Ilúvatar's other theme.

[Farael]

I always saw it as if the Third music was the one to give birth to the Children of Iluvatar, while the previous two shaped and gave life to Arda. We know that the only "thing" in Arda that the Ainur had no power over were the Children of Eru. They created mountains and flooded oceans, controlled winds and growing things (besides Elves, Men and Dwarves... oh, and Hobbits but everyone seems to forget them). Given that the first two songs were in part songs of the Ainur (and that's why Melkor could "interfere") I thought they were the creation of Arda, even if it was not yet created, it set the blueprings for it.

The third song is Eru's for the most part, unlike every other because it deals with the creation of the Children. The Ainur had lesser influence on it and so Melkor could not oppose it.

At least, that's the way I read it... I'm sure someone will bring up some comment from the Letters which I do not have and prove me wrong, but until then, those are my thoughts.