Thanks to everyone who's responded so far. It is most certainly not the self test tune. I don't think my friend's Atari 800 even had that option. This was not a simple collection of notes. It was raw and noisy and almost sounded like a badly sampled piece of music (low bit rate, poorly wired mic, clipping, etc). And I'm almost positive it involed PEEKing in memory locations, because I seem to remember we changed the start and ending values on the FOR loop to 0 TO 65535 trying to hear "the whole song." That just resulted in a bunch of squeals, static, silence, the little bit of music we'd already heard, more static.
Here is me trying to re-create the music. Don't judge me. I actually have a half decent singing voice. http://youtu.be/GEbINsaQgbs
And I am likewise shocked to find out that the self test music is the opening line of a classical music piece. I shouldn't be surprised, since every C-64 commercial in the early 80's had the same classical tune playing in the background. I can't remember the name or composer, but now it's stuck in my head.