Abstract approach to music

摘要

In this article we have outlined a formal framework for an abstract approach to211u001emusic and music composition. The model is formulated in terms of objects that 211u001ehave attributes, obey relationships, and are subject to certain well-defined 211u001eoperations. The motivation for this approach uses traditional terms and concepts 211u001eof music theory, but the approach itself is formal and uses the language of 211u001emathematics. The universal object is an audio wave; partials, sounds, and 211u001ecompositions are special objects, which are placed in a hierarchical order based 211u001eon time scales. The objects have both static and dynamic attributes. When we 211u001erealize a composition, we assign values to each of its attributes: a (scalar) 211u001evalue to a static attribute, an envelope and a size to a dynamic attribute. A 211u001ecomposition is then a trajectory in the space of aural events, and the complex 211u001eaudio wave is its formal representation. Sounds are fibers in the space of aural 211u001eevents, from which the composer weaves the trajectory of a composition. Each 211u001esound object in turn is made up of partials, which are the elementary building 211u001eblocks of any music composition. The partials evolve on the fastest time scale in 211u001ethe hierarchy of partials, sounds, and compositions. The ideas outlined in this 211u001earticle are being implemented in a digital instrument for additive sound 211u001esynthesis and in software for music composition. A demonstration of some 211u001epreliminary results has been submitted by the authors for presentation at the 211u001econference.