Abstract
Some pitch-class collections may be represented as subsets of a two-dimensional lattice or generalised Tonnetz. Whereas a well-formed scale of cardinality n is formed as a simple interval chain, and thus defined unambiguously by the size of its generating interval, there are a great number of inequivalent ways of forming connected n-subsets of the two-dimensional lattice defined by a given pair of basis intervals. Only very few of these connected subsets or lattice animals ever turn out to correspond to collections that possess the pairwise well-formed property. Pwwf scales are found to correspond to members of a small family of lattice animals that is independent of the generators at the basis of the lattice. Finally a method is shown for constructing a pair of generators that will yield any given heptatonic pwwf scale; the method is easily extended to other cardinalities.
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Wild, J. (2009). Pairwise Well-Formed Scales and a Bestiary of Animals on the Hexagonal Lattice. In: Chew, E., Childs, A., Chuan, CH. (eds) Mathematics and Computation in Music. MCM 2009. Communications in Computer and Information Science, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02394-1_25
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DOI: https://doi.org/10.1007/978-3-642-02394-1_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02393-4
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