Fractal images enjoy a great deal of popularity due to their aesthetically pleasing qualities. While the generation of fractal images is a topic that has received a lot of attention in the past, only a few attempts have been made to create musical compositions using fractals and their audible properties. This paper describes one possible process of mapping the elements from the Mandelbrot Set fractal to audible musical notes. The Mandelbrot Sound Map software tool has been created to implement the mapping of set elements to audible outputs. This software produces audible compositions based on a parameterized traversal of a specific portion of the Complex number plane containing the Mandelbrot Set, and creates musical files that can be listened off-line as well.