This chapter extends and adapts the constructs and procedures of the previous chapters for the analysis of atonal music. Atonal music is seen to be in flat space. To remnants of the chord distance rule are added principles involving atonal branching, atonal function, sensory consonance and dissonance, and fusion. These analytic tools are applied to passages in the music of Schoenberg and Webern. An attempt to analyze a 12-tone excerpt in Schoenberg results in relative failure, thereby showing the limits of the methods under consideration. A distinction is drawn between compositional system and heard structure, and reasons for the cognitive opacity of serialism are given. Future prospects are suggested, particularly with respect to compositional practice.
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