Well, I've finally finished the second installment of Math and Music, and I scheduled a talk on this for Saturday May 16th. There are power-point style slides from the first Math and Music here.
The first Math and Music talk focused on the development of a musical scale. This next talk will branch out a little and explore the "beats" that musicians often use in tuning and how these can be used to calculate the actual frequency of a note.
We'll also look at the Wave Equation - an important piece of mathematics that arises from attempts to understand the behavior of a vibrating string but which turns out to be useful in a wide variety of applications (including the invisibility equations!)
We'll also talk about harmony and harmonics, although I never did figure out exactly why woodwind and stringed instruments produce harmonic tones...
Math and Music
While I was at Portland State years ago, one of the physics professors, Laird Brodie, gave me and another lucky gentleman a demonstration of how harmonics work on a vibrating string. He stretched a wire (which looked like a typical guitar or piano string) onto a 3-foot-long bridge, then attached electric connections to it. He then turned out the lights in the classroom, induced a current through the wire, and turned on an adjustable strobe light. As he increased the frequency of the strobe flashes, we could see standing waves appear on the charged wire, waves which would sometimes appear to stand still. When he would double, triple, or quadruple the frequency of the strobes, the visible peaks and valleys on the charged wire would also double or triple. He explained to us that the large visible waves were whole notes and the smaller waves were harmonics. I was then able to visually understand how harmonic notes become audible when one moves one's fingers along the harmonic intervals along the neck of the guitar (or any other stringed instrument).