A general pitch interval representation: Theory and applications

Abstract

Abstract Pitch and pitch‐intervals are most often represented — in the western tradition — either by the traditional pitch naming system and the relating pitch‐interval names, or as pitch‐classes and pitch‐class intervals. In this paper we discuss the properties, relationships and limits of these two representations and propose a General Pitch Interval Representation (GPIR) in which the above two constitute specific instances. GPIR can be effectively used in systems that attempt to represent pitch structures of a wide variety of musical styles (from traditional tonal to contemporary atonal) and can easily be extended to other microtonal environments. Special emphasis will be given to the categorisation of intervals according to their frequency of occurrence within a scale. Two applications of the GPIR will be presented: a) in a system that transcribes melodies from an absolute pitch number notation to the traditional staff notation, and b) in a pattern‐matching process that attempts to discover repetition...