Interesting replies here! I like
Ibrin's distinction between innate talent and ability for
mighty and learned or developed force of Will for
Power. (We all know that Galadriel could be a bad girl at times.
) However, as
Ibrin suggests, perhaps the very fact that Tolkien apparently never capitalises
might or
mighty as he does with power/Power, demonstrates that the word for him does not have the significant reverberations in his thought that power/Power does. (Yikes! a word Tolkien might not have niggled over?)
Now, I have it on some authority, but cannot speak this of my own, having not read
The Lay of Leithian, and not owning the book to scurry away to verify the source, but, as I say, this authority of whom I speak says that therein Tolkien describes Daeron as 'the mightiest of the three [Elven musicians]' (the other two being Gelion and Maglor). Now, Daeron is associated with Luthian, so possibly his playing was what inspired her dancing. And we all know where her dancing led . . . .
Consequently here we might have an example of
might and its inflexions used without reference to physical prowess. *
EDIT: *unless we take this to refer to the prestidigital prowess of the piper.