[Lalwendë]

Firstly, you have to consider what Melkor does. Is it evil? I'll come to that later. But even if it is evil, and he was made that way by his father Eru, it is Eru's perogative to do what he likes. That's why the Why is so interesting.

And secondly, does Eru put the theme of the Music as a flawless thing?

Iluvatar called together all the Ainur and declared to them a mighty theme, unfolding to them things greater and more wonderful than he had yet revealed; and the glory of its beginning and the splendour of its end amazed the Ainur

The theme has might, wonder, glory and splendour. Is it flawless? We can only assume that if we want to read it that way. Now if we assume it is all good, then it's worth considering what Eru later says:

'Behold your Music! This is your minstrelsy; and each of you shall find contained herein, amid the design that I set before you, all those things which it may seem that he himself devised or added. And thou, Melkor, wilt discover all the secret thoughts of thy mind, and wilt perceive that they are but a part of the whole and tributary to its glory

This reveals that Melkor's discordancy is futile as it will not result in the things he assumes it will, only in things which in the end, will contribute to glory (for example snow and ice will result from his creation of cold). So what does Melkor assume his discordancy will result in? Now that brings me back to whether what Melkor does is 'evil'.

Melkor has all the powers of all his kindred, but instead of joining with them he seeks to follow his own path. This is interesting. He is the Mightiest and was made as the First of the Ainur, and it seems he decided he was going to challenge his Maker and have his own power. This is his 'sin', to attempt to seek his own way, not doing evil. There is nothing to say that Eru did not decide that 'evil' things like cold or despair or sadness were to be part of the theme; look at the words when he creates the vision of the Children:

The one was deep and wide and beautiful, but slow and blended with an immeasurable sorrow, from which its beauty chiefly came.

The Children are created with essential sorrow, which is also beautiful. So what we perceive as 'evil' can indeed be beautiful in Eru's eyes. All of Tolkien's stories are filled with strange combinations of sadness and joy, death and glory. It seems that Eru knew there needed to be Darkness in order for the Light to be all that more wonderful.

As to the why, I think it is Melkor's independence that rankles Eru. Melkor is filled with shame when he is 'found out' by Eru, presumably he has attempted something futile; his ongoing 'sin' then is to forget this lesson and continue, when he is in Ea, to pursue his goal of power and independence. If Eru wanted to create Ea with Darkness and Light, then it would have to be carefully balanced; I see that Melkor's discordancy puts that 'out of balance'.

It might in fact help to consider Tolkien's cosmology/theology not in terms of our Earthly Good/Evil axis but in terms of Light/Darkness, certainly that seems to be the way Eru intended them.

And just one more thing. Eru does trick Aule. He makes him think that he has smote down his Dwarves even before they have been given the Flame, but he hasn't:

Then Aule took up a great hammer to smite the Dwarves; and he wept. But Iluvatar had compassion upon Aule and his desire, because of his humility; and the Dwarves shrank from the hammer and were afraid, and they bowed down their heads and begged for mercy. And the voice of Iluvatar said to Aule: Thy offer I accepted even as it was made. Dost thou not see that these things have now a life of their own, and speak with their own voices? Else they would not have flinched from thy blow, nor from any command of thy will.' Then Aule cast down his hammer and was glad, and he gave thanks to Iluvatar, saying: 'May Eru bless my work and amend it!'