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/TnI classes. At the core of K-net theory lies the duality of objects (pitch classes) and transformations (Tn and T nI operators and their hyper-Tn and hyper-TnI 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. © 2009 Springer-Verlag.