Modular Arithmetic and Microtonal Music Theory

Autor/inn/en	AsKew, A.; Kennedy, K.; Klima, V.
Titel	Modular Arithmetic and Microtonal Music Theory
Quelle	In: PRIMUS, 28 (2018) 5, S.458-471 (14 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1051-1970
DOI	10.1080/10511970.2017.1388314
Schlagwörter	Arithmetic; Music Theory; Correlation; Numbers; Mathematics Instruction; Mathematical Models; Mathematical Concepts; Graphs; College Mathematics; North Carolina + Suchen Sie Ihr Suchwort? Addition; Arithmetik; Arithmetikunterricht; Rechnen; Musiktheorie; Korrelation; Zahlenraum; Mathematics lessons; Mathematikunterricht; Mathematical model; Mathematisches Modell; Grafische Darstellung
Abstract	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. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01