Extracting precise frequencies from FFT Bins using phase change between frames

Question

I have been looking through this fantastic article: http://blogs.zynaptiq.com/bernsee/pitch-shifting-using-the-ft/

While being fantastic, it is extremely hard and he

Answer 1

Signal frequencies that fall exactly on a bin frequency advance bin phase by integer multiples of 2π. Since the bin phases that correspond to the bin frequencies are multiples of 2π due to the periodic nature of the FFT there is no phase change in this case. The article you mention also explains this.