Expanded interval cycles
Adam H. Berliner, David Castro, Justin Merritt, Christopher Southard · Journal of Mathematics and Music · 2018
Pitch space is commonly represented using the face of a clock, in which the 12 pitch-classes are mapped onto the elements of Z12. 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.