Separatrix


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 line which separates points that are in a set from points which 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


Separatrix was first performed in Buffalo, New York at the North American New Music Festival in 1992. This recording is of a later performance that same year by violinist Nancy Dahn at the Banff Centre for the Arts:



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