Cognitive Constraints on Compositional Systems: Difference between revisions

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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 [[semiology|semiological]] terminology this may be called gap between the poeitic and esthesic processes. To explain, and eventually to help end, this Lerdahl proposes the concepts of [[musical grammar]]s, "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 are historically and fruitfully mixed freely, 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:
 
===Constraints on event sequences===
 
*''Constraint 1'': The musical surface must be capable of being parsed into a sequence of discrete events.
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*''Constraint 8'': The projection of a prolongational tree depends on a corresponding time-span tree in conjunction with a set of stability conditions.
 
===Constraints on underlying materials===
 
*''Constraint 9'': Stability conditions must operate on a fixed collection of elements.
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**[only certain divisions of the octave, 12 and 20 included, allow uniqueness, coherence, and transpositional simplicity, and that only the diatonic and pentatonic subsets of the 12 tone chromatic set follow these constraints (Balzano, 1980, 1982)]
 
===Pitch Space===
 
*''Constraint 15'': Any but the most primitive stability conditions must be susceptible to multidimensional representation, where spatial distance correlates with cognitive distance.
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He concludes, "Some of these constraints seem to me binding, other optional. Constraints 9-12 are essential for the very existence of stability conditions. Constraints 13-17, on the other hand, can be variously jettisoned." Examples given are [[Carnatic music|South Indian music]] which doesn't [[modulation (music)|modulate]] and isn't equally tempered (13 & 14) and music such as that of [[Claude Debussy]], [[Béla Bartók]], and others which "have developed consonance-dissonance patterns directly from the [[total chromatic]]." (14-17)
 
===Comprehensibility and value===
 
*''Aesthetic Claim 1'': The best music utilizes the full potential of our cognitive resources.