Mathematics and Music: An introductory exploration of set theory, chaos and fractals

In the summer of 2010 we, Lydia Short, math and piano graduate, and Sarah Rody, third year math major and piano minor, had only one task: find an idea that combines math and music and, from it, develop a project. After a broad search that covered everything from tuning theories to asymmetric rhythms, we decided on fractal music. We came up with two different approaches to composing fractal music. Lydia focused more creating music using fractal construction methods of Iterated Function Systems on a specific set of notes and times instead of a geometric shape.  Sarah focused on creating a fractal image of an Iterated Function System and mapping the image onto different musical scales. These constructions connect the mathematical concept of fractals to music in different ways, which create different sounds in their respective musical compositions.  These programs are just two of many examples of how mathematics and music connect.