What is Rhythmic “Well-Formedness?”
A chief concern for theories of musical rhythm and meter is distinguishing between well-formed versus malformed rhythms. But “well-formedness” encompasses many aspects, from grammaticality and typicality to perceptual coherence and aesthetic value. In this presentation, several types and/or sources of rhythmic well-formedness will be discussed: (a) stylistic well-formedness, based on the typicality or centrality of a rhythm (or family of rhythms) within the musical practice of a particular time and place, (b) notational well-formedness, based on the ease and possibility with which a rhythm may be captured in a give system of representation, (c) cognitive well-formedness, based on the ease with which a rhythm can be heard and remembered, which is closely related to (d) performance well-formedness, based on the ease and accuracy with which a rhythm can be reproduced by a human performer, and (e) theoretical well-formedness, based on the goodness of fit between a rhythm and a formal system for the construction of rhythmic patterns which takes into account aspects such as the kind and number of elements which may serve as primitives in the system, rules for their concatenation, constraints on their order and length, and so forth. It will be shown that various approaches to musical rhythm tend to highlight some kinds of well-formedness while paying less attention to others, and that different kinds of evidence and approaches (ranging from corpus studies to mathematical modeling to psychological experiments) are endemic to each. The importance of cross-cultural studies of rhythmic style, notation, perception, performance and theory will be stressed, and it will be argued that no matter what kind of rhythmic well-formedness is one’s particular concern, rhythm researchers should keep other aspects of well-formedness in mind.