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 Tn/TnI classes.1 At the core of K-net theory lies the duality of objects (pitch classes) and transformations (Tn and TnI 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.KeywordsRegistral SeparationInterval ClassSerial TransformationMusic TheoryPitch ClassThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.