I don't think the English language has a single word for it because it encompasses bits of different emotions. The closest single one I could think of might be "bittersweet".
Sort of a vibrant or vivid melancholy, maybe? Some songs by certain groups do that to me also - that song, "remind me" by royksopp always brings on those feelings. I think that listening to music makes you feel like everything in your body is opening up a little, loosening and relaxing and decompressing.
I'm not sure if there's a name for the feeling, but often, the reason we feel that way about certain pieces of music is because they feature minor keys instead of major keys.
Major keys = happy
Minor keys = sad
That said, I don't think either of your examples are in minor keys.