Two notions of well-formedness in the organization of musical pitch

Abstract

The attribute “well-formed” is used homonymously in two different approaches to the study of musical tone relations. The present article explores commonalities and differences of the underlying theoretical ideas. Fred Lerdahl (2001) uses the attribute “well-formed” (in extension of the GTTM tradition) in order to formulate constraints for the constitution of the basic space as a context-sensitive stratification of the chromatic pitches into layers. Norman Carey and David Clampitt (1989) use the term in order to formulate a criterion to select music-theoretically relevant scales from the larger domain of generated scales. The appearance of pitch hierarchies is common to both approaches and thus provides a starting point for the discussion. There are two other theoretical aspects, which motivate the the comparison between the two approches: (a) the distinction between generic and specific intervals and (b) the duality between step interval patterns and fifth/fourth foldings in the theory of well-formed modes.