You might wonder how it can be called a tragedy. The Greeks meant something a bit different than we mean by tragedy.
Here's Aristotle's definition with bolding from me:
Tragedy, then, is an imitation of an action that is serious, complete, and of a certain magnitude; in language embellished with each kind of artistic ornament, the several kinds being found in separate parts of the play; in the form of action, not of narrative; through pity and fear effecting the proper purgation of these emotions.So... serious, evoking pity and fear... but possibly having a happy ending.
To us it's not "tragedy" at all,
if it lacks a final fall.