Solution to Bach or Stravinsky?

Proof
From the payoff table:

There are two Nash equilibria:
 * $\left({\text{Bach}, \text{Bach} }\right)$
 * $\left({\text{Stravinsky}, \text{Stravinsky} }\right)$

Thus there are two steady states:
 * one in which both players always choose Bach
 * one in which both players always choose Stravinsky.

Either, but not both, experience their preferred music.