For an afterschool workshop in 2001, a small group of students met to compose their own music. My lesson plans where based on the project I read about in Creative Mathematics by William Higginson, Eileen Phillips, Rena Upitis and David Pimm. The basics are that just as we can transform a graph with different manipulations we can transform a piece of music to make new pieces of music. Once we have enough ‘pieces’ we can string them together and have created an entire composition.
The first day we saw how to manipulate a graph. I drew a puppy’s head and then flipped it backwards. Then we flipped it upside down. There are mathematical terms for each of these manipulations – reflection over the x or y axis. The image can be increase/decreased in size – transformed – or just moved somewhere else – translated. We finished with students at the piano or xylophone trying to pluck out 12-24 notes that sounded good to them.
The next class we saw that music can do the same thing only they call it something else. A translation is called transportation, reflection is called inversion/retrograde, and a change of scale is called diminution/augmentation. We spent the rest of our time composing our short sequence onto paper and acetate.
We spent the next few days using the acetate to flip and translate the individual chunks of music to see which sound good to our ears. The good ones were recorded on paper. Then we started stringing the pieces together for longer compositions. I worked along with the kids and I can still remember how to play my song. And I’m a better mathematician than I am a musician. I wish I could share the student’s finished work but they’re buried in some unknown archive which I hope to rediscover sometime in the future. Get a hold of Creative Mathematics if you’re interested.