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.