Music is not merely another kind of amusement, but a musical poet’s, a musical thinker’s representation of musical ideas; these musical ideas must correspond to the laws of human logic; they are a part of what man can apperceive, reason and express. Proceeding from these assumptions, I arrived at the following conclusions:

THE TWO-OR-MORE-DIMENSIONAL SPACE IN WHICH MUSICAL IDEAS ARE PRESENTED IS A UNIT. Though the elements of these ideas appear separate and independent to the eye and the ear, they reveal their true meaning only through their co-operation, even as no single word alone can express a thought without relation to other words. All that happens at any point of this musical space has more than a local effect. It functions not only in its own plane, but also in all other directions and planes, and is not without influence even at remote points. . . .

A musical idea, accordingly, though consisting of melody, rhythm, and harmony, is neither the one nor the other alone, but all three together. The elements of a musical idea are partly incorporated in the horizontal plane as successive sounds, and partly in the vertical plane as simultaneous sounds. The mutual relation of tones regulates the succession of intervals as well as their association into harmonies; the rhythm regulates the succession of tones as well as the succession of harmonies and organizes phrasing. And this explains why . . . a basic set of twelve tones . . . can be used in either dimension, as a whole or in parts.

The basic set is used in diverse mirror forms. The composers of the last century had not employed such mirror forms as much as the masters of contrapuntal times . . .

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. . . the last century considered such a procedure cerebral, and thus inconsistent with the dignity of genius. The very fact that there exist classical examples proves the foolishness of such an opinion. But the validity of this form of thinking is also demonstrated by the previously stated law of the unity of musical space, best formulated as follows: the unity of musical space demands an absolute and unitary perception. In this space, as in Swendenborg’s heaven (described in Balzac’s Seraphita) there is no absolute down, no right or left, forward or backward. Every musical configuration, every movement of tones has to be comprehended primarily as a mutual relation of sounds, of oscillatory vibrations, appearing at different places and times. To the imaginative and creative faculty, relations in the material sphere are as independent from directions or planes as material objects are, in their sphere, to our perceptive faculties. Just as our mind always recognizes, for instance, a knife, a bottle or a watch, regardless of its position, and can reproduce it in the imagination in every possible position, even so a musical creator’s mind can operate subconsciously with a row of tones, regardless of their direction, regardless of the way in which a mirror might show the mutual relations, which remain a given quality.

Arnold Schoenberg