Expanded interval cycles. Issue 1 (2nd January 2018) - Berliner, Adam H.; Castro, David; Merritt, Justin; Southard, Christopher
Abstract : Pitch space is commonly represented using the face of a clock, in which the 12 pitch-classes are mapped onto the elements ofZ 12 . Combining this form of representation with modular arithmetic results in the emergence of significant rotationally symmetric patterns, which can be used to generate pitch content and to effect a modulation between closely related collections within a composition. We generalize the situation to rotationally symmetric patterns with any number of intervals, and give necessary and sufficient conditions for when an interval pattern yields an analogous symmetry.