Psychological Bulletin 1961, Vol. 58, No. 3, 205-217

COMPLEX SOUNDS AND CRITICAL BANDS1 BERTRAM SCHARF Northeastern University

Studies of the responses of human given by the top curve in Figure 1. observers to bands of noise and other The ordinate gives the width (AF), complex sounds have led to the meas- in cycles per second, of the critical ure of what appears to be a basic unit band; the abscissa gives the center of hearing, the critical band. When frequency. As the frequency at the the frequency spectrum of a stimu- center of a complex sound increases, lating sound is narrower than the the critical band that is measured critical band, the ear reacts one way; around the center frequency becomes when the spectrum is wider, it reacts wider. another way. For example, experi- Not only does the critical band ments show that at values less than have the same values when measured the critical bandwidth, both loud- for several kinds of auditory response, ness and absolute threshold are in- it is also independent of such stimu- dependent of bandwidth; only when lus parameters as the number of the critical bandwidth is exceeded components in the complex (Scharf, do the loudness and the absolute 1959b) and the sound pressure level threshold increase with the width (Feldtkeller, 1955; Feldtkeller & (Gassier, 1954; Zwicker & Feldtkel- Zwicker, 1956). ler, 1955; Zwicker, Flottorp, & Prior to the experimental measures Stevens, 1957). of the critical band, Fletcher (1940) The critical band has also been had hypothesized the existence of a measured in experiments on auditory critical band for masking. He sug- discriminations that seem to depend gested that when a white noise just upon phase (Zwicker, 1952) and in masks a tone, only a relatively nar- experiments on the masking of a row band of frequencies surrounding narrow band of noise by two tones the tone does the masking, energy (Zwicker, 1954). In all four types of outside the band contributing little experiment—loudness, threshold, or nothing. Although attempts to sensitivity to phase, and two-tone test this hypothesis remain incon- masking—the value of the critical clusive, investigators (Bilger & Hirsh, band is the same function of its 1956; Hawkins & Stevens, 1950) have center frequency. The values of the been able to calculate values for the critical band, as a function of the fre- width of these hypothetical masking quency at the center of the band, are bands by assuming that the masking band and the just-masked tone have 1 This paper was completed while the author the same intensity. The calculated held a research grant, B2223, from the Na- values, which are labeled "critical tional Institute of Health, United States Pub- lic Health Service. The author wishes to ratios" in Figure 1, are smaller for the thank S. S. Stevens for detailed criticism and masking band than for the critical advice in the final preparation of the manu- band as measured in the experiments script. A. B. Warren and H. S. Zamansky are also thanked for reading and making sugges- cited above. As we shall see, this dis- tions about the final draft. crepancy is more apparent than real. 205 206 BERTRAM SCHARF 5000 ures of this phenomenon, using many tones and systematically varying the 2000 difference in frequency, AF, between o'ooo the lowest and highest components of the complex sounds.2 He varied the 500 AF by varying the number of equally intense tones, which were spaced at intervals of 20 cps. The number of tones was increased from 1 to 40 or until AF was equal to 780 cps. Each time a tone was added, the threshold CRITICAL RATIO for the whole complex was measured by a "tracking" method (Stevens, 1958). It was necessary, of course, 50 100 ZOO 500 1000 2000 5000 that all the tones in the complex have FREQUENCY IN CYCLES PER SECOND the same threshold when heard FIG. 1. The width, AF, of the critical band singly, for otherwise it would have and of the critical ratio as a function of the been impossible to determine the frequency at the center of the band. (The or- dinate gives the width, in cycles per second, precise cause of a change in the of the critical band—and of the critical ratio— threshold for a complex whose AF for the center frequencies shown on the ab- had been increased by the addition scissa. The top curve gives the values for the of a tone. Thus measurements were critical band which are based upon direct restricted to portions of the fre- measurements in four types of experiment; the bottom curve gives the values for the quency spectrum over which a sub- critical ratio which are calculated from meas- ject's threshold curve was flat. In urements of the masked threshold for pure order to study other portions of the tones in white noise. The points on the bottom spectrum, the multitone complexes curve are from Hawkins and Stevens—1950. This figure is adapted from an article by were presented against a background Zwicker, Flottorp, and Stevens—1957, p. 556 of white noise that had been tailored —which contains also a table of critical-band to raise the threshold for tones at all values.) (Adapted with permission of the the audible frequencies to the same Journal of the Acoustical Society of America') level, thus artificially flattening a subject's threshold curve. EXPERIMENTAL MEASURES OF THE Whether the background was CRITICAL BAND quiet, or consisted of a noise at 0 db. Four types of experiment in which SPL, at 20 db., or at 40 db., the critical bands have been measured same effect was noted: as soon as are reviewed: absolute threshold of AF exceeded a particular value whose complex sounds, masking of a band size depended upon the frequency at of noise by two tones, sensitivity to the center of the complex, the thresh- phase differences, and loudness. old for the multitone complex began to increase. Similar data were re- Threshold of Complex Sounds ported when bands of white noise When two tones, whose frequencies were substituted for the multitone are not too far apart, are presented simultaneously, a subject may report 2 Two or more tones constitute a complex hearing a sound even though either sound, i.e., a sound with energy at more than one frequency in contrast to a single or pure tone by itself is below threshold. tone with most of its energy concentrated at a Gassier (1954) made careful meas- single frequency. COMPLEX SOUNDS AND CRITICAL BANDS 207 complexes. The results indicate that Sensitivity to Phase the total energy necessary for a sound The critical band is also relevant to be heard remains constant so long to phase sensitivity, measured by a as the energy is contained within a comparison between the ear's ability limiting bandwidth. Although differ- to detect amplitude modulation ences between the two observers in (AM) and its ability to detect fre- these experiments were sometimes of quency modulation (FM). This pro- the order of 40%, the average size of cedure requires some explanation. the limiting bandwidths for both When the amplitude of a tone is multitone complexes and bands of modulated—i.e., alternately in- noise is approximated by the critical- 8 creased and decreased—a three-tone band curve of Figure I. complex is produced with the original Two-Tone Masking tone (the "carrier") at the center of the complex and a tone on either The masking of a narrow-band side (side bands). When the frequency noise by two tones provided a second of a tone is modulated over a narrow measure of the critical band. Using range, a three-tone complex is also a tracking method, Zwicker (1954) produced.4 The only important dif- measured the threshold of a narrow- ference between the three-tone com- band noise in the presence of two plex that is produced under AM and tones, one on either side of the noise. the complex that is produced under Increasing the difference in fre- FM concerns the phase relations quency, AF, between the two tones among the components. Conse- left the masked threshold for the quently, any difference in the ear's noise unchanged until a critical AF sensitivity to AM and FM would was reached, whereupon the thresh- presumably depend upon these phase old fell sharply and, in general, con- relations. tinued to fall as AF was increased Zwicker (1952) found, indeed, that further. The two subjects who served in order for a subject to just hear a in this experiment showed the same difference between a modulated and drop in threshold at approximately a pure, unmodulated tone, a smaller the same AF for a given center fre- amount of AM is required than FM. quency regardless of the SPL of the The ear is more sensitive to AM than masking tones. The critical-band to FM, however, only at low rates of curve of Figure 1 gives the approxi- modulation. As the rate of modula- mate values of AF at which the mask- tion is increased, the difference in ing effect of two tones is sharply re- sensitivity to AM and FM gradually duced. disappears. How do these results pertain to the critical band? The rate * GSssler (1954) measured a critical band of at which a tone is modulated deter- 165 cps at 1000 cps. Garner (1947) had writ- ten earlier that "the best estimate ... is that mines the frequency separation, AF, a band of frequencies no wider than 175 cps between the side bands of the three- around 1000 cps is necessary if temporal in- tone complex produced under the tegration of acoustic energy is to be perfect" modulation. It turns out that the (p. 813). His estimate was based upon meas- urements of the threshold changes for a wide- rate of modulation at which AM and band noise, an tinfiltered 1000-cycle tone, and a filtered 1000-cycle tone as a function of * For a lucid discussion of the intricacies of bandwidth which was varied by varying the modulation, consult Stevens and Davis (1938, duration of the signal. pp. 225-231). 208 BERTRAM SCHARF ference in sensitivity to AM and FM, implying that, beyond the critical band, the phase relations within the complex no longer serve as a significant cue in the detection of modulation. Loudness of Complex Sounds The critical band has been meas- ured most thoroughly in studies of the loudness of complex sounds as a function of bandwidth. Zwicker and "50 100 200 500 1000 2000 Feldtkeller (1955) demonstrated that BANDWIDTH IN CYCLES PER SECOND the loudness of a white noise is in- FIG. 2. The loudness level of a band of dependent of bandwidth until the noise centered at 1000 cps measured as a critical band is exceeded, whereupon function of the width of the band. (The the loudness begins to increase. parameter is the effective SPL of the noise. The dashed line shows that the bandwidth at Their procedure was straightfor- which loudness begins to increase is the same ward. They presented a band of at all the levels tested. This figure is adapted filtered white noise and a comparison from the book, Das Ohr als Nachrichtenem- tone alternately through a single ear- pfiinger, by Feldtkeller and Zwicker—1956, phone. The subject adjusted the in- p. 82.) (Adapted with permission of S. Hirzel Verlag) tensity of the tone until the tone and the noise sounded equally loud. The FM become equally difficult to de- overall SPL of the noise was held tect corresponds to values of AF that constant; only the bandwidth was are essentially the same as the cri- varied from judgment to judgment. tical-band values given in Figure 1. (Zwicker and Feldtkeller did not re- Zwicker's investigation showed, port the number of subjects or the moreover, that the critical band de- amount of variability; probably only termined by phase sensitivity is in- a few, well-trained subjects were dependent of the SPL of the modu- used and the variability was small.) lated tone and varies only as a func- Figure 2 shows what happens to the tion of the frequency of the "carrier" loudness of a band of noise when its which lies, of course, at the center of width is increased. These curves are the band. for bands centered at 1000 cps, Since the complexes produced un- which was the geometric mean of der AM and those produced under the two half-power points. At all FM differ primarily with respect to the SPLs tested, from 30 to 80 db., phase relations, the ear may be able the loudness of the noise remains to detect AM more easily than FM constant and the curve is flat up to a at low rates of modulation because it bandwidth of about 160 cps, where- is more sensitive to the kind of phase upon the loudness begins to increase. relations that occur under AM. The Within the critical band, the noises ear seems to be sensitive to the are as loud as a tone of equal inten- phase relations, however, only when sity, having the same frequency as the AF of the complex is less than a the center of the band. Functions critical band. When AF is greater similar in shape to those in Figure 2 than a critical band, there is no dif- were generated for bands centered at COMPLEX SOUNDS AND CRITICAL BANDS 209 500, 2000, and 4000 cps. The band- width at which loudness begins to increase defines the critical band for loudness, which was found to have approximately the same values as had been measured for threshold, two-tone masking, and phase sensi- tivity (see Figure 1). Zwicker and Feldtkeller studied continuous spectra, i.e., noises that have energy at every frequency be- tween the cutoff points. Bauch (1956) studied line spectra, i.e., sounds that have energy at two or -more separate frequencies. He measured the loudness of three-tone complexes, produced by amplitude modulation, as a function of the difference, AF, in cps between the lowest and highest components of the complex. Bauch obtained the same I 100 200 500 1000 2000 results with three-tone complexes OVER-ALL SPACING-if centered at various frequencies as FIG. 3. The dependence of the loudness of a Zwicker and Feldtkeller had ob- four-tone complex, centered at 1000 cps, on tained with bands of noise. For spacing and level. (Each point represents the values of AF less than a critical band, median of two judgments by each of 10 listen- loudness is constant except when ers. The symbol T means the comparison tone AF is so small that beats are heard. was adjusted; C means the complex was ad- justed. This figure is from Zwicker, Flottorp The loudness begins to increase as a and Stevens—1957, p. SSO.) (Reproduced function of AF only when AF exceeds with permission of the Journal of the Acoustical the critical band. Society of America) At the time that the critical band was being mapped out in Germany well with those being obtained across at the Technischen Hochschule Stutt- the sea. The experiments were con- gart (Bauch, 1956; Gassier, 1954; tinued at Harvard by S. S. Stevens Zwicker, 1952, 1954; Zwicker & with G. Flottorp from Norway and Feldtkeller, 1955) some of us at the E. Zwicker from Germany (Zwicker Psycho-Acoustic Laboratory at Har- et al., 1957). Four-tone complexes vard were puzzled by our failure to and bands of white noise, at various find an increase in the loudness of a center frequencies and various SPLs, four-tone complex as a function of were studied. In these experiments, AF. We had assumed that loudness 16 to 22 untrained subjects some- summation begins as soon as AF is times adjusted the complex sound increased. We were, however, study- and sometimes adjusted the compari- ing four-tone complexes whose AFs son until the two were equally loud. were smaller than a critical band. Figure 3 shows a typical set of results, When reports of the critical band those for four-tonecomplexes centered came from Germany, our results be- at 1000 cps. Each point is the median gan to make sense and, indeed, agreed of 20 loudness matches. Although the 210 BERTRAM SCHARF subjects were somewhat variable in In one procedure, a band of white their judgments, the medians are noise was divided in half at its center orderly and the lines through the frequency; the upper half was pre- data show a break at approximately sented through an earphone to one the same value of AF that had been ear and the lower half to the other measured in Germany. The critical ear. The loudness of the noise in band made the transatlantic journey both ears did not begin to increase safely and invariantly. with bandwidth until the overall Another investigation carried out width exceeded a value approxi- at Harvard (Scharf, 1959a) showed mately twice the critical band, i.e., that at low levels, between 5 and 35 until the noise in each ear was wider db. above threshold, where the loud- than a single critical band. In a sec- ness of a complex sound increases ond procedure, two narrow bands, more slowly with bandwidth than at each 100 cycles wide, were first pre- higher levels, the critical band must sented together to one ear and later be exceeded before loudness begins separately to each ear. When pre- to change as a function of band- sented together to a single ear, the width. loudness of the two bands increased Niese (1960), in Dresden, has also with the frequency separation be- studied loudness summation and the tween them. When, on the other critical band. He presented the hand, one band was presented to sound stimuli not only through ear- each ear, the loudness did not in- phones (as in all the previous experi- crease with the frequency separa- ments) but also through a loud- tion, no matter how great it was. speaker in a free field, i.e., in an The loudness did not increase be- anechoic room where sounds are al- cause the band of noise presented to most completely absorbed by spe- each ear was never wider than a cially constructed walls. The results critical band; it was always 100 for free-field listening are similar to cycles wide. Loudness summation those for earphone listening; the thus seems to depend only upon the loudness of a band of white noise be- distribution of energy in one ear, gins to increase with bandwidth suggesting that summation takes when the critical band is exceeded. place not at some higher level in the Niese found, however, that the loud- auditory system where nerve im- ness did not continue to increase in- pulses from the two ears join, but at definitely with bandwidth, but in- the periphery, probably in the inner creased about 8 db. and then re- ear. mained constant for bandwidths Still another aspect of loudness greater than 1000 to 5000 cps de- summation has been recently in- pending upon the center frequency. vestigated (Scharf, 1959b). The re- It may be that the loudness did not sults indicate that the loudness of a increase further because the avail- complex sound remains essentially able energy was spread to very low unchanged when only the number of and very high frequencies which con- components in the complex is varied. tributed little to the total loudness. The loudness of the complex increases In other experiments, Niese (1960) with AF when AF is greater than a ! tested 4the* 'assumption that loudness critical band, but at any given value summation is a peripheral process of AF the loudness is approximately occurring independently in each ear. invariant with the number of com- COMPLEX SOUNDS AND CRITICAL BANDS 211 ponents, provided the overall sound the indirect measurements of the pressure remains invariant. masking band and the assumptions The several experiments in loud- underlying them. ness summation, along with those on threshold, two-tone masking, and Indirect Measures of the Masking phase sensitivity provide a firm body Band of evidence for the critical band. If both Fletcher's hypotheses There remains, however, the ques- about the existence of a masking tion of the role of the critical band in band and about the equality of the the masking of pure tones by white intensities of the tone and noise are noise. accepted, it is possible to calculate the size of the masking band from the MASKING BANDS masked thresholds for pure tones in Although the empirical measures white noise. Only one empirical of the critical band are quite recent, operation is necessary. The thresh- the concept of a critical band was old for a tone is measured in the expounded some 20 years ago by presence of a white noise. From the Fletcher (1940) when he hypoth- intensity of the just-masked tone esized that: (a) a pure tone that is and the intensity of the masking masked by a white noise is in effect noise, it is fairly simple to calculate masked only by a narrow band of how large a band within the noise frequencies surrounding the tone, contains the same energy as the tone. and (6) the intensity of the part of The width of this band is, by defini- the band that does the masking is tion, the masking band. Its width is equal to the intensity of the tone. calculated by taking the ratio of the Fletcher (1940) presented some intensity of the tone to the intensity preliminary experimental results to per cycle of the noise. (Since a white support his thesis, but the projected noise contains all audible frequencies full-scale experiment has apparently at equal intensity, the intensity per not been reported. Nonetheless the cycle is uniform throughout.) For concept of a critical band has be- example, Hawkins and Stevens (1950) come important in theories about found that the ratio between the in- masking. Moreover, the acceptance tensity of a 1000-cycle tone (at its of Fletcher's hypotheses permits the masked threshold) and the intensity calculation of values for the masking per cycle of the masking noise is band from the measurement of the 63:1 or 18 db. Since the intensity in masking of pure tones by white noise each one-cycle band of noise is 1/63 (Hawkins & Stevens, 19SO). The the intensity of the masked tone, a calculated values for the masking band of frequencies 63 cps wide will band turn out to be about two-and- have an overall intensity equal to one-half times smaller than the em- that of the tone. Therefore, accord- pirical values for the critical band, as ing to the second hypothesis, the measured in experiments on loud- masking band is taken to be 63 cps ness, two-tone masking, etc. This wide for a tone of 1000 cps. Values discrepancy, however, may be re- for the masking band that are calcu- solved either by a modification of lated in the foregoing manner will be Fletcher's second hypothesis, or, bet- called "critical ratios," as suggested ter, by direct measurements of the by S. S. Stevens (see Zwicker et al., masking band. Let us turn first to 1957). 212 BERTRAM SCHARF Hawkins and Stevens measured reported threshold measurements, we the masked thresholds at many fre- can modify Fletcher's second asump- quencies from 100 to 9000 cps in the tion so that the masking band has presence of white noise at levels from the same values as the critical band. 20 to 90 db. They found that the Instead of assuming, quite arbi- ratio of the intensity of a just-masked trarily, that the intensities of the tone to the intensity per cycle of the masked tone and of the masking masking noise remains constant at band are equal, we can just as well all noise levels except the very lowest. assume that the intensity of the In other words, the critical ratio does masking band is two-and-one-half not change as a function of the level times as great as that of the masked of the masking noise. The critical tone. Over most of the frequency ratio is, however, different at dif- range, this simple modification of ferent center frequencies, as shown in Fletcher's second hypothesis yields Figure 1. The results of these experi- values for the masking band that are ments agree with similar measure- equal to the measured values of the ments that Fletcher and Munson critical band. A simple modification (1937) had made of the critical ratio succeeds because, as Figure 1 shows, for tones masked by a uniform mask- except for very low frequencies, the ing noise. critical band and the critical ratio Bilger and Hirsh (1956) also calcu- are the same functions of center fre- lated critical ratios from masking quency. Since this new assumption is data obtained with bands of white ad hoc and arbitrary, it will probably noise 250 mels wide. (The mel is a have little appeal. What we need is a unit of pitch.) The substitution of a more direct and straightforward 250-mel band, which is about five type of evidence of the existence of times as wide as the critical ratios the masking band. measured by Hawkins and Stevens, is consistent with the assumption Direct Measures of the Masking Band that the energy outside the masking band contributes nothing to the The direct measurement of the masking effect. If this, Fletcher's masking band requires the sampling fundamental assumption, is true the of the masked threshold for tones in critical ratio should be the same in the presence of bands of noise of dif- both experiments. The results of the ferent widths. If a masking band two independent experiments were, exists, the tone should become more in fact, in close agreement. difficult to detect as the bandwidth In all these experiments the calcu- of the noise is increased up to the lated value of the critical ratio de- value of the masking band. Increasing pends upon the measured value of the bandwith beyond the masking the masked threshold which may not band should not raise the threshold be very reliable. Blackwell (1953) for the tone any further. (In such has shown, for example, that the experiments, energy is added to the value obtained for a threshold de- noise as the bandwidth is increased, pends upon the psychophysical meth- unlike experiments on loudness sum- od employed in its measurement. mation where a constant amount of The congruence of the results of the noise energy is spread over a wider several experiments tends, however, frequency range in order to increase to negate this criticism. Using the the bandwidth.) Direct measure- COMPLEX SOUNDS AND CRITICAL BANDS 213' rrients of this type have been reported turned out to be approximately the by Fletcher (1940), Hamilton (1957), same as the critical ratios calculated and Schafer, Gales, Shewmaker, and in 1950 by Hawkins and Stevens (see Thompson (1950). Some of the re- Figure 1). This similarity is not sur- cent experiments suggest that the prising, for the values recommended masking band is larger than the crit- by Fletcher were, in effect, critical ical ratio and may approximate the ratios. While suggestive, Fletcher's critical band as measured for other results provided neither conclusive auditory phenomena. support for his hypotheses nor a solid In the first and most famous of basis for the direct measurement of these experiments, Fletcher (1940) the width of the masking band. measured the threshold for tones of Hamilton's (1957) more recent seven different frequencies ranging work provides a direct and precise from 125 to 8000 cps in the presence measure of the masking band. Meas- of bands of noise of various widths. uring the masked threshold for an No information about subjects, ap- 800-cycIe tone in the presence of paratus, or procedure was given. The bands of noise that were centered at results of this admittedly preliminary 800 cps and that varied in width experiment provided some evidence from 19 to 1100 cps, he found that up for the masking-band hypothesis; to a bandwidth of 145 cps the masked the masked threshold tended first to threshold increased as the width of increase and then to remain constant the masking noise increased. Beyond as the bandwidth of the masking 145 cps the threshold remained con- noise was increased. The results stant, indicating that the masking seemed also to justify the assump- band at 800 cps is 145 cps wide. The tion that, within the masking band, critical band measured in four other the intensity of the noise and the just- types of experiment is also about 145 masked tone are equal: a band of cycles wide at 800 cps (see Figure 1). noise, 30 cps wide, just masked a This coincidence of values is remark- tone lying at its center frequency and able in view of the variability in- having the same intensity. Precise herent in these experiments and determinations of the width of the Hamilton's apparent unfamiliarity masking band were not possible, with the other measures of the crit- however, because the data were ical band. highly variable and only a few band- A second important result in Ham- widths had been sampled. Of band- ilton's experiment shows that the widths having values in the vicinity difference (the signal/noise ratio) be- of those for the masking band, only tween the intensity of the 800-cycle one, 200 cps wide, was adequately tone at its masked threshold and the sampled. Nevertheless, relying heav- overall intensity of the masking noise ily upon the assumption that the is not constant, even when the width masking band and the just-masked of the masking noise is less than a tone are equally intense and upon critical band. The signal/noise ratio the threshold measurements made in decreases from about 0 db. for a band the presence of wide-band noise, 30 cps wide to almost — 4 db. for the Fletcher suggested values for the critical width of 145 cps. (Hamilton width of the masking band. These reports similar results by Bauman, values, which Fletcher cautioned Dieter, Lieberman, and Finney, might be wrong by a factor of two, 1953.) Fletcher had also found that 214 BERTRAM SCHARF a band 30 cps wide just masks a tone ing band can be estimated only ap- at its center when the signal/noise proximately. In the three frequency ratio is 0 db., i.e., when the intensi- regions that were tested, the results ties of the tone and the noise are suggest a masking band that is larger equal. This equality at a width of 30 than that given by the critical ratio, cps suggested that at the critical band- and one that could well be as large as width also, the tone and noise have a critical band. the same intensity. Hamilton showed, Schafer et al. (1950) interpreted however, that at the critical band- their results to indicate no change in width the signal/noise ratio is not the signal/noise ratio within the the same as at 30 cps. Accordingly, masking band. Hamilton (1957), on Fletcher's threshold measurements the other hand, did find a small but for a tone in a 30-cps-wide band of consistent change in the signal/noise noise probably lend no support to the ratio within the masking band. Since, critical-ratio hypothesis; they are, however, Schafer's observers were however, consistent with critical- too variable to permit a precise meas- band values for the masking band. urement of changes in the signal/ Although Hamilton studied only noise ratio, the small difference be- one frequency, his results provide tween the results of the two experi- valuable information because they ments is probably not significant. are orderly and self-consistent. Prob- There is also some question about ably the use of a forced-choice proce- what Schafer et al. measured. Their dure with well-trained subjects con- use of a tone "matched in pitch to the tributed to the preciseness of the re- masking noise" may account for some sults. In contrast, Schafer et al. of the disparity between their results (1950) report a more extensive ex- and Hamilton's. periment whose results are difficult to These two experiments, by Hamil- interpret. They measured the masked ton and by Schafer, seem to be the threshold for tones in three frequency only direct tests of the masking-band regions as a function of the band- hypothesis since Fletcher's original width of the surrounding noise. In- attempt. One related experiment stead of the usual white noise, they (Webster, Miller, Thompson, & Dav- used bands of synthetic noise com- enport, 1952) deserves mention. A posed of tones one cycle apart. Pre- white noise with octave gaps was liminary experiments indicated no used to mask tones at frequencies important difference between these corresponding to those in and near bands of synthetic noise and bands the gaps. The measurements of the of white noise. Twenty-five subjects masked thresholds seem to suggest served in the main experiments in that Fletcher's values for the mask- which a random method of limits ing bands are too small. was used to measure the masked The lack of extensive tests of the threshold for a tone that had been masking-band hypothesis prevents a matched in pitch to the masking definitive statement about the valid- noise. The results suggest the pres- ity of the hypothesis, and even less ence of a masking band, but since no may be said about the size of the sharp change in the masked thresh- bands. Nevertheless the net impres- old was observed as the bandwidth sion one obtains from the literature is was increased, the width of the mask- that a masking band does exist and COMPLEX SOUNDS AND CRITICAL BANDS 215

1 1 III III _lkcps that it may well be the same width 0 .25 .5 1 2 4 8 16 as the critical band.6 _lcb OTHER CORRELATES OF THE 0 4.8 12 16 20 24 CRITICAL BAND T 1 1 1 1 1 1 mel We have seen that the function 0 500 1000 2000 2500 3000 relating the critical band to the fre- A 1 1 1 ...I.I jnd quency at the center of the band is 0 200 400 600 8013 derived from four types of experi- "i 1 1 1 1 1 1 1 mm ment and that the width of the mask- 5 10 15 20 25 30 ing band may be the same as that of -0 the critical band. Of interest, also, FIG. 4. Representation on the basilar mem- brane of (1) frequency in kilocycles, (2) criti- is the resemblance that the critical- cal bands, (3) pitch (Stevens & Volkmann, band function bears to several other 1940), (4) just noticeable differences for fre- functions of frequency: the place of quency, the fifth line marks off distance in maximal displacement on the basilar millimeters on the basilar membrane. (This membrane, the difference limen for figure is adapted from the book, Das Ohr als NachrichtenempfUnger, by Feldtkeller and frequency, and the mel scale of sub- Zwicker—1956, p. 60.) (Adapted with per- jective pitch. These similarities have mission of S. Hirzel Verlag) been noted elsewhere with respect to the critical band (Zwicker et al., of the membrane. The boundaries of 1957) and also with respect to the the critical bands are not fixed, of critical ratio (Fletcher, 1940, 1953; course, since a critical band may take von Bekesy & Rosenblith, 1951). shape around any frequency. Perhaps the most interesting fact The mel and the jnd for frequency about the critical band is that it also correspond to constant distances seems to correspond to a constant on the basilar membrane (see the distance of about 1.3 millimeters third and fourth lines in Figure 4). along the basilar membrane. The It is, therefore, not surprising that first line in Figure 4 is a slightly the critical-band function looks very idealized schematization of the fre- much like the functions for the mel quency representation on the basilar scale and the jnd scale. Measured in membrane. The second line shows mels, the size of the critical band that 24 or 25 critical bands may be varies little, from 100 mels at low represented by equal-sized segments center frequencies to 180 mels at

5 high frequencies. The mel scale is Since the preparation of this article, not accurate enough, however, to Greenwood (i960) has reported an extensive study that confirms the suggestion that there distinguish 100 from 180 mels at op- is a masking band and that it is the same size posite ends of the scale, so that the as the critical band. Greenwood measured the pitch range of the critical band may, threshold for pure tones presented in bands of in fact, be fairly constant, perhaps white noise. He varied not only the width of the bands of noise around a given center fre- approximating 150 mels. quency, but also the sensation level of the The width of the critical band on noise and the frequency of the masked tone. the basilar membrane is determined Investigating bands of noise in five regions of from the map relating the frequency the spectrum, he found consistent evidence for of pure tones to the position of maxi- the existence of a fairly sharp masking band approximately the same size as the critical mal stimulation on the membrane band. (von Be'ke'sy, 1949). Although no di- 216 BERTRAM SCHARF rect physiological measures of the for mutual masking effects among the critical band have been reported, the bands. fact that throughout the frequency Other investigators are studying spectrum the critical band corre- temporal integration for short tone sponds to a constant length of the pulses (cf. Plomp & Bouman, 1959). basilar membrane lends support to Since short tone pulses are in effect the notion that this band may be re- multicomponent complexes whose garded as a fundamental unit of hear- bandwidth varies with time, the in- ing. tegration of energy at threshold would be expected to occur within FUTURE PROSPECTS the critical band. With the experimental basis for Clinical use of the critical band has the critical band reasonably well es- been attempted by deBoer (1960) in tablished, investigators are beginning the diagnosis of hearing loss. His re- to consider the relevance of the crit- sults suggest that the critical-band ical band to the loudness of pure mechanism may be disturbed in cer- tones, to temporal integration, to tain kinds of deafness. The related deafness, to speech perception, and problem of individual differences for to other auditory processes. the critical band has remained essen- Zwicker (1956, 1958), for example, tially uninvestigated except for some has argued that the loudness of an in- observations by Niese (I960) and tense pure tone is a composite loud- indications from earlier data (e.g., ness because the displacement of the Gassier, 1954) that the size of the basilar membrane is spread over critical band may vary from person many critical bands. Zwicker as- to person, just as thresholds do. sumes that the "loudnesses" corre- Although no answers have yet sponding to these critical bands sum- come forth, phoneticists are begin- mate to give the total loudness of the ning to ask about the role of the crit- tone. Similar assumptions underlie ical band in the perception of speech. Zwicker's (1958) system for the ob- Musicians may soon add their jective calculation of the loudness of problems. The quest has begun in a complex noise. The loudness of a earnest. Now that a fundamental noise is assumed to equal the sum of unit of hearing has been identified, the individual loudnesses of the com- it remains to discover its role in all ponent critical bands after allowance the many processes called hearing.

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