1) From the point of view of information theory, perception of melody presupposes the transmission of the melody. As first explicitly expressed by Yuki, the factor of “movement” dominates in the primitive stage of melody perception, but the melody perception has gradually developed into the present form in which position, or the “hereness” and “thereness” of each point of moving tone plays a more important rôle than the factor of movement in building up the perception of melody. These “hereness” and “thereness” can be given by the sequence of discrete and more or less prolonged tones. The sequence of discrete, extended sounds may be decomposed into the following two: the sequence of pitch intervals and the sequence of time intervals during each of which a pitch is extended. As the first step of the information theory approach toward melody perception, only the sequence of pitch intervals is studied in this paper. Several experiments were conducted in which then normal code of melody transmission was distorted or disturbed by a sort of noise, and the effect of deteriorated transmission was measured in terms of melody intelligibility scale constructed analogically to the scale of sentence intelligibility. 2) Preliminarily were analysed the frequencies of pitch intervals appearing in the most familiar musical melodies, for example, “Last rose of summer”, “Home, sweet home” and the like, with the finding that only ten pitch intervals appear with frequency greater than 1%. (See Table 1.) 3) Why the familiar melodies are mainly constructed with so few pitch intervals as ten will be accounted for by the assumption that melodies must be quantized if they are to be communicated exactly. Further, it should be necessary for communication that the rules of quantization must be shared as the common code of information transmission by people under the same historical and social background of music. So it is expected that melody transmission would be deteriorated if the normal pitch intervals as the shared code are distorted, extended or compressed, uniformly. The result of the experiment clearly demonstrates this effect. (Fig. 6) 4) It is a common observation that one can often guess the whole melody by listening only a part of it. An experiment was conducted to test how much the melody intelligibility increases as the length of presented melody increases. The result is shown in Fig. 7. 5) The third experiment is concerned with how the transmission of a pitch interval is reduced when a disturbing vibrato overlaps the two successive tones by which an interval is defined. The result is shown in Fig. 8. 6) Since the third experiment revealed that a disturbing vibrato reduces intelligibility of every elemental pitch interval, the effect of disturbing vibrato upon a melody intelligibility is examined in the last experiment. The result is shown in Fig. 9.
Problem. According to previous experiments, the effect of the figure upon the c.f.f of a flickering point on the ground proved to follow the next rules. (1) The effect decreases with an increase in the distance from the figure to the test point. (2) The effect increases within a certain limit with an increase in the light-intensity of the figure. (3) The disposition of the effect of the fringe of the figure depends on the structural character of the figure. The experimental curves obtained so far under various figural conditions have shown the tendency considerably similar to that of the theoretical curves obtainable both from Yokose's theoretical formula of the potential field and from Uchiyama's empirical formula under the corresponding figural conditions. We have then attempted an investigation, using the flicker method, to test statistically the function of the distance from the figure, the light-intensity of the figure, the subjects used (individual difference), the repetition of measurement and the interactions between these factors. Procedure. The dark-adapted subject was presented with a light-figure in the dark room and the c.f.f. of the flickering point projected on the ground was measured. The effect of the figure on the ground was estimated by the following equation: δ=100⋅(i-i0)/i0 where i0 is the c.f.f. value in case of no influencing figure and i is the c.f.f. value with one. The stimulus figures were contoured circles 4, 6.5, 9 and 14mm in semidiameter, illuminated at varied intensities 1, 10, 100 and 500 radlux. A flickering point 2mm in diameter was projected in the center of each circle. Results. Supposing that the δ-effect is an integration of the effects of the minute parts of the figure and the effect of the minute part is inversely proportional to the α power of the distance, we can formulate the following functional relation between the δ-effect and the distance (D): logδ=log2πc(α-1)logD where c denotes a constant and D corresponds to the semidiameter of each circle. Then we calculated α and c by the method of least squares in regard to each of the light intensities, of the subjects and of the measurements of our data. The obtained mean and standard deviation of α were respectively 2.04 and 0.45. There was no significant difference of α at the 1 per cent level within the light-intensities, the subjects and the measurements. We have further investigated the relation between c and the light-intensity (H). We supposed logc=βlogH+γ and computed β and γ by the method of least squares in regard to each subject and each measurement repeated. The mean and SD of β were respectively 0.11 and 0.13. These obtained figures indicate that there could hardly be established any definite functional relation between the δ-effect and the light-intensity. On the other hand, it may safely be assumed from our experimental data that the individual difference is larger under the weaker stimulus conditions than under the stronger ones and that the repetition of measurement reduces some fluctuations of the data. The above facts were also confirmed in our experiments conducted under the same figural conditions by the method of light stimulus thresholds.
The discrimination of purity of color stimulus was investigated in terms of the standard deviation of color matching on the purity dimensions for 473, 490, 540, 573, 612 and 542c in the dominant wave-length (mμ) on CIE (x, y) chromaticity diagram. The apparatus was essentially a type of color paper mixer; the results of the experiment thereby being limited to apply only to a part of color gamut reproducible by the mixing of surface colors of matte paper. The data were collected by 100 matchings by 5 observers, 20 matchings by each, for a stimulus color. The brightness of surrounding field was varied in three ways; darker (condition A), equal (condition B) and brighter (condition C) as compared with the stimulus. The stimulus brightness being constant, the phenomenal brightness of the stimulus was changed therefore by contrast effect from dark (in the condition C) to bright (in the condition A). It was found that high phenomenal brightness value generally improved the color matching accuracy but its characteristics was different from one half domain of the wave-length to another half. For the color stimuli of the dominant wave-length of 490-540-573mμ, the accuracy was more improved from the condition B to A than from C to B. On the other hand, for the stimuli of the dominant wave-length of 612-542c-473mμ, it was improved from C to B but not at all from B to A (Fig. 2 & Fig. 3). A psychological scale of chromatic saturation was formulated taking the standard deviation of color matchings as the unit. Every two chroma steps in Munsell chroma scale approximately corresponded with every ten units of standard deviation for the color stimuli of 612mμ and 473mμ in dominant wave-length. This was also partly true for 542cmμ. For the color of 490, 540 and 573mμ in dominant wave-length, this relation did not hold (Fig. 3). The psychological scale of chromatic saturation was transformed into iso-chromatic lines on CIE diagram. In comparison with the Munsell constant-chroma loci, they were more protruding in blue region. As a whole, they were displaced downward with respect to the Munsell's in the condition A and B. This discrepancy almost disappeared in the condition C, however. The isochromatic lines in the condition C significantly expanded, but the rate of expansion was not so great as the expansion of the constant chroma 1oci at low lightness value in the Munsell system (Fig. 4).
Most of the studies on brightness contrast have been carried in a dark room and concerned only with a brightness gradient between the test field (TF) and the inducing field (IF). But, in these cases, the influence of background (Bg) had not been taken into consideration as a factor to affect the brightness of both fields. To obtain a thorough understanding of contrast phenomenon, however, the interaction among these TF, IF and Bg should be examined in detail. Although Benary, W., Fuchs, W. and others emphasized the importance of the configurational rather than the physical factors, they nevertheless failed to pay special attention to the above mentioned interaction. In the present study, the change in the apparent brightness of the surface color (TF) was experimentally investigated in relation to the brightness of adjacent regions (IF and Bg) and the configurational factor (stimulus constellation). The following are the results obtained in the experiments wherein the achromatic colors were used as the stimuli. 1) The brightness contrast observed between surface colors on the white background was discovered to be very similar in tendency to that between transmitted lights in a dark room. Namely under one of such conditions as a decrease of brightness of the IF, an increase of the area of the IF and a decrease of the spatial distance between the TF and the IF, the contrast effect in creased. The interaction among these factors was also examined. As the spatial distance went beyond a certain limit, the influence of the other two factors almost diminished (Figs. 4, 5, 6 and 7). 2) Even if the brightness of the IF was kept constant, the contrast effect changed with the variation of brightness of the Bg. The brightness of the TF adjusted by subjects depended, therefore, not solely upon the conditions of whether the IF was brighter or darker than the TF, but rather upon that of whether it was brighter or darker than the Bg. In other words, the contrast effect increased with an increase in the brightness gradient between the IF and the Bg. Two types of the contrast effect were observed in the TF, the one tending toward the brighter value and the other, toward the darker. They yielded different types of curves as a function of the IF or of the Bg (Figs. 8 and 9). 3) In such a stimulus constellation, where the phenomenon of assimilation should take place according to Fuchs, it was not always observed. Whether the influence of an IF upon a TF takes the form of contrast or of assimilation seems to depend upon the brightness gradient and the spatial distance between them, and also upon the brightness of the Bg. It is suggested on the basis of this experiment that there are two kinds of potential tendencies operating simultaneously, i.e., the one toward contrast and the other toward assimilation, though in general the former is dominant over the latter. In this type of experiment, the influence of the set of subjects cannot be overlooked as indicated by the variation of the results among the subjects (Figs. 10 and 11).
According to Ishii (1), the three-dimensional vision of geometrical figures, such as Necker cube, Schröder staircase and others, depends upon the presence of Y and ↑ (arrow) form-factors in drawings. It must be noted, however, that these form-factors are constituted with vertical and oblique lines. Therefore the real cause of the depth impression of the Y and ↑ figures might be the three-dimensionality inherent in each single directional line-drawing. The purpose of the present study is to investigate what correspondence is found between the degree of slant and the apparent depth impression of a single line, and also what difference there is between monocular vision and binocular one to attain the depth impression in line-drawings. In the first experiment, the line figures of 7 slant-degrees, 10°, 20°, ……, 70°, were observed. The results are shown in Table 1 and Fig. 1. Comparing these results with those of the former experiment with the parallelogram (2), the authors concluded that a single line gives solid impression no less than a parallelogram. In the second experiment, the figures of the shape were used, which had the vertical lines under various conditions. The first group of figures were different from each other in the length of the vertical line. In the second group the distances between the vertical lines and the inclined ones were varied. And the third group had the vertical dot-lines which were drawn with various numbers of dots. The results, as in Figs. 2, 3 and 4, show that the role of the oblique line is important, the effect of vertical line being unimportant. In the third experiment, as in the first experiment, the figures of oblique line alone were observed with a single eye, as well as with both eyes, to compare the two cases. The results are shown in Fig. 5 and Table 6. According to these, it is clear that binocular viewing is superior to monocular one in accuracy and easiness of the depth perception of figures. The differences, however, are not so great as was expected. The above mentioned findings suggest that the depth vision of line-drawings is not due to binocular disparity.