Two algorithms for the instanciation of structures of musical objects

This is an extended and revised version of the paper: Symbolic and Sonic Representations of Sound-Object Structures published in M. Balaban, K. Ebcioglu & O. Laske (Eds.) “Understanding Music with AI: Perspectives on Music Cognition”, AAAI Press (1992, pp.64-109).<br />A representational model of discrete structures of musical objects at the symbolic and sonological levels is introduced. This model is being used for the design of computer tools for rule-based musical composition in which the low-level musical objects are not notes, but “sound-objects”, thereby meaning arbitrary sequences of messages dispatched to a real-time digital sound processor.<br />“Polymetric expressions” are string representations of concurrent processes that can easily be handled by formal grammars. These expressions may not contain all the information needed for synchronizing the whole structure of sound-objects, i.e. determining their strict ordering on (symbolic) time. In response to this, the notion of “symbolic tempo” is introduced: ordering all objects in a structure is possible once their symbolic tempos are known. Rules for assigning symbolic tempos to objects are therefore proposed. These form the basis of an algorithm interpreting incomplete polymetric expressions. The relevant features of this interpretation are commented.<br />An example is given to illustrate the advantage of using (incomplete) polymetric representations instead of conventional music notation or event tables when the complete description of the musical piece and/or its variants calls for difficult computations of durations.<br />Given a strict ordering of sound-objects summarized in a “phase table” representing the complete polymetric expression, the next step is to calculate the dates at which messages should be dispatched. This requires a description of “sound-object prototypes” along with their metric/topological properties, and various parameters related to the musical performance (e.g. “smooth” or “striated” time, tempo, etc.). These properties are discussed in detail and a time-polynomial constraint-satisfaction algorithm for the time-setting of sound-objects in a polymetric structure is introduced. Typical examples computed by this algorithm are shown and discussed