TEACHER NOTES

ISSUES RELATED TO THE PROBLEM

This exercise is very memory intensive. So that students have the time to wait for their computer, it is best to start it in class but allow additional time out of class for completion.

Prerequisites

The sine, cosine and exponential functions.

Time allotment - time management

This could be started at the end of a class period. The students should complete the work on their own time assuming they have easy access to computers running Mathematica.

Expectations

Students will have fun.

Future payoffs

Students get a quick and painless real-life application to the sine, cosine and exponential functions.

Extensions

The musically inclined may wish to listen to strange scales in which there are either more or less than 12 tones per "octave" by running through a power of two with exponents of the form 2^(i/n) where n is the number of tones in an "octave".

References and Sources

David Rusin's WWW page explains why there are 12 tones in an octave:
http://www.math.niu.edu/~rusin/papers/uses-math/music/12