The number of interviews needed to attend and number of programs needed to rank are so variable depending on your stats and fit with programs. I know people with great stats at top tier schools have been told by their school mentor/dean/advisor that they only need to rank 4-5 schools, whereas some people I've met at other less known institutions have been encouraged to rank everything (keep in mind it costs more to rank more), do as many audition rotations, and apply everywhere. I just wanted to throw this out there to add some more perspective and say that the "magic number" will be different for everyone here.
I think realistically, if you're concerned about the number of interviews or programs needed to rank, I would talk to an advisor or possibly a PD at your school institution (if they are approachable and available) and just straight up ask them based on your application. There's just too much variation here to really know what's best for you. For example, I know a couple of people that applied to only <10 programs and are ranking 4-6 and some that applied all over the nation and are ranking everything they get. If I said that I'm only planning to interview/rank X number of programs, I would hate for someone to read this and to think that X is the number they should aim for. It might be harmful to them in the long run.