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Re: music and math
Posted:
Mar 4, 1995 2:41 AM


On Friday, March3, Juliet Rogers wrote:
>Does anyone know of any texts or resources which use music to teach math? >
Juliet,
There are indeed connections between the two fieldsmuch more than anyone would realize...As a split personality, mathematician/musician, I should be connecting them even more in the classroom than I do.
Shari's response to you about the Sound Foundations is an excellent one. The materials are welldone and interesting. It is certainly a field use of math in music. There are other ways to employ music as a forum for mathematics. Because any music piece is a vast compilation of data, any form of data collection or probability/statistics instruction could turn to music for a number of investigations...Moreover, any music piece is a *patterned* compilation of organized data...There are a multitude of patterns to be found in any musical piece...You could almost give your students a free assignment to find a piece of music with patterns and I bet they all could...many with interesting patterns appropriate for downloading to some type of mathematically worthy discussion.
I, on the other hand, read your question from a different perspective. I was assuming, by your question, that you are looking for ways to demonstrate mathematic's interconnection with music. For example, we can certainly use the Pythagorean developed relationships between the arithmetic, geometric, and harmonic means to establish the interval relations between various pitches of the tempered musical scale...we can also use these relationships to establish the frequencies of overtones. I would suggest most History of Math resources would have information on this...if not, there is an old (mid1980's) article in Mathematics Teacher on this very topic and how to impletment it into the classroom.
A different twist that is not overly profound is the musical work of Milton Babbit in the twentieth century. Babbitt, a mathematician, worked a great deal in what is referrred to as "twelvetone music" where the composer establishes a "tone row" consisting of every one of the twelve pitches used in western music in some arbitrary order. Then, the composer may follow certain rules to manipulate the tone row to develop new sections of the music. What the rules are are essentially row operations on a matrix. An interesting way to give the students practice in learning what row operations are and how they work while simultaneously giving them a chance to create music (without having to have had a great deal of music theory)!
There are certainly other connections in the physics of music, soundwaves, etc. Also, various composers, such as J.S. Bach, were quite sophisticated mathematically and supposedly employed some mathematics undergirding some of their music. I will do some hunting and send you any references of resources I findhope that this is of some use to you...If anyone else out there would like some info, please write me.
Tim
***************************************************** Tim Hendrix (hendrix@uxa.cso.uiuc.edu) * Division of Mathematics Education * Department of Curriculum & Instruction * University of Illinois * ***************************************************** 382 Education Building * 1310 South 6th Street * Champaign, Il 61820 * ***************************************************** (217) 3333643 * *****************************************************



