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A Hypercube-Graph Model for n-Tone Rows and Relations

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Mathematics and Computation in Music (MCM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7937))

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Abstract

We investigate the representation of n-tone rows as paths on an n-dimensional hypercube graph with vertices labeled in the power set of the aggregate. These paths run from the vertex labeled by the null set to the one labeled by the full set, passing through vertices whose labels gradually accumulate members of the aggregate. Row relations are then given as hypercube symmetries. Such a model is more sensitive to the musical process of chromatic completion than those that deal more exclusively with n-tone rows and their relations as permutations of an underlying set. Our results lead to a graph-theoretical representation of the duality inherent in the pitch-class/order-number isomorphism of serial theory.

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Author information

Authors and Affiliations

  1. School of Music, Louisiana State University, Baton Rouge, LA, 70809, USA

    Robert W. Peck

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  1. Robert W. Peck
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Editor information

Editors and Affiliations

  1. Boston University, USA

    Jason Yust

  2. McGill University, Montreal, Canada

    Jonathan Wild

  3. University of Amsterdam, The Netherlands

    John Ashley Burgoyne

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Peck, R.W. (2013). A Hypercube-Graph Model for n-Tone Rows and Relations. In: Yust, J., Wild, J., Burgoyne, J.A. (eds) Mathematics and Computation in Music. MCM 2013. Lecture Notes in Computer Science(), vol 7937. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39357-0_14

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  • DOI: https://doi.org/10.1007/978-3-642-39357-0_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39356-3

  • Online ISBN: 978-3-642-39357-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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