Quaternion (1997)
(for string quartet)

First performed 1997 in San Francisco by Onyx Quartet

A quaternion is a mathematical way of representing a four-dimensional rotation in a three-dimensional space. Quaternion for string quartet uses abstract algebra – principally the properties of symmetry (inversion, transposition, retrograde) – to determine musical structures in which the instrumental actions of four performers are slowly rotated throughout the piece. The quaternion rotation is a means of cycling three-dimensional vectors, as determined by pitch, rhythm, and mode of attack, among four performers, each occupying a unique position within the traditional string quartet hierarchy.