Abstract
In his essay ‘What are twelve-note rows really for?’ (Tempo, Vol. 57, No. 225, July 2003, p. 36), Michael Graubart suggests that ‘twelve-note rows may give back to atonal music a goal-directed force and the possibility of closure’. He argues that by using a row, composers set up a pattern that can ultimately provide a sense of completion or closure to an atonal piece, although he admits that listeners may have trouble recognizing this completion. Closure in tonal music is in fact a powerful musical force, but one whose strength depends largely upon the hierarchy found in tonal melody and harmony. Consider the closure at the end of a piece. It is here that an authentic cadence signals the coming to rest of large-scale musical forces, both melodic and harmonic, on several levels of structure. We might make analogies, as Graubart does, between tonal closure and the pattern-completion possible with a twelve-note row, but one wonders if any row, or any twelve-note piece for that matter, can provide the type of multi-level completion that is possible within the tonal hierarchy.
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