"I'm stupid because I'm dead, I'm dead because I'm stupid
As is well known, Plato in Book III of his "Republic" recounts a conversation that occurred between Socrates and Adeimantus, in which the flute and the pipe was deemed by Socrates to be of inferior musical stature to stringed instruments (the lyre and the harp).
Socrates: But what do you say to flute-makers and flute-players? Would you admit them into our State when you reflect that in this composite use of harmony the flute is worse than all the stringed instruments put together; even the panharmonic music is only an imitation of the flute?
Adeimantus: Clearly not.
Socrates: There remain then only the lyre and the harp for use in the city, and the shepherds may have a pipe in the country.
Adeimantus: That is surely the conclusion to be drawn from the argument.
Socrates: The preferring of Apollo and his instruments to Marsyas and his instruments is not at all strange, I said.
For Nietzsche of The Birth of Tragedy the flute is unmistakably the most favorable instrument for its reference to Dionysiac rituals and ecstasy.
So, there is certainly a hyperbolic rejection of Schopenhauer's philosophy by Nietzsche on the grounds of the former philosopher's love of flute playing. However, hyperbol, especially in Nietzsche's case, just as in Kafka's is a style of writing which forces thought to "the limits of stupidity" as Deleuze explains in Difference and Repetition.
Moreover, after his collapse in Turin, Nietzsche is known to have mumbled now and then: "I'm stupid because I'm dead, I'm dead because I'm stupid.