I always interpreted it as the three "über-ages (empires, reiches, whatever you want to call it" of Éa- the shaping and undoing repeated three times up to the silencing of everything and demise of the earth. I could be way off, but it's just my inference.
As for the clash of Melkor and Eru, this is what I think:
Beginning of theme- Purity and innocence of the world and its people
Melkor and Iluvatar clash- Evil enters the world
Melkor's theme grows and overtakes Iluvatar's- Battle between good and evil. Evil gradually grows and leads to the undoing of the music's beauty and the overthrow of good.
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That best portion of a good man's life,
His little, nameless, unremembered acts of kindness and of love.
.................William Wordsworth
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