The MIT Linguistics Colloquium Series presents:
Jonah Katz
Massachusetts Institute of Technology
Friday, April 11, 2008
3:30 p.m., Room 32-141
In this paper, I argue that musical grouping obeys the logic of Optimality Theory (OT), producing a simple and explicit theory of grouping. Certain well-formedness conditions are argued to follow from domain-general constraints on the mental representation of temporal cognitive processes.
OT, developed by linguists studying phonological competence, models the interaction of violable constraints. The framework has formal similarities to the system of preference rules introduced in the Generative Theory of Tonal Music (GTTM, Lerdahl & Jackendoff 1983), but is more explicit and restrictive.
In the current approach, grouping is primarily determined by the family of surface disruption (SD) constraints, exemplified here by the rest constraint:
SD(REST): Each rest in the musical surface coincides with a group boundary at each level of structure.
Several of these SD constraints, interacting with one another in a strict ranking, will generate a single optimal grouping analysis for any unambiguous musical surface. Problems raised in GTTM concerning additivity and gradience are eliminated in a framework that assumes strict domination between constraints. Many well-formedness considerations fall out of the approach "for free," because it naturally aligns grouping boundaries at all levels of an analysis. Grouping overlap is given a new treatment as a naturally marked structure that emerges as optimal under special harmonic considerations.
The nested, hierarchical form of grouping is argued to follow from three domain-general considerations. The highest level of structure is due to the Unity of the Piece. The lowest level is a consequence of "chunking" (Miller 1956). Intermediate levels are due to the binarity principle, pervasive in language, verse, and musical reductions:
Binarity: If complex object G1 contains complex object G2, then G1 contains exactly two complex objects and nothing else.
Adopting OT for grouping analysis results in advances over GTTM in terms of empirical coverage and simplicity.
