The music of the Ainur

[Gayalondiel]

Then the voices of the Ainur, like unto harps and lutes...began to fashion the theme of Iluvatar to a great music; and a sound arose of endless interchanging melodies woven in harmony...
...But now Iluvatar sat and hearkened, and for a great while it seemed good to him, for in the music there were no flaws. But as the theme progressed, it came into the heart of Melkor to interweave matters of his own imagining...and straightway dischord arose around him...
...Then Iluvatar arose...and the Ainur percieved that he smiled; and he lifted up his left hand, and a new theme began amid the storm, like and yet unlike to the former theme...
...Then again Iluvatar arose...and behold! a third theme grew amid the confusion, and it was unlike the others.

To cut a long passage to not quite so long, this is a bit of the Sil that I just re-read, and it made me think. does anyone have information/theories/conjecture about what exactly the themes represent, and why there are three? I know the third is to do with the Children of Iluvatar, and that Manwe was chief instrument of the second. Is this something obvious that i've missed?