Abstract
The short paper below presents the definition of the pairwise well-formed scale concept, and a few of the significant mathematical and musical features entailed by that definition. The verifications that are easily available are supplied here; for the more difficult proofs which are here omitted, the reader is directed to my dissertation (Clampitt 1997). While the definition itself is quite abstract, the body of implications and equivalences that constitute the theory include several musically attractive properties. With the significant exception of one structural subcategory, all other pairwise well-formed scales participate in modulating cycles that generalize the maximally smooth cycles defined in Cohn 1996 and intersect with the Cohn functions defined in Lewin 1996.
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References
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Clampitt, D. (2009). Mathematical and Musical Properties of Pairwise Well-Formed Scales. 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_46
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DOI: https://doi.org/10.1007/978-3-642-04579-0_46
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04578-3
Online ISBN: 978-3-642-04579-0
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