Perception & Psychophysics1977, Vol. 22 (3), 282-286

Masking by combination tones and bands

DAVID Y. CHUNGBioacoustics Laboratory, Eye and Ear Hospital, Pittsburgh, Pennsylvania 15213

Masking of a pure tone by a cubic difference tone or band generated by two pure tones orby a pure tone and a narrow band of noise as a function of the level of the masker was measuredfor three subjects at three ratios of f2/f" 1.125, 1.2, and 1.3. The three maskers used were Calone, f, + f2 , and f, + NBN (60-Hz band of noise centered at f2 ) . At ratio 1.125, the amounts ofmasking produced by f, alone and f, + NBN were not significantly different for all subjects.For ratios = 1.125 and 1.2, f, + f2 produced the least masking at least in two of the subjects.I, + NBN was the best masker at ratios 1.2 and 1.3. These results show that the masking dataon cubic difference tone at very small ratios of f2/f, are not reliable due to the masking effectcontributed by f,. For higher ratios, the combination band has to be used instead of combina­tion tone because of the interaction between the signal and the cubic difference tone. Also thedivergence of the effectiveness in masking by the three maskers gives an estimation of thelevels of primaries at which the cubic difference tone is generated.

The features of the combination tones of the typef(k) = (k + l)f, - kf2 , where k is a small integerand fl < f2 , were studied extensively by Goldstein(1967) and Goldstein and Kiang (1968), using variousmethods, especially concellation [also called themethod of compensation (Zwicker, 1955)]. Theirdata convinced them that combination tones of thisclass are cochlear in origin and behave likestimulus tones. Their conclusion is supported byGreenwood's (1971) observations that combinationtones and bands produce masking at the frequenciesaround them. In his experiments, Greenwood usedmasking stimuli that were made up of (1) two tones,f l and f2 ; (2) a tone, f l , and a narrow band of noise50 Hz wide centered at f2 ; and (3) two narrow bandsof noise centered at f, and f2 • With the two-tonestimulus as masker, he found dips in masking on thelow-frequency slope of the masked audiogram thatcorresponded to the frequencies of 2f l - f2 , 3fl ­

2f2 , etc. He interpreted these dips in terms of theinteraction or beating between the signals and thecombination tones similar to those that have beenshown by Egan and Hake (1950) and Wegel and Lane(1924) for signals and harmonics of pure-tonemaskers. With the other two kinds of maskingstimuli, however, Greenwood found bumps onshoulders rather than dips to be evident in frequencyregion of the combination bands.

Greenwood (1972a) also measured signal-to­masker ratios using external bands of noise as

This study was supported by Grant 07790 from the NationalInstitute of Neurological Disease and Stroke. The author wishesto thank R. C. Bilger for his advice during all phases of this work.The present address of the author is Division of Audiology andSpeech Sciences, University of British Columbia, Vancouver,B.C., Canada V6T IW5.

masker. He then estimated the combination bandlevels by measuring the masked thresholds of thesignals at the point of maximum masking producedby the combination bands. The levels of thecombination bands can be calculated from the signal­to-masker ratios that were obtained previously froman external band of noise. Earlier, Greenwood(1972b) had found that the addition of a higher tonewith a higher intensity than the external maskingnarrow band of noise did not change the maskedthreshold at the maximum or on the lower slope ofthe masked audiogram by the noise alone in anysignificant extent. He also found that maskingpatterns produced by these external noise bands(centered at the cubic difference tone, CDT) plus thetone are almost identical to those by f, plus a narrowband of noise centered at f2 (NBN).

This study attempts to investigate masking asa method of studying combination tone by find­ing: (1) the effect of I, on the masking of a tone witha frequency in the vicinity of the CDT, and (2) thedifferences between f l + f2 and f , + NBN asmaskers of a tone at a frequency near the CDT.

METHOD

SubjectsOne female and two male college students served as subjects

in this study. One of them was the experimenter himself. SubjectsD.C. and M.F. were experienced in hearing experiments, whileJ.B. was not.

StimuliThe two-tone masker (f', + f2) was generated by a complex

waveform generator (Wolf & Bilger, 1972). Two tones with thesame amplitude and in sine phase with each other were generatedand stored on a computer tape. The third masker with the narrow­band noise was generated by passing a random telegraphic noisethrough a low-pass filter at 30 Hz to a multiplier. The other input

282

MASKING BY COMBINATION TONES AND BANDS 283

to the multiplier was from an oscillator with frequency at f,.The output was added to a pure tone of f', by an adder. The resul­tant was the masker, f, plus a narrow band of noise, 60 Hz widecentered at f,. Both components had the same sound pressurelevel. The nonlinear distortion components at the frequencies,2f, - f" were at least 50 dB down for the two-tone masker and55 dB down for the NBN masker, as measured by a Hewlett­Packard 358lA wave analyzer. The signal was 500 msec in dura­tion and had a rise-decay time of 16 msec. The signal always hada frequency of IO Hz above the frequency of the CDT. The maskerwas on continuously during each run. All stimuli were presentedmonaurally.

ProcedureAn adaptive procedure based on the four-interval-forced-choice

paradigm was used to estimate masked and unmasked thresholds.A randomly selected interval contained the signal. The periodbetween intervals was 300 msec. A pair of TDH-49 headphoneswas used for each subject. The left one was always silent. Thesubjects were instructed to push the button of the interval in whichthey detected a difference after the four intervals were presented.During each session, the same masker was used while its levelwas varied from 10 to 80 dB SPL in lO-dB steps. The sequencewas repeated three times with a total of 27 runs. There was aIO-min testing period after every four runs. Each session lastedabout 3 h. None of the subjects showed any recognizable sign offatigue at the end of each session either from the data or theappearance. After several practice trials, quiet thresholds andmasked thresholds were obtained under three different maskerconditions and three different f,/f, ratios. The ratios were 1.125(f. = 3,200 Hz), 1.2 (f', = 2,000 Hz), and 1.3 (f. = 2,000 Hz).The nine conditions are shown in Table I. A different f, wasused for the ratio 1.125 because of the limitation of the wave­form generator, which could only produce certain discretefrequencies.

RESULTS

The results of the three subjects are plotted inFigures 1-3. Each figure shows the masking func­tions of the three maskers in a given ratio of f2/f, forall three subjects. The ordinate is in dB masking andthe abscissa is in dB SPL of the masker.

Table 2 shows the results of the analyses of vari­ance calculated separately for each subject at eachratio of f 2/ L. For the ratio f 2 / L = 1.125, the maskereffect is significant only in subject M.F. with f, + f2

being the least effective masker. For subject D.C.,the masker effect is significant to 0.1 level with f, +

Table IThe Nine Different Conditions of the Experiment

Maskers

Ratios r, f , + r, r, +NBN

r, =3,200 Hz r, =3,200 Hz f, =3,200 Hz1.125 r, =3,600 Hz 60-Hz band centered

at 3,600 Hz

r, =2,000 Hz r, =2,000 Hz r, =2,000 Hz1.2 r, =2,400 Hz 60-Hz band centered

at 2,400 Hz

r, =2,000 Hz r, =2,000 Hz r, =2,000 Hz1.3 f, =2,600 Hz 6Q-Hzband centered

at 2,600 Hz

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Figure 1. The masking functions of the subjects in the ratioof f,lf, is indicated at the top of the figure, f, = 3,200 Hz. Theabscissa is in dB SPL of the masker and the ordinate is in dBmasking. Multiple ordinate scale is used. Each set of maskingfunctions for each subject has been shifted 20 dB on the ordinaterelative to the one below. Subject D.C., filled symbols; M.F., half­filled; and J .B., unfilled. The three maskers shown are f, alone(circles), r. + f, (triangles), and f, + NBN (squares). The fre­quency of the masked tone = 2f, - f, + 10 = 2,810 Hz.

f2 producing the least masking. For all subjects (Fig­ure 1), f', and f, + NBN are as effective as eachother in masking. At ratios 1.2 and 1.3, the maskereffect is significant to .05 level for subjects D.C. andM.F., and 0.1 for subject J.B. The masker f', + f2

is still the least effective masker for the former twosubjects at the ratio 1.2 (Figure 2), although it is notso definite for subject J.B. At the ratio 1.3, however,the masker f, alone remains the least effective maskerat higher masker levels (Figure 3).

The amount of masking due to the effect ofmasker level is, as expected, significant in allsubjects. Since the f, frequency in the ratio 1.125is different from that in the ratios 1.2 and 1.3, a fullanalysis of variance was not done. One can see, how­ever, that the masking due to L alone markedly de­creases as the ratio goes up. The same is true forf, + f2 , but the decrease is at a slower rate. For f',+ NBN, the masking at the ratio 1.125 to maskingat the ratio 1.2 is not decreased (the f'.s in the two

284 CHUNG

Table 2Analyses of Variance for Each Ratio of f2 If,

R=

Subject Source 1.125 1.2 1.3

Masker N* y y

D.C. Level y y yMasker by Level Y Y Y

Masker y y y

M.F. Level y y yMasker by Level Y y y

Masker N N* N*J.B. Level Y Y Y

Masker by Level N Y Y

Note- Y = significant, N = not significant; p < .05, except whereotherwise indicated. *p < .J.

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60 to 70 dB at the ratio 1.3. For the ratio 1.125, thedivergence is obvious only for subject M.F. andoccurs at the masker level of about 40 dB SPL.

DISCUSSION

Zwicker and Fast! (1973) compared the maskingproduced by the two maskers, (1) f', (2,000 Hz) + f2

(2,500 Hz) and (2) f', + NBN, 100 Hz wide centeredat f2 , and found that the difference in maskingthresholds between the two was about 9 dB. Thelatter produced a higher threshold than the former.They attributed the difference to the time structureof the masker. The artificial narrow band noise withthree components created by the authors seems tohave proved this point. That narrow band noise is abetter masker than a pure tone masker is not new.Egan and Hake (1950) compared the masking audio­grams of a pure 4oo-Hz tone and a narrow band ofnoise (90 Hz wide centered at 410 Hz), both at 80 dBSPL. At signal frequencies near the maskers, thenarrow band was a much more effective masker thanthe pure tone. The difference was as much as 18 dB.

Greenwood (1971) was aware of the interaction ofthe tonal masker and the pure tone signal. He wasable to show dips at the lower slope of the audiogramwhere the combination tones were located. He there-

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Figure 3. See caption of Figure 1, except that f, = 2,000 Hz.The frequency of the masked tone = 1,410 Hz.

10 20 30 40 ~O 60 70 80

LEVEL OF MASKER IN SPL

Figure 2. See caption of Figure I, except that f, = 2,000 Hz.The frequency of the masked tone = 1,610 Hz.

cases are different). From the ratio 1.2 to 1.3, thedecrease in masking, however, is large.

The interaction, Masker by Level, is significant inall cases with the exception of subject J.B. at theratio 1.125 (Figure 1). By examining the Figures 1-3,one can see in most cases that the three curves, whichcorrespond to the three maskers, diverge at a certainlevel of the masker depending on the case. Forexample, the three curves diverge when the SPL ofthe maskers are above 30 to 50 dB at the ratio 1.2 and

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MASKING BY COMBINAnON TONES AND BANDS 285

fore used either a narrow band centered at f2 or twonarrow bands centered at both C and f2 instead. In ourexperiments, by using the signal frequency at 10 Hzabove the combination tone frequency 2C - f2 , inthe case of the masker being C + f2 , the thresholdwas more a threshold of modulation than a tonalthreshold, as mentioned by a subject in Zwickerand Fastl's (1973) paper. By changing f2 into anarrow band, this modulation was no longerprominent. However, the change from one type ofmasker to another did not seem to affect the cri­terion, detection of a difference, used by the sub­jects. The modulation merely made it easier to bedetected.

For low ratios of f 21C, both the two maskers, Calone and C + NBN are both producing about thesame amount of masking. This does not disagreewith Greenwood's (1972b) finding that maskingproduced by a noise is not increased by adding ahigh-intensity and higher frequency tone to the noise.The most severe condition he used was an 80-dBSPL tone (C) added to a 35-dB narrow band of noise(50 Hz wide) centered at (C - 0.125 C) Hz. Thisfrequency is equivalent to a cubic difference toneproduced by two primaries having a ratio f 21C =1.125 (Figure 2D in Greenwood, 1972b). Both interms of the ratio and the SPL of C, the conditionsare very similar to the conditions shown in Figure 1,when masker level is 80 dB SPL. This is reasonable,because the level of the combination tone is expectedto be about 30 to 35 dB SPL (Goldstein, 1970). Sincethe curve in Figure 2D of Greenwood (1972b) doesnot indicate any shoulder, it shows that the addednoise does not increase the masking.

For the ratio f 21C equal to 1.2, the effects of mask­ing by the three maskers deviate. C alone acquires agentler slope, while f', + NBN becomes the mostprominent masker. C + f2 remains the lowest of thethree maskers for subjects D.C. and M.F. Here, thethree curves diverge at about 30-50 dB SPL inmasker level, depending on the subject. Assumingthat the divergence is due to the correspondence ofthe combination tones, this level should be where thecombination tone begins to occur. This implies thatthere are large individual differences in the levelwhere the combination tones arise. This assumptionis supported by the fact that when f2lf, = 1.3, thedivergence occurs at a higher level of masker, ataround 60 to 70 dB SPL. This is expected from thefact that increasing f 21C decreases the combinationtone level.

The interesting part of the results is that C aloneis a better masker than C + f2 for subjects D.C. andM.F. at ratios 1.125 and 1.2. For subject 1.B., how­ever, this is not true. The reason is obscure. From the

data, it seems that as the level of the masker getshigher the difference in masking between the two mas­kers becomes smaller. It is possible that at maskedthreshold measurement the difference in level be­tween the signal and the combination tone becomeslarger as the level of the masker increases, and there­fore the modulation becomes weak so that themasked threshold gets higher. Does modulation re­lease so much masking from the masker? There maybe some other mechanisms involved in this. Theresidual masking of C at the frequency of the eDT,therefore, should not be neglected for the ratio off 21C < 1.3. Above this ratio, the contribution ofr. on masking becomes minimal.

Greenwood (1972b) reported that at higherprimary levels the decrease in combination bandlevel became less as elf. was increased. There doesnot seem to have been such a trend in subjectsreported here except perhaps for subject 1.B. InFigure 13 of Greenwood's paper (1972a), the levelsthat show such effects are 85 and 95 dB SL. Bothare higher than the levels reported here. This may bethe reason why such a finding does not concur withthe data here.

Smoorenburg (1972) found significant inter­personal differences in the width of the audibilityregion. These differences cannot be accounted forby threshold differences. There was only 1 subjectout of 40 who could perceive a combination tonewhen the ratio f2lf, was smaller than 1.15 and thelevel of each component was 40 dB SL. From sucha finding, it is not surprising that subject 1.B.deviated from the other two subjects in that he didnot show a significant difference in the Masker byLevel effect when the ratio fjf, = 1.125. When theratio was higher, all subjects showed significance inthe Masker by Level effect. This is consistent withthe suggestion that the divergence of the maskingproduced by the three maskers is an indication of thepresence of the combination tone. Another reasonmay have been due to the lack of evidence insubject 1.B.

This study supports Greenwood's results in thatfor a masking experiment on eDT, the noise bandhas to be used. When masking with only two tones,f. + f2 is not a good indicator of masking. Thisstudy further shows that masking data with too lowa ratio (e.g., 1.125) are not reliable because of themasking contributed by the tone C. In Figure 7 ofZwicker and Fastl's (1973) paper, one can see verysimilar results between those obtained from themethod of compensation and those from maskingwith f. + NBN. The ratio they used was 1.25, which,as shown from our data here, could be large enoughfor a good estimate of the eDT level.

286 CHUNG

REFERENCES

EGAN, J. P., & HAKE, H. W. On the masking pattern of a simpleauditory stimulus. Journal ofthe Acoustical Society ofAmerica,1950, 22, 622-630.

GOLDSTEIN, J. L. Auditory nonlinearity. Journal of the AcousticalSociety ofAmerica, 1967, 41, 676-689.

GOLDSTEIN, J. L. Aural combination tones. In R. Plomp &G. F. Smoorenburg (Eds.), Symposium on frequency analysisand periodicity detection in hearing. Leiden, Holland: Sijthoff,1970. pp. 230-247.

GOLDSTEIN, J. L., & KIANG, N. Y.-S. Neural correlates of the auralcombination tone 2f1-f2. Proceedings of IEEE, 1968, 56,981-992.

GREENWOOD, D. D. Aural combination tones and auditorymasking. Journal ofthe Acoustical Society ofAmerica, 1971, SO,502-543.

GREENWOOD, D. D. Masking by combination bands: Estimation ofthe levels ofthe combination bands (n+Of1-nfh. Journal of theAcoustical Society ofAmerica, 1972, 52, 1144-1154. (a)

GREENWOOD, D. D. Masking by narrow bands of noise in proxim-

ity to more intense pure tones of higher frequency: Application tomeasurement of combination band levels and some comparisonswith masking by combination noise. Journal of the AcousticalSociety ofAmerica, 1972, 52, 1137-1143. (b)

SMOORENBURG, G. F. Audible region of combination tones. Jour­nal of the Acoustical Society ofAmerica, 1972, 52, 603-614.

WEGEL, R. L., & LANE, C. E. The auditory masking of one puretone by another and its probable relation to the dynamics of theinner ear. Physics Review, 1924, 23, 266-285.

WOLF, R. V., & BILGER, R. C. Generating complex waveforms.Behavior Research Methods & Instrumentation, 1972, 4,250-256.

ZWICKER, E. Der ungewohnliche Amplitudengang der nichtlinearenVerzerungen des Ohres, Acustica, 1955,5,67-74.

ZWICKER, E., & FASTL, H. Cubic difference sounds measured bythreshold- and compensation- method. Acoustica, 1973, 29,336-343.

(Received for publication November 8, 1976;revision accepted May 26, 1977.)