Signals and Noises


Separatrix is an early work for solo violin with computer processing. The title is a term drawn from mathematical descriptions of chaotic systems and fractal geometry: it is the boundary separating points that are in a set from points that are not. Rarely a straight line or smooth curve, the separatrix is more often a complex and intricate fractal shape.

Separatrix grew out of my exploration of the so-called Hénon-Heiles system, a chaotic system first described by the two astronomers for which it is named. Rather than mapping the output of the equations onto a 2D plane as is the usual practice, the output was instead mapped into a musical space (pitch and time) and printed out as a quasi-musical score. For example, the two pages below are the source of the beginning of the piece, starting from the red line in "measure" 8:

Separatrix source page 1

Separatrix source page 2

The violin is processed in real-time by a computer, adding some delay and pitch-shifting at various points in the piece. Separatrix was first performed by Diana Sachs at the North American New Music Festival in Buffalo, New York in 1992. This performance is by Nancy Dahn that same year, recorded at the Banff Centre for the Arts in Banff, Alberta.