Music is planned but meanwhile all we have are vanilla music. Nothing like playing as an orcish warlord laying waste to the Shire while listening to Mice on Venus. Warms the heart.
But don't be sad, my fellow Middle-Earthing, because you came to the right place! I'll not only tell you how to play your own music, I'll also tell you where to find fantasy-style music that fits Minecraft art style.
Creating a Resource pack
I suggest that you create a Resource pack instead of replacing music files in the game's location. This way you can remove and insert your musics back at any time in a glimpse, instead of messing with the local files.
Gealx3 from Planet Minecraft made a simple and easy tutorial for this: http://www.planetminecraft.com/blog/how-to-change-the-background-music-in-minecraft-1710/ (the tutorial says 1.8+, but it works for 1.7.10 too. I tested it).
Where to get the music
By now you probably have your resource pack ready to go, but no music. You're probably thinking "I'm going to download LOTR music from dubious websites, and for free!" No, no, no, I don't think that is a wise thing, simply because LOTR music doesn't really fits Minecraft. I don't know, it feels off. Every piece of music composed for the movies were made specifically for a scene, while Minecraft offers endless opportunities. Imagine mining iron ore while listening to The Battle of Pelennor Fields, it just doesn't work as it should.
But there is a free game called Battle for Wesnoth where you can find music that fits Minecraft. You can download it here: https://www.wesnoth.org/ (yes, it is free, and also a very good game. I recommend playing it with your friends, but if you guys are playing a free-for-all, please, it is not cool when everyone allies themselves against one lone person, really, it is not cool *wipes tears*).
You can check Wesnoth's music here: https://www.youtube.com/watch?v=U5gIr9B5-kU Play some songs to see if you like them.
Where to find the music in Wesnoth's folder
I suppose you already download and installed the game, great. Now locate where you installed the game and look for this folder:
Battle for Wesnoth x.xx.x\data\core\music
Here you can find all the musics already converted to .ogg, the same format used by Minecraft. Now all you have to do is select the musics you want and paste them in your Resource Pack (check the tutorial again, it says how to install the musics in the pack. Another thing, don't go around posting your own music resource packs around the web, contact the developers of the music first to get permission.
How to use the Resource pack
Open Minecraft > Options > Resource Packs and choose the one you just created. You can also use texture packs alongside your music pack without problems.