S. S. Stevens

A Scale for the Measurement of the Psychological Magnitude Pitch

A subjective scale for the measurement of pitch was constructed from determinations of the half‐value of pitches at various frequencies. This scale differs from both the musical scale and the frequency scale, neither of which is subjective. Five observers fractionated tones of 10 different frequencies at a loudness level of 60 db. From these fractionations a numerical scale was constructed which is proportional to the perceived magnitude of subjective pitch. In numbering the scale the 1000‐cycle tone was assigned the pitch of 1000 subjective units (mels). The close agreement of the pitch scale with an integration of the differential thresholds (DLs) shows that, unlike the DLs for loudness, all DLs for pitch are of uniform subjective magnitude. The agreement further implies that pitch and differential sensitivity to pitch are both rectilinear functions of extent on the basilar membrane. The correspondence of the pitch scale and the experimentally determined location of the resonant areas of the basilar ...

Brightness Function: Effects of Adaptation*

The method of magnitude estimation was used to investigate how the level of adaptation affects the power function relating brightness to luminance. With the left eye dark adapted and the right eye light adapted, a test field was presented briefly to one eye. The observers’ estimates generated a pair of brightness functions, one for each eye. The validity of these functions was checked by interocular brightness matching. The results are described by the equation ψ=k(L−L0)β, when ψ is brightness, L luminance, and L0 the absolute threshold. All the parameters—k, L0, and β—change systematically with light adaptation. The exponent β increases from 0.33 for the dark-adapted eye to 0.44 for the eye adapted to 1 lambert.

The Measurement of Loudness

This paper reviews the available evidence (published and unpublished) on the relation between loudness and stimulus intensity. The evidence suggests that for the typical listener the loudness L of a 1000‐cycle tone can be approximated by a power function of intensity I, of which the exponent is log102. The equation is: L = kI0.3. Intensity here is assumed to be proportional to the square of the sound pressure.In terms of sones, where 1 sone is the loudness produced by a tone at 40 db above the standard reference level, the equation for loudness L as a function of the number of decibels N becomes: logL=0.03N−1.2.Otherwise said, a loudness ratio of 2:1 is produced by a pair of stimuli that differ by 10 db, and this relation appears to hold over the entire range of audible intensities.At low levels of intensity, the loudness of white noise grows more rapidly than the loudness of a 1000‐cycle tone, but above the level of approximately 50 db the two loudnesses remain more nearly proportional. The suggestion is...

The Masking of Pure Tones and of Speech by White Noise

This report presents the results of a study of the monaural masking of pure tones by white noise at eight sensation levels (SL) from 20 to 90 db. The observed values of masking were employed to determine two basic functions: (a) The critical band width of a masking noise, i.e., the ratio, in decibels, between the level of a pure tone and the level per cycle of the noise that is just able to mask the tone. (b) The function relating the amount of masking to the effective level of the masking noise. With the aid of these two functions, a set of contours was constructed to represent the masked threshold for pure tones heard monaurally against background of white noise having an ideal flat spectrum at the ear of the listener. A study was also made of the masking by white noise of speech in the form of continuous discourse. Measurements of the threshold of detectability and of the threshold of intelligibility were made at the same eight noise levels used to mask pure tones.

Perceived Level of Noise by Mark VII and Decibels (E)

The calculation procedure Mark VII gives the perceived level of loudness or noisiness in PLdB. It utilizes a set of frequency‐weighting contours based on an average of 25 experimental contours. The standard reference sound is defined as a 13‐oct band centered at 3150 Hz. The perceived magnitude (loudness or noisiness) grows as the 23 power of the sound pressure, so that perceived magnitude doubles with each increase of 9 dB. The summation formula for the total subjective magnitude remains St = Sm + F (∑S − Sm), but the value of F is made to vary as a function of level in order to reflect the nonlinear growth (in log‐log coordinates) of broad‐band noise. As a result of the new reference sound at 3150 Hz, perceived level in decibels (PLdB) is approximately 8 dB lower than the older loudness level in phons. Except for the nearly constant difference of 8 dB, Mark VI and Mark VII give closely similar results for typical broad‐band noises. The 8‐dB downward shift makes it possible for a sound level meter with a...

Regression effect in psychophysical judgment

Psychophysical judgment, like all other kinds of judgment, involves a matching or equating of two different domains. When the judgment involves the matching of values on two perceptual continua, the observer tends, on the average, to constrict the range of his adjustments on whichever variable is placed under his control. When the observer adjusts each variable in turn, two different regression lines are produced. This regression effect presumably occurs whenever the results of the matching judgments yield less than a perfect correlation. Illustrative examples are given for the continua, loudness, vibration, brightness, and duration.

Sensory scales of taste intensity

The subjective intensity of taste was scaled by the method of magnitude estimation in which Os assigned numbers to designate the apparent strength ofstimulus concentrations. Substances used were sucrose, dextrose, maltose, fructose, saccharin, Sucaryl, sodium chloride, and quinine sulfate. For aqueous solutions of each substance, taste intensity was found to increase as a power function of concentration by weight. Some approximate exponents were: sucrose, 1.3; sodium chloride, 1.4; quinine sulfate. 1.0. The magnitude scale for sucrose was compared with the category scale obtained by a commonly used rating procedure. The category scale turned out to be highly nonlinear.

Loudness, Reciprocality, and Partition Scales

By the methods of magnitude estimation and magnitude production, judgments of softness were shown to be the reciprocal of judgments of loudness. The instruction to judge “distance” produces the same results as instructions to judge softness. Attempts to partition a segment of the loudness continuum into equal‐appearing intervals results in a systematic error that is greater the more variable are the judgments.

A psychological scale of weight and a formula for its derivation.

* Accepted for publication January 15, 1948. SS. S. Stevens, A scale for the measurement of a psychological magnitude, loudness, Psychol. Rev., 43, 1936, 405-416. 2 S. S. Stevens, J. Volkmann and E. B. Newman, A scale for the measurement of the psychological magnitude pitch, J. Acoust. Soc. Amer., 8, 1937, 185-190; and S. S. Stevens and J. Volkmann, The relation of pitch to frequency: a revised scale, this JOURNAL, 53, 1940, 329-353. ST. W. Reese, The application of the theory of physical measurement to the measurement of psychological magnitudes, with three experimental examples, Psychol. Monog., 55, 1943 (No. 251), 1-89. 4 E. H. Taves, Two mechanisms for the perception of visual numerousness, Arch. Psychol., 37, 1941, No. 265. SA discussion of the theory of scaling and a description of the criteria of a ratio scale are presented by Stevens (On the theory of scales of measurement, Science, 103, 1946, 677-680). A somewhat different presentation of this subject may be found in Reese, op. cit.

Relation of brightness to duration and luminance under light-and dark-adaptation

Abstract These experiments determined how the brightness of a brief flash grows with duration and intensity in dark-adapted and light-adapted eyes. Observers matched the brightness of a 1-sec flash to that of shorter flashes over a wide range of luminances. They also matched the briefer flashes to the 1-sec flash. The matching functions exhibit the brightness enhancement known as the Broca-Sulzer effect. The maximum enhancement shifts to a lower duration as the intensity is increased. Below about 10 msec in the dark-adapted eye the product of duration and intensity is constant for a given brightness (Blochs law). In an eye adapted to 95 dB (300 mL) this reciprocity was not found at the durations used, 0.15 msec and greater. The results accord with other evidence to the effect that brightness grows as a power function of luminance, but that two basically different exponents are involved. When the duration is above the region of the Broca-Sulzer enhancement, the exponent has the value13. When the duration is short enough for Blochs law to apply, the exponent is larger. Present evidence places the flash exponent between 0.4 and 0.5 for the dark-adapted eye.