The paper is a little bit hand-wavy about the mathematics of how CDs are sampled, how the Fourier transform works, and how frequencies are converted to semitones. But it does have references which mostly alleviates my desire for rigor :)

Once the author has a list of pitches though, the process of assigning pitches to instruments is very well laid-out. The key to locating the piano was that piano strings are hit in triplets, and each string in a triplet is tuned ever so slightly differently.

Signal processing was one of my favorite courses in college.