[[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 [[semiology|semiological]] terminology this may be called gap between the poeitic[[esthesic and esthesicpoietic]] processes. To explain this gap, and eventually to help end 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 further divides this into compositional grammar and listening grammar, the latter being "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 and the "gap" may only exist 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. This theory is outlined in the essay, and constraints on artificial compositional grammars are quoted below:
