ERIC Number: EJ1178557
Record Type: Journal
Publication Date: 2018
Abstractor: As Provided
Modular Arithmetic and Microtonal Music Theory
AsKew, A.; Kennedy, K.; Klima, V.
PRIMUS, v28 n5 p458-471 2018
In this article we discuss relationships between the cyclic group Z[subscript 12] 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.
Descriptors: Arithmetic, Music Theory, Correlation, Numbers, Mathematics Instruction, Mathematical Models, Music, Mathematical Concepts, Graphs, College Mathematics
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Authoring Institution: N/A
Identifiers - Location: North Carolina
Grant or Contract Numbers: N/A