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structure and not merely as a metrically organized row, we have to wait until it reaches its end. Then the complete form will appear to our analyzing mind as a new unit and not, as it appeared in meter, as an accumulation of single units. All the nonmetrical constituent parts of this new unit, although in their own rhythmic form clearly circumscribed, have now lost their individual meaning and are nothing but subordinate parts of this new entity. Now our place of observation has changed. We are no longer looking back on the past course of the row; we are above it, so to speak, and are looking down and can take in with one single glance the temporal form in its totality — indivisible, unrepeatable, unchangeable. We may say that musical time in this moment produced an effect which in normal time is nonexistent. This effect of comprehending as a new superunit what in the course of its development was built up by smaller units is borrowed from our spatial experiences, where this comprehensive judgment is a most commonplace fact — and yet it was the result of a strictly temporal operation. III Musical space is at least as far removed from our normal spatial concepts as was musical time in its rhythmic form of appearance from our temporal experiences. This seems strange, for even laymen without any musical training use the expression «ascending» for tone successions in which the second component has a higher number of vibrations per second, and conversely name «descending» any succession moving in the opposite direction. Actually there are in music no such spatial distinctions as high and low, near and far, right and left that correspond with the same definitions in real nonmusical space. Yet it is undeniable that successions of tones bring about effects of spatial feelings which in their obviousness are convincing even to the entirely untrained mind. Since neither the loudness nor the color of tones can produce or influence this effect, it must be the pitch relation among tones that is the reason for it. To understand the connection between the movement from tone to tone in music on the one hand and the feeling of spatial movement on the other, we must again, as we did in our discussion of the emotional effects of music, find the common denominator of both factors. This time the equation is: the physical effort which we know is necessary to change from one tone position to another equals the physical effort we imagine when we think of a change of position in our common physical experience. Going from one given tone up to a tone with a higher vibration frequency is accomplished, in human voices and in string and wind instruments, with an increase in the energy of tone production. The amount of energy involved in such movement may be almost undiscernible (as in a violinist’s progressing from the tone a of the open string to the next c), or it may be a tremendous physical effort, as when a tenor sings the same progression with full voice. But the absolute amount of energy involved counts only so far as our nonmusical interest in the performer himself or our sentimental reactions derived from his performance are concerned. It is the relative amount of energy that counts for our evaluation of musical
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