Mathematics and the Twelve-Tone System: Past, Present, and Future Author(s): Robert Morris Source: Perspectives of New Music, Vol. 45, No. 2 (Summer, 2007), pp. 76-107 Published by: Perspectives of New Music Stable URL: http://www.jstor.org/stable/25164658 . Accessed: 26/09/2014 08:08 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact
[email protected]. Perspectives of New Music is collaborating with JSTOR to digitize, preserve and extend access to Perspectives of New Music. http://www.jstor.org This content downloaded from 143.107.95.114 on Fri, 26 Sep 2014 08:08:19 AM All use subject to JSTOR Terms and Conditions Mathematics and the Twelve-Tone System: Past, Present, and Future Robert Morris Introduction the first major encounter of non-trivial mathematics and Certainlynon-trivial music was in the conception and development of the twelve-tone system from the 1920s to the present. Although the twelve tone systemwas formulated by Arnold Schoenberg, itwas 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.