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COMPLEX SOUNDS and CRITICAL BANDS1 BERTRAM SCHARF Northeastern University

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COMPLEX SOUNDS and CRITICAL BANDS1 BERTRAM SCHARF Northeastern University 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.
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