This paper addresses some issues arising from theories which represent musical structure in trees. The leaves of a tree represent the notes found in the score of a piece of music, while the branches represent the manner in which these notes are an elaboration of simpler underlying structures. The idea of multi-levelled elaboration is a central feature of the Generative Theory of Tonal Music (GTTM) of Lerdahl and Jackendoff, and is found also in Schenkerian theory and some other theoretical accounts of musical structure. In previous work we have developed computable procedures for deriving these tree structures from scores, with limited success. In this paper we examine issues arising from these theories, and some of the reasons limiting our previous success. We concentrate in particular on the issue of context dependency, and consider strategies for dealing with this. We stress the need to be explicit about data structures and algorithms to derive those structures. We conjecture that an expectation-based parser with look-ahead is likely to be most successful.