Expanded interval cycles. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Berliner, Adam H.; Castro, David; Merritt, Justin; Southard, Christopher
• Is Part Of: Journal of mathematics and music. Volume 12:Issue 1(2018)
• Page Start: 21
• Page End: 33
• Publication Date: 2018-01-02
• Subjects: circle of fifths -- modulation -- interval cycle -- expanded interval cycle -- Zn-orbiting sequence -- irreducible sequence; 00A65 -- 11A05 -- 11A07; Music theory -- Periodicals; Music -- Mathematical models -- Periodicals; Music -- Mathematics -- Periodicals; 781.2
• DOI: 10.1080/17459737.2018.1453950
• Languages: English
• ISSNs: 1745-9737

Abstract

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.