Apollo and Dionysos are often pictured as antagonists, and it's not hard to see why: Apollo represents law and order, shape and form, while Dionysos represents chaos, and liquidic shapelessness. And yet, there are no surviving myths which put the two into direct combat. In fact, myth records the opposite picture: the Tomb of Dionysos is located in Delphi, the Hellenic center of Apollo worship. One element of this relationship could be that the two are both necessary for the creation of art, with which both were associated- Apollo was the patron of all the arts, and Greek tragedy started as Dionysian ritual. Their relationship, in this regard at least, could be interpreted thus. Dionysos, with his connection to primal chaos and transcendence, helps the artist to gather the creative materials that are the very basis of all art; this done (symbolized as a 'death' of Dionysos), Apollo then helps to give this incoherent mass the aforementioned shape and form, making it comprehensible to both the artist and their audience. Without Dionysos, Apollo has nothing to work with, and without Apollo, Dionysos can only gibber meaninglessly. In short, there's always a way to synthesize two forces, even (or especially) contradictory ones.
