If...[Alban] Berg departs so radically from tradition, through his substitution of a symmetrical partitioning of the octave for the asymmetrical part… - George Perle

This intersecting of inherently non-symmetrical diatonic elements with inherently non-diatonic symmetrical elements seems to me the defining principle of the musical language of Le Sacre and the source of the unparalleled tension and conflicted energy of the work.

Collections of all twelve pitch classes can be differentiated from one another only by assigning an order to the pitch classes or by partitioning them into mutually exclusive sub-collections. The ordering principle is the basis of the twelve-tone system formulated by Schoenberg, the partitioning principle the basis of the system formulated around the same time by Hauer. In Schoenberg's compositional practice, however, the concept of a segmental pitch-class content is represented as well, as a basis for the association of paired inversionally related set forms. On the relation between Schoenberg and Hauer see Bryan R. Simms, "Who First Composed Twelve-Tone Music, Schoenberg or Hauer?" Journal of the Arnold Schoenberg Institute X/2 (November 1987).

The achievement of such a change of register through a sequential progression is a familiar procedure in the music of the "common practice." The significant distinction is that where Berg subdivides the registral span into equal, i.e., cyclic, intervals, his tonal predecessors subdivide it, in changing register through sequential transference, into the unequal intervals of the diatonic scale. As I pointed out in my last lecture, however, the qualitative transformation in the language of music which we have experienced in our century has a long prehistory. Beginning with Schubert, we occasionally find normal diatonic functions questioned in changes of key that progress along the intervals of the whole-tone scale, or the diminished-7th chord, or the augmented triad. An even more radical example of a cyclic progression in a tonal composition is...from Wagner (Die Walkure, Act III).