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{{Use Harvard referencing|date=January 2020}}
[[Fred Lerdahl]]'s '''"Cognitive Constraints on Compositional Systems"''' is a book chapter that 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 (composer)|Luigi Nono]], [[Karlheinz Stockhausen]], or [[Iannis Xenakis]]". (In [[semiology|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, ''[[Generative theory of tonal music|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==
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