[Voralphion]

The three themes of Illuvatar didn't correspond to the three ages of the world because the third age in LOtR wasn't the third age of the world, it was the third age of the sun and moon. Before the sun and moon there were the ages of the trees, and of these there were at least three because Melkor was imprisoned in the halls of Mandos for three ages. Before the ages of the trees there were the ages of the Valar in which they made the world, it says they toiled for ages uncounted.
As for the three themes of Illuvatar, I know for certain that the third theme was the theme concerning the children, as can be seen be the two separate movements in the theme, one slow and melodious (elves) and the other fast and endlessly repeated (men).
The first two themes involve the making of the world by the valar and their wars on Melkor for mastery of Arda.
I think the themes stopped at the time of the dominion of men as they were not bound to the music and fate as the elves were but could shape their lives as they wished, except of course the early men whose lives were entwined with the eldar, such as Tuor, Beren, Turin etc..