Stevens, S.S. (1957). On the psychophysical law. Psychol. Rev. 64, 153-181


Perceptual continua divide themselves into two general classes (StevensGalanter1957a). The nature of this division is suggested in a general way by the traditional dichotomy between quantity and quality. Continua having to do with {\it how much} belong to what we have called Class I, or prothetic; continua having to do with {\it what kind and where} (position) belong to Class II, or methatetic. Class I seems to include, among other things, those continua on which discrimination is mediated by an additive or prothetic process at the physiological level ... An example is loudness, where we progress along the continuum by adding excitation to excitation. Class II includes continua on which discrimination is mediated by a physiological process that is substitutive, or methatetic. An example is pitch, where we progress along the continuum by substituting excitation for excitation, i.e., by changing the locus of excitation. We know too little about physiological mechanisms to say whether all Class I continua are based on additive processes or all Class II continua on substitutive processes, but in those instances where the facts seem clear the parallels between function and physiology are at least suggestive. Until our knowledge stands improved, it is perhaps best to classify the perceptual continua by the pragmatic criteria of the way they behave and to hope that any uniformities we can discover will lead to deeper insights into basic mechanisms.

Four functional criteria are relevant to the distinction between prothetic and metathetic continua, although they have not all been tested with equal thoroughness. These four criteria concern the subjective size of the j.n.d., the form of category rating-scales, the time-order error, and hysteresis. It is likely, of course, that other criteria will be discovered if we continue to look for them.

1. Subjective size of the j.n.d. ... it is the growth in the subjective size of the j.n.d. as we go up the scale on a Class I or prothetic continuum that seems, in a sense, to "explain" at least two of the other three criteria... The point here is that on Class I continua the j.n.d.'s are not equal in subjective size. On continua of Class II (metathetic) the j.n.d.'s turn out to be approximately equal in subjective size when measured by magnitude scales of the continuum. The linearity between the mel scale of subjective pitch and the j.n.d. scale for frequency is a case in point ... and it seems reasonable to suppose that the same linear relation is approximated on such continua as position and inclination.

2. Category rating-scales. A category rating-scale is the function obtained when a subject judges a set of stimuli in terms of a set of categories labeled either by numbers or by adjectives. The form of these scales is different in the two kinds of continua. As shown by studies of a dozen perceptual dimensions (StevensGalanter1957a), the category scales on continua of Class I are concave downward when plotted against a ratio scale of the subjective magnitude. Category scales on continua of Class II {\it may be} linear when so plotted.

The chief factor that produces nonlinearity in the category scales of Class I is variation in the subject's sensitivity to differences. Near the lower end of the scale where discrimination is good the categories tend to be narrow, and by consequence the slope of the function is steep. Near the upper end, where a given stimulus difference is less easy to detect, the categories broadenand the slope declines. Only on Class II continua, where sensitivity (measured in subjectiveunits) remains relatively constant, is it ordinarily possible to produce category scales that are linearly related to subjective magnitude.

Prothetic continua of Class I on which category scales have proved nonlinear include apparent length, area, numerousness, duration, heaviness,lightness, brightness and loudness. Metathetic continua of Class II on which category scales have proved more or less linear include visual position, inclination, proportion, and pitch. On both types of continua alterations in the form of the category scale may beproduced by a variety of factors, including stimulus spacing (or relative frequency of presentation), landmarks, and differential familiarity...

3. Time-order error. The so-called "time-error" discovered by Fechner has been pursued in the theory and experiment for many decades ... It refers to the fact that the second of two equal stimuli tends to be judged greater than first. We have reason to believe that a systematic time-order error (as Guilford prefers to call it) is characteristic of judgments on Class I continua. On Class II continua we neither expect it nor do we generally find it ... ... Not only is the time-order error produced by other factors than time, but it also has nothing to do with order. Nor is it necessarily an error... If my thought is correct, that we are dealing here with an effect on category judgments that derives from an asymmetry based on the relativity of discrimination, a better name for it might be the "category effect"...

4. Hysteresis. ... The effect shows up in especially dramatic fashion in experiments on bisection and equisection. In a typical experiment on loudness the subject sits before a row of five keys which he presses to produce the tones (1000 cps). The levels produced by the two end keys are fixed, 40 dB apart, and the subject adjusts the levels controlled by the intermediate keys in order to divide a 40-dB interval into four equal-appearing steps in loudness. Where the subject sets the levels depends on whether he listens to the loudnesses in ascending or descending order. I found that in the ascending order he sets the bisecting level some 5 to 8 dB higher than in the descending order...