Honing, H. (1995). The vibrato problem: comparing two solutions. Computer Music Journal, 19(3), 32-49.
This article is about the formalization of musical knowledge. It describes an important music representation issue named the "vibrato problem," that characterizes the need for a knowledge representation that can deal with both the discrete and continuous aspects of music at an abstract and controllable level. 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 (1992; 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.
Full paper (pdf, and html with unpublished appendices).
All code in Common Lisp (in MCL; dmg)