In 1994, a young girl in Iceland witnessed Nirvana on MTV Unplugged. She was a student of classical violin at the time, but she was hooked, and when Unplugged came out on disc, she taught herself all the songs on guitar without the help of any lessons or formal training.

"I'm mixed between an educated musician and a self-taught one," Ólöf Arnalds says over the phone from Reykjavík. "I think my music is more American influenced—I really like listening to old American folk recordings, and I went through a period of really listening a lot to that kind of stuff. The Icelandic folk tradition is only oral and it's really weak, and because of the isolation and the poverty, there weren't any instruments. Also, the Lutheran Church banned workday singing and that kind of erased the Icelandic folk tradition. So we don't really have any, except the rímur, which is an oral form that's rhymed, midway between singing and reciting."

The delicate acoustic songs on Arnalds' debut album, Við Og Við, were each written for a family member or loved one. Her classically trained, clarion voice moves through gently thicketed pluckings of guitar and charango, sounding at turns lachrymose and hopeful. While it doesn't closely resemble American folk of any shade—not even the warped harpings of Joanna Newsom—it also sounds unlike anything else coming from Iceland, be it Björk, Sigur Rós, or even Múm, the electro-classical-folk band of which Arnalds is also a member.

Arnalds' second album, Ókídókí, is due out next, and it won't be as sparse as her debut—she says it will even include a pop song. "I've had [that song] in my system for seven years, so I sort of just had to record it and turn it into something. I feel really shy toward that song, and for a long time I thought about skipping it and not having it on the record, because it's a little bit like when you were a kid and you wore sunglasses and everybody said, 'Look at you! You're so cool, you have sunglasses!'" she laughs. "Of course, having sunglasses in Iceland is mostly only for the cold, because we don't really get the sun here."