I always associate hymns in a minor key with the medieval sound. Maybe it's because so many of the chants and so forth were in a minor key.
Once in a while, I'll hear something that makes me wonder about whether it's very deeply rooted in the medieval period. The violin theme from Ken Burns' "The Civil War" is an example. It's called "Ashokan Farewell," and it evokes such sadness and melancholy. It's a modern piece, but is so beautiful and mournful, I wonder if the composer used a medieval form for it. It always gives me goosebumps and brings a tear to my eye.