This paper is concerned with the type of data structures required for the accurate representation of tonal structure, in particular with the atomic/combinatorial nature of the non-terminal symbols within such representations. The theoretical commitments inherent in the form of Schenkerian representations will be examined, followed by a critical analysis of the consequences of these commitments for the descriptive adequacy of Schenkerian theory. Specifically, the structural phenomena examined here suggest that the form required of a successful tonal theory is a combinatorial syntax, an observation with important ramifications for the question of the computational architecture underlying our cognition of tonal music.