Abstract
Klumpenhouwer networks, or K-nets, are graphic representations of the intervallic relationships among elements of a set.1 Theorist David Lewin has suggested that K-nets may be applicable to Perle cycles, entities referred to by George Perle in his theory of twelve-tone tonality as cyclic sets. These entities are created through the alternation of inversionally related interval cycles. The present study seeks to broaden the applicability of K-nets in Perle’s theory by exploring their recursive nature at varying levels of structure.
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References
Foley, G.C.: Arrays and K-Nets: Transformational Relationships Within George Perle’s Theory of Twelve-Tone Tonality. Indiana Theory Review 23, 69–97 (2002)
Lewin, D.: Thoughts on Klumpenhouwer Networks and Perle-Lansky Cycles. Music Theory Spectrum 24(2), 196–230(2003)
Perle, G.: Twelve-Tone Tonality, 2nd edn. University of California Press, Berkeley (1996)
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Foley, G.C. (2009). K-Net Recursion in Perlean Hierarchical Structure. 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_36
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DOI: https://doi.org/10.1007/978-3-642-04579-0_36
Publisher Name: Springer, Berlin, Heidelberg
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