[Gwathagor]

I think we've got two kinds of "otherwordly" here, the first being simply part of Elvish nature and the second having its ultimate source in Aman. Elves like Thranduil, Legolas, and Thingol display the first kind, elves like Galadriel, Glorfindel, and Elrond display the second kind.

For the first kind, "hypernatural" or "extranatural" might be better terms than "otherworldly." It is, in its essence, earthy. Celtic-ish music would suit this well.

The second kind, is literally otherwordly, and appears in Elves who have had contact with the Valar/Maiar or who wield artifacts imbued with their power. This group would doubtless produce the sorts of ethereal music you describe, Bethberry.