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:
Pi actually reminds me a bit of "Nimrod" from Elgar's Enigma variations. The opening is only one note off, and then many of the later sequences in pi have the same large jumps that Nimrod does.
908234092830498230948203984023
984092384092834092384098230940
293423129192837917823793128372
891793821973821297897318297831
293178239781292398409238409283
409238409823094012972978312901
782379312837289179382197382129
789731829783129317823978129239
840923840928340923840982309401
297297831290178237931283728917
938219738212978973182978312931
782397812923984092384092834092
384098230940129729783129098230
940129729783129098230940129729
783129098230940129729783129098
23094012972978312555454