Modular Arithmetic and Microtonal Music Theory. Issue 5 (28th May 2018)

• Record Type: Journal Article
• Authors: AsKew, A.; Kennedy, K.; Klima, V.
• Is Part Of: PRIMUS. Volume 28:Issue 5(2018)
• Page Start: 458
• Page End: 471
• Publication Date: 2018-05-28
• Subjects: Group theory -- microtonal system -- modular arithmetic -- music theory; Mathematics -- Study and teaching (Higher) -- Periodicals; 510.711
• DOI: 10.1080/10511970.2017.1388314
• Languages: English
• ISSNs: 1051-1970

Abstract

Abstract: In this article we discuss relationships between the cyclic group and Western tonal music that is embedded in a 12-note division of the octave. We then offer several questions inviting students to explore extensions of these relationships to other n -note octave divisions. The answers to most questions require only basic properties of modular arithmetic and greatest common divisors. However, some questions ask students to explore additional topics such as Cayley graphs of groups. Thus, the questions can be adapted to fit into a course that appears as early in the curriculum as introduction to proof or as late as abstract algebra and number theory.