Geometric Proofs of the Common Tones Theorems

  • M BrianJ., Cartin
  • Published 2015


Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Geometric proofs are provided for the Common Tones Theorems for Transposition and Inversion [11, Chapter 5] of Mathematical Music Theory [2]. 

10 Figures and Tables


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