[Legate of Amon Lanc]

I will just quickly chime in now, with some corrective remark (I see Aiwendil already did that, but just shortly to point out the main misconception which was presented here) and some personal opinion on the Music following:

To sum it up, just what Aiwendil had said above, in a few short points, to correct the mistaken assumption made in the first post of this thread:

First theme is just the "setup": the original idea of Arda (untouched by discord yet).

Second one is response to the first discord.

The Children - BOTH Eldar and Edain - come only with the Third theme.

I think that much is clear from Ainulindalë itself. Personally, I take that also as "canon" - and if any other sources were different, then I would take this one's authority first over them. (And as I will show later, I believe there is a good reason for it in comparing to the parallel Tolkien might have used.)

Speculation and personal opinion follows from now on:

My personal belief is that the first theme is, in the philosophical sense, the original, unmarred "idea" of Eä. Now that this is laid out, Melkor can start to corrupt it. Once he does, there is the response - in my opinion, that is the part where Valar take their part, they are the active opposition, and it sort of refers to (or rather: is expressed in the history by) the wars in the beginning of Arda, before the coming of the Children. Third theme comes with the Children - and there, they are the active opposition, and that is the one before the final part.

If you want to use Christian metaphoric, I think the Christian tradition (especially strongly supported by the Roman Catholic church, where Tolkien's faith lay) can supply here very well and very nicely the comparison with the fall of the angels preceding the fall of Man. That is, I believe, something everybody is aware of, but it compares also to the Music: we can say, first theme is the beginning, and then, after the first discord, we descend to the "angelic level", the battle takes place on the "angelic plane", so to say: Valar vs. Melkor. Only with the Third theme, we descend into the realms where the battle takes place between Melkor and the Children.