In a previous post I looked at twelve-tone elements in the composition “Brasilia.” Another remarkable feature of that piece is the octatonic collection OCT1,2 embedded within the full chromatic set that makes up its first phrase. After the initial E-flat minor triad, all eight members of OCT1,2 are stated in (almost uninterrupted) succession, and the prepenultimate B-flat links OCT1,2 with the returning statement of E-flat minor.
Of the four pitch-classes excluded from OCT1,2, E-flat and G-flat comprise the tonality-defining beginning and ending gestures of the first phrase. The middle portion of the phrase can be considered OCT1,2 if non-members C and A are heard as subordinate embellishments to melodically predominant members of OCT1,2. From one possible voice-leading perspective, C is a neighbor-passing tone to B, and A is a neighbor tone to B-flat.
The use of the octatonic collection here is significant insofar as it can be conceived as a substitute for B-flat7, the dominant of the governing E-flat minor tonality of the piece. Jazz musicians sometimes use an octatonic scale over a dominant seventh chord when improvising, and theorists like Schoenberg, Berger, and others have shown the derivation of the octatonic collection from the double-semitonal transformation of a cycle of seventh chords whose roots are separated by the interval of a minor third. “Brasilia” manifests this melodically, stating the octatonic collection with pitches from B-flat7 (F, D), G7 (F, D, G, B), and E7 (B, G-sharp, E) as well as C-sharp minor sixth or B-flat half-diminished seventh (G-sharp, E, C-sharp, B-flat).
As I point out in the previous post, the B-phrase of this piece seems to prolong the dominant harmony of a tonic E-flat minor. Thus, like much tonal music, “Brasilia” is hierarchically self-similar: the tonic-dominant-tonic structure of the A-phrase is reflected on a higher level by the tonic-dominant-tonic (ABA) form of the whole piece.
For one final thought, notice how the register of melody notes in the A-phrase can be rearranged to depict the entire phrase as a long and almost unbroken string of falling thirds. This brings to mind the "ladder of thirds" which Peter van der Merwe argues is the underlying form of what he calls the "blues mode." It is crucial to recognize that the application of twelve-tone technique in "Brasilia" does not thereby jettison the norms of tonal music and the blues.