This is an interesting musical composition based on assigning digits to notes in the A-minor scale and adding a complex left-hand accompaniment. There's also some pi trivia on the visual side.
As a bonus, here's an entertaining (for math enthusiasts anyway) lecture from Michael Hartl at CIT suggesting that pi is not the most natural way of expressing the relationship between the linear size of a circle and its circumference. If you don't want to sit through all 51 minutes of it, you might prefer another video that does an excellent job of covering the basics of the idea in just over five minutes (and as a bonus shows you how to make a pie).
Essentially, Hartl et al argue that pi -- the ratio of a circle's circumference to its diameter -- is often less convenient than the ratio of the circumference to the radius. (After all, circles are generally defined in terms of radius.) Circumference divided by radius is 2π, which Hartl calls τ (tau). This makes a lot of trigonometry more intuitive, because there are τ radians in a circle, a fourth of circle (or a right angle) is τ/4 radians, and so on. It's certainly an interesting alternative way of looking at things.
Speaking of alternatives, I wonder what a song based on pi would sound like if expressed in octal rather than decimal notation, since a scale in Western music is thought of as having 8 notes. Or even better, how about duodecimal (base 12) notation, so that it corresponds to the chromatic scale including all sharps and flats?