what is minimum gpa required if I intend to apply for the department of music at Yale or Princeton?

It's not always so clean cut. Colleges, not just Yale and Princeton, look at a variety of aspects when determining their freshman class. I'm assuming that because you're into music, you'll have to curate some sort of portfolio, so I'm sure that'll have great weight in their decision. Nevertheless, they're still ivy league schools, so you should aim for at least a 4.3 GPA weighted, or close to a 4.0 unweighted.

Admission is competitive, so it's not possible to say. They look at your unweighted GPA, SAT/ACT scores, and prior successes in music.

If you aren't able to research this by yourself, you probably aren't up to their standards.