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: L_Aeq) 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.

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知覚とイメージの類同性の問題はイメージ研究の中心的課題になりつつある。しかし対象とされるイメージは視覚が主であり、運動行動と密接に関連する筋感覚的イメージについては未解決の問題が多い。本研究の目的は、におけるマグニチュード推定法を用いて知覚と筋感覚的イメージの類同性について検討を加えることにある。

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This research focuses on the relationship between the spatial self-position-detection with landmarks and the function of the visual field. 28 college students participated in the experiment were asked to move the center of the landmarks in virtual environment. By measuring the difference between the stopped positions under each condition and the exact central point of landmarks, the accuracy of the spatial position detection was quantified. The results indicate that the central visual field within 5 degrees and the visual field of 15 to 20 degrees of vision centered on the fixation point play a large role in the self-position-detection.

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　One unique feature of the piano is the continual decay of the sound after a key is pressed until the finger is lifted from the key. In this process, the sound from the piano attenuates the level while slightly changing the frequency structure.
　Further, when the pianist releases the key, but presses the forte pedal with the foot, the sound continues. The pianist can finely adjust the decay pattern that follows pressing a key by moving fingers and operating pedal. Thus, one of the major factors that can realize the expression of a brilliant piano performance is the decay of the sound itself, and the ability of pianist precisely control the characteristics of that decay to create a beautiful stream of sound. As shown in Fig.1, the dynamic characteristics of hearing greatly affect the perception of decaying sounds. The sound of a piano after a keystroke continues to attenuate, however, if the legato technique is performed with a finger held on a key or the forte pedal being pressed, the sounds played one after another will overlap. If dissonant sounds are generated over time, the sequence provides an unpleasant impression. If the decaying part of the preceding sound and the rising part of the following sound are superimposed, an acoustically dissonant sound is generated.
　Reflecting on the dynamic characteristics of hearing, due to the overshoot of the following sound, the decaying part of the preceding sound is masked, dissonance is not heard, and the melody progresses smoothly. Thus, it can be said that the variety of expressions from a piano is large because piano sound is a decaying sound, and the pianist skillfully adjusts attenuation patterns by using the dynamic characteristics of hearing.
　Dynamic characteristics of hearing can be investigated through psychophysical procedures under controlled conditions (Namba, S. 2013). However, it is not easy to describe the world of music in the heart, although this world is vividly expressed in excellent novels and essays. Research on the correspondence between the beauty of the sound of a piano in the world of the mind and as a precisely measured physical quantity is not highly remarkable. One reasons for this is the world of beauty in piano performances as depicted in novels is delicate, subtle and complex. Further, the physical quantities of piano sounds measured from various aspects are highly precise and complicated. Such complications are a barrier to finding psychophysical laws that reveal the relationship between the world of the mind and physical quantities.
　Historically, psychophysical measurements have not been benefical for assessing complex events. This is because of the difficulty in ensuring the reliability of experiments or in accurately controlling stimulus conditions in psychophysical experiments. In the case of a one dimensional attribute such as loudness, even if the physical quantity of sound is complex, it can be controlled by psychophysical methods. However, the tone quality that is an important attribute in the evaluation of piano sounds is multidimensional, and the physical quantity that affects the tone quality is also multidimensional. Therefore, it is not easy to find the psychophysical law between the two.
　If we can solve these problems, we should from the physical quantities, be able to correlate beautiful piano sounds that are described in novels. Not only that, it would be an important step on the path to elucidation the psychophysical relationships of complex events in daily life.
　Many studies on tone quality have been conducted in which target sound sources were selected to limit factors affecting the tone quality. Verbal expressions of tone quality, which is a multidimensional attribute, have been addressed also by selecting only a small number of adjectives. Further, statistical methods such as factor analysis were used in the selection process.
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