Peter Schat's Tone Clock: The Steering Function and Pitch-Class Set Transformation in Genen

Abstract

Dutch composer Peter Schat’s (1935-2003) pursuit of a compositional system that could generate and preserve intervallic relationships, while allowing the composer as much flexibility as possible to manipulate musical material, led him to develop the tone-clock system. Fundamentally comprised of the twelve possible trichords, the tone clock permits each to generate a complete twelve-tone series through the “steering” principle, a concept traced to Boulez’s technique of pitch-class set multiplication. This study serves as an overview of Schat’s tone-clock system and focuses primarily on the effects of the steering function in “Genen” (2000). Furthermore, I expand on the tone-clock system by combining transformational theory with Julian Hook’s uniform triadic transformations and my proposed STEER and STEERS functions, which express the procedures of the steering principle as a mathematical formula. Using a series of transformational networks, I illustrate the unifying effect steering has on different structural levels in “Genen,” a post-tonal composition.