Organized Time

This book presents a theory of temporal structure for music, making two main arguments. The first is that a single model of temporal structure, expressible in the form of a certain type of mathematical network, is common to all modalities, particularly rhythm, tonality, and form. As a result, we can develop tools to talk about the experience of musical time in abstraction from any particular modality, and make analogies from structural phenomena in one modality to another (e.g., formal counterpoint). The second argument is that each of these modalities is in principle independent: it has its own set of structuring criteria, and it may lead to structures that agree or disagree with each other. The resulting coordination or disjunction between modalities is of more direct aesthetic importance, typically, than anything that can be said about one isolated parameter alone. These claims have deep ramifications for theories of rhythm, tonality, and form: for instance, that it is possible to discuss formal structure without necessary reference to tonal features. Theories of harmony, key, formal function, hypermeter, and closure are developed in conjunction with analysis of a wide range of eighteenth- and nineteenth-century composers, surveys of classical repertoire, and observations about the history of musical styles. A number of mathematical tools for temporal structure are also proposed.