Composition with Twelve Tones:
Chapter 7

It has been mentioned that the basic set is used in mirror forms.

Example 4:

From the basic set, three additional sets are automatically derived: 1) the inversion; 2) the retrograde; and 3) the retrograde inversion. The employment of these mirror forms corresponds to the principle of the absolute and unitary perception of musical space. The set of Example 4 is taken from the Wind Quintet, Op. 26, one of my first compositions in this style.

Later, especially in larger works, I changed my original idea, if necessary, to fit the following conditions: the inversion a fifth below of the first six tones, the antecedent, should not produce a repetition of one of these six tones, but should bring forth the hitherto unused six tones of the chromatic scale. Thus, the consequent of the basic set, the tones 7 to 12, comprises the tones of this inversion, but, of course, in a different order.

In Example 5, the inversion a fifth below does not yet fulfill this condition. Here the antecedent of the BS plus that of the INV 5 consists of only 10 different tones, because c and b appear twice, while f and f # are missing.(BS means Basic Set; INV means inversion of the Basic Set; INV8, INV5, INV3, INV6 means inversion at the 8ve, 5th, minor 3rd, or major 6th from the beginning tone.)

My deepest appreciation to the translator Dr. Mikako Akutsu and her supervisor Prof. Dr. Higuchi for making this Japanese version of the Explore Arnold Schoenberg website a reality.
Lawrence Schoenberg