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{"created":"2022-01-31T13:17:25.976584+00:00","id":"lit28739","links":{},"metadata":{"alternative":"Studies from the Yale Psychological Laboratory","contributors":[{"name":"Scripture, Edward W.","role":"author"}],"detailsRefDisplay":"Studies from the Yale Psychological Laboratory 5: 76-80","fulltext":[{"file":"p0076.txt","language":"en","ocr_en":"ON BINAURAL SPACE.\nBY\nE. W. Scripture.\nThe fundamental fact of binaural space is that when two component sounds heard by the two ears are perceived as a single sound the resultant sound is \u201c localized in space.\u201d This \u201c localization in space \u201d is a direct experience of every person with binaural audition.\nAside from such problems as the influence of visual and muscular space on this localization, the fundamental problem is that of the localization of the resultant sound as dependent on the two components. The simplest sounds, tones, vary in pitch, intensity and duration. The only property which comes essentially into question in the case of the two components is that of intensity. The following paragraphs will present a hypothesis in respect to the law of localization as dependent on the intensity of the components.\nThe fundamental observation is as follows : When two component tones, e. g., from the telephones opposite the two ears, are heard as one tone, this tone is located in a certain direction in respect to the observer. When the intensities of the two components are equal, the resultant appears to be in the median plane, e. g., directly in front. As one of the components is weakened, the resultant appears to pass toward the side of the stronger one, finally reaching a line nearly opposite the ear\u2014the auditory axis\u2014and proceeding outward along it. The localization thus depends on the difference between the intensities of the components. Various observations lead me to believe that the following equations express this dependence.\nLet IR and IL be the intensities of the right and left components, and let d\u2014 IK \u2014 IL be the difference between the two intensities.\nLet the plane in which the resultant lies contain a system of rectangular coordinates, with the origin in the median plane, the axis X identical with the acoustic axis, and the axis Y perpendicular to X ; thus Y may lie anywhere in the median plane. Since the position of the sound with respect to these axes depends on the difference of intensity, we have x =/{d) and, since there is a definite relation between y and x, y \u2014 f(x).\nIn the experiments it is observed that when the two sounds are equal, i. e., ^ = 0, the resultant is located in the median plane, i. e., on the\n76","page":76},{"file":"p0077.txt","language":"en","ocr_en":"On binaural space.\n77\naxis I7at a certain distance m from the center. Thus for cl = o we have x = o, y \u2014 m. As the sound on the right is made louder we have IR > 1,4 and d positiv e ; when the sound on the left is made louder d becomes negative.\nAs one component becomes louder than the other, the resultant moves toward the side of the louder component ; indicating the right side by + and the left by \u2014 we have + x \u2014\n/(+'/) and \u2014 x =/(\u2014\u00ab). The resultant lies always on the positive side of the Y axis, which we can express by considering / as a function of the square of x, ory = jF(x2).\nThe path described by the resultant sound appears to me to be a curve of the form given by the equation\n\u00bba am\ny \u2014 me\nwhere m is the value for x = o and a is a constant of proportionality.\nOn the basis of these observations and considerations I venture to make the following two hypotheses : i. that the distance right or left of the median plane is proportional to the difference between the intensities of the two components, i. e., x = cd, when c is the factor of proportionality ; 2. that the relation between the distance from the median plane and the distance from the auditory axis is expressed by\n3.2\ny \u2014 me\nwhere m is the distance of the sound when .*= o(i. e., d= o), and a is a proportionality factor.\nThe values m and a depend on certain properties of the sounds used, but mainly on the absolute intensity. Sometimes the sound appears to remain always in the auditory axis, in which case m = o. A series of curv es for different values of m is shown in Fig. 22. The values from which the curves were plotted are given in the table.\nFig. 22.","page":77},{"file":"p0078.txt","language":"en","ocr_en":"Table of y \u2014me\tfor a\u2014 io.\n\n78\nE. IV. Scripture,\nC LO O 10M N NN O O tx o O 00 ro o \u00dc OvO f Cl O O O\n0 d o' o d o' o\n\u00ab O\nH M H H N N fO\n11 ill IT\n00 f^fo\u00f4 *h i/-> o\n\u00fc vO V\u00db N 10 TfO d n ion O C h rois O CnCO O co O' CO\nddddddo'd\n11 x:\n\u25a0t t>. lx CMn lO O ro co Cl tJ- vo CO00 + rsC' CsCO vO Cl O m roo O ^ih\nO O 0 O O 1\n1\", 0 ^ . \u00ab\nO m 't C\"0 vovO O'\nd d d o' \u00ab ci c\u00f4 ri-\nTf N ro N fO H fON VO CO \u00bbO O fo N OMX fO I\". C<0 co \u00ab O\nC\"0 N00 >OfOM O CO O\nOOOOOOOO\nN N N O\nIl II I I II\nO O co 0 CO im 10 VO\nC\tco\t<o\tO O\tPOO\tfO\t*h\tVOVO\n>m\tO''t *t\trocO\tO' tx\tw\tCl\tO' co\nC\tNH\tO\t'O >0\tH\trf\tCl tx\nfOM\td\t>m\tCMxiOM\to\tVO\t>-4 O\nOOOOOOOOOOOO\nfl xs\nk*-r\nO N c\\ Tt o O lx O NCMOIO Q mOOCO fOH -t CvCO >m tx \u00f6 M CO O' f -t- CO vC CO lONP!\no O O m co vo tx o fONHO\nd d d d d d d h h h \u00ab \u00ab\u25a0\nV*1\u00ab\nOOOOOHHPirOrJ\u2019 vovO\n\u00a7\u00bbm O \u00bbm vO O'CO M O' lx. vo m O OO o VO O O M txCO VO tx tx 0>CO rx rtCO N OMO rO H 0 C\"\u00fb m O O' COCO CO C\"C -TWihOOOOO 10 rj- rt\tf \u00f4 ci ci m *-\u00ab\u2019 d d d 0 o o o o d o\nh h ci pi ci ci co\no II \u00a3 J'k a\nco co vo O CO PO h rf vo\nINI\n-\u2022 M O -t\nI I\n0000000000000000000\n>\ttx\tlx vo\tO'Cl\ttx'C\t0\"0 O\tOCO\t0\"0\trOO\tO\tN\n>\tCO\ttJ-C/0\tCO\ttx\tci 10\tvo COCO\tO O\tN\tCl\tt fO O\tt\n8'0 tx\tfO\tH\t*m Cl\tVO o o\tvo 10O\tO\t10 Cl\tH\tH\nO O\tH\td\tPO't\t\u2018O txCO\tO Cl\t\u25a0<+\u25a0\ttx\tO' Cl\tvoCO\nOOOOOOOOOOO^mmvhi-icicici\nC m PO *0 lx O' \u2022t'\u00d4\nddddddodHMcipicif\u00f4f\u00f44i/i v\u00f4vd\n\u00a7CI tx VO IM tx t}-o fON^H C\"OC'!M,\u2019tH -t co Cl o O Cl O M tx O O CO Cl 00 tx Cl tx ^ txCO O tOO tx vo O'VO CO Cl txvofOn \u00abm O 0\"0 il \u00bb0 tx O' h d -fO O' fC 00 'TOrxiocociMHHOOOOOO\no ci'C' \u00f4od no d vA4 p\u00f4c\u00ee \u00ab h h n d d d o o d o d d d d o\nH IM M Cl Cl Cl PI Cl CO\nJ I I I I II II 11\nO O' Cl 00 KOO Tj-O IM o\ntx rf-O (\n. _ _ CO tx Cl CO vo -f Tj-v.\nO CO O co O' 'tCO Cl tO NNV.  ._ .. _ _______\nO' O' O' O'CO CO tx txsO VO >t CO P'1 >m O CO tx vo rf d O CO N t d O CO\ndddddddddddddddddo ddddddddo\nIl X 5\no \u00a9Sp\nC<c\nO'\troiotO N\tM\tPI\to H00 PI POO\tTfvo\ttoo\ntx\u00bbM\tt\t\u00bb0*0 t w\ttxiM\tvo tx tx tx vo d\ttxM\trj-vovo\n)IM\ttx vo\tco\tCl Cl CO VO\ttx\t\u00bbM\tVO o txCOM o\t00\t*M COO\nd\td CO't\tvoO rx&o\tO\t>m\td TiONO'H\td vo\ttx O' *m\nddddddddddddddddHMMMHMNNeiN \u00abt\u00f4\n!l\u201e\n\u00a9 H\n<\n8*m rf 0\"0 vovO O' *t *M O *m -f CvO >00 O' *t >m O ^ 't 0\"0 vo<0 O' o O C H P'1 CO 'to CO O pi to O' d VOCO ci O o t-CO d tx d lx Cl\ndddddddddoHHHHMpicicif\u00f4p\u00f4ttt\u00ef\u00f4 v\u00f4vd o tx\nM rot VOO txCO O' O","page":78},{"file":"p0079.txt","language":"en","ocr_en":"On binaural space.\n79\nThere still remains the fact that the plane of XV (which we have considered) may be in any position around the auditory axis; thus the sound may pass in front of, above, behind or below the head, or in any intermediate position. Four such positions are shown in Fig. 23. To fully\ndefine the apparent position of the sound, we must introduce a system of coordinates in which X is the auditory axial line through the head, Z is a line perpendicular to this at the central point in the head and extending in the direction which the subject considers to be directly in front, and Y is perpendicular to both X and Z. We thus have \u201ev = cd as before. Then in a case where the sound lies in the XZ plane to the front we have y = o and\nXn\nz \u2014 me aM.\nWhen the sound is upward in the XY plane we have x = 0 and\nxl\nurn\ny me \u2014","page":79},{"file":"p0080.txt","language":"en","ocr_en":"So\nE. IV. Scripture.\nThe complete relation is expressed by\nx = cd,\nyV\nam .\ny = me \u2022 sin \u00ab,\nXl\nam\nz = me - cos \u00ab,\nwhere \u00ab is the angle of elevation above the plane XZ.\nThis series of hypotheses agrees with the facts reported by Mr. Matsu-moto in the preceding pages, but cannot be proven until the experiments are repeated with tones of carefully measured intensities. I cannot say that I expect them to be confirmed just as they stand ; I propose them simply as an attempt to give definite form to our notions of one of the laws of binaural localization.","page":80}],"identifier":"lit28739","issued":"1897","language":"en","pages":"76-80","startpages":"76","title":"On binaural space","type":"Journal Article","volume":"5"},"revision":0,"updated":"2022-01-31T13:17:25.976590+00:00"}