Perception & Psychophysics 1989. 46 (2), 155-166 Binurl nd temporl integrtion of the loudness of tones nd noises DANIEL ALGOM John B. Pierce Foundtion Lbortory, New Hven, Connecticut Yle University, New Hven, Connecticut nd Br-Il University, Rmt Gn, Isrel nd ATALIA RUBIN nd LIOR COHEN-RAZ Br-Iln. University, Rmt Gn, Isrel Subjectsjudged the loudness of tones (Experiment 1) nd of bursts of noise (Experiment 2) tht vried in intensity nd durtion s well s in mode of presenttion (monurl vs. binurl). Both monurl nd binurl loudness, for both types of signls, obeyed the biliner-interction prediction of the clssic temporl integrtion model. The loudness of short tones grows s power function of both intensity nd durtion with different exponents for the two fctors (.2 nd.3, respectively). The loudness of wide-bnd noises grows s power function of durtion (with n exponent of pproximtely.6) but not of sound pressure. For tones, binurl summtion ws constnt but fell short offull dditivity. For noises, summtion chnged cross level nd durtion. Temporl summtion followed the sme course for monurl nd binurl tonl stimuli but not for noise stimuli. Notwithstnding these differences between tone nd noise, we concluded tht binurl nd temporl summtion re independently operting integrtive networks within the uditory system. The usefulness of estblishing the underlying metric structure for temporl summtion is emphsized. The integrtion of coustic stimultion over time nd the integrtionof stimultion over the two ers depict two widely documented uditory processes tht disply energy-dependent properties, t lest for threshold. For both types of summtion, loudness depends on the totl mount of energy in the stimulus nd is independent of how the energy is distributed over time or cross the two ers (e.g., Bbkoff & Algom, 1976; Hughes, 1938). Moreover, both temporl nd binurl summtion vry with the type (tone vs. noise) nd level (threshold vs. suprthreshold) ofthe stimulus (e.g., Algom, Adm, & Cohen Rz, 1988; Algom & Bbkoff, 1984; Algom & Mrks, 1984; Mrks, 1980). Despite the obvious similrities in opertion chrcteristics, these two energy-integrting networks in udition hve been studied independently, using mutully exclusive types of stimultion. In the present study, we report the results of combined investigtion of the two phenomen. We sked to wht extent, if ny, integrtion ofcoustic energy over time intercts with the integrtionof stimultion over the two ers. Do the rules tht govern binurl summtion chnge when the signls undergo temporl integrtion? Conversely, does the Preprtion of this pper ws supported by Nlli Grnt NS21326 to Lwrence Mrks, whose generous ssistnce nd vluble comments re grtefully cknowledged. We lso thnk Robert Melr for his most helpful comments on n erlier version of this mnuscript. Brbr Fulkner nd Elise Low provided skillful ssistnce t vrious stges of the completionof the mnuscript. Correspondence should be ddressed to Dniel Algom, John B. Pierce Foundtion Lbortory, 290 Congress Avenue, New Hven, CT 06519. course of temporl integrtion differ for monurlly nd binurlly presented stimuli? The present experiments enbled us to nswer these questions by directly compring temporl nd binurl integrtion for the sme suprthreshold stimuli. Binurl Summtion of Tones nd Noises Severl experiments hve exmined binurl summtion t threshold. For both tones nd noises, the binurl threshold is lower thn the monurl threshold, nd the verge difference is bout 3 db (e.g., Bbkoff& Algom, 1976; Chocholle, 1962; Hellmn & Zwislocki, 1963; Hughes, 1938; Shw, Newmn, & Hirsh, 1947). Mesurements of suprthreshold binurl summtion revel significntly greter binurl gins (when referred to soundpressure levels), indicting tht it is loudnesses, rther thn energies, tht dd (e.g., Levelt, Riemersm, & Bunt, 1972; Mrks, 1979b). For pure tones nd nrrow-bnd noises, the results re consistent with model of liner summtion. The estimtes of loudness of binurlly presented signl pproximte the sum ofthe loudness estimtes of the left nd right er components. A binurl sound is, on the verge, twice s loud s monurl sound ofthe sme sound-pressure level (SPL) (Algom & Mrks, 1984; Hellmn & Zwislocki, 1963; Levelt et l., 1972; Mrks, 1978, 1979, 1979b, 1980, 1987). To equl the loudness of binurl tone, monurl tone hs to be 10 db greter which, on the sone scle (i.e., loudness increses s the.6 power ofsound pressure). corresponds to doubling ofloudness (S. S. Stevens, 1956). Although 155 Copyright 1989 Psychonomic Society, Inc.
156 ALGOM, RUBIN, AND COHEN-RAZ Schrf & Fishken (1970) lso found tht the rtio of binurl to monurl loudness is constnt, their results suggest less thn complete summtion. For wide-bnd noise stimuli, on the other hnd, the binurl-monurl rtio increses with incresing sound pressure (Algom et l., 1988; Irwin, 1965; Mrks, 1980, 1987; Reynolds & S. S. Stevens, 1960; Schrf, 1968; Schrf & Fishken, 1970). Although Reynolds nd Stevens (1960) concluded tht the loudness of both monurl nd binurl noise stimuli grows s power function of sound pressure (but tht the exponents differ), Schrf nd Fishken (1970) nd Mrks (1980), s well s the mjority of other investigtions (see Schrf, 1978, for review), hve reported psychophysicl functions for noise tht re not power functions of sound pressure. Temporl Summtion of Tones nd Noises At threshold, the er integrtes the coustic energy of sinusoidl signllinerly up to criticl durtion of bout 250 msec; tht is, in this rnge, tenfold increse in durtion results in decrese in the signl intensity necessry for threshold by 10 db (Algom & Bbkoff, 1978; Algorn, Bbkoff, & Ben-Urih, 1980; Gmer & Miller, 1947; Wtson & Gengel, 1969). For brod-bnd noise stimuli, however, only prtil integrtion hs been found, with representtive vlue of 7-dB chnge in threshold for tenfold chnge in durtion (Bbkoff& Algom, 1976; Gmer, 1947; Miller, 1948; Penner, 1978). For suprthreshold levels of stimultion, not only re the dt sprse, but there pper to be some puzzling discrepncies. Some studies hve shown tht intensity hs to be decresed by 10 to 20 db for ech tenfold increse in durtion (Algom & Mrks, 1984; Smll, Brndt, & Cox, 1962; J. C. Stevens & Hll, 1966; see lso J. C. Stevens, 1976), wheres one study reported much steeper slopes (McFdden, 1975). Criticl durtions seem even more vrible, encompssing, t times, rnges of over 1:3 or 1:4 (Algom & Mrks, 1984; see lso the summry of results by Schrf, 1978). In fct, the very existence of criticl durtion for suprthreshold loudness hs been questioned (J. C. Stevens & Hll, 1%6; see lso McFdden, 1975). In ny cse, threshold nd suprthresholddt like my be described in terms of Gmer's (1947) well-known generl eqution, I x t = C, where I denotes stimulus power, t is durtion, nd the exponent is the slope of the line (reciprocity function) relting 10gI to logt. C represents constnt criterion loudness response such s threshold. Simple trdeoff between intensity nd time ( = 1) exists for threshold tonl stimuli only. Threshold noise stimuli yield prtil summtion ( < 1), wheres suprthreshold integrtion usully gives supersummtion ( > 1). Agin, despite such summry vlues, no universl greement hs yet been found on the exct size of the criticl durtion, especilly for suprthreshold stimuli, or on the exct nture nd slope of the trding function (see Algom & Bbkoff, 1984, nd Schrf, 1978, for recent reviews). Binurl nd Temporl Summtion Combined As noted, no experiment hs been reported tht directly compres monurl nd binurl temporl integrtion in the suprthreshold rnge. Their combined resolution, though probbly more complicted thn t threshold (see Bbkoff & Algom, 1976), should give more comprehensive ccount of their underlying uditory processes. EXPERIMENT 1 TEMPORAL INTEGRATION AND BINAURAL SUMMATION OF PURE TONES Method Subjects. Ten subjects (7 femles) with men ge of 23 yers (rnge: 20 to 29 yers) prticipted in the experiment. They reported hving no mjor hering problems. All subjects were screened for norml hering t frequencies of 1000, 2000, nd 4000 Hz, nd were required to hve monurl thresholds tht did not differ by more thn 2 db t 2000 Hz cross the two ers (method of limits). Four of the subjects hd previous experience with the method of mgnitude estimtion, lthough not necessrily injudging loudness. Otherwise, ll subjects were nive with regrd to the experiment. Apprtus. The 2000-Hz signl from Hethkit 16-72 genertor ws gted nd timed, nd ws then split into chnnels for the left nd right ers. All stimuli were trpezoid-shped, with l-msec rise/fll times. The signl in ech chnnel could be ttenuted independently before being fed to mtched set of hedphones (AKG-250A). Frequency nd durtion were monitored by Monsnto 120A counter-timer. Signl intensity ws clibrted in n rtificil er by Bruel nd Kjer precision sound-level meter (Mode! 2204). Procedure. The subject st in sound-shieldedbooth (Medtechnic Silent Cbin). Five different levels of sound pressure (30, 40, 50, 60, nd 70 db) were combined fctorilly with six different durtions (16, 32, 64, 128,256, nd 512 msec) to produce 30 different stimuli. These stimuli were presented both monurlly to ech subject's right er nd binurlly, producing 60 different stimuli in ll. The stimuli were presented one t time to the subject for judgment. Ech subject received two replictes of the entire threedimensionl [SPL (5) x durtion (6) x mode of presenttion (2) = 60 member] mtrix in session nd served in two sessions (seprted from one nother by t lest 1 dy), thus giving four judgments per stimulus in ll. The order of presenttion of the stimuli ws irregulr nd ws different for ech subject (orderly sequences tht occsionlly rise in rndom selection were intentionlly voided). The method ws free mgnitude estimtion. The subjects were instructed to ssign to the first stimulus whtever number seemed most pproprite to represent its loudness, nd to ssign numbers, in proportion, to succeeding stimuli. If no sound ws herd, the subject ws to ssign the number zero. The subjects were told tht they could use whole numbers, decimls, nd frctions s needed. In ddition, they were instructed to disregrd the pprent loction or length of the stimuli nd to judge only their loudness. The subjects mde their judgments verblly, communicting with the experimenter vi intercom. Results nd Discussion Metric structure: The integrtion of time nd intensity onto loudness. The mgnitude estimtes ofloudness given to ech stimulus were verged geemetriclly, nd these mens re plotted in Figure 1 s function of the SPL delivered to the right er. The prmeter is durtion; ech contour represents tones exposed for differ-
LOUDNESS SUMMATION FOR TONE AND NOISE 157 30 40 50 DECIBELS SPL - MONAURAL Figure 1. Monurl temporl integrtion. The verge mgnitude estimtes of loudness plotted s function of the sound-pressure level (SPL) delivered to the right er. The prmeter is durtion; ech contour represents tones exposed for different constnt durtion (t. -to = 16, 32, 64, 128, 256, nd 512 msec). ent constnt durtion. Assuming tht (1) multiplictive model is operting on the psychologicl representtions of time nd intensity trnsforming them onto loudness, nd (2) n pproprite (liner) judgment function exists for the mgnitude-estimtion response, the curves in Figure 1 should diverge. The clssic temporl integrtion model (I x t = C) implies tht when durtions re held constnt, s in Figure 1, differences in loudness increse linerly with incresing SPL. The loudness estimtes re plotted on liner scle to mke evident the metric impliction of the clssic multiplictive model for temporl integrtion: divergent interction tht is pproximtely biliner. Perhps the most striking feture of this fmily offunctions is their tendency to diverge from common origin t the lower left. There is systemtic chnge in the SPL seprting the functions from one nother. The complementry plot of binurl presenttions ppers in Figure 2. Although there pper to be some smll deprtures from monotonicity, these dt, s well s the monurl dt, seem to obey the implictions ofthe model under test firly well. It is possible to subject the biliner pttern implied by the multiplying rule to more rigorous visul test (beyond the mere divergence nicely illustrted in Figures I nd 2). To tht end, we first clculted the mrginl mens for ech level of the 2000-Hz tone; this ws ccomplished by verging the dt cross the six vlues of stimulus durtion. Then the mgnitude estimtes were plotted ginst the mrginl mens in grphs nlogous to those of Figures 1 nd 2. These re the test plots. If the mul- 60 70 tiplictive model holds, then ll of the functions in the test plots should be stright lines (llowing for vribility round the verge points) with slopes tht grow systemticlly lrger. Indeed, the slopes derived from the dt in Figures 1 nd 2 formed, in ech cse, the expected diverging fn of stright lines. Thus, the results support n underlying multiplictive rule of integrtion of both monurl nd binurl stimultion. I Binurl summtion nd loudness s function of pressure. Given fctorildesign of the type used in these experiments nd results consistent with bilinerity in the response domin, the mrginl mens provide vlid estimtes of the scle vlues (Anderson, 1974, 1981,1982). Figure 3 presents these clculted scle vlues for monurl nd binurl presenttions s function of SPL. These functions were produced by verging cross the different durtions in the two dt mtrices. The fits to the power functions (stright lines in the double logrithmic coordintes) re excellent (r 2 =.985 for the monurl function nd.996 for the binurl function). The slopes (exponents of the power functions) re.36 nd.42, respectively. Tht the loudness functions re closely (though, perhps, not fully) prllel cn be mde even more pprent by excluding the lowest (30-dB) vlue from the monurl dt set. (Filure ofcomplete temporl integrtion t the longest durtion for monurl stimultion probbly ffected judgments t this low SPL; see lso Figure 5, below.) The truncted function is bit steeper: the slope is.39, supported by n even better fit (r 2 =.989). Although these slopes re notbly smller thn the.6 ofthe sone scle, they re by no mens unusul within the frmework of suprliminl temporl summtion reserch. Three comprble studies (Algom & Mrks, 1984; f-.- -- 13 30 40 50 DECIBELS SPL - BINAURAL Figure 2. Binurl temporl integrtion. Sme s Figure 1, for tones delivered to both ers. 60 70
158 ALGOM, RUBIN, AND COHEN-RAZ U) & U) binurl 0.6 monurl <: Cl :::J -.l 0.6 Cl I- 0.4 & U) 0.2 &.: & / -.l 30 40 50 60 70 DECIBELS SPL Figure 3. Binurl summtion ofloudness s function of soundpressure level (SPL). Averge loudness functions of binurl nd monurl stimuli derivedfrom the mrginlmensof the dt plotted in Figures 1 nd 2. McFdden, 1975; J. C. Stevens & Hll, 1966) yielded verge mgnitude-estimtion exponents of.46,.40, nd.54 (noise), respectively. The smller exponents in the present study my stem from greter difficulty in judging stimuli tht vry in durtion nd loci s well s intensity (Algom & Mrks, 1984; J. C. Stevens & Hll, 1966; S. S. Stevens & Greenbum, 1966). Binurl summtion cn be ssessed from inspection of the horizontl seprtion between the monurl nd the binurl loudness functions. Complete binurl summtion implies tht sound presented to two ers should be just twice s loud s the sme sound presented to one er. According to the eqution for sones, for exmple, loudness doubles with 1O-dB increse in sound pressure. Given the sone scle, it follows tht monurl stimulus must be 10 db greter thn binurl stimulus for them to pper eqully loud, s demonstrted by Algom nd Mrks (1984) nd Mrks (1978, 1979, 1979b, 1980). Figure 3 gives lower vlue for the binurl gin; t ll but the lowest levels of sound pressure, the difference seprting the binurl nd monurl functions is bout 7 db. Most likely, the results ofthis experiment re commensurte with only prtil summtion ofloudness cross the two ers.f Although Algom nd Mrks (1984) nd Mrks (1978, 1979, 1979b) demonstrted liner dditivity nd binurl gin of bout 10 db for tones, other studies hve similrly indicted less thn complete summtionof round 7 db (Cusse & Chvsse, 1942; Schrf, 1969; Schrf & Fishken, 1970; see lso Irvin, 1965). In fct, Mrks hs lso obtined less thn complete summtion in couple of experimentl conditions (e.g., Mrks, 1979b, p. 270; Mrks, 1980, Experiment 5). Tht summtion ws systemticlly less thn perfect is lso cler from inspection oftble 1, which summrizes the rtios of equl SPL binurl nd monurlloudnesses. On the verge, the subjects judged sound herd with two ers s 1.5 times s loud s sound ofthe sme intensity herd with one er. Similr binurl-monurl rtios of 1.7: 1, 1.65:1, nd 1.5:1 were obtined by Schrf nd Fishken (1970), Jnkovic nd Cross (1977), nd Mrks (1980), respectively. No systemtic effect either of durtion or of pressure is evident in the clculted rtios. Rescling the present dt to n exponent of.6 (i.e., "correcting" the response scle to sones) increses the mount of binurl loudness summtion (the binurl rtio becomes 1.84: 1) but does not suffice to mke the dt fully dditive. However, (smll) subdditivity is pprently common result with tones. Binurl summtion nd loudness s function of durtion. Figure 4 shows how loudness grows s function of durtion for both monurl nd binurl presenttions. These functions were produced by verging cross the different SPLs in the dt mtrices. It is cler tht loudness grew pproximtely s power function of the durtion of the tone for both modes of presenttion. The stright-line segments hve slopes of.31 (binurl function, r? =.980) nd.23 (monurl function, r'2 =.930). It is lso cler, however, tht n increse in durtion bove 256 msec brought bout little, if ny, chnge in loudness for the monurl condition. (No visible discontinuity- criticl durtion-ppers in the binurl dt.) Therefore, better description of the dt cn result from confining the power fit to only the first five monurl dt points-those flling t or below the criticl durtion. This gives slope of.27 with gretly improved fit (r =.977). Thus, over ll except the longest durtion, the monurl nd binurl functions virtully prllel one nother nd hve slopes in the vicinity of.29 (their geometric verge). This exponent differs from the exponents for loudness s function of pressure obtined erlier. Although the bsolute vlues differ somewht, J. C. Stevens nd Hll (1966) reported similr reltionship between exponents. Their exponent for loudnesss s function ofsound energy equlledbout 80% oftheir exponent for loudness s function ofdurtion; the present dt yield exponents for intensity tht re pproximtely 70% of those for durtion. Over their liner segments, the verge horizontl seprtion between the monurl nd binurl functions in Figure 4 is pproximtely.5 logrithmic units. Tht is, Tble 1 Averge Binurl-to-Monurl Loudness-Judgment Rtios for Tones t Different Sound-Pressure Levels (SPLs) nd Durtions SPL Durtion (in msec) (in db) 16 32 64 128 256 512 Men 30 2.46 1.02 2.09 1.01 1.42 2.07 1.67 40 0.83 1.21 1.51 1.28 1.43 1.8 1.34 50 0.89 1.47 1.02 1.81 1.32 1.58 1.34 60 1.39 1.23 1.2 1.77 1.61 2.07 1.54 70 1.24 1.37 1.55 1.57 1.44 1.98 1.52 Men 1.36 1.26 1.47 1.48 1.44 1.9 1.48
LOUDNESS SUMMATION FOR TONE AND NOISE 159 0.7 1.2... biric.ro l <: rrcvuro! C) C) -J 0.5 C) l- -- 0.3 I- <..:) C) 0.1 -..J / 1.5 /./ 1.8 Figure 4. Binurl summtion of loudness s function of durtion. Averge loudness functions of binurl nd monurl stimuli derived from the mrginl mens of the dt plotted in Figures I nd 2. 2.1 LOG DURATION lms) on the verge, threefold increse in the durtion of monurl tone ws needed for it to pper eqully s loud s binurl tone of the sme intensity. This binurl gin (the difference in log durtion between eqully loud monurl nd binurl stimuli) entils corresponding power-function exponent for loudness reltive to durtion. Given the presently derived binurl-monurl loudness rtio (of bout 1.5:1), the implied exponent for loudness is bout.35. This vlue is firly close to the directly derived exponents for durtion s well s to the comprble loudness exponents for durtion reported by J. C. Stevens nd Hll (1966). Thus, loudness seems to grow pproximtely s the cube root of durtion. Time-intensity trdeoff ssessed from the binurl gins in pressure nd durtion. The two indexes of binurl gin, nmely, the difference in decibels nd the difference in Gog) durtion between eqully loud monurl nd binurl stimuli, provide for n estimtionofthe timeintensity trdeoff. For equl-durtion monurl nd binurl tones (i.e., collpsing the durtion dimension in the response mtrix), the monurl tones hd to be ugmented by 7 db for them to pper eqully loud. For equl SPL monurl nd binurl stimuli (i.e., collpsing the soundpressure dimension in the dt mtrix), the monurl tone hd to be tripled in durtion to sound eqully loud. This yields time-intensity trding reltionship chrcterized by slope of -7 db per tripling of durtion; tht is, for loudness to be judgedequl, intensity hs to be decresed by 15 db for ech tenfold increse in durtion. Time-intensity trdeoff ssessed from loudness functions t ech durtion. Tble 2 presents prmeters of 2.4 2.7 the power fits pplied to the loudness functions t the different durtions for monurl nd binurl presenttions. This is no obvious trend in the derived exponents cross either mode (monurl vs. binurl) or durtion. The verge is bout.40, consistent with the vlue derived on the bsis of the mrginl mens. Moreover, the fits to the power functions re gin excellent. To obtin trditionl time-intensity trdeoff functions, the six loudness functions were horizontlly intersected t the sme ordinte vlues for both modes of stimultion. Thus generted, one such pir of monurl nd binurl trding functions for (the sme) equl loudness is shown in Figure 5. For both conditions, s stimulus durtion incresed, the intensity necessry to produce n equl-loudness judgment decresed. This trding reltionship does not, however, obey rule ofsimple reciprocity becuse the liner region ofech function does not hve slope of -1. The slopes, bsed on the five shortest durtions for the monurl mode nd ll durtions for the binurl mode, hve men of -1.75. On the verge, then, intensity hd to be decresed by 17.5 db for ech tenfold increse in durtion. This trding reltionship is very much like the one derived erlier nd is quite (though not fully) consistent with those obtined by Algom nd Mrks (1984), Smll et l. (1962), nd J. C. Stevens nd Hll (1966) in their studies of suprthreshold integrtion. Note, though, tht the ltter two studies used wide-bnd noise s stimulus, in contrst to the 2000-Hz tone used here. Note, too, tht lthough criticl durtion of pproximtely 256 msec chrcterizes the monurl dt, no comprble chnges re detectble in the slope of the respective binurl trding function. Loudness functions nd binurl gins ssessed from the time-intensity trdeoff. The monurl nd binurl trding functions in Figure 5 provide for yet nother estimtion of the binurl gins. Over their liner rnges, the verticl seprtion between the monurl nd the binurl functions is bout 6.7 db, vlue virtully identicl to the 7-dB binurl gin derived on the bsis ofthe mrginl mens. Given the binurl-monurl rtio derived erlier (in the vicinity of 1.5) this implies loudness function reltive to SPL with n exponent of pprox- Tble 2 Prmeters of the Psychophysicl Power Function for Loudness Reltive to Sound-Pressure Level t Six Different Durtions for Monurl nd Binurl Listening Durtion (in msec) 16 32 64 128 256 512 Men Monurl Binurl b r 2 b r 2 -.7.34.97 -.64.34.92 -.72.36.99 -.59.38.99 -.64.38.97 -.56.4.99 -.5.36.98 -.55.4.99 -.52.4.99 -.45.42.99 -.58.42.99 -.3.42.99.38.39 Note- = intercept, b = power-function exponent.
160 ALGOM, RUBIN, AND COHEN-RAZ -J -, 70... \ \. 60 binurl.... monurl -..J Q: ::J lj) lj)... <. 50 "<, ---. Q: Q... CJ \ <: ::J 40 C)... lj) 16 32 64 128 256 512 DURATION ims) Figure S. Equl-loudness contoursgiving the combintions of durtion, pressure, nd mode of listening (binurl vs. monurl) tht produced the sme subjective loudness. imtely.51. The horizontl seprtion ofthe curves-the difference in durtion between eqully loud monurl nd binurl stimuli-gives the binurl gin in time. The trding functions indicte roughly 2.S-fold binurl gin. Given the corresponding 6.7-dB gin in pressure, this yields time-intensity trding rtio of -6.7 db/2.5 msec (or pproximtely -18 db/to msec). Incidentlly, the 2.5-fold binurl gin in durtion lso implies scle for loudness which grows s the.43 power oftone durtion. Clerly, then, these estimtes for loudness s function of SPL nd s function of durtion, s well s the ssessment of the time-intensity reciprocity, closely correspond to the respective vlues derived erlier on the bsis of the metric properties of the dt tken s whole. Moreover, both sets ofestimtes, it should be recognized, were obtined independently of subjects' numericl judgments. Wht is the reltionship between temporl nd binurl summtion? The overll pttern ofthe response rry remins strikingly uniform regrdless of the type of summtion tested. The rules shown to govern the binurl summtion oflong supercriticl tones lso pply to much shorter tones regrdless oftemporl summtion tht the ltter undergo. Moreover, temporl summtion ofsuprthreshold tonl stimuli follows the sme course regrdless of whether the tones re presented to just one er or to both. This outcome, nmely the totl lck of mutul influence or interction between the two integrtion processes, suggests tht they re bsed on orthogonl, possibly identicl, mechnism(s). The underlying network of integrtion, to be thought of s neurl orgniztion t some high level in the uditory system, sums these types of input in n dditive mnner. EXPERIMENT 2 TEMPORAL INTEGRATION AND BINAURAL SUMMATION OF BROAD-BAND NOISES Method Subjects. Eight subjects (5 femles) prticipted in this experiment. Their ges rnged from 19 to 32, with men of 22 yers. The criteri for selection were those used in Experiment 1. None of these subjects hdtken prt in Experiment 1, but two hd previous experience in judging loudness. Apprtus nd Procedure. The production of the stimuli ws identicl to tht used in the previous experiment, except tht Generl Rdio 1390-B rndom-noise genertor providedthe trpezoid shped, l-msec onset nd l-rnsec offset, bursts of noise. The mkeup of these stimuli nd the detils of the method nd procedure were like those used in Experiment 1. The set of stimuli gin comprised ll 60 combintions of six durtions (16-512 rnsec), five SPLs (30-70 db), nd two modes of presenttion (monurl nd binurl) of white noise. The response of the hedphones ws essentilly flt between 300 nd 5000 Hz; there were few dips nd rises tht in no cse exceeded 2 db. Ech subject mde four judgments per stimulus in ll. Agin, the method ws free-mgnitude estimtion. The subject's tsk ws to ssign numbers in proportion to loudness. Results nd Discussion Metric structure. Figures 6 nd 7 present the fctoril plots for the monurl (right er) nd binurl presenttions, respectively. Both fmilies offunctions re linerly divergent, s they should be if they reflect biliner interction. They both pss the visul test of bilinerity obtined by spcing the stimuli in the horizontl xis ccording to the mrginl mens. Both fmilies of functions ppered s fn of stright lines. 3 To first pproximtion, then, these results imply tht the subjects did use simple multiplictive process when they estimted loudness. -.. l ll) 20 16 12 30 40 DECIBELS 50 60 70 SPL - MONAURAL Figure 6. Monurl temporl integrtion of noise. Sme s Figure 1, for wide-hnd noise bursts.
LOUDNESS SUMMATION FOR TONE AND NOISE 161 I-- l.jj 42 30 30 40 Figure 7. Binurl temporl integrtion ofnoise. Smes Figure 2, for wide-bnd noise bursts. 50 DECIBELS SPL - BINAURAL Loudness of wide-bnd noise s function of pressure. Figure 8 gives the monurl nd binurl loudness functions with respect to SPL, bsed on the mrginl mens of the respective response mtrices. The dt for both conditions pper somewht bow-shped, curvture tht hs been noted severl times before for noise (Mrks, 1980; Pollck, 1951; Schrf & Fishken, 1970). A striking chrcteristic of the binurl nd monurl functions, s shown in Figure 8, is the systemtic chnge in the number of decibels seprting them. The results of Irvin (1965), Mrks (1980), Reynolds nd S. S. Stevens (1960), Schrf (1968), Schrf nd Fishken (1970), nd recently, of Algom et l. (1988) showed similr chnge with level for noise stimuli. At low levels, the monurl noise hd to be bout 4 db greter thn the binurl noise to be judged s loud, but this difference incresed to bout 9 db, in the present set of short noise bursts, t levels round 70 db. If we grnt power functions to describe the growth of loudness (the exponents re.68 nd.60, respectively, for the binurl nd monurl dt; 1'2 =.96 nd.98, respectively), then the rtio of binurl to monurl loudness increses continuously with incresing SPL. By wy of contrst, the dt on pure tones (Experiment 1) show decibel difference tht remins roughly constnt t 7 db for the entire 30-70 db rnge. 4 More importnt to the present purpose thn the form of these prticulr psychophysicl functions is the demonstrtion tht binurl summtion of brief noise stimuli obeys exctly the sme rules tht govern binurl summtion of much longer noise stimuli. Tht these brief stimuli presumbly undergo concurrent process oftemporl integrtion does not seem to lter the course of binurl summtion in ny systemtic fshion. Both for long noises beyond the criticl durtion nd for brief 60 70 noises below the criticl durtion, binurl summtion is prtil t low SPLs, incresing to greter summtion t high SPLs. Different rules of interurl integrtion, then, pply to wide-bnd noises nd to nrrow-bnd signls, regrdless of durtion. Loudness of wide-bnd noise s function of durtion. Figure 9 presents the loudness functions for monurl nd binurl presenttions with durtion s the rgument. The fits to the power functions re good (r 2 =.989 for the monurl function nd.995 for the binurl function). There is only slight difference in slope (b), the binurl function being bit steeper (b =.62 nd.65 for the monurl nd binurl conditions, respectively). Figures 8 nd 9 seem to imply tht the growth of loudness with either incresing pressure or incresing durtion is greter for noises (present experiment) thn for pure tones (Experiment 1). It is not cler why the loudness functions for durtion, while following power lw, should differfor tones nd noises. A possible clue comes from the exmintion of the time-intensity trding functions for equl loudness derived in previous studies. Typiclly, tones yield shllower reciprocity functions thn do noises, with slope closer to -1.0 (Algom & Mrks, 1984; see lso Schrf, 1978), which implies greter role for durtion in noise. Ifwe tke the monurl nd binurl loudness functions for durtion to prllel one nother, n dditionl scle for loudness cn be derived. The verge horizontl seprtion between the functions in Figure 9 is bout.4 log L.u :<: Cl :::J 1.0 30 binurl monurl 40 50 DECIBELS 60 SPL.>.:>.:"/ L.u 0.4 -- / -J I-- -q: I-- L.u 0.8 <.:l -J. -0.4 f Figure 8. Binurl summtion ofthe loudness ofnoises s function ofsound-pressure level (SPL). Sme s Figure 3, for functions derived from the mrginl mens of the dt plotted in Figures 6 nd 7. 70
162 ALGOM, RUBIN, AND COHEN-RAZ LOG DURA TlON (ms) Figure 9. Binurl summtion of the loudness of noises s function of durtion. Sme s Figure 4, for functions derived from the mrginl mens of the dt plotted in Figures 6 nd 7. 1.6.>. <: t <> -..J //.:: tu f--,:;" 0.4.::/ i:: 1.0 0.8 0.6 0.4 0.2... bincurol mo.iourot../../ /. /. 0.2 Y 1.2 1.5 ::/ 0.2 <:)./ / -..J -0.8... / 30 40 50 60 70.. DECIBELS SPL - BINAURAL Figure 10. The growth of the loudness of noisebursts s function of stimulus mgnitude for six different durtions. The dt re those presented in Figure 7, plotted in double-logrithmic coordintes. units. This binurl gin mens tht 2.S-fold increse in the durtion of monurl noise burst is needed for it to sound eqully s loud s binurl burst of the sme SPL. Given n verge binurl-monurl loudness rtio of 1.88 (Tble 3), this yields loudness function which is bout the.69 power of durtion. Time-intensity trdeoff for noise. Power fits were ttempted to the judgments t ech durtion, seprtely for 2.1 2.4 2.7 the monurl nd binurl dt. Good only s first pproximtion (note the curvture or bowing in the shpe of the curves in the exmple provided in Figure 10), the fits seem, nevertheless, stisfctory for convenient summry (Tble 4). At ll durtions, the exponent of the binurl function is greter thn the exponent of the corresponding monurl function. The men difference is.066, quite consistent with the vlue [ difference of.08 (.68-.60) between binurl nd monurl listening] derived erlier on the bsis of the mrginl mens. The log-log plots of the loudness estimtes t the six durtions were intersected t severl rbitrry ordinte levels for both monurl nd binurl listening. Figure 11 plots one such set ofcorresponding pirs of pressure nd durtion, t both monurl nd binurl modes of presenttions, necessry to produce n equl-loudness judgment. There is fundmentl difference between tones nd noises in the wy they interct binurlly, nd, consequently, in their respective courses of temporl integrtion. The monurl nd binurl trding functions for tones were essentilly prllel, reflecting virtully identicl course of temporl integrtion for both listening conditions. This ws not so with noises: The reciprocity functions for monurl nd binurl listening re nonprllel, converging t the lower right. The binurl function hs slope of pproximtely -1.4, wheres the monurl function hs significntly steeper slope of round -2.0. Clerly, the integrtion of monurlly presented noise stimuli follows different time course thn does the integrtion of binurlly presented stimuli. The verticl seprtion between the monurl nd binurl functions decreses grdully from bout 12 db t the shortest du- Tble 3 Averge Binurl-to-Monurl Loudness-Judgment Rtios for Noisest Different Sound-Pressure Levels (SPLs) nd Durtions SPL Durtion (in msec) (in db) 16 32 64 128 256 512 Men 30 1.37 1.68 1.8 0.83 1.27 1.45 1.4 40 0.81 2.07 1.75 1.43 2.02 2.52 1.76 50 0.7 1.7 2.8 1.39 1.45 2.3 1.89 60 1.99 1.28 2.17 2.70 2.53 2.52 2.19 70 1.96 2.10 2.53 2.55 2.26 1.71 2.18 Men 1.56 1.76 2.21 1.78 1.9 1.75 1.88 Tble 4 Prmeters of the Psychophysicl Power Function for Loudness Reltive to Sound-Pressure Level t Six Different Durtions for Monurl nd Binurl Listening Durtion (in msec) 16 32 64 128 256 512 Men -1.89-1.45-1.32-1.05-1.12-0.7 Monurl b 0.68 0.56 0.56 0.56 0.66 0.56 0.60 r? 0.92 0.95 0.97 0.96 0.96 0.99-1.78-1.3-1.06-1.4-0.92-0.6 Note- = intercept, b = power-function exponent. Binurl b 0.72 0.6 0.58 0.76 0.68 0.64 0.66 r" 0.95 0.98 0.98 0.96 0.98 0.98
-.J :::,. 60 -.J Q:: ::::> 50 lj) lj) 0:: Q Cl <: ::::> () lj) 40 -. \.... \ -,.... :.. binurl mnur/ <: 128 256 512 30 '.. 16 32 64 DURA TlON ims) Figure 11. Equl-loudness contours for noise, giving the combintions of durtion, pressure, nd mode of listening (binurl vs. monurl) tht produced the sme subjective loudness. rtions to bout 4 db t durtion of.5 sec. These dt for noise, then, suggest nonconstnt binurl gin in decibels t the different stimulus durtions. Perhps the simplest wy to interpret these results is to relte them to the rther widely documented dt on the growth of loudness for noise. Regrdless of its form (prticulrly whether or not power function), the loudness of wide-bnd noise increses with incresing SPL more rpidly under binurl thn under monurl listening. Given tht binurl nd monurl loudness vries the sme wy s function of durtion (see Figure 9), the different rtes of growth with incresing sound pressure must result in different vlues of the time-intensity trdeoff, s Figure 11 clerly demonstrtes. The most importnt empiricl outcome of this experiment, then, is the different slopes demonstrted for the temporl integrtion of monurl nd binurl noise signls. This contrsts with the results obtined for tones (Experiment 1) nd for threshold-level noises (Bbkoff & Algom, 1976) collected under similr conditions. GENERAL DISCUSSION LOUDNESS SUMMATION FOR TONE AND NOISE 163 L = c.r', (1) When the sme dt re plotted in terms of stimulus energy (I), power fits re gin ble to describe the function reltionship (t lest to good first-order pproximtion): L = cl/. (2) Following Mrks (1974) nd J. C. Stevens nd Hll (1966), the reltionships given by Equtions 1 nd 2 cn be combined into single sttement tht includes the effects of both energy nd durtion. The generl formul for loudness below the criticl durtion, then, cn be written From Eqution 3, nother simple reltionship cn be secured, nmely, the combintions of energy nd durtion necessry to produce ny constnt level of loudness: nd (3) (4) where = dig. The reltionship expressed by Eqution 4 is, of course, Gmer's well-known formul for relting time nd energy, lredy given in the introduction. Of mjor interest here is the question of how the empiricl vlues, derived under the different experimentl conditions, mp onto the prmeters depicted by Equtions 1-4. In prticulr, do different vlues pply to monurl nd binurl modes oflistening? How does the spectrl distribution of sounds ffect the functionl reltionships under considertion? Given the model depicted by Eqution 3, the loudness equtions for monurl (m) nd binurl (b) listening, respectively, cn be written (5) For the ske of simplicity, we ssume tht the two ers re eqully sensitive, so tht single eqution suffices to describe monurl hering (cf. Mrks, 1978). Given these equtions for monurl nd binurl listening, binurl stimultion below the criticl durtion will show perfect binurl summtion t ll SPLs only ifdo = d..., go = g..., nd cjc... = 2. Given tht these re true, n immedite corollry shows tht the slopes ofthe time-intensity trding functions should be the sme for monurl nd binurl listening. Tht is, we expect prllel equlloudness contours, or tht o =... (Eqution 4). (6) Derivtion of Equl-Loudness Contours furtoofuremuycombmwm Despite some vribility, the dt clerly demonstrte the generl nture of temporl summtion for suprthreshold loudness: loudness increses with both incresing durtion nd incresing intensity (then, beyond the criticl durtion, it becomes reltively independent ofdurtion). Thus, t short durtions, the dt imply tht loudness (L) grows s power function of durtion (d): Bmurl nd Temporl futegrtion for Tones Thedt for pure tones (Experiment 1) stisfy the equlexponent, equl reciprocity-slope requirements but they fll short of full binurl summtion in tht co/c... < 2. Binurl summtion is constnt, yet is only prtil t bout 7 db. The verge vlues of d nd g (reltive to sound energy) were.29 nd.20, respectively. Tht is, d is pproximtely 1.5 times lrger thn g. Eqution 3 thus cn be specified s
164 ALGOM, RUBIN, AND COHEN-RAZ or, if we tke the correct vlue of g to be.3 (the sone function), it cn be rewritten nd (7) Idelly, the equl-loudness contours should hve slope of round 1.5 (=-.29/.2 or.4351.37). The slope derived on the bsis of the trdeofffunctions turned out to be bout 1.7. Thus, Eqution 4 cn be rewritten It1.5 = C, (8) (9) implying tht the exponent for the psychophysicl power function should be 1.5 times lrger for durtion thn for sound energy. More importnt to the present purpose thn the prticulr numericl vlues is the demonstrtion tht, for pure tones, the temporl integrtion ofmonurlly nd binurlly presented stimuli follow the sme course. Consequently, binurl summtion ofshort sinusoidl signls does not depend on their durtion. (The binurl gin ws constnt cross the different-durtion stimuli.) The lck of binurl X temporl interction in loudness implies tht neither process exerts ny systemtic influence on the other. Binurl summtion of short signls, the loudness of which is ffected by durtion, obeys the sme rule of summtion tht governs the binurl summtion oflonger signls, the loudness ofwhich is independent ofdurtion. Binurl nd Temporl Integrtion for Noises For noises, the results re more complicted. The prmeters differ for monurl nd binurl hering such tht B» "* gm nd, of course, cjc; is not constnt. Interestingly, however, db = d m, which mens tht the psychophysicl function for durtion is the sme for monurl nd binurl listening. Given tht db = d; nd gb "* gm, it follows tht b "* m. Indeed, the timeintensity trding functions (see Eqution 4) differ for monurl nd binurl listening. They cn be respectively specified (10) (11) where C, is set to equl C m Clerly, temporl integrtion of noises bursts differs for monurlly nd binurlly presented stimuli. For both modes of stimultion, time plys more prominent role thn does sound energy, but the monurl trding function hs much steeper slope. As result, binurl summtion decreses s durtion increses. For noise bursts, then, there is n interction between temporl nd binurl integrtion. Temporl Summtion versus Binurl Summtion Does the obtined interction imply n uthentic influence of one integrtion process on the other? Not necessrily. For long-durtion wide-bnd noise stimuli, lying well beyond the limit for temporl integrtion, binurl summtion hs lredy been shown to increse with incresing level (e.g., Irvin, 1965; Mrks, 1980; Reynolds & S. S. Stevens, 1960; Schrf & Fishken, 1970). Given the time-intensity trdeoff for constnt loudness, shorter stimuli must be more energetic. And, to be sure, binurl summtion is greter for these stimuli thn for longer (hence softer) ones. Tht different courses of temporl summtion pply to monurl nd binurl listening is n importnt finding first reported here. However, it bsiclly reflects the different rtes of growth for monurl nd binurl loudness (of wide-bnd noise), rther thn ny genuine influence oftemporl integrtion on binurl summtion. This lck ofmutul influence becomes, therefore, fct to be fitted into complete theory ofloudness processing. 5 Cognitive Algebr of the Processing of Temporlly Integrted Loudness A unique nd novel feture of the present study is the explicit estblishment of the underlying metric structure for temporl summtion. Trditionl mesurement solutions (cf. Algom & Bbkoff, 1984; J. C. Stevens, 1976) ssumed tht (1) subjects were in fct judging loudness, nd (2) their numericl responses provided vlid mesure of loudness. Both ssumptions re risky nd need empiricl justifiction. This is prticulrly true of uditory temporl integrtion, in which mjor theoreticl effort is imed t reconciling the liner (or close to liner) energy integrtion produced by the system with the eqully demonstrble fct of nonliner reltionship between sound intensity nd loudness (e.g., the sone scle; Zwislocki, 1969; see lso the review oftheories by Algom & Bbkoff, 1984). Consequently, it is not lwys prim fcie cler which set ofvlues to cll loudness (cf. Mrks, 1979b). However, even if we grnt tht the output from suprliminl temporl processing does correspond to loudness, the question still remins whether the puttive numericl rtios represent ctul rtios ofloudness. Hence, treting the subjects' mgnitude estimtes s the true scle vlues to be integrted into the prescribed psychologicl eqution (such s the clssic multiplictive model suggested for temporl integrtion) my be mbiguous or even misleding. It is the opinionof the present uthors tht filure to vlidte the scle vlues under concern stisfctorily hs dversely ffected the work on temporl summtion. The logic behind the present nlysis owes much to Anderson's (1981, 1982) theory of functionl mesurement. In this nlysis, we rgue for the explicit determintion of the integrtion function tht combines seprte stimulus components into unitry response. Besides providing the explicit "cognitive lgebr" used when pe0 ple judge the loudness ofdifferently shped suprliminl signls (i.e., estblishing Lite underlying metric structure for temporl summtion), the multiplictive model estblished here plys vitl role in the derivtion of the psychophysicl functions s well. Indeed, this model provides the needed criterion to vlidte the overt numericl estimtes (see Anderson, 1981, for detils of the relevnt theorems).
LOUDNESS SUMMATION FOR TONE AND NOISE 165 REFERENCES ALGOM, D. (1979). Auditory temporl integrtion: Detection versus discrimintion. Unpublished doctorl disserttion. Br-nn University, Rmt Gn, Isrel. ALGOM, D., ADAM, R., & COHEN-RAZ, L. (1988). Binurl summtion nd lterliztion of trnsients: A combined nlysis. Journl of the Acousticl Society ofameric, 84, 1302-1315. ALGOM, D., & BABKOFF, H. (1978). Discrimintion of equl-energy, eqully detectble uditory stimuli. Psychologicl Reserch, 40, 149-157. ALGOM, D., & BABKOFF, H. (1984). Auditory temporl integrtion of threshold: Theories nd some implictions of current reserch. In W. D. Neff (Ed.), Contributions to sensory physiology (Vol. 8, pp. 131-159). New York: Acdemic Press. ALGOM, D., BABKOFF, H., & BEN-URIAH, Y. (1980). Temporl integrtion nd discrimintionofeqully detectble equl-energy stimuli: The effect of frequency. Psychologicl Reserch, 42, 305-318. ALGOM, D., & COHEN-RAz, L. (1984). Visul velocity input-output functions: The integrtion ofdistnce nd durtion onto subjective velocity. Journl ofexperimentl Psychology: Humn Perception & Performnce, 10, 486-501. ALGOM, D., & MARKS, L. E. (1984). Individul differences in loudness processing nd loudness scles. Journl ofexperimentl Psychology: Generl, 113, 571-593. ANDERSON, N. H. (1974). Algebric models in perception. In E. C. Crterette & M. P. Friedmn (Eds.), Hndbook ofperception: Vol. 2. Psychophysicl judgment nd mesurement (pp. 215-298). New York: Acdemic Press. ANDERSON, N. H. (1981). Foundtions ofinformjion integrtion theory. New York: Acdemic Press. ANDERSON, N. H. (1982). Methods ofinformtion integrtion theory. New York: Acdemic Press. BABKOFF, H., & ALGOM (GoMBOSH), D. (1976). Monurl nd binurl temporl integrtion of noise bursts. Psychologicl Reserch, 39, 137-145. BRINDLEY, G. S. (1960). Physiologyofthe retin nd visul pthwy. London: Arnold. CAUSEE, R., & CHAVASSE, P. (1942). Differences entreie seuil de l'udition binuriculire et Ie seuil monuriculire en function de l frequence. Comptes Rendus de L Societe de Biologie, 86, 301-302. CHOCHOLLE, R. (1962). Les effects des interctions interurles dns I'udition. Journl de Psychologie Normle et Pthologique, 59, 255-282. EKMAN, G. (1956). Discriminl sensitivity on the subjective continuum. Act Psychologic, 12, 233-243. GARNER, W. R. (1947). Effect offrequency spectrum on temporl integrtion in the er. Journl ofthe Acousticl Society ofameric, 19, 808-815. GARNER, W. R., & MILLER, G. A. (1947). The msked threshold of pure tones s function of durtion. Journl ofexperimentl Psychology, 37, 293-303. HELLMAN, R. P., & ZWISLOCKI, J. J. (1963). Monurl loudness function t 1000 cps nd interurl summtion. Journl ofthe Acousticl Society ofameric, 35, 856-865. HUGHES, J. W. (1938). The monurl threshold: Effect of sublirninl contrlterl stimulus. Proceedings ofthe Royl Society, London, 124b, 406-420. IRWIN, R. J. (1965). Binurl summtion of thenn! noises of equl nd unequl power in ech er. Americn Journl ofpsychology, 78, 57-65. JANKOVIC, I. N., & CROSS, D. V. (1977, April). On the binurlddi tivity ofloudness. Pper presented t the meeting ofthe Estern Psychologicl Assocition, Boston. LEVELT, W. J. M., RIEMERSMA, J. B., & BUNT,A. A. (1972). Binurl dditivity of loudness. British Journl ofmthemticl & Sttisticl Psychology, 25, 51-68. MARKS, L. E. (1974). Sensory processes: Thenew psychophysics. New York: Acdemic Press. MARKS, L. E. (1978). Binurl summtion of the loudnessofpure tones. Journl ofthe Acousticl Society ofameric, 64, 107-113. MARKS, L. E. (l979). Sensory nd cognitive fctors in judgments of loudness. Journl ofexperimentl Psychology: Humn Perception & Performnce, 5, 426-443. MARKS, L. E. (l979b). A theory ofloudness nd loudness judgments. Psychologicl Review, 86, 256-285. MARKS, L. E. (1980). Binurl summtion ofloudness: Noise nd twotone complexes. Perception & Psychophysics, 27, 489-498. MARKS, L. E. (1987). Binurl versus monurl loudness: Supersummtion oftone prtilly msked by noise. Journl ofthe Acousticl Society ofameric, 81, 122-128. McFADDEN, D. (1975). Durtion-intensity reciprocity for equl loudness. Journl ofthe Acousticl Society ofameric, 57, 702-704. MILLER,C. A. (1948). Perception ofshort bursts ofnoise. Journl of the Acousticl Society ofameric, 20, 160-170. PENNER, M. J. (1978). A power lw trnsformtion resulting in clss of short-term integrtors tht produce time-intensity trdes for noise bursts. Journl ofthe Acousticl Society ofameric, 63, 195-201. POLLACK, I. (1951). On the mesurement ofthe loudness of white noise. Journl ofthe Acousticl Society ofameric, 23, 654-657. REYNOLDS, G. S., & STEVENS, S. S. (1960). Binurl summtion of loudness. Journlofthe Acousticl Society ofameric, 32, 1337-1344. ScHARF, B. (1968). Binurl loudness summtion s function ofbnd width. In Y. Kohsi (Ed.), Reports ofthe 6th Interntionl Congress on Acoustics (Vol. I, pp. 25-28). Tokyo: Mrzen A-3-5. ScHARF, B. (1969). Dichotic summtion of loudness. Journl of the Acousticl Society ofameric, 45, 1193-1205. ScHARF, B. (1978). Loudness. In E. C. Crterette & M. P. Friedmn (Eds.), Hndbook ofperception: Vol. 4. Hering (pp. 187-242). New York: Acdemic Press. ScHARF, B., & FISHKEN, D. (1970). Binurl summtion of loudness: Reconsidered. Journl of Experimentl Psychology, 86, 374-379. SHAW,W. A., NEWMAN, E. G., & HIRSH, I. J. (1947). The difference between monurl nd binurl thresholds. Journl ofexperimentl Psychology, 37, 229-242. SMALL, A. M., JR., BRANDT, J. R., & Cox, P. C. (1962). Loudness s function of signl durtion. Journl ofthe Acousticl Society of Americ, 34, 513-514. STEVENS, J. C. (1976). Equl-senstion functions generted by the method of mgnitude estimtion. Journl ofthe Acousticl Society ofameric, 59, 473-474. STEVENS, J. C., & HALL, J. W. (1966). Brightness nd loudness s function of stimulus durtion. Perception & Psychophysics, 1, 319-327. STEVENS, S. S. (1956). The direct estimtion of sensory mgnitudesloudness. Americn Journl ofpsychology, 69, 1-15. STEVENS, S. S., & GREENBAUM, H. B. (1966). Regression effect in psychophysicl judgment. Perception & Psychophysics, I, 439-446. WATSON, C. S., & GENGEL, R. W. (1969). Signl durtion nd signl frequency in reltion to uditory sensitivity. Journl ofthe Acousticl Society ofameric, 46, 989-997. ZWISLOCKI, J. J. (1969). Temporl summtion of loudness: An nlysis. Journl ofthe Acousticl Society ofameric, 46, 431-441. NOTES I. It is often possible to test the model nlyticlly by pplying nlysis ofvrince (ANOVA) to the dt (Anderson, 1974, 1982). Legitimte ppliction of ANOVA, however, requires tht the dt hve resonbly uniform vrince, condition tht typiclly does not hold with mgnitude estimtes. By contrst, functionl dependencies between the mens nd the stndrd devitions of mgnitude estimtes, violting ssumptions of ANOVA, re often encountered in psychologicl reserch (cf. Algom & Cohen-Rz, 1984; Mrks, 1978, 1980). As generl rule, the stndrd devitions of these estimtes increse nerly in proportion to the mens of the estimtes- reltionship tht is sometimes clled Ekmn's lw (Ekmn, 1956). This phenomenon chrcterized ll ofthe present dt sets. Nonetheless, we ttempted n ppliction ofanova to the binurl dt (Figure 2)-the set coming closest to displying resonbly (though not fully) uniform vrince. The results confirmed the conclusions drwn from the grphic disply. There ws highly significnt pressure x durtion interction [F(20,18O) = 2.60,
166 ALGOM, RUBIN, AND COHEN-RAZ p <.0 Il, the better prt of which (78%) ppered in the biliner component. The biliner component ws highly significnt [F(I,18O) = 13.9, p <.Ol], wheres the reminder of the interction ws insignificnt [F(l9,18O) = 1.89,p >.05l. A similr ANOVApplied to the monurl dt yielded nonsignificnt interction [F(l2,180) = 1.11, P >.05l. As noted erlier, however, lthough strightforwrd ppliction of ANOVA is questionble, the visul ppernce of the dt bers out the predictions of the multiplictive model quite convincingly. 2. In fct, three simple possibilitiesexist: (1) Loudness is ddedlinerly cross the two ers, but this complete binurl summtion corresponds to 7-dB increse in SPL; (2) summtion is perfect cross the two ers, but the vlues of loudness tht re summed in the binurl system differ from sones nd re rther conunensurte with the empiriclly derived power-function exponents of round.4; or (3) loudness should be counted in sones (i.e., the present scle pproximtes the sone function), nd the 7-dB binurl gin obtined here indictes less thncomplete loudness summtion. One wy to ssess these lterntives is to derive their implictions fully nd them compre them with the empiriclly obtined vlues. Thus, becuse liner summtion mens tht binurl loudness is twice monurl loudness, binurl gin (N) entils corresponding power-function exponent, which equls log2/(n/20). A 7-dB binurl gin-tken to correspond to complete summtion-implies n exponent of.86. This vlue is not only incomptible with the empiriclly derived exponents (t round.4) nd the sone scle, but lso with the gret bulk of loudness exponents reported in the literture (cf. Mrks, 1974). Conversely, given psychophysicl scle for loudness which is.4 power of pressure nd complete binurl summtion, one cn clculte the implied binurl gin (the difference in decibels between eqully loud monurl nd binurl stimuli). The bove ssumptions yield gin of round 15 db, vlue tht is clerly t odds bothwith the empiriclly obtined rtio of7 db nd with previously obtined estimtes. We must, perforce, reject the first two lterntives bove s possible explntions of the present dt. 3. The pproprite ANOVAs yielded overll interction terms tht were highly significnt [F(20,14{» = 1.88 for the monurl dt nd 1.98 for the binurl dt, p <.01 in both cses]. As noted bove, however, these re hrdly tests of bilinerity becuse mgnitude estimtion tends to yield nonuniform vrinces. Most importnt, however, the divergent biliner interctions re clerly evident upon visul inspection of the results. 4. Tht the binurl-to-monurl loudness rtio grows lrger with incresing SPL cn be glenedfrom inspection ofthe rnrgini mens vis-vis intensity (the lst column in Tble 3). A log-log plot of this rtio s function of SPL yields stright line (fitted by lest squres) with slope of.096. It ppers, therefore, tht the binurl-to-monurlloudness rtio increses s power function of SPL with n exponentof.096. Recll tht the difference in exponents between the binurl nd the monurl loudness functions (reltive to SPL) comes quite close to this vlue. Thus, there is good greement between thesetwo wys of looking t the binurl summtion of the loudness of noises (cf. Reynolds & S. S. Stevens, 1960). By contrst, no obvious trend in the binurl-tomonurl loudness rtios is evident cross the different durtions. 5. An importnt quntittive property of the dt deserves mention. Both for tones nd for noises, the slopes () of the reciprocity functions re substntilly different from wht is usully found for threshold-level stimuli. For both types of signls, given chnge in intensity could be offset by smller reltive chnge in durtion to mintin constnt loudness (supersummtion). Yet in order to mintin just-detectble senstion of loudness, givenchnge in intensity must be offsetby either n eqully lrge chnge in durtion (complete summtion, tones) or lrger reltive chnge in durtion (prtil summtion, noises) (Algom & Bbkoff, 1984; Bbkoff& Algom, 1976; Mrks, 1974). Why should the nture ofthe time-intensity trdeoff differ for threshold nd higher levels? It is tempting to consider the possibility tht the difference is relted to the synthetic versus the nlytic chrcteristics ofthe respective processes. Thus, it my be rgued tht equl-energy, but differently pckged (with respect to durtion nd intensity), sounds re eqully detectble becuse they pper perceptully equl. At superthreshold levels, on the other hnd, lthough it is possible to mintin equl loudness, the different time-intensity configurtions cn be redily nlyzed. Brindley (1960) hs dubbed these two kinds of opertions s Clss A nd Clss B, respectively. Appeling s this explntion might seem, it certinly is incorrect. We (Algom, 1979; Algom & Bbkoff, 1978; Algom, Bbkoff, & Ben-Urih, 1980) hve shown tht even t threshold, equl-energy, eqully detectble stimuli re nevertheless clerly distinguishble from one nother. Rther, the present dt point towrd the possibility tht the vrition in the mgnitude of the fctor is cused by differences in intensity processing between threshold nd higher level stimuli (but scling ofdurtion remins reltively constnt). Be tht s it my, this gin is fct to be incorported into generl theory of loudness or uditory integrtion. (Mnuscript received August 9, 1988; revision ccepted for publiction Jnury 23, 1989.) Announcement Chnge in Editorship Psychobiology The Publictions Committee ofthe Psychonomic Society tke plesure in nnouncing tht Pul E. Gold, University of Virgini, hs ccepted the editorship ofpsychobiology, beginning in 1990.