Magic vs. Power

[Salocin]

I believe the word you are looking for is not power but virtue. Elves are given more "virtue" than men and Valar and Maia are given even more. This comes from the idea that middle earth "magic" is a granting of a measure of power/virtue from Eru to others.

I think that it was the natural fibre of her own being that allowed her to manipulate the water in such a way that it connected with things that appeared to be unrelated to the Hobbits, but in fact were all things to which the reality of Galadriel extended.

I would disagree. She was able to make the water reveal images, but she was not able to control what images they showed. She got this power from her ring which was the ring of water. The ring served as sort of an amplifier for her inate virtue as well being able to channel it in certain ways. Obviously a hobbit would not be able to use the ring in such a way. This would be explained as there "base" virtue being significantly lower so even with the multiplier of the ring they would not have much power. I doubt even an ordinary elf would be able to use the ring in the ways Galadrial could. I think you got it right when you said

If you use this ideaology, and my "blanket" illustration on the Great Rings themselves, it clearly explains why they give power according to their owner. Frodo was a mortal, a small mortal even, and had very little power over his surroundings, as his part in the music was probably very different that that of someone like Gandalf. This made his being, even with the ring, still pretty weak.

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