Representing Musical Time

An examination of a crucial issue in processing music by computer and in other abstract and formal approaches to music. The relations of time specified in musical scores and found in bodies of musical performances have a complex and sometimes indeterminate structure, and even the nature of musical time can be in question. Complicating factors such as partially determined ordering of events are found not only in music of the 20th century, when composers explicitly employed such indeterminacy, but also in music where the indeterminacy is only implicit in the interpretation of the notation.;This work analyzes in detail the essential issues of the nature of musical time, possible formulations of musical temporal relations, taking account of indeterminacy, and systems for the measurement of musical time. Representations are classified according to their expressive power and computational complexity. Existing systems of musical representation are related to these formulations, and some generic representations of music are proposed and analyzed. The most expressively powerful representations are shown to be computationally intractable, while those of least computational complexity are shown to be incapable of representing some types of music. A perfect system of representation is therefore impossible, and different representations are appropriate for different purposes.