Webern’s Twelve-Tone Rows through the Medium of Klumpenhouwer Networks

Abstract

The theory of Klumpenhouwer networks (K-nets) in contemporary music theory continues to build on the foundational work of (1990) and (1991), and has tended to focus its attention on two principal issues: recursion between pitch-class and operator networks and modeling of transformational voice-leading patterns between pitch classes in pairs of sets belonging to the same or different T_n/T_nI classes.¹ At the core of K-net theory lies the duality of objects (pitch classes) and transformations (T_n and T_nI operators and their hyper-T_n and hyper-T_nI counterparts). Understood in this general way, K-net theory suggests other avenues of investigation into aspects of precompositional design, such as connections between K-nets and Perle cycles, K-nets and Stravinskian rotational or four-part arrays, and between K-nets and row structure in the “classical” twelve-tone repertoire.