The Women in Science Initiative at Brandeis has put together a nice series of talks : Art of Science.
This month's featured Professor Diana Dabby and her work creating musical variation utilizing chaos.
The term "chaos" means something specific in mathematics. It's reserved for dynamical systems, that is systems that change over time according to mathematical rules, that exhibit sensitivity to initial conditions.
We're familiar with this idea in terms of the "butterfly effect": that something as small as the flap of a butterfly's wings can be the deciding factor as to whether a hurricane forms half-way round the globe. This term was coined by Edward Lorenz, an american meteorologist and mathematician. He discovered it while running simulations for the weather patterns in the early 1960's. In one of these simulations, he decided to save time and put in fewer numbers after the decimal, and was surprised to find that the behavior was completely different.
Professor Dabby uses a set of equations that Lorenz created to describe the weather to generate her musical variations. Solutions to these equations tend to have a similar shape, a little bit like a butterfly.
One is shown in the poster. Dabby finds a solution to these equations and then connects that solution to the musical notes of the original song. She then changes the initial conditions to get a different solution, and uses the connection she built before to make a new song.
An interesting thing that she shared was that she had actually met Lorenz and that she's tried to find other chaotic systems that make aesthetically pleasing variations and no others have worked as well. She played a number of variations that she had created and discussed their similarities when considered through the lens of Schenkerian analysis.
Here's a link to her her variation generating app so you can try it out.
And a link to one of her papers for more detail: 1996 Chaos paper
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