A Theoretical Model of Musical Form

Musical form is one of the most central aspects of musical structure, as it concerns the overarching organization principles of music across genres and styles. Therefore, understanding the formal characterization of musical form is a central topic in music theory, computational music analysis, MIR, and music generation. Numerous theoretical accounts of form have been developed in music theory, largely in repertoires of common-practice tonality. This paper makes a theoretical contribution proposing a formal model that characterizes the main aspects of musical form and lends itself to computational implementation. In our paper, we characterize musical form by the following aspects: (a) segmentation, (b) hierarchical grouping structure, (c) meter and hypermetrical structure, (d) repetition structure, and (e) form-functionality. As the structures of hierarchical segmentation as well as form-functionality have previously been conceptualized in terms of a recursive tree-shaped hierarchy, we ground our model in formal abstract generative grammars. Our model extends this hierarchical analysis by an account of the rhythmical properties of form as well as repetition structure. The harmonic layout defines constraints for motivic content (pitch and rhythm). Our approach also captures repetition structure by modelling the location and degree of variation of repeated ideas. This is achieved via variable binding. We exemplify our theoretical contribution by a detailed analysis and discuss its applicability for theory, computational modelling, and music generation.