Reflections towards a generative theory of musical parallelism

Abstract

Parallelism plays a core role in Lerdahl and Jackendoff's (1983) GTTM, as it rules the emergence of motivic, metrical, grouping and even formal structures. Due to the high amount of detail and complexity characterising associational structures, neither explicit model nor systematic methodology of parallelism-based structural inference has been included into the GTTM. This paper develops a methodological and computational answer to this problem founded on a computational modelling of pattern extraction operations. The paper focuses in particular on the methodological interest of the pattern mining formalism, and in particular its application to the formalisation of grouping and metrical structure inference and to the understanding of the possible interdependences, between these two levels of representation, but also more generally between parallelism and phenomenal accents. Concerning grouping structures, an attenuation of the strong hierarchy postulate is suggested, opening the framework to the study of structural polysemy and polyphony. A generalisation of the pattern mining formalism indicates a bottom-up understanding of musical variation and ornamentation, through the construction of a syntagmatic network whose connectivity is constrained by basic tonal principles.