Edvard Grieg - Notturno Op 54, No 4, for Piano (1891).

I first heard this piece at an exhibit of Norwegian art at the Elvehjem (now the Chazen) Museum of Art in Madison, Wisconsin, around 1980.  It pretty much overshadowed the most beautiful paintings in the exhibit and stopped me in my tracks while I took in its chilling and deep mournfulness. 

Thirty years later, it retains its spell over me.  It's performed here by Mark Gasser: