In Greek mythology, Apollo and Dionysus are both sons of Zeus. Apollo is the god of reason and the rational, while Dionysus is the god of the irrational and chaos. The Greeks did not consider the two gods to be opposites or rivals, although often the two deities were interlacing by nature.
The Apollonian is based on reason and logical thinking. By contrast, the Dionysian is based on chaos and appeals to the emotions and instincts. The content of all great tragedy is based on the tension created by the interplay between these two.