The Third Torus and Counterpoint

Guerino Mazzola, Maria Mannone, Yan Pang

Research output: Chapter in Book/Report/Conference proceedingChapter


This chapter deals with the mathematics of the third torus group ℤ3 × ℤ4 and its symmetries and then applies these structures to music theory, in particular to counterpoint.

Original languageEnglish (US)
Title of host publicationComputational Music Science
PublisherSpringer Nature
Number of pages9
StatePublished - 2016

Publication series

NameComputational Music Science
ISSN (Print)1868-0305
ISSN (Electronic)1868-0313

Bibliographical note

Publisher Copyright:
© 2016, Springer International Publishing Switzerland.


  • Major Scale
  • Music Theory
  • Pitch Class
  • Strong Dichotomy
  • Torus Group


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