The nature of tonal brightness.

Originally published in Proceedings of the National Academy of Sciences, 22, 514-21, 1936.

by E.G. Boring and S.S. Stevens

Psychological laboratory, Harvard University

It is well known that tones can be characterized as bright or dull. When intensity does not alter greatly, tonal brightness seems to vary with pitch: high tones are bright, and low tones are dull. Thus Rich [1] concluded that brightness and pitch are identical as tonal attributes. Abraham [2] concluded that the brightness of tones produced by a Seebeck siren is a function of the ratio of the size of the hole in the siren disc (II) to the size of the closed interval between holes (I). For values of H/I from about 1.0 to 0.1 he concluded that brightness varies inversely with H/I. By an analysis of what he supposed these waves forms to be he decided that brightness is not due to the presence of higher partials, for the reason that his analyses did not persistently show an increase in the higher partials for the brighter tonal complexes. He thus was led to suppose that brightness depends upon the form of the primary wave in the complex. Ogden [3] later accepted Abraham's conclusion.

Apparatus.

For stimuli we cut sirens from cardboard (0.04 in, thick). Each siren is a disc of 16-in. diam. The holes are sectors, 0.75 in. in radial dimension, with the ends cut exactly along radii and the sides cut approximately as arcs about the siren's center. In this way we avoided the ambiguity that arises with the circular holes of the Seebeck siren, where it is hard to say just what is the exact duration of the hole and of the interval between holes. Moreover, the radial width of these holes is so large in relation to the spread of the blast of air that it probably constrains the air very little.

The air-blast was delivered from a tank at a pressure of 5 lb. per sq. in. The nozzle pressure was reduced by the friction of a long rubber tube (16 ft. long, 1/4 in. inside diam.). The nozzle was a piece of V2-in. round brass, drilled with a hole 0.16 in. diameter, streamlined conically back 1/2 in. from the end. The orifice was fixed about 0.25 in. from the face of the disc.

The sirens were rotated on induction motors, which ran as synchronous motors at 1800 rpm on light loads, and which maintained great constancy at 1650 rpm with the sirens as loads.

Among 24 stimuli prepared for investigation, the nine listed in table 1 yielded the most significant results. The stimuli 1B, 2B and 3B are identical. 1A, 1B and 1C provide variation of the mean linear velocity (V) of the holes, with H/I I and the frequency (F) constant. 2A, 2B and 2C give variation of frequency (F), with H/I and V constant. 3A, 3B and 3C provide variation of the ratio of the hole to the interval between holes (H/I), with V and F constant. Preliminary experimentation with other discs in which H varied with I constant, and I varied with H constant, revealed no significant auditory changes other than those dependent on the ratio H/I.

Table 1.  Description of stimuli.

Velocity

These sirens yield complex tonal masses and a simple comparative judgment of two such complexes is not easy. However, there is no exception (among 5 observers) to the rule that brightness varies directly with linear velocity (V). (See table 2.) So also does loudness. All observations show that 1A is brighter and louder than 1B, and 1B brighter and louder than 1C. When the loudness of the two members of the comparison are equated subjectively by throttling the tube to the nozzle for the louder sound, the difference in brightness is much reduced, the judgment of brightness becomes more difficult, and two of the five observers reversed their judgments for one or the other of the two stimulus pairs. It is apparent that brightness is not loudness, since a difference in brightness persists when the difference in loudness is eliminated, but it also appears that brightness tends to vary directly with loudness. Since it is known that brightness also tends to vary with pitch [1], we advance the hypothesis that brightness varies directly with both the intensity and the frequency of the stimulus, after the manner of tonal density [4,5].

Figures 1-3.  Harmonic spectra of the sounds 1A, 1C, 3A, and 3C.

The paired stimuli (1A-1 C and 3A-3C) are subjectively equated in loudness. Abscissa: logarithmic scale of frequencies of harmonic partials. Ordinate: intensity as ratio of third partial = 1.0. The properties of the stimuli are:

Figure 1 shows that brightness depends on V, since 1A is brighter than 1 C when H/I and F are constant.

Figure 3 shows that brightness does not depend on H/I, since 3A and 3C are not demonstratively different in brightness when H/I varies, and V and F are held constant.

The frequency spectra for 1A and 1C are shown in figure 1. These analyses of the sounds were made by means of a General Radio Type 636-A Wave Analyzer. They gave no evidence of Abraham's Knall frequency, well below the siren's fundamental, or of any other frequencies below the fundamental. A few inharmonic partials were found, but they were of insufficient intensity to appear in the charted spectra. Figures 1A and 1 C show the harmonic components of the stimuli 1A and 1 C, plotted as ratios of the third partial as unity, for all these tonal complexes that have been analyzed turn out to be dominated by the third partial. Since the analyzed stimuli were subjectively equated for loudness, the charts must be examined for the effect of frequency upon brightness. It will be seen that the brighter sound, 1A, weights the upper partials more than does the duller sound, 1C. 1A has less of the first and second partials than 1 C, has the seventh partial fully as strong as the third, and has the partials in the fourth octave (8 to 15) more prominent than they are in 1C. The visually perceived difference between the plotted spectra is quite as great as the auditorially perceived difference between the brightness of the two sounds, for these spectra are taken for the small difference of brightness that occurs when the sounds are of equal loudness.

TABLE 2.
Comparative judgments for different pairs of stimuli.

At the left is shown the category of judgment (and whether loudness was or was not equalized). Each column shows the two frequencies with which each of the two stimuli was preferred as brighter, etc. The table summarizes 136 judgments. Among these there were only 8 equality-judgments, and these have been divided equally between the two sides of the column. Thus "7-0" in the upper left corner of the table means that the sound 1A (V = 264 cm./sec.) was 7 times judged brighter than the sound 1B (V = 198 cm./sec.), and no times less bright.

Figures 4-6 also demonstrate the dependence of brightness upon velocity and its independence of the ratio H/I when frequency is constant. These graphs are wave-forms traced from the patterns on a cathode-ray oscillograph. The sounds were got from a cardboard Seebeck siren with round holes. The properties of their stimuli are shown in the legend of the figures. 4A, 5A and 6A are the dull sounds ; 4C, 5B and 6B are brighter (and also louder). 4B lies qualitatively between 4A and 4C. The series 4A-4B-4C duplicates Abraham's condition and shows brightness varying directly with V and inversely with II/I. The pair 5A -5B shows brightness varying directly with both V and II/I. The pair 6A-6B shows brightness varying directly with V when H/I is constant. The conclusion is inescapable that it is a change in the velocity V, and not the change in the ratio H/I, which causes the difference in brightness.

Figures 4-6 also show the typical appearance of the wave-forms of bright sounds (4C, 5B, 6B) and of dull sounds (4A, 5A, 6A).

Figures 4-6.  Oscillograms of seven siren sounds.

The sounds increase in brightness in the orders 4A-4B-4 C, 5A-5B and 6A-6B. They are not equated for loudness. C = the compression-phase when the hole opens, and E = the expansion-phase when the hole closes. The properties of the stimuli are:

Figure 4 shows that brightness increases when V increases and H/I decreases.

Figure 5 shows that brightness increases when V increases and H/I increases.

Figure 6 shows that brightness increases when V increases and H/I is constant.

Hence brightness depends upon V and not upon H.

Frequency.

The series of stimuli 2A-2B-2C gives a decrease of frequency (F) when V and H/I are constant. In all cases 2A is judged brighter than 2C, and usually 2A is also judged to be louder, although the difference in loudness seems less than the difference in brightness. 2B was judged brighter than 2C in all cases but one. They are nearly equal in loudness, and there is no consistency as to the direction in which the difference of loudness is reported. When the differences of loudness are eliminated by subjective equation, the order of decreasing brightness is still 2A-2B-2C, although here two observers showed confusion in distinguishing between 2A and 2B.

This finding supports the preceding conclusion that brightness tends to increase when the frequencies of the various components of a tonal complex are increased, or when the total intensity of the complex is increased.

The H/I Ratio.

The series 3A-3B-3C provides an increase in II/I with V and F constant. This is the parameter which Abraham accepted as the condition of brightness. We do not find it possible to obtain consistent comparative results for brightness with these stimuli. It is clear that the stimulus 3B is not so loud as 3A and 3C. Hence there is a tendency for observers to report 3A and 3C as brighter than 3B. When the loudnesses of the pairs are equated subjectively, the judgments of brightness become difficult and contradictory. See table 2. The harmonic spectra of 3A and 3C, shown in figure 3, support this conclusion : the spectra are not obviously different. It is now clear that brightness does not depend upon the II/I ratio, except that the departure of this ratio in either direction from unity tends to increase loudness, and with it brightness in lesser degree.

A similar conclusion has already been reached from a consideration of the wave-forms of figures 4-6.

The Relation to Abraham's Finding.

The chief ground for Abraham's conclusion is found in his data for the relative brightness of sounds obtained from a special Seebeck siren. In this siren, on each of five different circumferences, 24 circular holes were cut. All holes were the same size. On the circumference of least radius the diameter of a hole approximately equaled the space between the holes, i.e., H = I, and H/I = 1.0. On the outer circumference, since the holes were not made larger, the space between holes became about ten times as large as the holes; H/I = 0.1. Abraham found that the brightness of the sound increased consistently as H/I decreased from 1.0 to 0.1. However, he had not controlled the velocity, which was more than five times as great on the outer circumference as on the inner. The changes of brightness which he observed should have been ascribed to V and not to H/I.

Abraham considered the possibility that brightness depends upon the predominance of upper partials and rejected the hypothesis. He worked without the advantage of modern means for the electrical analysis of sounds and he assumed incorrectly that a siren, in which H/I 1.0, would have a simple wave-form with the phases of compression and expansion unequal. Figure 4 shows what actually happens to the wave-form when Ii/ I varies under Abraham's conditions with V, and figure 3 shows what happens to the harmonic analysis when H/I varies without V. The general conclusion, based upon the inspection of oscillograms, is that the brighter siren sounds tend to have more and sharper peaks-- a conclusion that is consistent with the finding that they have relatively strong upper partials.

The Relation of Brightness to Density.

One of us (Stevens) has shown that tones possess an attribute of density, which increases with the intensity or the frequency of the stimulus, and can be held constant if intensity and frequency be varied inversely in the right amounts [4,6] We have shown that brightness is a similar function of intensity and frequency. The question arises as to whether brightness and density can be identified as the same tonal attribute.

Neither of us is able to distinguish between brightness and density in making these comparative judgments. One of us (Stevens) is accustomed to making judgments of tonal density and asserts that at no time has he ever been able to distinguish density from brightness. The other of us (Boring) learned to judge density after he had learned to judge brightness, and, although his mechanisms of judgment (visual surrogates) are different for the two tasks, he finds that brightness and density always covary and are thus indistinguishable for him as attributes of the sound. Two other observers have given judgments of density (see table 2) and in most instances have reported the relations of stimuli with respect to density the same as they had previously reported for brightness. One of these observers had been trained to make judgments of density in a previous experiment [4]. However, these observers both reported 2B (330 c.p.s.) as denser than 2A (495 c.p.s.) but 2A as brighter than 2B. After repeated trials neither of us is able to agree with this inversion. We think that the other observers have shifted their criteria in these cases and are judging the coherence of the tonal mass and not the attribute that has been established as density. These tonal masses offer in the patterns of their complications many new dimensions of difference, and the maintenance of a single criterion is doubtless more difficult than it is for pure tones.

Working with pure tones, one of us (Stevens) has tried to get observers to make two tones of different frequencies equal in brightness by varying the intensity of one tone. This is the method that has been used to establish the laws of variation for the other tonal attributes—pitch, loudness, volume and density. Observers, who are accustomed to making judgments of density, find it impossible to equate these two tones in brightness, if they are instructed to regard brightness as different from density. On the other hand, observers, who are unfamiliar with density, are able to make consistent judgments of brightness, and for them brightness turns out to increase with both the intensity and the frequency of the stimulus, according to the relationship which has with other observers been established for density.

It seems to us, therefore, that brightness and density covary to such an extent that the two attributes ought, at least tentatively, to be identified. It is probable that two attributes, whose laws of dependence upon the parameters of the stimulus differ by an amount that is small with respect to the probable error of the judgments, would never come to be distinguished. They would remain practically identical until the probable error of judgment could be reduced. In this sense at least we think that tonal brightness is tonal density as that attribute has been previously established [4].

Conclusion.

The brightness of tones and tonal complexes varies directly with the intensity and with the frequency of the stimulus, after the manner of tonal density. Tonal brightness and tonal density are thus probably to be identified. Of the two terms density is to be preferred, since it has been definitely established by quantitative measurement and is therefore less equivocal than brightness.

Footnotes

1. G. J. Rich, "A Study of Tonal Attributes," Amer. Jour. Psychol., 30, 121-164 esp. 153-158 (1919).
2. O. Abraham, "Zur psycholgischen Akustik von Wellenldnge and Schwingungszahl," Z. f. Sinnesphysiol., 51, 121-152, esp. 130-152 (1920).
3. R. M. Ogden, Hearing, New York, Harcourt Brace and Co., esp. 10-12, 58-62 (1924).
4. S. S. Stevens, "Tonal Density," Jour. Exper. Psychol., 17, 585-592 (1934).
5. S. S. Stevens, "The Attributes of Tones," Proc. Nat. Acad. Sci., 20, 457-459 (1934).