Okay, so now that we've established that the badger folk (or Melinae sapien, if you want to be politically correct) are trading their ore to the humans for cat food. Now we need to determine what kind of culture exchange they'll have.
To look at one particular issue, what kind of human music would badger folk prefer? Of course, individual badger folk will have different preferences, but in a similar way that Americans liked British Rock best back in the day, badger folk will like a specific type of human music best.
We can assume that badger folk have similar musical preferences to that of real badgers.
(Note: If you are questioning the hard-science tag, see Can hard-science apply to social sciences and other academic fields? and Is the use of the [Hard-Science] tag acceptable in questions with a non-hard premise?)
(Note: This isn't opinion based. I'm asking for hard-science answers based on zoomusicology (or other fields), not opinion based-answers.)