Of course, many bands have been inspired by
Tolkien over the decades; music with ME references seemed to come almost weekly, back in the late 60's and early 70's. I think I've seen lists, though a lot gets left out.
Plus, there have been a number of classical composers who tried to evoke ME in their works, and there are the film soundtracks.
Different sorts of music will bring ME to mind to different people, for many reasons. But I was thinking specifically of music that might actually have been
heard in ME; that Eivor piece happened to strike me as something at least close to possible -- as does the Slider song Desert Loon posted -- thanks for that! Also maybe Loreena Mckennitt (of whom I've been a fan for years, BTW).
Within those parameters, electric and electronic music would be out -- though, as I say, perfectly admissible in other contexts; After all, Games Workshop fans appear to think the universal music 40,000 years from now will be today's heavy metal!
With the exception of some of the anachronistic aspects of
the Shire, the situation of ME seems mostly modeled on 5th/6th century Europe -- in fact, the
Battle of the Pelennor Fields was based on a description of the Battle of the Catalaunian
Fields in 451. We don't really have music from that period, not to mention the
languages Tolkien spent much of his professional life trying to reconstruct.
Attempts at that kind of reconstruction for music are going on now; here's a sample:
Judgement on its success, or otherwise, will be subjective, to say the least, but they are trying to incorporate scanty evidence of Old or Proto-Germanic elements.
I daresay Tolkien, had he seen or heard anything like this, would have hated it, and (especially with all the "pagan" symbolism and gutteral sounds) would have immediately assigned it to
Dunland, or some such place. Which, come to think of it, might be quite appropriate.
I have to say it's the only band I've heard of to have its own shieldwall!