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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Mathematical and Musical Properties of Pairwise Well-Formed Scales
verfasst von : David Clampitt
Erschienen in: Mathematics and Computation in Music
Verlag: Springer Berlin Heidelberg
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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
.