I think this is a nice writeup, but I would argue with the claim [The error is] "Pretty much exactly the resolution of the FFT we used. It's very hard to do bet

I think this is a nice writeup, but I would argue with the claim [The error is] "Pretty much exactly the resolution of the FFT we used. It's very hard to do better given the inputs." The 19hz error being explained by the FFT resolution only makes sense for a classification-based loss/error that used the (FFT_bins / 2) as classes. Since the proposed network is using regression, even though you have a frequency resolution of 19hz, you should be able to estimate pitch with finer resolution if you are using any popular non-rectangular window because it can be fit to match the shape of the main lobe. You would only expect such a large error at the very low frequencies, where there wasn't much to interpolate on because the next harmonic would overlap. For an example see figure 4 in PARSHL, (One of the original sinusoidal analysis frameworks where the frequency of each harmonic is estimated by fitting to a parabola) https://ccrma.stanford.edu/~jos/parshl/parshl.pdf https://ccrma.stanford.edu/~jos/parshl/parshl.pdf A neural network should be able to do much better than parabolic fitting.