Difference thresholds for interaural intensity*. Ervin R. Hafter, Raymond H. Dye, John M. Nuetzel, and Howard Aronow. Department of Psychology, University of ...
Differencethresholdsfor interauralintensity* Ervin R. Hafter, Raymond H. Dye, John M. Nuetzel, and Howard Aronow Departmentof Psychology, University of California,Berkeley,California94720 (Received 16 August 1976; revised8 November 1976)
In an earlier paper, we examinedthe distributionof binaural resolvingpower by measuringthreshold increments of interauraldelayas a functionof overalldelay [Hafter and De Maio, J.AcouSt.SocAm. 57, 181-187 (1975)]. In the current study, similar measureswere made for interaural incrementsof intensity. As before,the stimuli were bandpassclicks of either low (0.1-2 kHz) or high (3-4 kHz) frequency.For overall interaural differencesas great as 24 dB, it seemsthat performancewas basedon the interaural differences,and not on the monaural increments/decrementsthat are concommitantwith a binaural change in level. As was the casewith time, sensitivityto interaural intensitywas reasonablyconstantacrossthe
range tested,indicatingthat, unlike the case'for vision,spatialresolutionin the auditory systemis not concentratedin the center.A simplebinaural trading ratio which convertsintensityto time can be shown to fit the data for low-frequencyclicks quite well. However, the fit to high frequenciesis so poor as to suggestthat separatemechanisms were usedfor detectingtime and intensity.Finally, a numberlike the binaural masking-leveldifference(MLD) was computedfor the two kinds of clicks. Surprisingly,the MLD's for low and high frequencies werea similar7.2 and 8.0 dB. PACS numbers:43.66.Pn, 43.66.Cb
INTRODUCTION
In 1958, Mills measured the minimum audible angle (MAA) that could be detected between two locations of tones in the free field and found that sensitivity was less for peripheral locations than for those near the midline.
These
data are
often
cited
as evidence
for a
MAA's for 250, 500, and 750 Hz, confirming the doralpant role of interaural time in low-frequency localization.
A question of allotment of resourc9s , similar to that asked for interaural time, can be posed for interaural intensity.. That is, over the large range of interaural
from center.
Mill's results do not distinguish between
intensity differences (IID) to which the system is sensitive (e.g., Egan, 1965), howis resolution(AIID) distributed? Rowlandand Tobias (1967) useda B•k•sy
the resolution
of interaural
audiometer to measure Arid for pure tones of 250, 2000,
tapered auditory localization space. i.e.. one whose resolution falls off as the sound source moves away time
and interaural
inten-
sity, since time differences produced in the free field by displacing loudspeakers are confounded by differences of intensity which result from the acoustic shadow cast by the head. Independent manipulation of intensive and temporal cues can only be attained by presenting the stimuli via headphones. The
mechanisms
of sound localization
are
confronted
with a problem faced by all sensory systems; that is, the need to maintain accuracy while covering the entire range of sensitivity. In the case of the visual systems, acuity is concentrated at the fovea. Thus things which are straight ahead are much better resolved, visually,
than those toward the side (Mandelbaumand Sloan, 1947). In contrast, the case for the resolution of interaural differences of time is quite different. Using headphones to present acoustic transients that could be
delayed to one ear, Halter and DeMaio (1975) measured just noticeable differences (JND's) of delay (At) as a function of the overall delay (t).
For both low- (0.1-2
kHz) and high- (3-4 kHz) frequencyclicks, they found
and 6000 Hz.
Their subjects varied the level of a tone
presentedat 20, 35, or 50 dB HL (ISO)in thepresence of a tone of 20, 25, 30, 35, 40, 45. or 50 dB HL at the other ear. They found that while overall level affected the increment thresholds just as it does for monaural listening, there was little effect of interaural difference. Hershkowitz and Durlach also measured just-
noticeable AIID's aS a function of IID; they used 500-Hz tones presented at 50 dB to one ear and either 50, 40, 30, 20 or - 5 dB SL to the other. They too found sensi-
tivity to be little affected by the baseline interaural difference. At least in terms of low frequencies, both of these studies may be difficult to interpret in terms of localization. As noted above, differences of intensity that occur in the free field with low-frequency tones are
not primary cues for localization (Feddersenel al., 1957). Clearly, suchlarge interaural differencesare never seen in the "real" world, where the head shadow at 250 Hz is essentially nonexistent and at 500 Hz is still quite small.
that, at least at high levels, At increased by only a factor of about 2 over a range of 500 /zsec. From this they concluded that the interaural delay line postulated
The purpose of the present study was to look further into the issue of intensity resolution versus range. By use of both low- and high-frequency, bandpass clicks
by Jeffress (1948) maintains a relatively constant acuity
we hoped to compare the results to those we had found for At VS t (Hafter and DeMaio, 1975). The signals
throughout, with only a shallow decline in sensitivity from center to periphery. These data are in close agreement with results from Hershkowitz and Durlach (1969) who measured At as a function of I for 500-Hz
tones. Also, by converting Mills's azimuths into interaural time differences, Halter and DeMaio show that
the At/t functionsfor transientscomparewell with 829
J. Acoust. Soc. Am., Vol. 61, No. 3, March 1977
were
dichotic
acoustic
transients
with bandwidths
of
either 0.1-2 or 3-4 kHz. Theshold increments of Arid were then determined for various fixed values of IID.
Because a change of interaural intensity is necessarily accompaniedby a mortaural change in at least one of the Copyright ¸ 1977 by the AcousticalSociety of America
829
830
Hafteret aL: Differencethresholdsfor interauralintensity
24O
830
Prior to every binaural run, the subject was seated in a soundproof room while the computer presented a continuous stream of cliotic-clicks, spaced 20 msec apart. His instructions were to place the headphones in such a way that the intracranial'image produced by these clicks sounded centered. In the actual tests, each interval contained a single dichotic click.
160
•2o
For the binaural conditions, the baseline FID referred to the difference
between
SAME-DIFFERENT pair.
channels
in the first
click
of a
Thus:
IID= 20 log{(voltsleft)/(volts right)]. 0
I00
•
•0
Creating a &LID was done by incrementing the left channel while simultaneously decrementing the right. Thus:
400
t,•sec FIG.
1.
AIID =20 1Og{(volts left + incrementleft)/(volts left)]
Threshold values of interaural
tion of overall delay (t).
delay (At) as a func-
-20 log[(voltsright + decrementright)/
Data represent averages from two
subjects in an experiment by Halter and DeMaio (1975). The upper curve (filled circle) is for high-frequency clicks (3-4
kHz); the lower curve (filled square) is for low-frequency clicks
0.1-2
kHz).
(volts right)] . The level of the clicks
with an LID of 0 was 48 dB SPL.
For binaural conditions, the settings were symmetrical, so that an IID of 12 dB meant that the right ear received 48 +6 =54 dB SPL while the [eft ear received
channels being incremented, separate monaural thresh-
olds (AI) were gathered with the same Listeners. Our hope was to parcel out the role of monaural cues, if any, in what appears to be binaural perforrm•ce. EXPERIMENTAL
PROCEDURE
StimuLiin theseeXPeriments were clickswithbandwidths of either 0.1-2 or 3-4 kHz. They were produced
6 =42.
54.5 on the right and 41.5 on the left.
For monaural
conditions, the channel contaIning the lower level was simply disconnected.
I.
48-
In keeping with this convention, for the condition IID :12, a AIID of 1 dB meant that the DIFFERENT clicks were
Thus the mortaural control for
IK) =12 dB was the increment threshold (AI) obtained with a mortaural level (I) of 54 dB SPL.
by ringing electronic filters with brief rectangular
A trial lasted 2300 msec, with 300 msec'between the two clicks and 1500 msec for response. Subjects used
pulses(20 •sec) whichhada reasonablyflat spectrum
two levels labeled "SAME" and "DIFFERENT." Visual rein-
over the range of the fiRers.
forcement was given immediately after each response. Thresholdswere measuredfor IID's of 0, 4, 6, 12, 16,
Pulse widths and heights
were controlled in the early part of the studyby a
PDP-8/L laboratorycomputer;later a changewasmade to a PDP-11/20. In either case, the computergenerated the transients, controlled the experimental sessions, and recorded the data. /,eveIs were set by choice of appropriate inputs to two digital-to-analog converters which generated the voltages.
ALl levels were
and 24 dB. For each value of IID, a subject ran at least two sets of 200 trials
at different
values
of AIID in order
to produce two points of a psychometric function.
It
was required that one point fall in the range of percent
correct from 64%to 75%, and that the other point fall in the range from 75% to 86%. AIID's were tested until
tested using a method proposed by Patterson and Green
two such points were found.
(1970)wherebyclicks are repeatedat a rate whichis
verted to yes/no d"s and a linear interpolationfitted •o estimatethresholdlevel performancefor d.' =1.0.
fast enoughto be integrated by a voltmeter but slow enough to prevent direct interclick
The data were then con-
interference.
Stimulus pulses were shapedby Krohn-Hite (3500) filters, one for each cha•nel. These filters have roll-
offs of 24 dB/octave. Identicalsettingswere accompushed by presenting identical pulses to each filter and then adjusting the frequency controls to produce a
'straight-LineLissajouspattern on an oscilloscope. Amplifiers, attenuators, and mixing circuits were then used to drive a matched pair of Telephonics TDH-39 headphonessuspendedin an Auraldome headset.
II.
RESULTS
AND
DISCUSSION
Figure 1 shows the results from Halter and DeMaio
(1975). It plots average thresholdsacross subjectsfor hateraural time (At) as a function of overall delay (t). These data are shown for comparison to those for AIID VS liD.
A. Low frequencies Results from the low-frequency
clicks are shown in
The subjects were three of the authors, RD, JN, and HA. Each is in his 20's. They had no known hearing losses within the frequency ranges tested. Subject JN had extensive listening eXPerience in other binaural experiments, while the others had none. RD received ap-
the three subjects. Thresholdsare estimatesfor a dt
proximately
ferences.
30 hours of training before data were col-
lectedwhile HA receivedapproximately20 suchhours• J. Acoust. Soc. Am., Vol. 61, No. 3, March 1977
Figs. 2. These curves are composites of the data from of 1.0. It is well known that tasks which require lat.eralization can often produce considerable individual dif-
Thus the thresholds {or each subject are in-
cluded in Table
I.
831
Haftereta/.: Difference thresholds for interaural intensity
af',#1/•..................
831
perfect summationof information. It seems unlikely
.•.4
that such independentprocessing of monaural channels
2.0 .•0
was takingplace. For the smaller values of IID, where the functionsare quite separate, there is no question:
i.6.3.2 .2.8
1.2
clearly, those data are indicative of binaural interaction. The primary reason for the diminishing difference between the two functions is the improvement in strictly
Uonaural
2.4
2.0 •
Binaural
.! L•I 1.2
mortaural performance sometimes described as a near
miss to Weber's law (PennerandViemeister, 1973).• Indeed, this difference in slope alone, with a rising AIID versus IID for the binaural cases compared to a falling AI versus I for mortaural cases, should help
.4
dispel any fear that the former were based on monaural 0 •
2
4
4q 50
6
a
51 52
I0
12
53 •
I•
•
IIDd8 IBinaural)
5•
•
1aSSPLl•naural)
cues.
B. High frequencies FIG. 2.
Solid points show threshold increments of interaural
intensity differences (AIID) for low-frequency (0.1--2 kHz) clicks plotted as a function of the overall inter• ity difference (I/D). Untilled points are for monaural increments (zl/) and are plotted as a function of the monaural soundpressure level against which they were presented. (Further explanation of the scales can be found in the text. )
The lower plot shows performance with the binaural stimuli while the upper plot is the one obtained for the mortaural conditions. We must remember that, at least logically, the mortaural conditions can be thought of as subsets of the binaural.
Where signals are added to one
ear while subtracted from the other, it is possible for the listener to operate entirety on the bases of incre-
mentsand/or decrementsin the individualchaaneIs. The separate scales of Fig. 2 were chosento help clarify this problem, with the data plotted in a way such
The composite results with high-frequency clicks are
shownin Fig. 3. As before, the individual data are listed
in Table
I.
The slight increase of interaural ,XIID as a function of IID was 'a bit.more pronounced for the high frequencies than for the low. Nevertheless, over an interaural range of 24 dB, the increase was only from 1.46 to 2.12 dB. We should also note that, as in the case of the Low frequencies, the binaural detection cannotbe accounted for in terms
of the confounded
monaura[
cues.
C. Concentration of spatial acuity
This project, tike the one before it (Halter and
DeMaio, 1975), examinedthe extentto whichinteraural acuity is concentrated in the lateralized "center."
As
before, little suchconcentration wasfound. Spatialfoveation is so pronounced in vision that one is inclIned
that the outer scale reflects the magnitude of the monaural change inherent in each binaural condition. Thus
to ask why it should not be .so for hearing. One possibility is that evolutionary pressures ha.re worked to
a binaural AI/I) of 3 dB is also represented by a 1.5-dB increment (decrement) in the individual channels. A
make soundlocalization a first-order orienting process, useful primarily for pointing far more accurate [ocalizers, the eyes. From this point of view, uniformity in
similar
double scale is used for the abcissa
which shows
the base difference, IID. There, for example, where an IID of 16 dB refers
to a case of 40 dB in one ear and
56 dB in the other, the comparablemonaura[value (56 dB) is shown as $ dB re 48 dB on the lower scale. As in the case with interaural
time
TABLE I.
we found little
evidence of a concentration of binaural acuity in the
regions of small interaural differences, i.e., the center of lateralization space. Rather, performance was virtually constant over the range of 24 dB. This picture of a reasonably uniform interaural resolution is in keeping
with the results with low-frequency tones (Rowlandand
Tobias, 1967; Hershkowitzand Durlach, 1969). The phenomenoIogy here was quite interesting.
For
the 24-dB differences, all of the subjects reported the impression of a sounddisplaced completely to one side. Yet it seems clear that the binaural system was working, aad working well. It is true that for the largest values of IID, we cannot rule out completely the possibility that purely monaura[ listening produced the allegedly binaural performance.
Threshold values of the monaurgl increments
and the interaural intensity differences (AIID's) for the individual subjects. Thresholds were defined as the estimated levels necessary for performance of d' = 1.0.
But to have done so would have re-
quired independentevaluation of the two channels, one going up in level and one going down, followed by nearly J. Acoust.Soc. Am., Vol. 61, No. 3, March 1977
Monaura[ (0.1-2 I re dB SPL
kHz)
Monaural (3-4
kHz)
HA
RD
JN
HA
BD
JN
0
2.95
1.17
1.45
1.54
1.37
2.29
2
2.26
1.51
1.73
2.37
1.51
1.99
3
2.08
1.38
1.84
2.60
1.69
2.47
6
1.59
1.50
1.87
2..24
1.17
1.59
8
2.21
0.85
1.22
1.45
1.39
1.53
12
1.47
1.31
1.33
2.47
1.25
0.83
Binaural (0.1-2kHz)
Binaural (3-4 kHz)
IID (dB)
HA
HA
RD
RD
JN
JN
0
2.51
1.55
1.14
1.92
1.22
1.23
4 6 12
2.04 2.09 1,60
1.94 2.19 1.65
1.19 1.29 1.94
2.00 2.14 1.62
1.16 1.17 1.39
0.89 0.64 0.82
16 24
2.58 2.40
2.06
1.65
1.93
1.69
1.54 2.32
1.86 1.96
1.94 2.07
832
Hafteretal.: Difference thresholds for interaural intensity
41MII• ' ' ' "'"' ' ............
832
across lateralization space. Hershkowitz and Durlach.
(1969) suggesteda useful way for relating interaural ZO &o
,1.6
M0naural ,2.8
L2 .2.4
•
Binaural
time to interaural intensity in which the values of At and AIID are compared at a given level of performance. To this end, we took the threshold value At at t =0 /zsec from the earlier paper and.divided it by the AIID at IID = 0 dB in the present paper. Taking the quotient of these two numbers is one way to define a time-intensity
trading ratio.
.8,LB • i
The trading ratios, so found, were 11.0
/zsec/dBfor the tow-frequencyclicks and42.5 /zsec/dB
4.2
for the high. By treating the ratios as scaling factors, we could use the ! and At data of Fig. I to compute hypothetical values of IID and AIID. O •
FIG. 3.
2
4
6
8
4•
50
51 52
16 12 5) •
I• •
These are shown in
•
liDriB(Binaural)
Fig. 4, plottedfor comparisonwiththe valuesobtained
•
IdSSPL(•naural)
from Lhepresent experiment.
The dashedcurve is for the lower frequencies (0.1- 2
Solid points show threshold increments of interaural
intensity differences (AIID) for high-frequency (3-4 kHz) clicks plotted as a function of the overall intensity difference (IID). Unfilled points are for menaural increments (A/) and are plotted as a function of the menaural soundpressure level against
kHz) while the solid curve is for the higherfrequencies (3-4 kHz). The pointsare the binauraldatafrom
which they were presented.
the notion that for the low-frequency clicks, detection of intensity was based on a simple transformation of in-
(Further explanation oœthe scales
can be found in the text. )
auditory resolution makes sense. Of course one must
be cautiouswith this kind of speculation,and indeed, anotherinterestingfact shouldbe considered. That is, for large valuesof spatial azimuth, there is a diminution in sensitivity as measuredby the minimum audible angie (Mills, 1958). Feddersenet el. (1957) have used
Figs. 2 and 3. The difference between the two predictions is striking. From these data, we cannot reject
tensity into time. This does not prove a trade; indeed the correspondence between points and prediction might
be fortuitous. But, the relation is compelling. If time and intensity do trade with low-frequencyclicks, then we should note that recent evidence
has shown the trade
to be incomplete. Also using0.1-2-kHz clicks, Smith (1976)examined/hediscriminabilityof stimuli with in-
probe microphones to determine the IID's for various
Letaural time disparities
azimuths. Supposewe apply their measurements to
intensity.
Milis's for 4 kHz, a tone similar in frequency to our high-frequencyclicks. Using twice the reported MAA's to take accountof Mills's psychephysicalprocedures, we
500-Hz tones, Smith foundthat time and intensity were not identical. That is, for a givenvalue of AIID, no value of At couldbe foundwhichwas not at least partially
computed AIID's of 0.8 dB for an IID of 0 and 2.6 dB at
discriminable.
an rid of 7.5 dB. Certainly these results are unlike
thosefrom thepresentexperiment. Where, then, is the discrepancy? The distinction would seem to lie in dif-
ferencesbetweenlisteningin the free field and through earphones. Feddersen et el. show that for the example
frequency(4 kHz) the IID ceasesto growbeyondabout
45ø. Thismeans thatregardless of s.ensitivity, there
from those with differences
As Hafter and Carrier
of
(1972) had shown for
What is equally interesting is the complete lack of correspondence for the high frequencies. This does not seem particularly
surprising when one considers
allO
20
.........
is no way, based on intensity, that a listener could hear differences in the angles beyondthat point. While the
angieat whichthe IID functionsgo flat differs according to frequency, such a region exists for all high frequencies.
Thus, it seems that two things must be true. From the present experiment we knowthat sensitivity to interaural intensity is virtually constant over a range of 24 dB, a value much greater than is needed to contend
zo I.õ
with any differencesfoundin nature. On the other hand,
).4
the physics of soundassures that for moderate to large
1.2
ß
values, interaural intensityis unaffectedby azimuth,
andso thehighsensitivityto AIID is essentiallywasted, and real spatialacuity, i.e., that for angles, diminishes.
Interaural level
FIG. 4. Predictions of AIID detectionbasedon a simpletime-
D. Trading ratios The present data, in conjunction with the At vs t re-
suits from Hafter and DeMaio (1975), provide sufficient inforn•tion to study the role of time-intensity trading J. Acoust. Soc. Am., Vol. 61, No. 3, March 1977
intensity trade.
The open and closed points are the data for
low- andhigh-frequencyclicks, respectively, taken from Figs. 2 and 3. The lines showthe results of a hypothetical trading mechanism (see text).
The dashed carve is for the
few frequenciesandthe solid is for the high frequencies.
833
Hafteret al.: Difference thresholds for interauralintensity
the/ateralization of tones, but direct trading of time for intensity has been reported for high-pass clicks
(Harris, 1960). Figure 4 showsthat if time and inten-
' 833
Hire filters. Therefore, the most ptausible description seems to be that clicks are different from other signals. at least with respect to binaural masking and frequency.
sity do intergct for such stimuli, the degree of interaction must be variable
across
the extent of lateralization
III.
space. Therefore, if a simple trading model is at all applicable to high-frequency clicks, the relation is certainly a complex one. More likely, the poor fit indicates the existence of separate intensity-sensitive sensitive
E.
and time-
mechanisms.
Binaural detection vs monaural:
SUMMARY
(1) Both low- (0.1-2 kHa) andhigh- (3-4 kHa) frequency clicks were used to measure sensitivity for in-
crements of interaural intensity (AIid) as a function of the overall interaural intensity difference (riD}. The average level was 48 dB SPL. Also measured were comparable monaural thresholds, these to be used as a control for monaural detection in the presumably bin-
MLD-like
phenomena
aural
Possibly the most important function of the binaural system is to reduce masking and, in effect, increase
tween the binaural
the amount of information
that can be retrieved
from
a
conditions.
(2) From the large discrepancies in performance beconditions and the monaural controls.
it seems likely that, even for interaural differences of
noisy world. The most commonly used index of this
as high as 24 dB, detections were based entirely on in-
ability is the maskinglevel difference (MLD). In recent years, special interest has centeredon a class of MLD's
teraural
for which the signal and masker are spectrally identical.
Wightman(1969), Halter andCarrier (1970), and Y0st (1970) used tones, while Jeffress and McFadden(1971), narrow bands of noise; but, in each case, MLD's were determined with the signal-to-mask ratios and phases held constant. The data here may lend themselves to
just such an analysis. In the studies mentioned, the conditions comparable to ours were those in which the signal-to-mask phase (usually referred to as a) was zero. Thus, the only effect of adding signal in either the homophasic (signal in phase at the two ears) or antiphasic
(phasereversed) conditions,was to changeintensity. It is not uncommon to consider strictly monotic masking as an acceptable substitute for the usual diotic refer-
ence in computing MLDs, since for detection of tones
in noise, the two casesare identical (Jefftess et al., 1956). By makingthis assumption,and then treating all of the data as if the increments
had accrued
from
adding a click-signal to a click-musket, we can compute what is essentially an MLD. The computation is complicated by the fact that for cases which we will call
signalplus noise, oneear received48 +•IID+• • • AIID dB while the other ear received 48- « liD- « AIID dB. Unfortunately, the symmetrical apportionment of lid and
information.
and not on the loudness incre-
ments and/or decrements in the individual channels. (3) As in the case with interaural differences of time
(Halter and DeMalo, 1975), sensitivity to increments of interaural intensity was shownto decrease little over a
large portionof lateralization space. Mills (1958)measured sensitivity to angular change in the free field and showedthat acuity drops for large azimuths. His resuits stem from the physics of sound, and not from a lack of resolving power in the listener. (4) When the JND's for At were divided by the JND's for AriD, a binaural time-intensity trading ratio emerged which couId be used to evaluate the possible role of temporal cues in intensity discrimination. These computations were used to attempt a fit to the Arid vs
rid data for each of the two frequency ranges. The resuits suggested that while the low-frequency clicks may well have been lateralized on the.basis of time cues, such was surely not the case for the high-frequency Clicks.
(5) Finally, a number muchlike the MLD of binaural masking was computedfor clicks heard in the center of the head, i.e., those for Iid= 0 dB. Interestingly, these numbers were nearly identical for the two kinds of clicks
AIID decibelsresultsin an asymmetricalapportionment ' tested (7.2 dB for low-frequency clicks and 8.0 dB for
of sound pressure. The severity of the problem increases considerably with increasing Iid, so we have
chosento make the comparison only for lid = 0 dB, where the asymme[ry at threshold values is slight. The supposed antiphasic signals were computed using only the channel that was incremented in the binaural conditions; this seemed the most appropriate for comparison to the monotic reference. Averaging across subjects, the MLD's thus found are 7. 2 dB for the low-frequency clicks and •. 0 dB for the high. This near identity of the MLD's for the two kinds of stimuli seems surprising in
light of previous results (e.g., Hirsh and Burgeat, 1958; McFadden, Jefftess, and Lakey, 1972), where traditionally, the MLD has been shownto decrease sharply at higher frequencies. In view of the considerable differences in the predictions from trading in Fig. 4, it seems unlikely that perromance with t.he 3-4 kHz clicks was based on lower frequencies in the skirts of the KrohnJ. Acoust. Soc. Am., Vol. 61, No. 3. March 1977
high-frequencyclicks). ACKNOWLEDGMENT
We would like to thank Alice Brilmayer preparation of the manuscript.
for her help in
*This research was sponsoredin part by a grant from the National
Institutes
of Health.
1TheWeberfractioncompares theactualintensityof theadded "increment" (at threshold) to the intensity present before addition. This comparison makes more sense for the mortaural ease than for the binaural, and that is why we have chosen to call •/the
sum of the intensity added and the intensity
al-
ready present. When the log of the increment added is plotted against the log of the intensity present, it gives the familiar masking function. It is this function which shows the near miss to Weber's
law.
Penner and Viemeister
(1973) found
the slope of this function to be 0.92 for low-pass (780 Hz) clicks and 0.98 for high-pass (2040 Hz) clicks. For our
834
Hafteret al.: Differencethresholds for interauralintensity
monaural dejections. we found slopes of 0.95 for the low-
frequency clicks and 0.96 for the high-frequency clicks.
Egan. J.P.
(1965). "Masking-Level Differeries as a Func-
tion of Interaural Disparities in Intensity of Signal and Noise," J. Acoust. Soe. Am. 38, 1043-1049. Fedclersen, W. E.. Sandel. T. T., Teas, D.C., and Jefftess, L. A. (1957). "Localization of High-Frequency Tones," J. Acoust.
Soe. Am.
29,
Soc.Am. 28, 416-426. Jefftess,
I.. A..
(1970). "Masking-Level
Differences Obtained with a Pulsed Tonal Masker," Soe. Am. 47, 1041-1047.
J. Acoust.
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