SOURCE: "The Twelve Tone Method," in Schoenberg and His Circle: A Viennese Portrait, Schirmer Books, 1986, pp. 183-218.

In the following essay, Smith provides an overview of Schoenberg's twelve-tone method.

Several Viennese composers outside of the Schoenberg circle were concerned with repeated pitch structures and some even with the concept of chromatic completion (the structurally geared use of all twelve pitch classes) coincidentally with Schoenberg. However, the idea of an ordering within the twelve-tone set, and the application of the four systematic operations of transposition, inversion, retrogression, and retrograde-inversion, which brought about a musically constructive method for twelve-tone composition, were Schoenberg's alone. They did not come to him in a single insight but rather developed slowly over a number of years.

The composer probably most concerned, besides Schoenberg, with finding a substitute for the long-range structural functions of tonal harmony was Anton Webern. Of all of Schoenberg's pupils, he...