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Re: music and math
Posted:
Mar 4, 1995 2:41 AM
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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 fields--much 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 well-done 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
down-loading 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 "twelve-tone 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 find--hope 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 *
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382 Education Building *
1310 South 6th Street *
Champaign, Il 61820 *
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(217) 333-3643 *
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