Beyond the Regular: A Formalization of Non-Isochronous Metrical Structure

Meter perception is the process of inferring metrical structure, a hierarchical and regular mental framework of beats, from an auditory signal. Research on meter perception revolves around the question how listeners perform this task. Formal theories provide a complete abstract representation of metrical structure. Thereby, they provide a clear overview of its key properties and can be implemented into cognitive models, which may in turn clarify the cognitive processes behind meter perception. Most existing formal theories of metrical structure disregard patterns that contain nonisochronous (unequally spaced) beats, while many musical pieces from non-Western musical cultures, such as Balkan or African, induce such meters. Recently, London (2012) proposed a theory of metrical structure that is grounded in empirical perceptual studies and cross-cultural, by incorporating non-isochronous metrical structure. However, this theory is not formal: it is not completely and unambiguously specified. This thesis is concerned with formalization of the theory of London. Formalization reveals multiple ambiguities and inconsistencies within the theory of London, which are evaluated by defining additional rules to the formalization and analyzing the effect of these rules on the space of possible meters. In future research, the proposed formalization may be implemented into a cognitive model of meter perception. Such a cognitive model may provide insight into the cognitive processes behind meter perception within a cross-cultural paradigm.