The Vibrato Problem. Comparing two Ways to Describe the Intraction between the Continuous Knowledge and Discrete Components in Music Representation Systems
Henkjan Honing
Abstract:
The Vibrato Problem.
Comparing two ways to describe the interaction between the continuous and
discrete components in music representation systems.
Henkjan Honing
In a number of timebased domains (e.g., animation, music, sound or speech)
a distinction can be made between the discrete, symbolic aspects and the
continuous, numerical aspects of the underlying representation. In such a
`mixed' representation it becomes necessary to describe the interaction
between both types of description. This issue of interaction will be
discussed by comparing two approaches in the domain of music. In this
domain the need for a knowledge representation that can deal with both
the discrete and continuous aspects at an abstract and controllable level
is charaterized by the vibrato problem. Two formalisms of functions of time
that support this notion will be compared: the approach used in the Canon
family of computer music composition systems (Dannenberg, McAvinney and
Rubine 1986; Dannenberg 1989; Dannenberg, Fraley and Velikonja 1991) and
the Desain and Honing (1992a; 1993) Generalized Time Functions (GTF). The
comparison is based on a simplified version of the Dannenberg's Arctic,
Canon, and Fugue systems (referred to as ACF), obtained from the original
programs using an extraction technique, and a simplified version of the
GTF system that was made syntactically identical to ACF. In general, both
approaches solve the vibrato problem, though in very different ways. The
differences will be explained in terms of abstraction, modularity,
flexibility, transparency, and extensibility -- important issues in the
design of a representational system for music (Honing 1993b). The GTF
formalism, that was developed for the music domain, is expected to be
useful in other timebased representations as well, i.e., representationsystems where knowledge about the domain is essential in maintaining isomorphism
between the realworld and its representation.