This got me curious: what does pi sound like? And the answer is that it's actually surprisingly tonal. The opening "31415" firmly establishes the key, and thereafter there's sonorous intervals to keep everything fairly well-behaved; the few out-of-place notes can be dealt with by an appropriate sort of rhythym. If you're gonna try it I recommend it as far as:

31415926535897932384626433832795028841971693993751

So that you get a nice 5-1 ending.