Composition with Twelve Tones:
Chapter 5

After many unsuccessful attempts during a period of approximately twelve years, I laid the foundations for a new procedure in musical construction which seemed fitted to replace those structural differentiations provided formerly by tonal harmonies.

I called this procedure Method of Composing with Twelve Tones Which are Related Only with One Another.

This method consists primarily of the constant and exclusive use of a set of twelve different tones. This means, of course, that no tone is repeated within the series and that it uses all twelve tones of the chromatic scale, though in a different order. It is in no way identical with the chromatic scale. (Curiously and wrongly, most people speak of the "system" of the chromatic scale. Mine is no system but only a method, which means a modus of applying regularly a preconceived formula. A method can, but need not, be one of the consequences of a system. I am also not the inventor of the chromatic scale; somebody else must have occupied himself with this task long ago.)

Example 1:

Example 1 shows that such a basic set (BS) consists of various intervals. It should never be called a scale, although it is invented to substitute for some of the unifying and formative advantages of scale and tonality. The scale is the source of many figurations, parts of melodies and melodies themselves, ascending and descending passages, and even broken chords. In approximately the same manner the tones of the basic set produce similar elements. Of course, cadences produced by the distinction between principal and subsidiary harmonies will scarcely be derived from the basic set. But something different and more important is derived from it with a regularity comparable to the regularity and logic of the earlier harmony; the association of tones into harmonies and their successions is regulated (as will be shown later) by the order of these tones. The basic set functions in the manner of a motive. This explains why such a basic set has to be invented anew for every piece. It has to be the first creative thought. It does not make much difference whether or not the set appears in the composition at once like a theme or a melody, whether or not it is characterized as such by features of rhythm, phrasing, construction, character, etc.

Why such a set should consist of twelve different tones, why none of these tones should be repeated too soon, why, accordingly, only one set should be used in one composition – the answers to all these questions came to me gradually.

Discussing such problems in my Harmonielehre (1911), I recommended the avoidance of octave doublings. To double is to emphasize, and an emphasized tone could be interpreted as a root, or even as a tonic; the consequences of such an interpretation must be avoided. Even a slight reminiscence of the former tonal harmony would be disturbing, because it would create false expectations of consequences and continuations. The use of a tonic is deceiving if it is not based an all the relationship of tonality.

The use of more than one set was excluded because in every following set one or more tones would have been repeated too soon. Again there would arise the danger of interpreting the repeated tone as a tonic. Besides, the effect of unity would be lessened.

Justified already by historical development, the method of composing with twelve tones is also not without esthetic and theoretical support. On the contrary, it is just this support which advances it from a mere technical device to the rank and importance of a scientific theory.

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 cooperation, 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. For instance, the effect of progressive rhythmical subdivision, through what I call "the tendency of the shortest notes" to multiply themselves, can be observed in every classic composition.

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, as will be shown later, a basic set of twelve tones (BS) 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; t least, they seldom did so consciously. Nevertheless, there exist examples, of which I want to mention only one from Beethoven’s last String Quartet, Op. 135, in F Major:

Example 2:

The original form, a, „Muss es sein,“ appears in b inverted and in Major; c shows the retrograde form of this inversion, which, now reinverted in d and filled out with passing notes in e, results in the second phrase of the main theme. Whether or not this device was used consciously by Beethoven does not matter at all. From my own experience I know that it can also be a subconsciously received gift from the Supreme Commander.

The two principal themes of my Kammersymphonie (Chamber Symphony) can be seen in Example 3 under a and b. After I had completed the work I worried very much about the apparent absence of any relationship between the two themes.

Example 3a:

Example 3b:

Directed only by my sense of form and the stream of ideas, I had not asked such questions while composing; but, as usual with me, doubts arose as soon as I had finished. They went so far that I had already raised the sword for the kill, taken the red pencil of the censor to cross out the theme b. Fortunately, I stood by my inspiration and ignored these mental tortures. About twenty years later I saw the true relationship. It is of such a complicated nature that I doubt whether any composer would have cared deliberately to construct a theme in this way; but our subconscious does it involuntarily. In c the true principal tones of the theme are marked, and d shows that all the intervals ascend. Their correct inversion e produces the first phrase f of the theme b.

It should be mentioned that 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 Swedenborg'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 quantity.