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Application of algebraic structures to music

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  • application of algebraic structures to music (en)
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  • July 2021 (en)
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  • On pp. 79–80 Boulez speaks of "isomorphic families", "a double network of privileged series", "dividing" a series and "the whole is multiplied by each of its parts in turn", thereby creating "multiple isomorphic relationships", objects "multiplied by themselves", etc., but where is this expression "pitch multiplication"? (en)
dbp:reference
  • Koblyakov, Lev. 1990. Pierre Boulez: A World of Harmony. Chur: Harwood Academic Publishers. . (en)
  • Heinemann, Stephen. 1998. "Pitch-Class Set Multiplication in Theory and Practice." Music Theory Spectrum 20, no. 1 : 72–96. (en)
  • Slonimsky, Nicolas. 1947. Thesaurus of Scales and Melodic Patterns. New York: Charles Scribner Sons. . (en)
  • Krenek, Ernst. 1937. Über neue Musik: Sechs Vorlesungen zur Einführung in die theoretischen Grundlagen. Vienna: Ringbuchhandlung. (en)
  • Rahn, John. 1980. Basic Atonal Theory. Longman Music Series. New York and London: Longman. Reprinted, New York: Schirmer Books; London: Collier Macmillan, 1987. (en)
  • Boulez, Pierre. 1971. Boulez on Music Today. Translated by Susan Bradshaw and Richard Rodney Bennett. Cambridge, Massachusetts: Harvard University Press. . (en)
  • Antokoletz, Elliott. 1993. "Middle Period String Quartets". In The Bartok Companion, edited by Malcolm Gillies, 257–277. London: Faber and Faber. ; . (en)
  • Morris, Robert D. 1982. Review: "John Rahn, Basic Atonal Theory. New York: Longman, 1980". Music Theory Spectrum 4:138–154. (en)
  • Schillinger, Joseph. 1941. The Schillinger System of Musical Composition. New York: Carl Fischer. . (en)
  • Hibbard, William. 1969. "Charles Wuorinen: The Politics of Harmony". Perspectives of New Music 7, no. 2 : 155–166. (en)
  • Morris, Robert D. 1997. "Some Remarks on Odds and Ends". Perspectives of New Music 35, no. 2 : 237–256. (en)
  • Fokker, Adriaan Daniël. 1987. Selected Musical Compositions. Utrecht: The Diapason Press. . (en)
  • Heinemann, Stephen. 1993. Pitch-Class Set Multiplication in Boulez's Le Marteau sans maître. D.M.A. diss., University of Washington. (en)
  • Howe, Hubert S. 1965. "Some Combinational Properties of Pitch Structures." Perspectives of New Music 4, no. 1 : 45–61. (en)
  • Randall, James K. 1962. "Pitch-Time Correlation". Unpublished. Cited in . (en)
  • Schuijer, Michiel. 2008. Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts. Eastman Studies in Music 60. Rochester, New York: University of Rochester Press. . (en)
  • Winham, Godfrey. 1970. "Composition with Arrays". Perspectives of New Music 9, no. 1 : 43–67. (en)
  • Hanson, Howard. 1960. Harmonic Materials of Modern Music. New York: Appleton-Century-Crofts. (en)
  • Eimert, Herbert. 1950. Lehrbuch der Zwölftontechnik. Wiesbaden: Breitkopf & Härtel. (en)
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  • Multiplication (music) (en)
  • Moltiplicazione (musica) (it)
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