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.
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Nolan, C. (2009). Webern’s Twelve-Tone Rows through the Medium of Klumpenhouwer Networks. In: Klouche, T., Noll, T. (eds) Mathematics and Computation in Music. MCM 2007. Communications in Computer and Information Science, vol 37. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04579-0_37
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DOI: https://doi.org/10.1007/978-3-642-04579-0_37
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