor sensation, by means of which we can feel also the angular direction of a source of sound, for we have a fine sense for this movement of the eyes. This muscular sensation of the eyes is supplementary to the sensation of rotation of the head, by means of which we can chiefly estimate the direction of a sound.\nFrom these considerations it is clear that by long practice the association has been established between a particular acoustic sensation\u2014corresponding to the stimulation by the sound from a particular direction\u2014and the rotatory sensation\u2014which is required for bringing the source of sound into the visual fixation line or into the auditory axis\u2014and moreover the association has been established between the acoustic sensation and the oculo-motor sensation. After the associations between these factors have been established, either one of these factors by itself is able to call forth other factors. It is not necessary that the rotatory sensation or muscular sensation, which gives us the measure of the angular departure of a source of sound from the fixation line of the eyes, should arise always by an actual movement. Though this is the original case, the sensation of innervation or reproduced motor sensation called forth by association with the acoustic sensation may take the place of the actual motor sensation.\nOur final conclusion is thus that an acoustic sensation receives its spatial form primarily from the space idea which is given to us by the visual, tactual and motor sensations. Acoustic space presupposes the existence of the space form of other sensations. We have only to give an account of how the perception of the position of sounds arises on the basis of the already existing space which was given to us by other sensations. As to the further problem of the ultimate origin of the space form of perception, its solution must be sought in the visual and tactual perception.","page":75}],"identifier":"lit28738","issued":"1897","language":"en","pages":"1-75","startpages":"1","title":"Researches on acoustic space","type":"Journal Article","volume":"5"},"revision":0,"updated":"2022-01-31T12:57:33.358957+00:00"}