Composition with Twelve Tones:
Chapter 10

The unlimited abundance of possibilities obstructs the systematic presentation of illustrations; therefore, an arbitrary procedure must be used here.

In the simplest case, a part of a theme, or even the entire theme, consists simply of a rhythmization and phrasing of a basic set and its derivatives, the mirror forms: inversion, retrograde, and retrograde inversion. While a piece usually begins with the basic set itself, the mirror forms and other derivatives, such as the eleven transpositions of all the four basic forms, are applied only later; the transpositions especially, like the modulations in former styles, serve to build subordinate ideas.

Example 5:

Example 5 shows the basic set (with its inversions in the octave and fifth) of my Wind Quintet, op. 26. Many themes of this work simply use the order of one of the basic forms.

Example 6:

The main theme of the first movement uses for its first phrase the first six tones, the antecedent; for its second phrase, the consequent of the BS. This example shows how an accompaniment can be built. As octave doubling should be avoided (see page 126), the accompanying of tones 1-6 with tones 7-12, and vice versa, is one way to fulfill this requirement.

Example 7:

Example 7 proves that the same succession of tones can produce different themes, different characters.

Example 8a:

Example 8b:

Example 8c:

Example 8d:

Example 8e:

Example 8, the principal theme of the Rondo of this Quintet shows a new way of varying the repetitions of a theme. The production of such variants is not only necessary in larger forms, especially in Rondos, but useful also in smaller structures. While rhythm and phrasing significantly preserve the character of the theme so that it can easily be recognized, the tones and intervals are changed through a different use of BS and mirror forms. Mirror forms are used in the same way as the BS. But Example 9 shows a more complicated procedure.

Example 9:

At first a transposition of the retrograde is used three times in succession to build melody and accompaniment of this subordinate theme of the Rondo from the same Quintet. The principal voice, the bassoon, uses three tones in each of the four phrases; the accompaniment uses only six tones, so that the phrases and the sets overlap each other, producing a sufficient degree of variety. There is a definite regularity in the distribution of the tones in this and the following Example 10, the Andante from the same Quintet.

Example 10:

Here also the form used, the BS, appears three times; here also, some of the tones appear in the principal voice (horn) while the others build a semi-contrapuntal melody in the bassoon.

Example 11:

In the Scherzo of the same work (Example 11), the main theme starts with the fourth tone after the accompaniment has employed the preceding three tones to the BS. Here the accompaniment uses the same tones as the melody, but never at the same time.

Example 12:

In Example 12, inversion and retrograde inversion are combined into a contrapuntal unit which is worked out in the manner of the elaboration of the Rondo.