Honing, H. (1994). The Vibrato Problem. Comparing two ways to describe the interaction between the continuous and discrete components in music representation systems. (Research Report CT-94-14). Amsterdam: Institute for Logic, Language and Computation (ILLC).


In a number of time-based 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 time-based representations as well, i.e., representation systems where knowledge about the domain is essential in maintaining isomorphism between the real-world and its representation.

Full paper (with unpublished appendices).