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Published in:
2009 | OriginalPaper | Chapter
Webern’s Twelve-Tone Rows through the Medium of Klumpenhouwer Networks
Author : Catherine Nolan
Published in: Mathematics and Computation in Music
Publisher: Springer Berlin Heidelberg
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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
n
I classes.
1
At the core of K-net theory lies the duality of objects (pitch classes) and transformations (T
n
and T
n
I operators and their hyper-T
n
and hyper-T
n
I 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.