5. Made up, at it is, of two determinants, quality and intensity, every psychical element must have a certain degree of intensity from which it is possible to pass, by continual gradations, to every other degree of intensity in the same quality. Such gradations can be made in only two directions: one we call increase in intensity, the other decrease. The degrees of intensity of every qualitative element, form in this way a single dimension, in which, from a given point, we may move in two opposite directions, just as from any point in a straight line.
This may be expressed in the general statement: The various intensities of every psychical element form a continuity of one dimension .
The extremities of this continuity we call the minimal and maximal sensation or feeling, as the case may be.
In contrast with this uniformity in intensifies, the qualities have more variable attributes. Every quality may, indeed, be so arranged in a definite continuity that it is possible to pass uninterruptedly from a given point to any other points in the same quality. But the various continuities of different qualities, which we may call systems of quality, exhibit differences both in the variety of possible gradations, and in the number of directions of gradation. In these two respects, we may distinguish, on the one hand, homogeneous and complex, on the other one-dimensional, two-dimensional, and many-dimensional systems of quality. Within a homogeneous system, only such small differences are possible that generally there has never arisen any practical need of distinguishing them by different names. Thus, we distinguish only low quality of pressure, hot, cold, or pain, only one feeling of attention or of activity, although, in intensity, each of these qualities may have many different grades. It is not to be inferred from this fact that in each of these systems there is really only one quality. The truth is that in these cases the number of different qualities is merely very limited; if we were to represent it geometrically, it would probably never reduce entirely to a single point. Thus, for example, sensations of pressure from different regions of the skin show, beyond question, small qualitative differences which are great enough to let us distinguish clearly any point of the skin from another at some distance from it. Such differences, however, as arise from contact with a sharp or dull, a rough or smooth body, are not to be reckoned as different qualities. They always depend on a large number of simultaneous sensations, and without the various combinations of these sensations into composite psychical compounds, the impressions mentioned would be impossible.
Complex systems of quality differ from those we have been discussing, in that they embrace a large number of clearly distinguishable elements between which all possible intermediate forms exist. In this class we must include the tonal system and color-system, the systems of smells and tastes, and among the affective systems those which form the subjective complements of these sensational systems, such as the systems of tonal feelings, color-feelings, etc. It is probable also that many systems of feelings belong here, which are objectively connected with composite impressions, but as feelings are simple in character, such are the various feelings of harmony or discord that correspond to the different combinations of tones.
The differences in the number of dimensions have been determined with certainty only in the case of certain sensational systems. Thus, the tonal system is one-dimensional. The ordinary color-system, which includes the colors and their transitional qualities to white, is two-dimensional; while the complete system of light-sensations, which includes also the dark color-tones and the transitional qualities to black, is three-dimensional.
6. In the relations discussed thus far, sensational and affective elements in general agree. They differ, on the other hand, in certain essential attributes which are connected with the immediate relations of sensations to objects and of feelings to the subject.
1) When varied in a single dimension, sensational elements exhibit pure qualitative differences, which are always in the same direction until they reach the possible limits of variation, where they become maximal differences. Thus, in the color-system, red and green, blue and yellow, or in the tonal system, the lowest and highest audible tones, are the maximal, and at the,same time purely qualitative, differences.
Every affective element, on the contrary, when continuously varied in the suitable direction of quality, passes gradually into a feeling of opposite quality. This is most obvious in the case of the affective elements regularly connected with certain sensational elements, as, for example, tonal feelings or color-feelings. As sensations a high and low-tone are differences that approach more or less the maximal differences of tonal sensation; the corresponding tonal feelings are opposites. In general, then, sensational qualities are limited by maximal differences, affective qualities by maximal opposites. Between these opposites is a middle zone, where the feeling is not noticeable it all. It is, however, frequently impossible to demonstrate this indifference-zone, because, while certain simple feelings disappear, other affective qualities remain, or new ones even may arise. The latter case appears especially when the transition of the feeling into the indifference-zone depends on a change in sensations.
Thus, in the middle of the musical scale, those feelings disappear which correspond to the high and low tones, but the middle tones have still other, independent affective qualities which do not disappear with these opposites.