Tonal density.

Originally published in Journal of Experimental Psychology, Volume 17, pages 585-92, 1934.

S.S. Stevens, Harvard University

One of the Os in Rich's experiment on tonal volume [1] reported, "The larger [lower] tones seem to have a greater diffuseness. It seems as if the smaller [higher] tones fill space more compactly, what they fill." Similar characterizations of the phenomenal aspects of tones have appeared in the protocols of several Os in more recent experiments. An O in an experiment performed by Gundlach and Bentley [2] described high tones as "denser" and "compacter" than low tones. Likewise, in Moul's a experiment, where she sought to obtain phenomenal descriptions of the "thickness" or volume of tones, one finds that a noise was characterized as "tight, hard, impenetrable" by an O who described a tone of 700 cycles thus: "The tone somehow carries the meaning of "giveyness," of penetrability, of a certain looseness, a certain softness in the sense that a vapor is soft." Another O in the same experiment experienced a tone of woo cycles as "thick, dense, compact." The same tendency of Os to experience high tones as dense, hard, compact, impenetrable was present in the author's 4 experiment on tonal volume and suggested that, density might be a discriminable aspect of tonal stimuli, different from volume, pitch and loudness. The present experiment was undertaken to test this possibility.

The Os used in the experiment were Dr. J. Volkmann (V), Mr. E. B. Newman (N), Dr. J. G. Needham (Ne), and Mr. H. S. Odbert (Od). V and N had observed in the experiment on tonal volume and were well trained in the technique used in that and in the present experiment. Furthermore, they had both described tones as being more or less dense at one time or another. Ne and Od had never heard of tonal density and had, therefore, to be trained in its recognition. The training was accomplished by presenting them with a high tone followed by a low tone and asking them to notice the difference in the density of the two. They immediately reported that the higher one was more dense. They were then presented with a loud tone followed by a weak tone. In this case they both described the loud tone as being more dense than the weak tone. Their judgments thus fell into line with the reports of V and N.

The experimental procedure was to present alternately two tones of different pitch and to require the O to equate them in density by changing the intensity of one of the tones. This result was achieved by the use of an oscillator (General Radio, type 508-A) in a circuit so designed that by means of a switching device [5] two tones of different pitch could be presented alternately at the rate of about 40 per min. One of the tones was of fixed intensity, whereas the intensity of the other could be changed by a small variable resistance held in the hands of the O. The O adjusted the intensity, taking as much time as he desired, until the two tones seemed equal in density, and the voltage was read directly from a voltmeter connected across the output of the oscillator. Two Jensen "Concert Junior" dynamic speakers were used as the source of sound. These speakers were mounted close to the head of the O, one over each ear. The observing was done in a sound-room lined with a 2-in. blanket of rock wool designed so as to minimize the reflection of the sound by the walls.

Each of six comparison tones was equated to the standard tone (500 cycles at 60 db above threshold) in both density and intensity. Equations were made in respect of both aspects during each of five observational periods by each O. The difference between the value at which a given tone was judged equal to the standard in density and the value at which it was judged equal in intensity was taken as a measure of the amount by which the two tones differed in density for the particular O.

The results are shown in Table I. Values are given in both volts and db. The values in db were computed from the liminal value which was empirically determined as .001 volts. It will be noted that the magnitude of the difference between the value at which a given tone was judged equal to the standard in density and the value at which it was judged equal in intensity is approximately the same for each O. One can thus average these differences for the purpose of plotting a contour representing equal density.

The results of matching 6 tones to the standard frequency 500 cycles at the intensity level of 1.0 volt, or 60dB above the threshold value of .001 volt.

Each entry is the average of 10 observations.

Frequency V N Ne Od
Density: Volts dB Volts dB Volts dB Volts dB
400 2.04 66.18 1.34 62.54 2.35 67.42 1.51 63.58
450 1.63 64.24 1.16 61.28 1.92 65.51 1.35 62.60
475 1.22 61.72 1.10 60.82 1.72 64.71 1.19 65.51
525 .82 58.38 .94 59.46 .99 59.99 .90 59.08
550 .69 56.78 1.05 60.08 .85 58.59 .85 58.59
600 .44 52.86 .99 59.99 .77 57.73 .75 57.50
400 1.35 62.60 .94 59.46 1.53 63.69 1.12 60.98
450 1.18 61.42 .98 59.82 1.38 62.80 1.13 6.06
475 1.05 60.42 .98 59.82 1.34 62.54 1.07 60.58
525 .98 59.82 1.04 60.34 1.26 62.00 1.05 60.42
550 1.01 60.08 1.29 62.22 1.23 65.80 1.05 60.42
600 .87 58.79 1.38 63.80 1.25 61.94 1.05 60.42
Difference between Density and Intensity in dB
400   3.58   3.08   3.73   2.60
450   2.82   5.46   2.75   5.54
475   1.40   5.00   2.17   .93
525   -1.44   -0.88   -2.01   -1.34
550   -3.30   -2.14   -3.21   -5.83
600   -5.93   -3.85   -4.21   -2.92

Table II shows the coefficients of variation (100 A.D./Mean) for the data of Table I. The average coefficient of variation of the judgments in terms of density is larger in the case of every O than the average coefficient of the intensitive judgments. This difference may be interpreted as meaning that the differential limen for density is larger than the differential limen for intensity. A similar relationship has been found to obtain for volume. A comparison of the coefficients of variation for the volumic judgments obtained in the author's experiment on tonal volume with the present coefficients for density reveals the fact that the coefficients are of comparable magnitude, an equivalence which suggests that Halverson's [6] technique of the determination of differential limens is not adequate as a means of showing the univocal status of volume as an attribute. Had Halverson's Os been judging density instead of volume, the magnitudes of the resultant limens would not necessarily have revealed the fact.

Coefficients of variation of the results obtained from 4 Os

Each coefficient is based upon 10 observations.

Frequency V N Ne Od
400 15.25 8.06 7.53 8.01
450 13.87 6.90 9.01 8.74
475 12.13 4.27 10.52 7.48
525 9.39 6.8 10.51 5.56
550 14.64 8.22 12.24 5.53
600 8.41 10.20 7.79 12.80
Average 12.28 7.41 9.60 6.02
400 11.40 9.04 6.99 6.61
450 9.49 6.84 4.49 5.31
475 7.24 5.61 6.42 4.58
525 5.82 5.38 7.62 4.95
550 8.51 5.43 8.94 5.90
600 7.14 8.18 7.44 7.43
Average 8.27 6.75 6.98 5.80

Average of the average coefficients for density:  8.83
Average of the average coefficients for intensity:  6.95

Density is established as a discriminable aspect of tones distinct from loudness and volume by the nature of the contour shown in Fig. 1.  There, the curve is plotted from the differences between the values at which two tones are matched in density and the values at which they are matched in loudness, so that the Os can not have confused density with loudness. The fact that they have not confused density and volume is apparent from the fact that this contour has a negative slope, whereas contour for equal volume, plotted in the same coordinates, has a positive slope. The function means that in order that two tones may be equal in volume, the higher 'tone must be made louder than the lower tone. To make them equal in density, however, the lower tone must be made louder than the higher.

Figure 1
Figure 1. Contour representing equal density of 6 tones equated to a standard tone (500 cycles, 60 db above the threshold), as plotted in positive and negative deviations of frequency and intensity from the standard, which is represented as the point 0,0 in the graph. Each point is the average of the data from 4.0s.

The introspections of the Os show general agreement as to the phenomenal basis of their judgments. V and Od, however, stated that density was not "penetratingness" or "piercingness." They thought it might be possible to match two tones for "piercingness," but were uncertain as to whether the matches would be different from the equations they made for density. V also had some difficulty at first in getting the higher tones to lose their density when the loudness was decreased, a difficulty which tended, however, to disappear with practice. Towards the end of his series V said: "Low tones intrinsically lack density, but to make a high tone lose its density it must be made quite faint. Then it becomes much like a faint cloud. It loses its hard center, or rather, the hard center spreads out."

N stated: "The density of tones is not very hard to judge. It is one of the most direct judgments I have made. Density is very much the same as the penetrating quality of the tone. The thing I am judging as density is right in the middle of the tone; it is the core of the tone, whereas what I was judging as volume was the limits of the tone-- the outer edge. Sometimes I get visual imagery. Then the low tones of poor density seem like attenuated smoke and the dense tones appear as solid, heavy smoke."

The report of Ne was: "Some tones are thick-- others are thin or diffuse. The high tones are packed solidly. They are solid all the way through. If one of these tones is weakened in intensity, it becomes more scattered. Then it is thinner and less dense."

Od was confused at first by the difference in pitch between the two tones, but quickly overcame this difficulty. He reported: "Density seems to be somewhat analogous to saturation; that is, it is the ratio of the amount of tone to the amount of silence it is diluted in. It is the concentration of the tone-- the amount per unit something or other. It is difficult to express."

The physiological basis of density is not obvious. One would like to think of it as dependent upon the density of the nervous impulses reaching the cortex via the auditory nerve. Volume, then, might depend upon the spread of these impulses, as Boring [7] suggested, and intensity might depend upon the total number arriving per unit time. Such a situation is conceivable in terms of a resonance theory, but, in view of the present state of our knowledge, it is perhaps wiser to limit ourselves to some such statement as the following. The interaction of a sound wave with the auditory mechanism of a subject who has been instructed to observe tonal density sets up a dynamic pattern of neural excitation which is differentiated so as to issue in a specific discriminatory response. Since the response when the instruction is to judge density is different from the response which results when the subject is set to observe volume or intensity, it must follow that the total neural pattern is differentiated differently in each case, but the precise nature of the crucial neural pattern and the manner of its arousal by the cochlear mechanism remains obscure.

Another notion suggested by the outcome of this experiment is that the existence of density as a phenomenal dimension may account for the fact that weak tones are commonly .referred to as soft. In the usual description given of a tone of slight density one finds such adjectives as "soft," "penetrable," loose," diffuse;" whereas dense tones are called "hard," "solid," "impenetrable." For a given pitch, the dense tones are the loud tones; the tones which lack density are the weak tones. Hence, it may be that, in the absence of a convenient antonym for loud, the word soft came to be used, because it expresses one of the phenomenal characteristics of weak tones.


1. In several previous experiments density has been reported as one of the phenomenal aspects of tones.

2. The ease with which Os are able to equate in density two tones which differ in pitch by changing the intensity of one of the tones indicates that density is a discriminable aspect of tonal stimuli.

3. The average coefficients of variation of the equation of two tones for density are larger than the coefficients of the equation of two tones for intensity, and the coefficients for density are approximately equal to the corresponding coefficients for volume.

4. The form of the contour for equal density, as plotted against frequency and intensity (Fig. 1), shows that the Os did not confuse density either with loudness or with volume.

5. The physiological basis of the experience of tonal density is at present obscure.

(Manuscript received June 14, 1933)


1. G. J. Rich, A preliminary study of tonal volume, J. EXPER. PSYCHOL., 1916, 1,19.

2. R. Gundlach and M. Bentley, The dependence of tonal attributes upon phase, Amer. J. Psychol., 1930, 42, 538.

3. Emeline R. Moul, An experimental study of visual and auditory `thickness,' Amer. J. Psychol., r93o, 42, 551 f.

4. S. S. Stevens, The volume and intensity of tones, to be published in Amer. J. Psychol. The apparatus used in the present experiment is described in this paper.

5.  S. S. Stevens, A switch for the presentation of electrically generated tonal stimuli, to be published in Amer. J. Psychol.

6.  H. M. Halverson, Tonal volume as a function of intensity, Omer. J. Psychol., 1924, 35, 360-367.

7.  E. G. Boring, Auditory theory with special reference to intensity, volume and localization, Amer. J. Psychol., 1926, 37, 167 f. The idea is more specifically stated by the same author in Physical Dimensions of Consciousness, 1933, 85.