ANDREW MEAD

Milton Babbitt, Set Theory and Twelve-Tone Composition

Abstract

In certain theoretical circles, pitch-class set theory and twelve-tone theory are considered distinct disciplines. However, from the very beginning of his compositional career, Milton Babbitt has demonstrated both in his music and his writings that twelve-tone composition, as he practices it and as he examines it in the works of Schoenberg, Webern and Stravinsky, is grounded on and revealing of the range of properties and relationships to be found among unordered collections in the total chromatic.

The presentation traces the arc of Babbitt's compositional practice from its roots in Schoenberg's hexachordal combinatoriality and Webern's trichordally derived rows through trichordal arrays and all-partition arrays to the use of super-arrays, with particular attention to their implications for set theory. The various stages of his development will be illustrated with analytical vignettes, including portions of the two piano works, Partitions and Post-Partitions. A technique for comparing collectional structures employing a non-interval-preserving pitch-class operator will be introduced in order to illustrate the deep-structural similarities amongst certain compositional constructions, while revealing their individual differences. This will be illustrated with examples from the trichordal arrays of a number of works from the 1950's.

Biography of Andrew Mead