The relative role of beats and combination tones in determining theshapes of masking patterns: II. Hearing-impaired listeners

Jose¤ I. Alca¤ntara, Brian C.J. Moore �

Department of Experimental Psychology, University of Cambridge, Downing Street, Cambridge CB2 3EB, UK

Received 4 June 2001; accepted 4 December 2001

Abstract

Masking patterns were measured for hearing-impaired subjects with varying degrees of hearing loss. In one set of conditions,three subjects were tested using narrowband noise (‘noise’) and sinusoidal (‘tone’) maskers and narrowband noise signals. Themaskers had centre frequencies of 0.25, 0.5, 1.0 and 4.0 kHz and levels of 60, 80 and 100 dB SPL. Masking patterns for both thenoise and tone maskers showed irregularities (‘dips’), especially for signal frequencies up to 500 Hz above the masker frequency.The irregularities occurred for all masker levels and for all subjects for at least one masker frequency and they occurred for arelatively constant range of masker-signal frequency separations, suggesting that they were the result of beat detection. In anotherset of conditions, masking patterns were measured using two subjects, for a 2.0-kHz tone masker with a level of 100 dB SPL andtone and noise signals. For the tone masker alone (baseline condition), the masking patterns again exhibited prominent dips above,and sometimes below, the masker frequency. The addition of a lowpass noise to the masker, intended to mask combination tones,had little effect for one subject. For the other subject, who had near-normal absolute thresholds at low frequencies, the noiseelevated thresholds for masker-signal frequency separations between 500 and 1500 Hz. For this subject, an extra tone with afrequency equal to the masker-signal frequency separation, added in place of the lowpass noise, had a very similar effect to thatproduced by the lowpass noise, suggesting that he was detecting a simple difference tone in the baseline condition. The addition ofa pair of high-frequency tones (MDI tones ^ intended to reduce the detectability of beats) to the masker elevated thresholds forsignal frequencies from 1500 to 2500 Hz for one subject and from 1500 to 3500 Hz for another subject. The addition of lowpassnoise and MDI tones to the masker produced masking patterns very similar to those observed when the MDI tones alone wereadded to the masker. Overall, the results suggest that the irregularities in the masking patterns were caused mainly by the detectionof beats and not by the detection of combination tones. = 2002 Elsevier Science B.V. All rights reserved.

Key words: Masking pattern; Beat; Combination tone; Hearing-impaired

1. Introduction

A masking pattern is obtained by measuring thethreshold for detecting a narrowband signal as a func-tion of the signal frequency, in the presence of a ¢xedmasker. It is thought to represent, at least crudely, theexcitation pattern evoked by the masker (Wegel and

Lane, 1924; Moore and Glasberg, 1983). Masking pat-terns have been measured extensively for normallyhearing subjects (Wegel and Lane, 1924; Egan andHake, 1950; Ehmer, 1959; Greenwood, 1971; Zwickerand Fastl, 1990; Moore et al., 1998; Alca¤ntara et al.,2000) but less data are available for hearing-impairedsubjects, and most studies have used only a restrictedrange of masker and signal frequencies (Leshowitz andLindstrom, 1977; Florentine et al., 1980; Tyler, 1986;Murnane and Turner, 1991; Nelson and Schroder,1996, 1997). The general aim of this study was to char-acterise the shapes of masking patterns obtained usingsubjects with cochlear hearing impairment and to ex-plore the factors in£uencing the shapes of the maskingpatterns.

0378-5955 / 02 / $ ^ see front matter = 2002 Elsevier Science B.V. All rights reserved.PII: S 0 3 7 8 - 5 9 5 5 ( 0 2 ) 0 0 2 9 1 - 5

* Corresponding author.Tel. : +44 (1223) 333574; Fax: +44 (1223) 333564.E-mail address: bcjm@cus.cam.ac.uk (B.C.J. Moore).

Abbreviations: ERB, equivalent rectangular bandwidth of theauditory ¢lter; MDI, modulation detection interference; PTC,psychophysical tuning curve; TDT, Tucker-Davis Technologies

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Masking patterns show a variety of complex non-monotonic features that cannot readily be explainedin terms of the distribution of cochlear activity (Green-wood, 1971; Zwicker and Fastl, 1990; Moore et al.,1998; Alca¤ntara et al., 2000). These may include‘dips’, secondary peaks, and ‘plateaus’. Also there aresystematic di¡erences between the shapes of maskingpatterns measured using narrowband noise and usingsinusoidal maskers and/or signals. It is generally ac-cepted that the two main cues responsible for thesee¡ects are £uctuations in level (beats) and combinationtones, produced by the interaction of the masker andthe signal. Opinions di¡er as to the relative importanceof these two types of cue in determining the shapes ofmasking patterns.In a recent study using normal-hearing subjects, Al-

ca¤ntara et al. (2000) studied the masking patterns pro-duced by a 2.0-kHz sinusoidal masker, for that maskeralone and when a variety of other components wereadded to the masker. These included a lowpass noiseto mask combination tones and a pair of high-fre-quency tones, with the same frequency separation asthe 2.0-kHz masker and the signal, to interfere withthe detection of beats (Yost et al., 1989).The results suggested that beats strongly in£uenced

the masking patterns for masker-signal frequency sep-arations up to 300 Hz. Combination tones, in con-trast, in£uenced the masking patterns for masker-sig-nal frequency separations between 300 and 1000 Hz.When combination tones were masked, beats in£u-enced signal thresholds for masker-signal frequencyseparations up to 700 Hz. The relative importanceof beats and combination tones in determining theshapes of masking patterns for hearing-impaired sub-jects is as yet unclear. However, psychoacousticalstudies suggest that combination tones of the type2f13f2 are reduced in level or absent when the primarytones fall in a region of hearing loss (Leshowitz andLindstrom, 1977; Smoorenburg, 1972). Also, the levelof distortion product otoacoustic emissions in hearing-impaired subjects is reduced compared to those mea-sured in normal-hearing subjects (Gorga et al., 1993).On the basis of these ¢ndings, we would expect thatcombination tones would have little or no in£uence onthe shapes of masking patterns for hearing-impairedsubjects. Thus, irregularities in the patterns should beascribed mainly to the detection of beats (Carney andNelson, 1983). This prediction was tested in the currentstudy.The stimuli used in the present study are very similar

to those used in earlier studies with normally hearingsubjects (Moore et al., 1998; Alca¤ntara et al., 2000).The reader is referred to those studies for ‘reference’data on normally hearing subjects.

2. Materials and methods

2.1. Subjects

Six subjects with bilateral symmetrical sensorineuralhearing loss (air-bone gaps95 dB) took part in thestudy, although none participated in all seven condi-tions. Their ages and assumed aetiologies of the hearinglosses are shown in Table 1. They were tested usingonly one ear; this was the ear that they used for thetelephone. All had previous experience of psychoacous-tical masking experiments. The subjects received prac-tice until their performance appeared stable. This tookonly 2^3 h. No systematic changes in performance oc-curred during the course of the experiment. All werepaid for their involvement in the study. Their absolutethresholds in dB SPL are displayed in the ¢gures asdashed lines.

2.2. Procedure

The masker was presented in three observation inter-vals and the signal was gated on synchronously with themasker in one of those intervals, chosen randomly fromtrial to trial. The subject indicated, by pressing one ofthree buttons, the interval thought to contain the signal.Lights on the response box provided immediate feed-back as to the correctness of the response. A run wasstarted with the signal at a level about 20 dB above theexpected threshold value, as determined in practice tri-als. After three successive correct responses the signallevel was decreased, while after a single incorrect re-sponse it was increased. This procedure tracks the sig-nal level corresponding to 79.4% correct (Levitt, 1971).The initial step size was 5 dB. After four reversals thestep size was decreased to 2 dB and a further eightreversals were obtained. The threshold was estimatedas the mean of the signal levels at the last eight rever-sals. Runs were discarded when the standard deviationof the levels at the last eight reversals exceeded 5 dB.Initially, two threshold estimates were obtained for eachcondition. If the two estimates di¡ered by more than2 dB, at least one additional estimate was obtained andthe two closest estimates were averaged. Absolutethresholds were estimated using a similar procedure.

2.3. Stimuli

The main masker was either a sinusoid or an 80-Hzwide band of noise. For brevity, these will be referredto as the ‘tone’ and ‘noise’ maskers. The maskers werepresented at a level of 100, 80 or 60 dB SPL and werecentred at either 0.25, 0.5, 1.0, 2.0 or 4.0 kHz. Thesignal was also either a sinusoid or an 80-Hz wide

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band of noise (‘tone’ and ‘noise’ signals). The startingphase of the tone masker was 0‡ and that of the tonesignal was 90‡. Hence, when the tone signal and thetone masker had the same frequency, the powers ofthe signal and masker added. We discuss later the in-£uence of this choice of phase on the outcome. Thethree masker bursts each had a steady state durationof 200 ms, and 10-ms raised-cosine rise/fall times. Theinter-stimulus interval was 500 ms. The signal was gatedsynchronously with one of the masker bursts, and wasalso 200 ms in duration.All stimuli were generated digitally using a Tucker-

Davis Technologies (TDT) System II, controlled by aPC. The noise signals were generated by adding sinus-oids spaced at 5-Hz intervals, with equal componentamplitudes and phases drawn randomly from a uniformdistribution in the range 0^360‡; this gives a good ap-proximation to Gaussian noise (Hartmann, 1987). Adi¡erent randomly generated noise was used for everystimulus. When both the masker and signal were noisewith the same centre frequency, independent samples ofnoise were used for the signal and masker. Unlike trueGaussian noise, the overall energy of the noise signalsdid not vary signi¢cantly from stimulus to stimulus.The spectral slopes of the noise bands were essentiallyin¢nite. The sampling rate was 25 kHz and stimuli wereconverted to analogue form using two channels of aTDT DD1; one for the signal and one for the masker.The levels of the signal and masker were controlled in-dependently by two TDT PA4 programmable attenua-tors. The signal and masker were subsequently mixed(TDT SM3) before being passed to the headphone bu¡-er (TDT HB6), a ¢nal manual attenuator (Hat¢eld2125) and one earpiece of a Sennheiser HD414 600 6headphone.Sound levels are speci¢ed as levels close to the ear-

drum. The calibration was based on average measure-ments for three subjects (not those of the presentstudy), using a Rastronics Portarem 2000 system. Theprobe microphone was positioned within 4 mm of theeardrum as recommended by the manufacturer, usingthe on-screen display to monitor standing waves in theear canal and to place the valley in the frequency re-sponse curve above 8.0 kHz (Siegel, 1994). For a ¢xedinput voltage, the standard deviation of the sound level

across subjects was typically about 1 dB for frequenciesup to 1.0 kHz, about 2 dB for frequencies from 2.0 to6.0 kHz, and about 3 dB from 6.0 to 8.0 kHz.Subjects were tested in an IAC double-walled sound-

attenuating chamber. To check that the results wouldnot be unduly in£uenced by distortion products gener-ated in the earphones, measurements were made of theearphone output using a Bru«el and KjTr 4153 arti¢cialear, ¢tted with a Bru«el and KjTr 4134 microphone,connected to a Hewlett Packard 35670A dynamic signalanalyser. For a sinusoidal input, harmonic distortionoccurred mainly for the odd harmonics, and all har-monics had levels at least 62 dB down from the levelof the primary tone. We also checked for intermodula-tion distortion products, especially of the type 2f13f2.These were at least 82 dB lower in level than the moreintense of the two primary tones. Simple di¡erencetones were at least 78 dB lower in level than the pri-mary tones.

3. Results

3.1. Condition 1: masking patterns for a noise or tonemasker, for di¡erent masker frequencies, usinga noise signal

In condition 1, we used a noise or tone masker and anoise signal (our previous results with normally hearingsubjects indicated that similar results were obtained us-ing tone and noise signals, except for the special casewhen the signal frequency equaled the masker fre-quency (Moore et al., 1998)).The use of noise or tone maskers was intended to

allow a dissociation of the e¡ects of beats and combi-nation products in determining the shape of the mask-ing patterns; beats should be more salient for the tonemasker than for the noise masker, as the inherent am-plitude £uctuations in the noise masker should make itmore di⁄cult to detect the beats. The e¡ect of maskercentre frequency was also intended to allow this disso-ciation. The range of masker-signal frequency separa-tions over which beats in£uence the masking patternshape should be no more than about 700 Hz (Alca¤ntaraet al., 2000). Also the frequency range over which beatsplay a role should not vary with masker frequency, asthe beat rate depends on the absolute value of themasker-signal frequency separation. In contrast, the fre-quency region over which combination tones might bedetectable should depend on the masker-signal fre-quency ratio (Goldstein, 1967; Smoorenburg, 1972).Fig. 1 shows the masking patterns for subjects HC

(top) and PG (bottom), for noise (open symbols) andtone (¢lled symbols) maskers and noise signals. Forsubject HC, the three masker frequencies tested were

Table 1Ages and aetiologies of the subjects

Subject Age Aetiology

HC 65 UnknownPG 62 Me¤nie're’sKS 72 Noise-inducedSN 45 GeneticET 78 Noise-inducedDT 74 Noise-induced

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0.25 kHz (circles, left), 1.0 kHz (squares, middle) and4.0 kHz (diamonds, right). Due to subject PG’s highabsolute thresholds at 250 Hz, it was not possible touse this frequency; therefore masker frequencies of 0.5(circles), 1.0 (squares) and 4.0 kHz (diamonds) wereused. The masker level was 100 dB SPL for all maskerfrequencies except 250 Hz, in which case the level was95 dB SPL; it was not possible to test using a maskerlevel of 100 dB SPL at 250 Hz due to output limitationsof the equipment used. All thresholds are expressed indB SPL and plotted against signal frequency, which isscaled in ERB units, where ERB stands for the equiv-alent rectangular bandwidth of the auditory ¢lter (Glas-berg and Moore, 1990). The corresponding frequency inkHz is shown at the top of each panel. The equationrelating ERB number to frequency is:

ERB number ¼ 21:4 logð4:37F þ 1Þ ð1Þ

where F is the frequency in kHz. The ERB scale ap-proximates a logarithmic scale for frequencies above 1.0kHz. Note that this scale is based on average ERBvalues for normally hearing listeners ; it does not re£ectthe ERB values for the hearing-impaired subjects testedhere. For normally hearing people, masking patternshave approximately the same shape, regardless ofmasker frequency, when plotted on a ERB scale(Moore et al., 1998).Consider ¢rst the results for the on-frequency signal

for the noise masker (open symbols). The only detec-tion cue for this condition is the change in overall levelproduced by adding the signal to the masker (Bos andde Boer, 1966). Consistent with this, the noise signallevels at the peaks of the masking patterns were closeto the overall masker levels. Averaged across the threecentre frequencies used, the signal level at threshold was0.03 dB above and 1.1 dB below the levels of themaskers, for subjects HC and PG, respectively. Forthe 0.25-kHz noise masker, thresholds tended to de-crease fairly smoothly with increasing masker-signal fre-quency separation. However, the masking patterns forboth subjects showed distinct irregularities for the 1-and 4-kHz maskers. These took the form of ‘dips’,mainly on the high-frequency sides of the masking pat-terns, for signal frequencies within 500 Hz of themasker frequency. These are similar to the dips foundfor normal-hearing listeners using a noise masker andnoise signal (Moore et al., 1998). The dips, on both thelow- and high-frequency sides of the masking patterns,occurred at roughly constant masker-signal frequencyseparations for the di¡erent masker frequencies, sug-gesting that they re£ect the detection of irregular beatsand not combination tones.We turn now to the masking patterns obtained using

the tone masker (¢lled symbols). The peaks of themasking patterns were much lower in level than forthe noise masker. For both subjects, the signal tomasker ratio at threshold for the on-frequency signal,

Fig. 1. Masking patterns for subjects HC (top) and PG (bottom) for 250-Hz (left), 1-kHz (middle) and 4-kHz (right) noise (open symbols) andtone (¢lled symbols) maskers presented at 100 dB SPL. Signal thresholds in dB SPL are plotted against signal frequency, expressed as ERBnumber (bottom scale) and kHz (top scale). Absolute thresholds are shown by the dashed lines. Error bars show W1 S.D. Error bars are omit-ted when they would be smaller than the symbol used to represent a given point.

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averaged across masker frequency, was about 318 to319 dB. These values are comparable to those foundusing normal-hearing subjects under similar conditions(Hellman, 1972; Hall, 1997) and they probably re£ectthe detection of within-interval £uctuations in level pro-duced by adding the noise signal to the tone masker.For PG at all masker frequencies, and HC at 1.0 and

4.0 kHz, the masking patterns showed dips when thesignal frequency was close to the masker frequency.These dips, which occurred both above and below themasker frequency, presumably re£ect the detection ofirregular beats. The very low signal thresholds for sig-nal frequencies close to the masker frequency indicatethat both subjects were very sensitive to this cue. Forsignal frequencies within W 100 Hz of the masker fre-quency, thresholds were around 75 dB SPL, whichmeans that the beat depth was approximately 1.0 dB(mean peak to valley ratio).Normal-hearing subjects would probably not detect

beats with 1-dB depth if tested at the same sensationlevel, but they would if tested at the same absolute level(Riesz, 1928). The relatively good performance of ourhearing-impaired subjects may re£ect the in£uence ofloudness recruitment, which can lead to better thannormal intensity discrimination for signals at low sen-sation levels (Jerger et al., 1959; Buus et al., 1982a,b;Schroder et al., 1994).For subject HC, the 0.25-kHz tone masker produced

more masking (W4 dB) than the noise masker for sig-nal frequencies more than one octave above the maskerfrequency. A similar ¢nding was reported by Moore etal. (1998) for normal-hearing subjects, and was attrib-uted to the ability to listen in the ‘dips’ of the envelopeof the noise masker (see also Buus and Florentine,1985). In all other cases, the tone masker producedless masking than the noise masker. This probably oc-curred because the inherent £uctuations in the noisemasker reduced the salience of envelope £uctuationsproduced by adding the noise signal to that masker(Dau et al., 1997). The tone masker had no inherent£uctuations, so any envelope £uctuations produced byadding the signal to it would be highly salient.In summary, the irregularities in the masking pat-

terns for both the noise and tone maskers that occurredabove and sometimes below the masker frequency, forconstant masker-signal frequency separations, canprobably be attributed to the detection of envelope £uc-tuations rather than to the detection of combinationtones.

3.2. Condition 2: masking patterns for di¡erent maskerlevels

Masking patterns were measured for three di¡erentmasker levels : 100, 80 and 60 dB SPL. The masker and

signals were 80-Hz wide narrowband noises. The ra-tionale for including this condition was two-fold: (1)to determine if the non-monotonic features present forthe 100-dB SPL masker were also present for the twolower level maskers; (2) to determine the degree of non-linearity in the growth of masking for signal frequenciesabove the masker frequency.Fig. 2 shows the masking patterns for subject HC

(top two panels and bottom-left panel) who was testedusing masker frequencies of 0.25 (circles), 1.0 (squares)and 4.0 kHz (diamonds), and for subject KS (bottom-right panel) who was tested only using a masker fre-quency of 1.0 kHz, due to the onset of illness. Themasker levels were 100 dB SPL (95 dB SPL for the0.25-kHz masker) (un¢lled symbols), 80 dB SPL (¢lledsymbols) and 60 dB SPL (partially ¢lled symbols). Thesignal levels at the peaks of the masking patterns wereclose to the levels of the maskers. Dips in thresholdoccurred just above the masker frequency for the 1.0-and 4.0-kHz maskers for subject HC, and for the 1.0-kHz masker for subject KS, for all three masker levels.Moreover, the size and location of the dips were largelyinvariant with masker level. This is consistent with theidea that the dips result from the detection of a form ofbeats.In most cases, the masking patterns grew approxi-

mately linearly with masker level, which is what wouldbe expected from previous work using hearing-impaired

Fig. 2. Masking patterns for subject HC for a 250-Hz (upper-leftpanel), 1-kHz (upper-right panel) and 2-kHz (lower-left panel) noisemasker and KS for a 1-kHz (lower-right panel) noise masker at 100(open symbols), 80 (partially ¢lled symbols) and 60 dB SPL (¢lledsymbols). The signal was a noise band. Otherwise, as for Fig. 1.

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subjects (Florentine et al., 1980; Murnane and Turner,1991; Nelson and Schroder, 1997). The only exceptionwas for subject HC, for whom there was some evidenceof non-linear growth of masking for signal frequenciesabove that of the 1.0-kHz masker; signal thresholdsincreased by almost 30 dB when the masker level wasincreased from 80 to 100 dB SPL. This non-linearity issimilar to that observed for normal-hearing subjects(Moore et al., 1998), and is not surprising, given thatHC had only a small hearing loss in the frequency re-gion around 1.0 kHz.

3.3. Condition 3: masking patterns for a severelyhearing-impaired subject

Masking patterns were measured for 100-dB SPL 1-kHz and 2.0-kHz noise and tone maskers, and a noisesignal for one subject (SN) with a severe to profoundhearing loss. The rationale was to examine the in£uenceof beat detection when mean absolute thresholds werevery high (v70 dB SPL).Fig. 3 shows the masking patterns for the 1.0-kHz

(top panel) and 2.0-kHz (bottom panel) maskers, forthe noise (un¢lled symbols) and tone (¢lled symbols)maskers. The masking patterns have some features incommon with those shown in Figs. 1 and 2. For thenoise masker, there were well-de¢ned peaks at themasker frequency, with prominent dips for signal fre-quencies around 500 Hz above the masker frequency.For the tone masker, the signal threshold when the

signal frequency equaled the masker frequency wasmuch lower, and dips were present for signal frequen-cies both above and below that of the masker. Themuch lower thresholds obtained for the on-frequencysignals and the tone masker probably re£ect a sensitiv-ity to the within-interval £uctuation in level producedby adding the noise signal to the tone masker. Thise¡ect is similar to that shown in Fig. 1 for subjectHC, who has a smaller hearing loss (note that the ordi-nate is scaled di¡erently for Figs. 1 and 3). Thus, thesensitivity to this cue was not greatly a¡ected by thedegree of hearing loss.The dips for signal frequencies adjacent to the

masker frequency probably re£ect a sensitivity to themore regular envelope £uctuations produced by the in-teraction of the signal and masker. These beat-like £uc-tuations resulted in lower thresholds for the tonemasker than for the noise masker, probably becausethe inherent £uctuations in the noise masker made thebeats less salient or less detectable (Egan and Hake,1950; Dau et al., 1997). Indeed, for the tone masker,the masked thresholds were close to the absolutethresholds for masker-signal frequency separations ofabout 100 Hz, even though the masker itself wasmore than 20 dB above the absolute threshold. As forsubjects HC and PG in conditions 1 and 2, this subjectappeared to be very sensitive to £uctuations in the levelproduced when the noise signal was added to themasker, especially for signal frequencies close to themasker frequency. Signal levels at the dips adjacent tothe tone masker frequency were about 78 dB SPL. Thismeans that when the signal was added to the masker,beats with a peak to valley ratio of about 1.4 dB weredetectable.

3.4. Interim discussion

The results so far suggest that the irregularities in themasking patterns were mainly caused by the detectionof envelope £uctuations and not by the detection ofcombination tones. We base this conclusion on threeobservations:1. Dips in the masking patterns, when present, oc-curred over a ¢xed range of masker-signal frequencyseparations, irrespective of masker centre frequency.If combination tones had been detected, the dipswould have occurred for roughly a ¢xed masker-sig-nal frequency ratio.

2. Dips were sometimes observed for signal frequenciesboth below and above the masker frequency. Detec-tion of combination tones produces dips only forsignal frequencies above the masker frequency(Greenwood, 1971).

3. The positions and magnitudes of the dips did notvary greatly with masker level, whereas the dips pro-

Fig. 3. Masking patterns for a subject with a severe to profoundhearing loss for 1-kHz (top) and 2-kHz (bottom) noise (open sym-bols) and tone (¢lled symbols) maskers and noise signals. Otherwise,as for Fig. 1.

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duced by combination tone detection (in normallyhearing subjects) are markedly in£uenced by maskerlevel (Moore et al., 1998; Alca¤ntara et al., 2000).To provide a more direct test of the importance of

beats and combination tones in determining the shapesof masking patterns, a number of conditions were in-cluded in which extra components were added to a 2.0-kHz masker (conditions 4^7 described below). In theseconditions, a tone masker and tone signal were used inorder to maximise the audibility of beats and combina-tion tones. In addition, a noise signal was used. Therationale for including these conditions was the sameas described in Moore et al. (1998) and Alca¤ntara et al.(2000). Condition 4 was a baseline condition, involvingthe tone masker alone. In condition 5, a lowpass noisewas added to mask combination tones produced by theinteraction of the signal and the masker. In condition 6,a high-frequency tone pair (called modulation detectioninterference, MDI, tones) was added to introduce beatsof the same rate as produced by the interaction of themasker and the signal, thereby interfering with the de-tection of beats (Yost et al., 1989). Condition 7 used acombination of the lowpass noise and the MDI tones.Two subjects with di¡erent patterns of hearing loss

were used. Subject ET had relatively constant absolutethresholds, around 75 dB SPL, for frequencies between1.0 and 6.0 kHz. Subject DT had normal thresholds at1.0 kHz, a rapid increase (worsening) in thresholds forfrequencies between 1.0 and 2.0 kHz, and relativelyconstant thresholds, around 65 dB SPL, for signal fre-quencies above 2.0 kHz.

3.5. Condition 4: masking patterns for a tone maskerand tone or noise signals

Fig. 4 shows the masking patterns for the baselinecondition for subjects DT (left) and ET (right). Forthe tone signal (open symbols), the masking patternsfor both subjects have distinct peaks at the masker fre-quency. The level in the interval containing the maskerplus signal would have been about 1.2 dB above thatfor the masker alone. This indicates quite good inten-sity discrimination, comparable to that measured fornormal-hearing subjects. The peaks of the masking pat-terns for the noise signal (¢lled symbols) were substan-tially lower in level, around 77 dB SPL, re£ecting theuse of the cue of a within-interval £uctuation in levelproduced by adding the signal to the masker.It should be noted that the magnitude of the peak at

the masker frequency for the tone signal was in£uencedby our decision to add the masker and signal with 90‡starting phase, so that their powers added. If thresholdsare actually determined by the peak values of the stim-uli (Goldstein, 1999), it might be more appropriate toexpress the signal thresholds as the level that would

have been needed if the signal and masker were addedin phase. This would result in a reduction of the thresh-olds. For example, for both DT and ET, the thresholdfor the 2-kHz tone signal was 95.2 dB SPL. The equiv-alent level if the signal and masker were added in phasewould be 83.4 dB SPL, which is markedly lower. How-ever, even when signal thresholds are expressed in thisway, local peaks in the masking patterns still occur,indicating that beats are more salient than steady di¡er-ences in level.For subject ET, dips extending 500 Hz on either side

of the masker frequency occurred for both types ofsignal. Subject DT’s masking pattern showed two dipsfor signal frequencies above the masker frequency, the¢rst between 2.05 and 2.25 kHz and the second between2.5 and 3.5 kHz. Again, these dips occurred for bothtypes of signal. There was a monotonic reduction inthreshold for frequencies below 1.75 kHz.It is likely that the dips adjacent to the masker fre-

quency were caused by the detection of beats. The tonesignal level at the minima was about 70 dB SPL forboth subjects, indicating that when the signal wasadded to the masker, beats with a peak to valley ratioof about 0.5 dB were detectable. Signal levels at theminima of the dips were very similar for the tone andnoise signals, suggesting that the detectability of thebeats was not a¡ected by their somewhat irregular na-ture for the noise signal.For subject ET, and for frequencies between 2.75 and

7.0 kHz, thresholds were lower for the noise than forthe tone signal. It is very unlikely that beats played arole for such large masker-signal frequency separations.Probably, subject ET was able to detect the within-in-terval £uctuations in level that occurred when the noisesignal was added to the tone masker.The second dip in subject DT’s masking patterns,

which extended from about 2.5 to 3.5 kHz, is di⁄cultto explain in terms of beats, as beats at a rate of 1.5kHz would probably not be detectable. Also, an explan-ation in terms of beats would not account for the local

Fig. 4. Masking patterns for subjects DT (left) and ET (right) for a2-kHz tone masker at 100 dB SPL and tone (open symbols) andnoise (¢lled symbols) signals. Otherwise, as for Fig. 1.

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increase in threshold around 2.5 kHz. The dip canprobably be attributed to the detection of distortionproducts (combination tone(s) for the tone signal andcombination band(s) for the noise signal). The type ofdistortion product is clari¢ed by the results describedlater.The presence of a second dip for DT, but not for ET,

can be explained by their di¡erent patterns of hearingloss. Subject DT’s relatively low absolute thresholdsbelow 1.0 kHz meant that any combination tones fall-ing below the masker frequency (e.g. 2f13f2 or f23f1)would probably be audible, thereby in£uencing thehigh-frequency side of the masking pattern. On the oth-er hand, subject ET’s relatively high absolute thresholdsat low frequencies made it unlikely that combinationtones would be detected even if they were present.The absence of dips on the low-frequency sides of themasking patterns for DT is also explicable in terms ofhis improving absolute thresholds with decreasing fre-quency below 2.0 kHz, which were associated with rap-idly decreasing masked thresholds. If the results wereexpressed as amount of masking, dips would be appar-ent on the low-frequency side.

3.6. Condition 5: masking patterns for a tone maskerplus a lowpass noise, for tone and noise signals

In this condition a continuous lowpass-¢ltered whitenoise was added to the 2.0-kHz tone masker. The noisewas generated using an Ivie Technologies IE-20B noisegenerator and then passed through four Kemo VBF 8/04 ¢lters in series set to lowpass, each with a 33-dBpoint of 1800 Hz; the slope of the skirt of each ¢lterwas 90 dB/octave. The level of the noise was chosen asfollows. The level of the signal in the region of the dipsin the masking patterns for the baseline condition wasused as a starting point. This was about 70 dB SPL. Itwas reasoned that the level of any combination prod-ucts would be at least 10 dB below this level (Smooren-burg, 1972; Zwicker, 1981). The total noise powerpassed by each auditory ¢lter in the frequency regionof the combination tones was required to be about 5 dBabove the combination tone level to ensure masking(i.e. approximately 65 dB SPL). Assuming that theERB of the auditory ¢lters for the hearing-impairedsubjects at a centre frequency of 1600 Hz was not lessthan the ‘normal’ value of 200 Hz, the spectrum levelrequired to give a total noise power at the output of theauditory ¢lters of at least 65 dB is 42 dB. This was thespectrum level used in this experiment. The cut-o¡ fre-quency of the lowpass noise was chosen so that thenoise would mask combination tones below 2.0 kHzwhile producing negligible masking above 2.0 kHz, rel-ative to that produced by the main 2.0-kHz masker.Fig. 5 shows the masking patterns measured without

the lowpass noise (open circles, data reproduced fromFig. 4) and with the lowpass noise (¢lled circles) ; whenlowpass noise was present, thresholds were measuredonly for signal frequencies at and above the maskerfrequency. For subject ET (top), the addition of thelowpass noise had very little e¡ect for either the tonesignal (left) or the noise signal (right), suggesting thatcombination tones played little or no part in determin-ing the shapes of the masking patterns. In contrast, thelowpass noise raised thresholds for subject DT (bot-tom), for signal frequencies between about 2.5 and 3.5kHz for the tone signal and between about 2.25 and 3.0kHz for the noise signal. The lowpass noise largelyeliminated the second, but not the ¢rst, of the twodips. This suggests that, in the baseline condition, com-bination tones in£uenced the detection of signals withfrequencies between 2.25 and 3.5 kHz.It is not clear what type of combination tone was

responsible for the second dip in the baseline conditionfor DT. Both the cubic di¡erence tone, 2f13f2, and thesimple di¡erence tone, f23f1, would have fallen in afrequency region where absolute thresholds were rela-tively low, and the lowpass noise would have maskedcombination products of both types. It was decided,therefore, to include a supplementary condition for sub-ject DT where an extra tone was added to the 2.0-kHzmasker without the lowpass noise. This tone had a fre-quency equal to f23f1, where f1 was the masker fre-quency (2.0 kHz) and f2 was the frequency of the signal.

Fig. 5. Masking patterns for subjects ET (top) and DT (bottom) fora 2-kHz tone masker at 100 dB SPL and tone (left) and noise(right) signals. The results for the 2-kHz masker alone (open sym-bols) are taken from Fig. 4. The ¢lled symbols show the e¡ect ofadding a lowpass noise to the masker. Otherwise, as for Fig. 1.

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The extra tone had a level of 75 dB SPL and it waspresented continuously. This tone should consistentlymask the simple di¡erence tone, but, as explained be-low, it would not always mask the cubic di¡erence tone,thus allowing us to determine whether the dip around3.0 kHz was caused by the detection of the former orthe latter.Fig. 6 shows the results, for the tone signal (left) and

noise signal (right), for the 2.0-kHz masker alone (opensymbols) and with the extra ‘f23f1’ tone (¢lled sym-bols). The extra tone e¡ectively ‘¢lled in’ the secondof the two dips in the masking patterns for the baselinecondition. The e¡ect of the extra tone was very similarto that of the lowpass noise (see Fig. 5, bottom). Acritical case occurs for a signal frequency of 3.5 kHz.The extra tone had a frequency of 1.5 kHz, while the2f13f2 combination tone, if present, would have had afrequency of 0.5 kHz. A 1.5-kHz tone would be ex-pected to produce very little masking of a 0.5-kHztone, as the absolute threshold was much higher at1.5 kHz than at 0.5 kHz, and there is little downwardspread of masking for this subject. However, the extra1.5-kHz tone produced a clear elevation of the signalthreshold at 3.5 kHz, strongly suggesting that the dip inthe baseline condition around 3.0 kHz was caused bydetection of the simple di¡erence tone.The origin of the di¡erence tone is not clear. Mea-

surements of the distortion introduced by the head-phone (made in the way described under Section 2)indicated that the level of the simple di¡erence tonewas less than 4 dB SPL for an input signal consistingof a 100-dB SPL sinusoid at 2 kHz and a second sinus-oid with a level of 70 dB SPL at 3 kHz; these arecomparable to the masker and signal used with subjectDT in the region of the second dip. The simple di¡er-ence tone produced by the headphone would have beenbelow DT’s absolute threshold. Therefore, the di¡er-ence tone must have arisen either in the middle ear(Dallos, 1973; Rosowski, 1996) or the cochlea (Rhode,1977).

3.7. Condition 6: masking patterns for a tone maskerplus MDI tones for tone and noise signals

Condition 6 was the same as condition 4, except thattwo equal-level high-frequency (‘MDI’) tones weregated on synchronously with the 2.0-kHz tone masker,in every interval. The two tones were generated digitallyin the same way as described previously for the maskerand signal stimuli. The combined level of the MDItones, for both subjects, was 100 dB SPL. For subjectDT, the lower of the MDI tones had a frequency of 5.0kHz and the upper had a frequency of 5.0 kHz plus thefrequency separation between the masker and the sig-nal. For example, if the masker and signal frequencies

were 2.0 and 2.1 kHz, respectively, the MDI tone fre-quencies were 5.0 and 5.1 kHz; if the masker and signalfrequencies were 2.0 and 1.5 kHz, then the MDI tonefrequencies were 5.0 and 5.5 kHz. When the signal fre-quency was equal to the masker frequency, a single 5-kHz tone was added to the masker with a level of 100dB SPL.For subject ET, the MDI tones were as described

above, except that the lower tone had a frequency of3.0 kHz, and the upper had a frequency of 3.0 kHz plusthe frequency di¡erence between the masker and thesignal. Pilot studies had indicated that MDI tonesaround 5.0 kHz had little e¡ect and MDI tones around4.0 kHz had only a moderate e¡ect. In contrast, MDItones around 3.0 kHz had a large e¡ect. This probablyhappened because ET’s absolute thresholds were quitehigh at 5 and 4 kHz, but improved at 3.0 kHz. There-fore, the sensation level of the MDI tones would havebeen higher for the ‘3.0-kHz’ MDI tones, leading to agreater MDI e¡ect (Yost et al., 1989). For ET, thresh-olds were not measured for signal frequencies above 2.5kHz, as the MDI tones would have had a ‘direct’ mask-ing e¡ect for higher frequencies.Fig. 7 shows the results for the tone signal (left) and

noise signal (right), for the baseline condition (opensymbols) and the tone masker plus the MDI tones(¢lled symbols). Consider ¢rst the results for ET(top). Addition of the MDI tones had a pronouncede¡ect for both the tone and noise signals, on both sidesof the masking patterns. Thresholds were elevated formasker-signal frequency separations up to 250^500 Hz.The large dips in the masking patterns for the baselinecondition were substantially reduced in size, althoughfor the tone signal small dips remained on either side ofthe masker frequency, and for the noise signal there wasa single dip centred at the masker frequency. These

Fig. 6. Masking patterns for subject DT for a 100-dB SPL tonemasker and tone (left) and noise (right) signals. The results for the2-kHz masker alone (open symbols) are taken from Fig. 4. The¢lled symbols show the e¡ect of adding an extra tone to themasker, with frequency equal to f23f1, where f1 is the masker fre-quency and f2 is the signal frequency. Otherwise, as for Fig. 1.

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residual dips probably occurred because the MDI tonesdid not completely prevent envelope £uctuations frombeing detected, especially when the £uctuations oc-curred at a low rate.For DT (bottom), the MDI tones elevated thresholds

for masker-signal frequency separations up to 750 Hzon the low-frequency sides of the masking patterns, and1000 Hz on the high-frequency sides. The elevation onthe high-frequency side resulted in the second dip beingpartially ¢lled in. We presented evidence earlier thatthis dip was caused by detection of the simple di¡erencetone. The MDI tones probably a¡ected the second dipbecause they produced a simple di¡erence tone of thesame frequency as that produced by the interaction ofthe 2.0-kHz masker and signal. The threshold elevationproduced by the MDI tones for signal frequencies wellbelow the masker frequency might also partly havebeen a consequence of the MDI tones producing a sim-ple di¡erence tone, which then had a direct maskinge¡ect on the signal. However, the threshold elevationproduced by the MDI tones for signal frequencies with-in about 250 Hz of the masker frequency was likely tohave been caused by interference with the detection ofenvelope £uctuations.

3.8. Condition 7: masking patterns for a tone maskerplus lowpass noise plus MDI tones, using tone ornoise signals

In condition 7, the lowpass-¢ltered noise of condition

5 and the MDI tones of condition 6 were presentedtogether with the 2.0-kHz masker. The levels of thenoise and MDI tones were as previously described.Our main interest was to compare the results for thiscondition with those for condition 5, where the lowpassnoise was present but there were no MDI tones. Thelowpass noise should have been e¡ective in maskingboth simple and cubic di¡erence tones. Therefore, anye¡ect of adding the MDI tones to the lowpass noise canbe attributed to interference with the detection of enve-lope £uctuations, rather than to masking of combina-tion tones.Fig. 8 shows the results for the tone signal (left) and

noise signal (right). Results for the 2.0-kHz masker pluslowpass noise are indicated by open symbols, and re-sults for the 2.0-kHz masker plus lowpass noise plusMDI tones are indicated by ¢lled symbols. For ET(top), the MDI tones resulted in elevated thresholdsfor signal frequencies from 2.05 to 2.5 kHz, for boththe tone and noise signals, suggesting that, in the ab-sence of the MDI tones, the detection of beats had astrong in£uence. The fact that thresholds did not de-cline monotonically with increasing masker-signal fre-quency separation suggests, as before, that the MDItones were not completely e¡ective at eliminating beatsas a cue, especially when the beat rate was low.For DT (bottom), the MDI tones resulted in elevated

thresholds over a more limited range of signal frequen-cies, from 2.05 to 2.25 kHz for the tone signal and from

Fig. 7. As for Fig. 5 but showing the e¡ect of adding the MDItones to the masker (¢lled symbols).

Fig. 8. As for Fig. 5 but showing the e¡ect of adding lowpass noiseand the MDI tones to the masker (¢lled symbols).

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2.05 to 2.125 kHz for the noise signal. The MDI toneshad no e¡ect in the region of the ‘second dip’ observedin the baseline condition, which is consistent with ourinterpretation that the second dip was not caused bybeat detection, but was due to the detection of a simpledi¡erence tone. The results again suggest that the MDItones were not completely e¡ective at eliminating beatsas a cue.For both subjects, the thresholds obtained with the

lowpass noise plus MDI tones were very similar tothose obtained with the MDI tones alone. As discussedearlier, the simple di¡erence tone produced by the MDItones probably had the e¡ect of masking any simpledi¡erence tone produced by the interaction of the signaland the 2.0-kHz masker. However, the MDI tonesshould not always have been e¡ective in masking thecubic di¡erence tone. Thus, the fact that thresholds inthe presence of the MDI tones were una¡ected by thepresence or absence of the lowpass noise suggests thatcubic di¡erence tones had no in£uence on thresholds.This is consistent with previous research suggesting thatthe non-linearity giving rise to cubic di¡erence tones isreduced or abolished by cochlear damage (Leshowitzand Lindstrom, 1977; Gorga et al., 1993; Robles etal., 1991).

4. Discussion

With the exception of DT, there was no indicationthat the results were in£uenced by the detection of com-bination tones. In the case of DT, a secondary dip inthe masking pattern for signal frequencies more than500 Hz above the masker frequency was probably theresult of detection of the simple di¡erence tone pro-duced by the interaction of the masker and the signal.His ability to detect this tone depended on the fact thathe had near-normal absolute thresholds in the fre-quency region where the f23f1 tone would have oc-curred. There was no evidence for any subject that cu-bic di¡erence tones in£uenced the masking patterns.This contrasts with what is found for normally hearingsubjects, for whom the high-frequency sides of themasking patterns can be strongly in£uenced by the de-tection of cubic di¡erence tones (Greenwood, 1971;Moore et al., 1998; Alca¤ntara et al., 2000). Cubic di¡er-ence tones may have little e¡ect for hearing-impairedlisteners because the tones are absent, as a result ofdamage to the active mechanism in the cochlea, orare not audible because of the relatively high absolutethresholds of the listeners.The results suggest that temporal envelope £uctua-

tions (primarily beats) strongly in£uenced the shapesof the masking patterns for masker-signal frequencyseparations up to W 500 Hz. In an earlier study using

normal-hearing listeners, Alca¤ntara et al. (2000) foundthat the addition of MDI tones to a 2.0-kHz tonemasker had the e¡ect of elevating tone signal thresholdsfor masker-signal frequency separations up to W 300Hz. The addition of a lowpass noise, in contrast, raisedthresholds for masker-signal frequency separations be-tween 300 and 1000 Hz. This suggests that beats pro-vided the main detection cue when the signal frequencywas close to the masker frequency and combinationtones provided the main detection cue for largermasker-signal frequency separations, corresponding tofrequency ratios between 1.15 and 1.5. When MDItones were used in addition to a lowpass noise, thresh-olds were elevated by the MDI tones for masker-signalfrequency separations up to 700 Hz. This suggest that,when combination tones are not audible, beats can in-£uence thresholds over a relatively wide frequencyrange.At ¢rst sight, some results of Yost et al. (1989) ap-

pear to be inconsistent with our argument that the MDItones can a¡ect beat detection for beat rates up to 700Hz. They found that MDI decreased markedly withincreasing modulation rate of the signal and interferer(when both were modulated at the same rate), and itwas essentially absent when the modulation rate was200 Hz. However, this result was obtained using a sig-nal carrier frequency of 4000 Hz and an interferer car-rier frequency of 1000 Hz. It is likely that the reducedMDI at higher modulation rates was caused at leastpartly by increasing resolution of the spectral sidebandsof the interferer in the peripheral auditory system,which would have reduced the e¡ective modulationdepth, a point noted by Yost et al. (1989). Thus, itremains at least possible that MDI can operate forbeat rates up to several hundred Hz when the interfereris composed of a pair of tones with a high centre fre-quency, as in our experiments.The results for the hearing-impaired subjects gener-

ally indicated a high sensitivity to beats of low andmoderate rates. However, we did not ¢nd evidence foran in£uence of beat detection on the masking patternsfor beat rates above 500 Hz. The small di¡erence be-tween the normal and hearing-impaired subjects mayre£ect the poorer temporal resolution abilities whichsometimes accompany cochlear hearing loss, especiallywhen stimuli are presented at low sensation levels (Buusand Florentine, 1985; Moore and Glasberg, 1988;Glasberg et al., 1987). However, beat detection in ourhearing-impaired subjects appeared to be essentiallynormal for beat rates up to a few hundred Hz, whichis consistent with earlier work on modulation detection(Moore and Glasberg, 2001).The strong in£uence of beat detection on the masking

patterns indicates that the shape of a masking patterncannot be used as an indicator of the excitation pattern

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of the masker, or, more generally, to give an estimate offrequency selectivity. Even when MDI tones were addedto the masker to reduce the salience of beats, irregular-ities still occurred in the masking pattern. This appearsto be an inherent problem when narrowband maskersare used. The in£uence of beats on measures of theupward spread of masking might be reduced by usinga noise with a relatively large bandwidth (Buus, 1985).Alternatively, the notched-noise method (Patterson andMoore, 1986; Glasberg and Moore, 1990) can be usedto characterise frequency selectivity (the auditory ¢ltershape) at a given centre frequency; this method appearsto be relatively una¡ected by beat detection. If auditory¢lter shapes are measured for several centre frequencies,the shape of the excitation pattern evoked by a givensound can then be calculated from the measured audi-tory ¢lter shapes (Glasberg and Moore, 1990; Mooreand Glasberg, 1997). This approach may be morestraightforward for hearing-impaired than for normallyhearing subjects, as the shapes of the auditory ¢ltersvary less with level for the former (Moore and Glas-berg, 1997).Consistent with the idea that auditory ¢lters vary

little with level for hearing-impaired subjects, thegrowth of masking measured for our subjects, for sig-nals frequencies above the masker frequency, wasnearly linear, i.e. a 20-dB increase in masker level re-sulted in roughly a 20-dB increase in signal threshold.This linear behaviour contrasts with the more rapidnon-linear growth of masking typically found for nor-mally hearing subjects (Egan and Hake, 1950; Zwickerand Fastl, 1990). The greater linearity in the hearing-impaired subjects probably is the result of damage tothe active mechanism in the cochlea (Murnane andTurner, 1991; Oxenham and Moore, 1995; Oxenhamand Plack, 1997; Nelson and Schroder, 1997). How-ever, subject HC did show some evidence of non-lineargrowth of masking (see Fig. 2), suggesting that the ac-tive mechanism was still partially functioning.Finally, it is worth considering the relative merits of

measures of frequency selectivity based on the use of¢xed maskers, as in the present experiments, and ¢xedsignals, as in the measurement of psychophysical tuningcurves (PTCs) (Chistovich, 1957; Small, 1959). The for-mer may be regarded as providing a crude approxima-tion to the excitation pattern evoked by the masker(Moore et al., 1998; Zwicker and Fastl, 1999), whilethe latter characterise tuning at one centre frequency(one place on the basilar membrane). PTCs may beless a¡ected than masking patterns by combinationtones, because of the low signal level that is typicallyused (about 10 dB SPL). However, PTCs can still bestrongly in£uenced by beats and by o¡-frequency listen-ing (Johnson-Davies and Patterson, 1979; O’Loughlinand Moore, 1981).

5. Summary and conclusions

Masking patterns were measured for hearing-im-paired subjects with varying degrees of hearing loss.Both ‘tone’ and ‘noise’ maskers were used. The resultsshow the following:

1. Masking patterns for both noise and tone maskersshowed irregularities (‘dips’), especially for signalfrequencies up to 500 Hz above the masker fre-quency. The dips occurred for all masker levelsand for all subjects for at least one masker fre-quency. Further, the dips occurred for a relativelyconstant range of masker-signal frequency separa-tions, suggesting that they were the result of beatdetection.

2. The addition of a lowpass noise to a 2-kHz tonemasker, intended to mask combination tones, hadlittle e¡ect for one subject. For a second subject,who had near-normal absolute thresholds at low fre-quencies, the noise elevated thresholds for masker-signal frequency separations between 500 and 1500Hz. For this subject, an extra tone with a frequencyequal to the masker-signal frequency separation,added in place of the lowpass noise, had a very sim-ilar e¡ect to that produced by the lowpass noise,suggesting that he was detecting a simple di¡erencetone when the lowpass noise was absent. There wasno evidence that cubic di¡erence tones in£uenced theresults, for any condition.

3. The addition of a pair of high-frequency tones (MDItones ^ intended to reduce the detectability of beats)to a 2-kHz tone masker elevated thresholds for sig-nal frequencies from 1500 to 2500 Hz for one subjectand from 1500 to 3500 Hz for another subject. Thee¡ect for signal frequencies within 500 Hz of themasker frequency can be attributed to the MDItones reducing the detectability of beats. The e¡ectfor signal frequencies well above 2500 Hz can beattributed to the MDI tones producing a simple dif-ference tone, which masked the di¡erence tone pro-duced by the main masker and signal.

4. The addition of lowpass noise and MDI tones to a 2-kHz tone masker produced masking patterns verysimilar to those observed when the MDI tones alonewere added to the masker.

5. Overall, the results suggest that the irregularities inthe masking patterns were caused mainly by the de-tection of beats. The hearing-impaired subjects testedhere showed a sensitivity to beats similar to thatfound for normally hearing subjects. There was noevidence that cubic di¡erence tones in£uenced theresults. Detection of the simple di¡erence tone in£u-enced the results for one subject with near-normalabsolute thresholds at low frequencies.

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Acknowledgements

This work was supported by Phonak AG (Switzer-land), the Medical Research Council (UK), and by aEuropean Union TAP project (SPACE). We thankHiva Fassihi and Bhashkar Mukherjee for gatheringsome of the data and Brian Glasberg for writing thecomputer programs to run the experiments.

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