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.