Ciro Scotto

Harmonic Process and Formal Structure in Some Recent Music by Boulez

This paper models the harmonic process and formal structure of two relatively recent works by Pierre Boulez, incises (1994, 2001) and sur incises (1996, 1998) and compares their structure to the serial and pitch-class multiplication techniques of earlier works, such as Le marteau sans maître (1954). While the theoretical literature modeling the serial processes in the early works provides some insight into their harmonic and formal structures, very little has been written about recent compositions. Boulez appears to abandon the technique of pitch-class multiplication for generating pitch-class sets and the serial techniques that structured his early works in favor of a more gestural and controlled chance technique in the later works. My forthcoming publication in Perspectives of New Music, however, connects Boulez’s earliest serial works to his most recent works through transpositional combination, an operation that generates pitch-class sets. Moreover, the article proves the formal and functional equivalence of pitch-class multiplication and transpositional combination, so the latter operation not only generates the domains and serial structures of Le marteau sans maître, but also many of the harmonic pitch-class structures in Sur incises as well. Since the theoretical foundation for transpositional combination is transformation theory, the latter theory provides additional tools for modeling harmonic processes and formal structures. In the earlier works, transpositional combination and Boulez’s unique serial structures create a compositional space, a structured topology of pitch-class sets that provides a logical global framework for the progression of domain pitch-class sets. This paper constructs a new global framework for the later compositions that replaces the serially generated framework with a transformational network. Nevertheless, the latter theoretical construct exhibits many similarities to the earlier serial compositional space, such as a logically constructed global framework that allows for local indeterminacy.