Fade in on bin size would be a periodic function of the bin size and wouldn't have such regular harmonic decay.

In the osciolograph you can see that that low fundamental has a 2nd order periodic harmonic decay on a log scale display, a fixed periodic window size overlap wouldn't decay in a log fashion. The artifacts introduced from window overlap would compress as they move up the scale and the period's f function gets represented closer and closer on the graph. You can see this as the little spikes that get closer and closer as s/t is represented by less and less space.

You can see a sub-fundamental peak from the resonator and IMD, sympathetic vibrations from resonance and then there is an other harmonic series from the piano's other elements (body resonance and sympathetic vibrations form other strings) this is what defines the instrument's timber palette. If we had an osciolograph of a higher key say an A6 two octaves higher you would get less resonance and less pronounced sub fundamental peaks, this is why a piano's higher keys sound more tinny and less reverberant and full as the energy put into resonator and body of the instrument is not going to cause as much sympathetic vibrations or body resonance at higher frequencies.

In a more complex sound than a single tone one can expect the window function's overlap to add more noise to the signal but not so much as to generate a periodic decay outside the set of the bin size. Anyway we are way out of bounds for what was initially a pretty simple question.

Overthinking things for no reason.

 

Thank you everyone for such an informative and in depth conversation. I am overwhelmed by the number of replies, and just how deep it all goes. A special thank you to Qrchack for a detailed response that really speaks to what I am trying to wrap my head around. I should have mentioned in my original post, but I was also seeing anomalies when using a pure sine tone, and Qrchack has helped explain why I am seeing this inaccurate readout. The piano example has too many confounds. Once again thank you to all of you, I have learned a lot!