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Paradigmatic Classification

  • Guerino Mazzola
Chapter
Part of the Computational Music Science book series (CMS)

Summary

Paradigmatic classification deals with formation of classes of objects which belong to specific paradigms. Here, paradigms are fields of equivalence or association. In a more general setting than in mathematics, equivalence is not necessarily understood as being a transitive relation. We give motivation of the paradigm concept from musicology, semiotics and poetology, and mathematics. Our taxonomy yields two types of paradigms: by transformations and by similarity—however, in practice, they often appear in mixed form. In a mathematical perspective, the first type is covered by group theory, the second by topology. This means that fuzzy concepts in the humanities are not a priori useless, they can be incorporated into exact reasoning by means of a refined paradigmatic reconstruction.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Guerino Mazzola
    • 1
  1. 1.School of MusicUniversity of MinnesotaMinneapolisUSA

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