Imaginary transformations

Document Type

Article

Publication Date

11-1-2010

Abstract

We investigate classes of discrete musical operations that function in ways that correspond to the imaginary units i, j, and k of the quaternions (i.e. orthogonal square roots of-1). In particular, we focus on musical transformations of order 4 that are mutual square roots of a central involution. We define imaginary transformations as members of groups of operations acting on the set of pitch classes in an octatonic collection and as members of subgroups of various triadic-transformational systems. These structures include quaternion, Pauli, (almost) extraspecial, and dicyclic groups, among others. © 2010 Taylor & Francis.

Publication Source (Journal or Book title)

Journal of Mathematics and Music

First Page

157

Last Page

171

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