The Scottish Play

I haven't read a lot of Shakespeare, but I have read some of his more famous comedies and tragedies. In the majority of the cases, the case for which category his work lies in is pretty simple. Light hearted banter, misunderstandings which are cleared up at the end and a couple of marriages - comedy. Everyone you liked in the play dies - tragedy. Macbeth, however, is rather difficult to categorise. It's been considered a tragedy, but given that the story ends with the deaths of a traitorous murderer and his equally evil wife and the restoration of some sort of order to a kingdom that's been freed from their grasp, I would say that the story has a pretty happy ending. Sure, the play is dark enough and bloody enough, but strictly speaking, given that it ends on an upbeat note (more or less), it should be classified as, well, not perhaps a comedy, but certainly something other than a tragedy.