Mathematics and the Twelve-Tone System: Past, Present, and Future

  • Robert Morris
Part of the Communications in Computer and Information Science book series (CCIS, volume 37)


Certainly the first major encounter of non-trivial mathematics and non-trivial music was in the conception and development of the twelve-tone system from the 1920s to the present. Although the twelve-tone system was formulated by Arnold Schoenberg, it was Milton Babbitt whose ample but non-professional background in mathematics made it possible for him to identify the links between the music of the Second-Viennese school and a formal treatment of the system. To be sure, there were also important inroads in Europe as well,1 but these were not often marked by the clarity and rigor introduced by Babbitt in his series of seminal articles from 1955 to 1973 (Babbitt 1955, 1960, 1962, 1973).


Music Theory Compositional Space Array Column Combinatorial Array Cardinality Operator 
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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Robert Morris
    • 1
  1. 1.Eastman School of MusicUniversity of RochesterRochesterUSA

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