A hierarchical and deterministic approach to music grammars and its application to unmeasured preludes

We discuss the notion of a music grammar and formulate a set of requirements which define a certain genre of music grammars to which our work relates. Motivated mainly by our requirement for cognitive adequacy, we develop a model characterised by a hierarchical structure and by sequential parsability with strictly bound memory resources. In the course of doing that, we define the LR(k, n) property and explore some of its mathematical implications. As an instance of our model, we develop a grammar for unmeasured preludes, having Louis Couperin’s Prelude number 7 in A-minor as initial coverage. We evaluate our grammar by means of proving some of its formal properties (in particular LR(k, n)), and by means of applying a parsetree based performance algorithm which is based on the parse tree produced by the grammar. The performance is then evaluated by experts in order to verify the grammar’s descriptive adequacy. We conclude by discussing some of our ideas for further research.