I have a couple of references that, if I remember correctly, indicate that the song of Illuvatar is derived from the ancient Greek concept of Musica universalis; however, I'm having difficulty locating the precise quotes at the moment, but I will update this answer when I locate them.
OK, here's the reference I was thinking of. In Tolkien the medievalist , Bradford Lee Eden wrote:
A cursory examination of Tolkien's biograph and letters indicates that Tolkien himself did not refer to [the music of the spheres] in the construction of his mythology. Yet, as a classicist and medievalist, the "music of the spheres" concept would have been deeply ingrained into his educational training...the entire history of Middle-earth follows an interesting decay and descent in the uses and appearances of music that closely follow Boethius's model regarding the three types of music in medieval cosmological theory.
The "Boethius" mentioned above is this man, whose work De institutione musica introduced to much of the Western world the medieval concepts of Musica mundana and Musica divina (the music of the spheres/world and the music of the gods, respectively).
There's a lot more supporting material in Mr. Eden's article, but I think this captures the essence of the argument.