G. T. Fechner proposed his logarithmic law between physical continuum of stimulus and an attribute of sensation in 1860. Fechner also proposed the distinction between outer and inner-psychophysics. Outer-psychophysics deals with the relation between the observable participant's response and stimulus. In outer-psychophysics, it can be postulated that the response is located on the interval scale when the logarithmic law between stimulus and response is established.
In inner-psychophysics, the logarithmic law is established in mind on the assumption that the equality of subjective size of just noticeable difference (jnd). However, it is difficult to verify the equality of jnd using empirical procedures. Bergson strongly criticizes that Fechner's law is based on an assumption that cannot be verified.
Zwislocki (1991) defines that the measurement entails matching of common attributes of things or events. According to his definition of “Natural Measurement”, we can match the different things or events on the common psychological continuum. As a result, matching operation can ensure the point of subjective equality (PSE) to be a common attribute among different objects. When an appropriate measure is applied, the same PSE from different things or events confirms the same point on the continuum of common attribute of sensation. The PSE is a physical measure. It can be measured using objective or empirical procedure. An important role of psychophysics is to find an appropriate physical measure. Usually, the standardized physical measure of adequate stimulus is modified on the basis of psychophysical data and reflects the characteristics of sensation. Therefore, a good relationship between subjective response to adequate stimulus and a standardized measure can be expected.
It is true that the relation between the loudness judgment of various kinds of nonsteady sounds and a standardized index (e. g. equivalent continuous A-weighted sound pressure level: LAeq) exhibits a high coefficient correlation. However, a law derived from the experimental results depends on the psychophysical method used. For example, the method of category scaling results logarithmic law and magnitude estimation results power law.
The result of the experiment using the scale discriminative method was introduced to verify whether the logarithmic law or the power law was valid for the loudness judgment. The results showed that participants' quantitative judgments were well adapted to the experimental procedure. Torgerson (1960) suggests that the participants seem to judge the stimulus taking a different strategy depending on the purpose of the experiment. In daily life situations, we are very adaptive to quantitative behavior for satisfying the purpose of the behavior. This poses a problem of ecological validity in psychophysics. Therefore, it is necessary to select the appropriate stimuli and method to simulate the daily life situations in the psychophysical experiments.
Main attributes of auditory sensation are loudness, pitch and timbre. Both loudness and pitch are one dimensional, but timbre or tone quality is multidimensional. It is difficult to constitute rating scale of tone quality expressed by only one physical dimension, and at present, it is far from to establish a general psychophysical rule for applying to tone quality. However, if the sound source is limited, a possibility of establishing a physical scale to predict tone quality. Some examples of the machine sound's tone quality control were introduced.