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A Geometric Language for Representing Structure in Polyphonic Music

In 1981, Deutsch and Feroe proposed a formal language for representing melodic pitch structure that employed the powerful concept of hierarchically-related pitch alphabets. However, neither rhythmic structure nor pitch structure in polyphonic music can be adequately represented using this language. A new language is proposed here that incorporates certain features of Deutsch and Feroe’s model but extends and generalises it to allow for the representation of both rhythm and pitch structure in polyphonic music. The new language adopts a geometric approach in which a passage of polyphonic music is represented as a set of multidimensional points, generated by performing transformations on component patterns. The language introduces the concept of a periodic mask, a generalisation of Deutsch and Feroe’s notion of a pitch alphabet, that can be applied to any dimension of a geometric representation, allowing for both rhythms and pitch collections to be represented parsimoniously in a uniform way.