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Fred Lerdahl's "Cognitive Constraints on Compositional Systems" cites Pierre Boulez's ''Le Marteau sans Maître'' (1955) as an example of "a huge gap between compositional system and cognized result," though he "could have illustrated just as well with works by Milton Babbitt, Elliott Carter, Luigi Nono, Karlheinz Stockhausen, or Iannis Xenakis". (In semiological terms, this is a gap between the esthesic and poietic processes.) To explain this gap, and in hopes of bridging it, Lerdahl proposes the concept of a musical grammar, "a limited set of rules that can generate indefinitely large sets of musical events and/or their structural descriptions." He divides this further into compositional grammar and listening grammar, the latter being one "more or less unconsciously employed by auditors, that generates mental representations of the music". He divides the former into natural and artificial compositional grammars. While the two have historically been fruitfully mixed, a natural grammar arises spontaneously in a culture while an artificial one is a conscious invention of an individual or group in a culture; the gap can arise only between listening grammar and artificial grammars. To begin to understand the listening grammar Lerdahl and Ray Jackendoff created a theory of musical cognition, ''A Generative Theory of Tonal Music'' (1983; ISBN 0-262-62107-X). That theory is outlined in the essay. Lerdahl's constraints on artificial compositional grammars are: ==Constraints on event sequences== *''Constraint 1'': The musical surface must be capable of being parsed into a sequence of discrete events. * *(Ligeti, computer music ) *''Constraint 2'': The musical surface must be available for hierarchical structuring by the listening grammar. * *(grouping structure, metrical structure, time-span reduction, and prolongational reduction. "Associational" factors such as motivic development and timbral relations are ignored, but for "Timbral Hierarchies" see Lerdahl 1987 ) *''Constraint 3'': The establishment of local grouping boundaries requires the presence of salient distinctive transitions at the musical surface. * *(minimal music ) *''Constraint 4'': Projections of groups, especially at larger levels, depends on symmetry and on the establishment of musical parallelisms. *''Constraint 5'': The establishment of a metrical structure requires a degree of regularity in the placement of phenomenal accents. *''Constraint 6'': A complex time-span segmentation depends on the projection of complex grouping and metrical structures. *''Constraint 7'': The projection of a time-span tree depends on a complex time-span segmentation in conjunction with a set of stability conditions. *''Constraint 8'': The projection of a prolongational tree depends on a corresponding time-span tree in conjunction with a set of stability conditions. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Cognitive Constraints on Compositional Systems」の詳細全文を読む スポンサード リンク
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