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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Badness of Serial Fit Revisited
verfasst von : Tuukka Ilomäki
Erschienen in: Mathematics and Computation in Music
Verlag: Springer Berlin Heidelberg
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David Lewin introduced the notion of Badness of Serial Fit, or BSF, to analyze the relation between two twelve-tone rows. It is based on Milton Babbitt’s idea of the protocol made of the shared ordered pairs of pitch classes of two rows and aims to evaluate how distinctive the protocol is. While BSF has been mentioned several times in the music theory literature, so far little progress has been made in the analysis of its properties. This paper formalizes BSF in terms of partial orders and links the musical discourse to the pertinent literature in mathematics and computer science. BSF is analyzed in terms of computational complexity and it is shown to be related to the notion of “presortedness” used in the analysis of sorting algorithms. It is proven that the logarithms of the values of BSF define a metric for twelve-tone rows. This new metric is several orders of magnitude finer than any other measure discussed in the literature.