Brightness and loudness as functions
of stimulus duration 1
JOSEPH C, STEVENS AND JAMES W. HALL LABORATORY OF PSYCHOPHYSICS. HARVARD UNIVERSiTY
The brightness of white light and the loudness of white (1948) and by Small, Brandt, and Cox (1962) for white noise were measured by magnitude estimation for sets of noise. White noise provides a more suitable stimulus stimuli that varied in intensity and duration. Brightness and for this kind of problem than pure tones, because the loudness both grow as power functions of duration up to a intensity of a white noise (unlike tones) can be rapidly critical duration, beyond which apparent magnitude is es modulated without effecting a material change in the sentially independent of duration. For brightness, the critical sound spectrum. Thus a prominent click is heard at duration decreases with increasing intensity, but for loudness the onset of a tone but not at the onset of a noise. the critical duration is nearly constant at about ISO msec. How the loudness of white noise grows with intensity Loudness and brightness also grow as power functions of in has been the subject of several investigations (S. S. tensity. The loudness exponent is the same for all durations, Stevens, 1966a). Like brightness, the loudness of white but the brightness exponent is about half again as large for noise obeys the general psychophysical power law short durations as for long. The psychophysical power func proposed by S. S. Stevens (1961) tions were used to generate equal-loudness and equal-bright IjJ ~ k¢.8 (1) ness functions, which specify the combinations of intensity E and duration T that produce the same apparent magnitude. where if; is subjective magnitude, and ¢ is the physical Below the critical duration ET equals k for equal brightness, magnitude. Of special concern here is how the constants and Era equa Is k for equal loudness. The value a is about of the power function depend on the duration of the 0.7 for threshold and about 1.25 for supraliminal loudness. stimulus.
Apparafus for Producinc Visual Flashes The present paper concerns the way apparentbright The flash source was a fast-decaying 4-wattfluores ness and apparentloudness vary with duration throughout cent lamp (Sylvania's "Deluxe Cool White") that could the dynamic range of vision and hearing. Interesting be activated at a high intensity level for almost any similarities and differences between these two senses duration longer than about 0.5 rnsec, The operation and come to light from a comparative study of brightness circuitry are described by Gerbrands and J. C. Stevens and loudness over wide variations of time and intensity. (1964). Reasonably square pulses of light can be pro The principal method was to obtain magnitude esti duced at durations as short as 0.5 msec. and at mates of a matrix of stimuli covering a wide range of luminances as intense as 5 or 6 lamberts (L), about 10 intensity (50 dB for brightness, 73 dB for loudness) and 107 dB re 10- L. of duration (2000-fold for brightness, 100-fold for From a distanceof 35 emtheobserverviewed foveally loudness). From the numerical estimates of a group of a portion of the lamp (diameter 1.25 em, visual angle observers it is possible (1) to state how brightness and 203') from inside a dark booth (see Fig. 1). On a signal loudness grow with duration and with intensity, and (2) from the experimenter the observer pressed a key, to generate a family of equal-sensation functions that which, after a delay of 0.5 sec., triggered the flash. specify combinations of duration and intensity that The brief delay between pressing and seeing was found arouse a given level of apparentbrightness orloudness. to favor concentration on the flash. Just to the left of Except for certain procedural details, the investiga the target appeared a reel fixation spot. Throughout the tion of visual brightness was a repetition, with similar experimental session the observer viewed this spot outcome, of an earlier experiment by Raab (1962). The with his right eye while holding his head steady in a range of intensity was extended 10-fold (10 dB) in the chin rest. A black mask prevented his left eye from present study. Alba and S. S. Stevens (1964) used the seeing the target. method of brightness matching in order to study the The intensity of the flash was controlled by means of same problem, and S. S. Stevens (1966b) has proposed neutral density filters. a simple model to show how brightness may depend on intensity and duration. Procedure for Scaling Briglltness An analogous model for loudness has not,apparently, Before an experimental session, the observer was been worked out. Data on supraliminal loudness arenot dark-adapted with red goggles for 10 min., and then for very numerous, and there appear to be some puzzling another minute or two he sat in the dark booth. discrepancies. Of most relevance to the present study The observers were instructed to assign numbers are the equal-loudness functions measured by Miller proportional to the subjective brightness of the flashes
Perception & Psychophysics, 1966, Vol. I comment 1966, Fsucnonomic Press, Goleta, Calif. 319 and to disregard any apparent variation in the duration of the flashes. For the first flash presented to him, the observer was asked to decide on an appropriate number to stand for the subjective brightness; to all subsequent booth neutrol woll stimuli he then assigned numbers proportional to sub filters jective brightness. I mosk Altogether, 60 stimuli (i.e., combinations of peak clear gIOSS~ ~ luminance and duration) were presented in a series of six experiments (see Table 1). Approximatelyone-sixth I fixation lamp of these stimuli were used in each of the six experi I ments, but in order to tie the results of all six experi I ments together, one particular stimulus (200 msec. at 85 dB re 10-10 L) was presented in every experiment. I I The sequence of the various experiments differed from one observer to another. left eye mosk \. I Each stimulus was presented twice in an experi ~~kright eye mental session, except that the first stimulus was chin rest ~ presented three times with only the last two judgments counted. This procedure was adopted because extensive experience with the method of magnitude estimationhas Fig. 1. Schematic diagram of the visual apparatus (not to scale). shown that the original number assigned as a "modu lus," whether by the experimenter or by the observer variation, such as duration or quality (qualitative himself, is not always exactly the same as the "effec variation as a function of duration constitutes a promi tive" modulus implicit in the subsequent judgments. nent feature of the shorter bursts). Sixty combinations The order of the stimuli was irregular with respect of physical magnitude (peak SPL) and duration were to brightness and differed from one observerto another. presented in a series of six experiments as specified The dimmest stimulus was neverpresented immediately by Table 2. One stimulus, 80 msec. at 81 dB peak SPL, after the brightest, and all the stimuli were presented was presented in each of the six experiments. The once before any was presented a second time. The time order of these experiments differed from one observer between presentations was about 15 sec. If an observer to another. felt that he had not seen a given flash properly, he could Each stimulus was presented twice in a session, except ask for another presentation. for the first stimulus (always one of intermediate loud Altogether 21 persons (graduate students, staffmern ness), which was presented three times altogether; only bers, and employees) served as the observers. Someof the last two judgments of this stimulus were counted them served in only one experiment, others in 2, 3,4, as magnitude estimates. In each session the order of 5, or all 6 of the experiments, but 10 persons served in the stimuli was irregular with respect to loudness, each of the six experiments. No person ever served in except that all the stimuli were presented once before more than one experiment on the same day. any was presented a second time. The order of stimuli also differed from one observer to another. Apparatus for Producing Bursts of Noi se Twelve persons served as observers in all six An electronic switch (Grason-Stadler Type 829-S-14) experiments. Ten of them were undergraduate students, was used in conjunction with an interval timer (Grason one a graduate student, and one a staffmember. Before Stadler Type 471) to gate the filtered output (low-pass the first session the observers were asked to make 20,000 Hz) of a white noise generator. The gated signals magnitude estimates of the lengthofafewline segments were then passed through a decade attenuator to a pair in order to given them familiarity with the method and of PDR-8 earphones. The duration and the intensity of the bursts were monitored throughout the experiment Table 1. The combination of physical magnitude and duration with an oscilloscope and a voltmeter. used as stimuli in Experiments 1 through 6 on brightuess. For The interval timer was set to deliver repeatedbursts Experiments 1 to 3. the first stimulus was 200 msec, 85 dB. The of noise, separated by 900-msec. intervals of silence. asterisks mark the first stimuli for Exp eriments 4 to 6. On a given stimulus presentation the observer pressed a switch for as long as he wished to hear the repeated Peak luminance Duration in milliseconds in dB re 1O-10L o.s 1 2 5 10 20 50 100 200 500 1000 bursts. The observer sat in a sound isolation booth and listened binaurally. 105 2 4 3 2 5 3 2 4 3 2 3 95 5 6 4 5 6 4 5 6 4 5 6 85 2 1 3 2 1 3 2 1 ALL 2 1 Procedure for Scal ing LOUdness 75 5 6 4 5 6 4 5 6 4* 5* 6* The task was to make magnitude estimations of 65 1 3 2 1 3 2 1 3 2 1 apparent loudness, disregarding any other perceived 55 4 5 6 4 5 6
320 Perception & Psychophysics, 1966, Vol. I Table 2. The combination of physical magnitude and duration min. After a rest of two or more hours, he returned for used as stimuli in Experiments 1 through 6 on loudness. the actual experimental session, which lasted 30 to 40 min. Peak SPL in dB re Duration in milliseconds 0.0002 dyne/cm 2 5 10 18 30 50 80 130 200 300 500 Results of Seal ing Brightiless 36 2 4 6 4 2 6 4 6 2 6 For each stimulus the geometric mean of the bright 51 3 2 4 5 4 2 6 1 6 2 66 6 5 2 1 4 3 2 4 5 3 ness estimates was computed. In order to tie together 81 5 6 1 2 3 ALL 1 3 5 6 the results from the six different experiments, the fol 96 4 1 3 5 (, 1 3 4 2 1 lowing procedure was adopted. For eachexperiment, the 109 1 3 5 3 5 3 1 5 1 5 geometric mean for the stimulus common to all six experiments (85 dB, 200 msec.) was multiplied by a to improve their understanding of the task. No person factor b that made the resulting product (b times the served in more than one session in one day (typically, geometric mean) equal 10. Thenall the geometric means sessions were separated by several days), and none of for a given experiment were multiplied by the same the observers had previously served in any of the six factor b. This computation preserves the ratios among experiments on brightness. the geometric means of a given experiment and allows the results of all six experiments to be plotted in a Measurement of the Auditory Threshold single pair of coordinates. The absolute threshold of a dozen observers (only The transformed geometric means are plotted as one of whom served in the scaling experiment) was functions of duration in the log-logcoordinates of Fig. 2. measured at each of the 10 durations listed in Table 2 The parameter is peak luminance in dB re 10-10 L. and also at durations of 800 and 1000 msec, The order Three features of the outcome, all of which have been of presentation of the durations was irregular and dif observed in earlier studies (Alba & S. S.Stevens, 1964; ferent for each observer. Raab, 1962) may be noted again here. (1) For each For this experiment a recording attenuator (Grason intensity level there is a "critical duration," shorter Stadler Model E-3262-A) was inserted between the than which apparent brightness clearly depends on the electronic switch and the earphones. The observer duration, and longer Ullinwhichbrightness is essentially operated a two-position switch, which when pressed independent of the duration. Below the criticalduration, caused an immediate I-dB increase or I-dB decrease of the data can be fitted fairly well by straight lines whose attenuation in the recording attenuator. A light flash slopes equal approximately 0.45. In other words, to a signaled the observer that the noise burst was about to first approximation the brightness grows as a power occur. The task was to press the switchin one direction function whose exponent is about 0.45. This exponent is (increased attenuation) if the noise was heardand in the larger than the exponent of the "standard"bril function other direction (decreased attenuation) if the noise was (0.33) that relates subjectivebrightness to the luminance not heard. The threshold was "tracked" by this stair of a target that lasts 1 sec. and is viewed by the dark case method (the Bekesy method) until a reasonably adapted eye (J. C. Stevens & S. S. Stevens, 1963). (2) In stable value was achieved. the region of the -critical duration, there usuallyoccurs The observer practiced the technique for about 10 an enhancement (shown by the dotted "humps" in Fig. 2),
50.0 Brightness ~ 30.0 105dB
20.0 o 95dB en en 65d8 o -1:1------55d8 Fig. 2. How apparent brightness grows as a function of stimulus duration at six 5.0 10 30 50 100 200300 500 1000 levels of peak luminance measured in 10 Durotton in milliseconds dB re 10- L. Perception & Psychophysics, 1966, Vol. 1 321 which is the well-known Broca-Sulzer phenomenon. 1958; Luce, 1959; J. C. Stevens & S. S. stevens, 1961). For an unknown reason, a Broca-Sulzer hump failed to The larger space between the functions for 55 and 65 dB show up in the topmost function of Fig. 2 (105 dB). The is consistent with Equation (2). flattened appearance of this function is puzzling. It Figure 2 seems to imply thatthe growth of brightness resembles the topmost function in a similar plot of with intensity follows the same power law fordurations Raab's results (see S. S. Stevens, 1966b) at a level of longer than about 100 msec, Except for the function at" 95 dB-a level that revealed the enhancement in the 105 dB, it would also appear that a power function may present study. Why the topmost functions of these two hold for durations shorter than about 5 msec. The different experiments should have the same curiously spacing of the functions is such that, as suggested by flattened shape is not clear, especially since a Broca Aiba and S. S. stevens (1964), the exponent for short Sulzer hump occurred in the brightness matches of durations must be larger than that for the longer Aiba and S. S. Stevens (1964) at a level of 103 dB. durations. Because the critical duration varies with (3) The critical duration decreases withthe intensity lev intensity between about 10 and 100 msec,; the brightness el, from about 150 msec, at55 dB to about 5 msec. at 95 functions should consist of two sections, the upper dB. This decrease in the critical duration was present portion of which would be steeper than the lower. but had a smaller magnitude in the matches of Alba The data are displayedin another way in Fig. 3, where and S. S. Stevens than in either Raab's magnitude esti the adjusted geometric means for the stimuli between mations or those of the present study. 65 and 95 dB are plottedas a function of peak luminance, with duration as the parameter. Also plotted in Fig. 3 Brightness as a Function of Intensity are the geometric means obtained by Raab (see S. S. If, for the longerdurations, apparentbrightness grows Stevens, 1966b) for peak luminance between 65 and 90 as a power function of luminance, then the horizontal dB and for a dozen durationsbetween 0.5 and 2000 msec, portions of the functions of Fig. 2 ought to be spaced Although the data for intermediate durations could at equal intervals in these log-log coordinates. This is probably be fittedbetter with two straight-line segments, approximately true, with the obvious exception of the power functions were fitted by least squares to the data lowest function (55 dB). Between 65 and 105 dB, an for all durations. The obtained slopes (exponents) were increase of 10 dB produces nearly a constant two-fold plotted as circles and squares in Fig. 4. The two sets increase in subjective brightness. Below 65 dB, the of exponents follow the same trend, but Raab's exponents growth of brightness seems to be steeper. Near the are slightly larger throughout. The exponents range absolute threshold (roughly 50 dB for a 20 target), the from about 0.3 for the longer durations to about 0.45 growth of sensory magnitude with intensity is known to for the shorter durations. The transition from the one be rapid. The generality of this finding throughout the exponent to the other for the intermediate durations sensory domain has led to a more general form of the appears to be gradual rather than abrupt; presumably power law: this happens because with decreasing duration the (2) steeper segment of the two-segment function comes more and more to dominate in the least-squares where 30.0 20.0 Fig. 3. How apparent bright ness grows as a function of stimulus magnitude for a number of different stimulus durations (in milliseconds). Upper part: ., present experiment. Lower part: .:: experiment by Raab (1962). The peak luminance of the most in ~ ., tense stimulus plotted was 95 Ct: dB (upper) and 90 dB (lower) re 1.0 ~_~_---L._----'-__.L-_--L..._---.i.._----'__.L..._-'------'---'.__~_-'---_-'-_--J.---J 10-10 L. Lines fitted by the Relative intensity (subdivision 10 decibels) method of least squares. 322 Perception & Psychophysics, 1966, Vol. 1 is about one and a half times larger for short than for c; 0 long flashes. If the exponent of the bril function is as Q) and S. S. Stevens (1964) give a smaller estimate of the ::: 0.3 ~ Loudness difference (0.33 and 0.40). 0 Figure 4 also shows that, in contrast to brightness, - o Brightness - Stevens C 0.2 the exponent of the loudness function (triangles) is Q) c; El Br ightness - Raab 0 essentially invariant with duration. This functional dif 0- W" ference between the eye and the earisdiscussed below. Duration in milliseconds The Equal-Brightness Functions and Bloch's Law Fig. 4. How the exponents of the loudness and brightness func The straight lines of Fig. 3 were used to generate a tions shown in Figs. 3 and 7 depend upon the duration of the family of equal-brightness functions that relate peak stimulus. luminance and duration. Several horizontal cuts were made through the power functions of Fig. 3. The peak The exponent of the "standard" brightness function luminances in decibels and the durations in milliseconds (the so-called bril scale) has been given a value of marked by the intersections were plotted in Fig. 5, and 0.33, a value estimated from the results of a variety of straight-line segments were fitted to the points. This methods in different laboratories (see S. S. stevens, procedure does noteliminate the deficiencies in the data, 1966b). It is not unusual, however, for the method of nor does it preserve the Broca-Sulzer hump. On the magnitude estimation to yield a value slightly smaller other hand, it clarifies certain relations. than 0.33 (J. C.Stevens & S. S. Stevens, 1963). Moreover, The dotted lines of Fig. 5 mark the "critical dura the likelihood of obtaining a low exponent appears to tions," longer than which brightness is essentially increase when a task is made more difficultor compli independent of duration. The equations of the dotted cated (Marks, in press). lines are very nearly the same for both sets of data in Both sets of data in Fig. 4 suggest that the exponent Fig. 5. Brightness a;'" 100 .0 Q) .>t:. o Q) 60 0010 from J. C. Stevens a.. o o o 100 s: Q) ..c o o 80 Q) u c o o c 70 : E :: Fig. 5. Two families of equal-brightness functions giving the combinations of peak .=! Data from Raab 60 luminance and duration that produce the same apparent brightness. Upper: present o experiment. Lower: experiment by Raab. 50 The points were obtained by making hori zontal cuts through the brightness func 10 100 1000 tions of Fig. 3 at several brightness values milliseconds Duration in t/J. Perception & Psychophysics, 1966, Vol. 1 323 suggests that the time it takes for the development of 100.0 109 d8 visual sensation depends on the level of stimulation. 50.0 That the time required for maximum sensation grows <::I 96d8 shorter with increased intensity has been recognized 30.0 0 0 by virtuallyeveryinvestigatorof the problem.According 20.0 81 d8 to Bills (1920), various functions have been proposed 0 Q) the fourth root of intensity. McDougall's measurements .~ 3.0 0 51 dB in 1904 suggest the fifth root of intensity, and the dotted E 2.0 Q) a:: 0 lines of Fig. 5 suggest the thirdrootof intensity. Those lines have slopes (exponents) of -3.2 (upper line) and 1.0 36 d8 -3.3 (lower line). 0.5 The slope values in Fig. 5 raise the interesting possi bility that the time required for maximum sensation may grow in simple inverse proportionto the subjective 0.2 brightness that is finally attained; for if brightness 20 30 50 100 200 300 500 1000 grows as the cube root of intensity (the bril function) Duralion in milliseconds and if the reciprocal of duration atmaximumbrightness Fig. 6. How subjective loudness grows as a function of stimulus also grows as the cube root of intensity (as shown by duration at six levels of stimulus magnitude (in dB peak SPL). the dotted lines), thenitfollowsthatthe critical duration grows in inverse proportionto the maximumbrightness. The straight-line segments to the left of the dotted The equal-brightness contours of Aiba and S. S. Stevens, lines have slopes equal to -1.0. This means that a however, show a variation of the critical duration that decade increase in duration may be traded for a decade is too small to obey the cube-root relation. decrease in peak luminance, and vice versa. This rela tion of reciprocity between time and intensity, demon Results of Scaling LOUdness strated in Fig. 5, means that Bloch's Law holds at The loudness estimates were processed in the same suprathreshold levels, as noted by Aiba and stevens and way as were the brightness estimates. In order to tie by Raab, On this point all three studies agree. Because together results from the six different experiments, the time and intensity are interchangeablebelow the critical geometric means for each experiment were multiplied duration, the exponent that governs the power function by a factor b: the value of the factor b was chosen so relating subjective brightness to duration must have a that the product of b and the geometric mean for the value of 0.4 or 0.5. Figure 2 shows that this conclusion stimulus 81 dB for 80 msec, (the one presented in all is approximately correct. six experiments) equalled 10. In Fig. 6 the 60 adjusted geometric means are plotted as a function of duration The Rise-Time of Visual Sell"afion with peak SPL as the parameter. In Fig. 7 they are The negative slope of the dotted lines in Fig. 5 plotted as a function of peak SPL with duration as the Fig. 7. How tbe subjective loud ness of white noise grows as a function of stimulus magnitude for 10 diHerent stimulus durations (in milliseconds). Tbe most intense stimulus {or each function was 109 dB peak SPL. Lines fitted by the Relative intensity (subdivision = 20 decibels 1 method of least squares. 32<1 Perception & Psychophysics. 1966, Vol. 1 between the exponents thatgovern the loudness functions 120 Loudness for intensity and duration. Figure 6 reveals no variation of the "critical dura tion" with the level of intensitynor anything resembling ~ o/~ 50 a Broca-Sulzer hump. Instead, the relation between ® loudness and duration seems to be about the same over a great portion of the dynamic range of hearing. This 0/' 20 N generalization needs qualification, however, when it E comes to loudness near the absolute threshold...... u Q) c: 0/ ~ 10 The lines in Fig. 7 were fitted to the points by the >- "0 ~ method of least squares, and the slopes (exponents) are N plotted in Fig. 4 to show that, unlike visual brightness, 0 0 0/ ~ 5 0 the loudness of a white noise seems to be governed by o 0 the same exponent regardless of the duration. The average of the obtained exponents was 0.54 and the ~ ~ 0/~2 ~ standard deviation, 0.01. The loudness functions of Fig. on Q; 7 seem to differ from one another with respect only to .c IjJ ~ 1 u 0 the constant kofEquation (I), thatis to say, with respect Q) 0 (;) 0 to the stimulus magnitude that is required to produce 30 a given level of loudness. Using bursts of tone at 1000 Hz instead of noise, Wright (1965) found the exponent 20 of the loudness functions to be constant. Hisfive obser vers estimated the loudness of a number of intensity levels at durations of 10, 30, 100, 300, and 500 msec. of noise in The Equal-Loudness Contours and the Critical Duration Fig. 8. Equal-loudness functions giving the combinations of The functions of Fig. 7 were used to generate a duration and peak sound pressure level that produce the same suh family of equal-loudness functions relating peak SPL jective loudness. The points were obtained by making horizontal and duration-an auditory analogue of the family of cuts through the functions of Fig. 7 at several Ievels of apparent loudness Perception & Psychophysics, 1966, Vol. 1 325 The fits are often good, although the various studies c fail to yield precisely the same slope. For noise, Miller 0 uc (1948) measured an average slope of -0.88 for three :: 10 listeners (i.e., -8.8 dB offsets a 10-foldchange in dura :;; ~ tion), and Small, Brandt, and Cox (1962) measured an 0 o, average slope of -1.25 for 12 listeners, the same slope obtained in the present experiment. Both Miller and ~'" Small et al stated that the critical duration depends on a the level of intensity. The evidence offered for this a. 2 dependency does not seem to be definitive, and, in any '"~ case, in neither study is the apparentvariationas large C'" I 5 10 50 100 500 as the variation measured for visual brightness. Overa Duration of the noise in milliseconds range of intensities comparable to that used in the present experiment on loudness (70 dB), the critical Fig. 9. The value or the constant k or the psychophysical power duration in Miller's experimentappears to have changed runction tor loudness, plotted as a function or stimulus duration, by a factor of 1.5 or less. Small and his co-workers in log-log coordinates. measured a change of approximately 3-fold between 20 and 60 dB above threshold. constant k of the power functions presented in Fig. 7 The slope of -1.25 obtained here implies thatsubjec are plotted in log-log coordinates. The straight-line tive loudness grows less rapidly with respect to sound segments in Fig. 9 show that the value of k grows energy than with respect to duration. The formula approximately as the 0.34 power of duration up to about relating peak energy E and duration T for equal loud 150 msec. and beyond 150 msec, remains approximately ness below the critical duration is constant. If this model is correct, then the general log E ~ -1.25 log T + log C (3) formula for loudness (below the critical duration) can or be written: (4) L = cTaEf3 (5) Equation (4) implies that the exponent of the psycho physical power function should be 1.25 times largerfor 1n the present experiment the values of a and f3 were duration than for sound energy. A comparison of the 0.34 and 0.272, Le;; a is 1.24 times larger than S. slopes of the functions in Figs. 6 and 7 confirms this Since the correct value of 13 is thought to be about 0.3 expectation. (the sane function), Equation (5) can be rewritten: L = cTD.375ED.3 (6) Is There a Critical Duration for Loudness? Although the equal-loudness functions can be des Equation (4) for the equal-loudness contours follows cribed quite well by two straight-line segments, the directly from Equation (6). points in Fig. 8 could be fitted by other types of functions, such as a logarithmic or exponential curve. Reciprocity and Threshold Several different formulas have from time to time been The absolute threshold of audibility (average from 12 proposed to describe the relation between duration and observers) is plotted as the bottom function of Fig. 8. intensity at the absolute threshold. Considering the This function resembles the equal-loudness contours nature and the precision of the psychophysical methods in its double-segmented shape, but it appears to differ available for the determination of thresholds and equal from them in two ways. First, the critical duration at loudness, it may not prove feasible to decide on the threshold is about 230 msec., rather than 150 msec , basis of fit alone from amongall the alternative formulas Thus, between about 0 and 10 dB sensation level (SL) and theories. Whether the critical duration should be a shift takes place in the critical duration, as is apparent thought of as a real discontinuity is therefore debatable; also from the experiments of Miller and of Small, but it is nevertheless clear that a sharp change in the Brandt, and Cox. Second, the slope of the audibility slope of the equal-loudness function does occur in the function (-0.7) is substantially different from that of vicinity of 150 msec. Small, Brandt, and Cox reported the equal-loudness functions (-1.25). that the critical durationdiffers widelyfrom one listener A slope of -0.7 agrees reasonably well with Miller, to another and that the transition between the two seg who obtained -0.8, with Garner (1947), who obtained ments of the functions is more gradual for the averaged -0.88, and with Small, Brandt, and Cox, who obtained results than it is for the individual results. Thus, the -0.77. Note that in that experiment Small et al also real sharpness of the change is partially smoothedover obtained a slope of -1.25 for equal-loudness contours by the process of averaging. between 10 and 60 dB SL. Thus the evidence is strong However that may be, the equal-loudness contours of that stimulus magnitude and duration do not offset each Fig. 8 provide a reasonable and simple description of other in the same way at thresholdand at higher levels. the empirical findings. 1n Fig. 9 the values of the At threshold, furthermore, the slope for noise does not 326 Perception & Psychophysics. 1966. Vol. 1 equal -1,0. Over a similar range of duration, the slope Ekman, G. Two generalized ratio scaling methods. J. Psuchol., for a pure tone may be closer to -1,0, and nearly' 1958, 45, 287-295. perfect energy summation may take place. Although Ekman, G., Berglund, B" & Berglund, U. Loudness as a function of the duration of auditory stimulation. Rep., Psychol. Lab. reciprocity has often been claimed for pure tones, at Univ. Stockholm, 1966, No. 205. least one extensive study of the question (Yntema,1955) Gamer, W. R. Effect of frequency spectrum on temporal integration yielded results much closer to those reported here for in the ear. J. Acoust. Soc. Amer., 1947, 19, 808-815. noise. Garner (1947) pointed out that simple reciprocity Gerbrands, R., & Stevens, J, C. A high-intensity flash source. for tones clearly breaks down, not only at the critical Amer. J. Psuchol., 1964,77,643-646. Luce, R. D. On the possible psychophysical laws. Psuchol. Rev., duration, but also toward very short durations, as the 1959, 66, 81-95. spectrum of the tone burst comes more and more to Marks, L. E. Brightness as a function of retinal locus. Percept. resemble that of noise; and he suggests that perfect & Psychophys., (in press), temporal summation may occur only when the stimulus Miller, G. A. Perception of short bursts of noise. J. Acoust. Soc. is confined to a "critical band." Broader spectra, Amer., 1948, 20, 160-170. Raab, D. Magnitude estimation of the brightness of brief foveal such as broad-band noises or very short tones, yield stimuli. Science, 1962, 135, 42-43. less than perfect summation. Other interpretations of Small. A. M., Jr., Brandt, J. F., & Cox, P. G. Loudness as a the same facts are, however, given byZwislocki(1960), function of signal duration. J. Acoust. Soc. Amer., 1962, 34, and the present experiments demonstrate that the 513-514. degree of summation for noises depends on the intensity Stevens, J. C., & Stevens, S. S: Physiological zero and the psycho physical law. In Proc. 16th Tnt. Conor. Psuchoi., Amsterdam: level. North Holland. 1961. Pp. 192-193. In any case, the measurements of thresholdandequal Stevens, J. C., & Stevens, S. S. Brightness function: Effect of loudness alike seem to fit the formula suggested by adaptation. J. Opt. Soc. Amer., 1963, 53, 375-385. Garner for relating time and energy, namely: Stevens, S. S. To honor Fechner and repeal his law. Science. 1961. 133, 80-86. ETa = k (7) Stevens, S. S. Matching functions between loudness and ten other continua. Percept. & Psychophys., 1966a, 1, 5-8. It is curious that, for the same noise spectrum, the Stevens, S. S. Duration, luminance, and the brightness exponent. factor a should assume values both greaterand smaller Percept. & Psucnotihus ; 1966b, 1,96-100. than 1,0, depending on the stimulus level. There seems Wright, H. N. Loudness as a function of duration. J. Acoust. Soc. to be no analogous phenomenon in vision. The change Amer., 1965.37,1174. (Abstract) in the factor a between threshold and higher levels be Yntema, D. B. The probability of hearing a short tone near thresh old. Unpublished doctoral dissertation, Harvard University, 1955. comes, therefore, a fact to be fitted into a complete Zwislocki, J. Theory of temporal auditory summation J. Acoust.. theory of temporal summation in audition. Soc. Amer., 1960, 32, 1046-1060. Nole References 1. This research was supported in part by National Institutes of Aiba, T. S., & Stevens, S. S, Relation of brightness to duration Health Grant NB-02974 and in part by National Science Foundation under light- and dark-adaptation. Vision. Res., 1964, 4, 391-401. Grant GB-3211 (Laboratory of Psychophysics Report PPR-327). Bills, M. A. The lag of visual sensation in its relation to wave length and intensity of light. Psuchol. Monogr., 1920, 28, No.5. (Accepted tor publication August 1, 1966.) Perception & Psychophysics, 1966, Vol. 1 327