Amusia is like colour blindness for music. Affected people can’t grasp the subtleties and structure of music despite having having intact hearing. The problems seems to be with the relevant auditory brain systems.
BBC Radio 4 science programme Frontiers recently had an edition on this curious condition that explores the neuroscience of why this occurs and talks to people with the music perception difficulties.
They also link to a musical listening test so you can test your own abilities.
Link to Frontiers page on amusia.
realaudio of programme.
Link to good BBC article on amusia.
Mind Hacks 
Is colour blindness a good analogy here? I thought that many people with colour blindness do not have intact vision, in the sense that they often are missing (or have unusual varients of) types of cones in their eye. I wonder if a better analogy might be face blindness, where the physical aspects of vision can be intact, but certain types of information don’t seem to be completly processed?