While one can certainly identify elements of tragedy in literatures around the world, tragedy in its purest form has only arisen at certain times and places:
What we seem to see here is a major cultural shift, followed by a peacetime during which certain artists have the time and luxury to consider the changes that took place. Most cultural changes are gradual, or the jump is not that dramatic. But sometimes you get cultural changes such as we saw with the Renaissance.
Above is a cusp catastrophe model of cultural change. It is rare for a culture to move along the front edge of the topological map. More commonly, cultures evolve along the back side of the map. We can see what will happen if one moves from one stable section to another along the front of the map -- sudden, surprising changes. One can imagine that during such changes, people will have a desire to figure out what, exactly, just happened. And that's where tragic art comes in. The bigger the jump, the purer the tragedy that will be written.
Coincidentally, during long periods of stability, we tend to see epics written, providing confirmation for that culture.
Tragedy affirms the new cultural forms, while trying to make sense of them.
Comedy arises out of conservative impulses, to ridicule the excesses of the new.
Drama tends to combine the genres. Novels, especially. These can in some ways be seen as storytelling for storytelling's sake.