Melodic Variation by Arrows

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


The ideas of tangent objects described in Section 7.5 are applied to define contrapuntal intervals as tangential “arrows” from the cantus firmus to the discantus tone. This formalism fits with the idea that the discantus is a kind of melodic variation around the cantus firmus line. The ring structure of the set of such arrows is discussed and motivated from the musical perspective.


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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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