From the OED:
Quote:
a. Gr. katastrophe overturning, sudden turn, conclusion, f. kata-strephein to overturn, etc., f. kata down + strephein to turn.
1. ‘The change or revolution which produces the conclusion or final event of a dramatic piece’ (J.); the dénouement.
|
So neither the etymology nor the first definition requires the sudden turn to be for the worse (what Tolkien called "dyscatastrophe").