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ERIC Number: EJ853595
Record Type: Journal
Publication Date: 2009-Sep
Pages: 7
Abstractor: ERIC
Reference Count: 9
ISBN: N/A
ISSN: ISSN-0025-5769
Introducing Group Theory through Music
Johnson, Craig M.
Mathematics Teacher, v103 n2 p116-122 Sep 2009
The central ideas of postcalculus mathematics courses offered in college are difficult to introduce in middle and secondary schools, especially through the engineering and sciences examples traditionally used in algebra, geometry, and trigonometry textbooks. However, certain concepts in music theory can be used to expose students to interesting and straightforward examples of abstract notions in higher algebra, such as groups and rings. In this article, the author defines inversions, shows how they are used in composing music, and shows how sets of inversions can be given a structure that then leads in a natural way to the definition of a group, a subgroup, and a co-set. The author begins by enumerating a piano keyboard as a means of organizing pitch relationships. (Contains 11 figures.)
National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: orders@nctm.org; Web site: http://www.nctm.org/publications/
Publication Type: Journal Articles; Reports - Descriptive
Education Level: High Schools; Middle Schools; Secondary Education
Audience: Teachers
Language: English
Sponsor: N/A
Authoring Institution: N/A