As an African American born in Brooklyn in 1945, I am embarrassed to define this expression, "twentieth century music". In my formal musical education, this expression normally refers to the music of Schoenberg (and his school), Bartok, Stravinsky, Hindemith, and many other mostly European composers, and including my own American composition teachers, Leon Kirchner, Roger Sessions and David DelTredici. Perhaps it is best to refer to this body of music as "twentieth century music in the European classical tradition", and thereby distinguish it from jazz, blues, rhythm and blues, rock, rap and other specifically American (and, I do indeed emphasize, basically African American) musical categories. To whatever extent it might be helpful, I plan to use examples from these American repertoires, as well as from the European tradition.
Arnold Schoenberg greatly simplified the discussion of linear and periodic structures by inventing the twelve-tone technique. The twelve-tone row is a module which can be presented in a linear or a periodic fashion, and in the twelve-tone works of Schoenberg, Berg, Webern and others we can examine how this functions in the smaller and larger aspects of the musical architecture.
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