The problem is that there is almost never a single "current frequency" in a song. Unless it's a pure sine tone, there are multiple overtones; when you have multiple instruments that gets progressively more complicated.
Yes, fourier transform could tell you which frequencies are present. You'd have to look at the documentation for the FFT package you're using (the badlogic code) to get information about how to invoke it. Their sample programs, such as the FFTTest, are likely to be particularly informative.
Not a trivial project, but should be a fun one. Good luck!