Ensemble Timing in Computer Music

Abstract

The precision of computers makes possible computer music ensemble interactions that are both arbitrarily complex and tightly constrained. Such control is useful in the simulation of expressive playing, where it is necessary to introduce slight deviations in the time trajectories of individual voices and insure that the ensemble cohesion is not disturbed. Furthermore, it opens up a realm of compositional timing arrangements that would be impossible or extremely difficult with human performers alone. Many such examples, although implemented on the player piano, can be found in the music of Conlon Nancarrow. Similarly, Henry Cowell wrote music with complex rhythms for an obscure instrument called the Rhythmicon, music that was later implemented on computer by Leland Smith (Smith 1973). Finally, the author's composition Silicon Valley Breakdown (1982) for computergenerated tape includes a variety of complex timing arrangements such as canons in which each of several voices has an independent, continually varying tempo and all voices finish their material simultaneously at a predesignated point in time. Despite the potential for interesting ensemble interactions, computer music programs have tended to neglect or deal in a clumsy manner with both interand intra-voice timing and phrasing, due to both the lack of generality of the programs and a lack of clarity concerning timing issues. This made the simulation of expressive playing in arrangements of traditional music tedious and timing arrangements on the order of complexity of Silicon Valley Breakdown next to impossible. The problem is that the composer is protected from direct access to scheduler behavior. Furthermore, no facility is provided for applying an arbitrary expression or function call to a parameter value. Some recent programs such as Pla (Schottstaedt 1983) and FORMES (Rodet, Potard, and Barriere 1984) have alleviated these problems. However, in order to gain the desired control over timing, the task of specifying tempo and ensemble behavior must be properly handled. The appropriate construct for describing ensemble timing interaction is the time map, which provides precise, yet flexible phrasing control. The time map allows the composer to specify, either graphically or by a functional definition, a distortion of a time trajectory such that complex tempo variations combined with precise coincidence control can be obtained. The time map approach is also a useful way to think about performance analysis. It must be stressed that the time map method is an approach rather than an implementation and can be adapted to a variety of environments. Therefore, although implementation issues and sample prog ams are discussed in this paper, no detailed description of a particular implementation is given.