Magic in Arda
Broadly speaking magic is a term that Men (and Hobbits) use to explain that which is beyond their understanding. They might call a Morgul dagger and the Mirror of Galadriel both magic because they cannot do it... or at least most of them cannot, but we'll get to that. First off the most impressive and wide ranging expressions of direct power upon the world is divine, or angelic depending on how you want to see the Ainur.
In the beginning before time there was Eru from his wandering thoughts were born the Ainur, some greater which were called in later years the Valar and some lesser which were called the Maiar and each had after the manner of the part of Eru's mind of which they were born power and understanding over certain concepts.
In his own time Eru reveals to them a great music which enraptures all of them and he asks them to sing it, but one of the Valar Melkor who was wisest to the mind of Eru, though he did not know all of it and mightiest, though not as mighty as his Maker decided to make his own song. Other spirits joined him for he was mighty and fair to their eyes and a great din of Discord rose against the Music which Eru had set out and the Music and the Discord rang one against the other a long time until at the last Eru made a third theme which the Ainu who sang it could not wholly understand. In the midst of that song the Singers as if in waking dream the history of Arda and though they did not see all of it clearly they did bear witness to the Children of Iluvatar (elven name for Eru) who were the Elves and Men. Many of the Ainur were were entranced by them for good or for ill, for they had been part of the Third Theme which only Iluvatar understood
But when the song was over the Ainu, the Timeless Ones discovered that their work had not simply drawn a waking dream over them but had made Ea The Universe That Is, under the dominion of time and in this universe is Arda, the physical world of Middle Earth, within it one can find aspects of the Music and the Discord still ringing out still.
That is why a lot of the deep magic in Lord of the Rings is presented as song, because it is a continuation and a refinement of the song of creation. Of all the beings on Arda of course the Ainu of which Sauron was one just as his master Melkor are the best at this expression of power, because they were a part however small of the original singing. Sauron was there when Aule sang that iron would be magnetic and Melkor sag that it would rust and wear away, perhaps he even added some small flourish to it. Now among the Children the best at magic are the elves who are most like the Ainu in their love of the world which they will never leave. Not to say that every elf can sing a bank of mist into being or even make fire in wet kindling, but it is a common power of elven song to make the listener have waking dreams, elven glamor if you will.
But of course that same power exists within the Discord, the power to overawe and terrify as Melkor did in his challenge, the power to deceive and to hide one's heart and this Men who do not have as much time to study and meditate upon the world as the elves have an easier time grasping. This is not D&D style sponsored magic, you do not have to pray to Melkor to use it, but you do have to think like him, you have to be willing to
break things on some level.
That does not mean all the works of Discord are blatantly destructive, it can be really subtle. For instance the Three Rings were made by the elves using lore than Sauron, as Annatar, taught them so Discord and what they broke was... the natural progression of ages and the passing of the elves, for a while at least. When Sam and Frodo get to Lothlothien and describe the place as from another age, they are exactly right, that age is the First Age when the elves were still at the height of her power because Galadriel bore the Ring of Adamant and
she said so. This was in effect a transgression against the will of Eru... for all the good it undoubtedly did.
So what does that mean for the practice of sorcery that is begotten in the primordial will of evil incarnate? Well that will be for you guys and Eriol to consider.