-1 is an exponent, and a hyperbola has an area of rapid decay followed by slower decay. That has nothing to do with the question, which is whether the decay also varies according to n, the partial. That is the question that physics has to answer. It probably does, but then, it is probably negligible compared to the hyperbolic decay.

I believe that research has shown that the decay of a piano tone has two distinct regions that don't follow a smooth curve such as one exponential or a hyperbola. I also believe that there is no doubt that the higher partials decay more quickly. To put it another way, the relative amplitudes of the various partials change substantially as the note decays.

I hope to be able to check some recordings in about two days. That will be on Friday. Unfortunately, I will only be looking at recordings of one or two notes from one or two pianos, so I don't think any large questions will be answered.

About the hammer, however: remember that I'm curious about the relation between force and the relative lower partial amplitude. If the hammer is nonlinear, that will only mean that the amount of force delivered to the wire is nonlinear. So, while the overall amplitudes of the lower partials may make sudden leaps, isn't it possible, and predicted by Fourier, that the relative amplitude of the lower partials will remain constant? (Although, yes the upper partials will also enter the picture and affect the tone.)

But, yes, the recently posted pictures of soft and hard strikes appear to contradict that expectation. I hope to see if there is a predictable pattern. Do the same lower partials always tend to get louder as force increases? Is there a predictable relation between their amplitude and the amplitude of the fundamental? In predictable increments or within predictable ranges of increments? If so, of course, the question of the causes arises. Sympathetic resonance of other strings picked up by the mic (which would make sense for the 5th partial, at least)? Unisons (but shouldn't they couple, as much as they ever do, as force increases)? Difference or sum tones created by the interaction between the lower partials and the upper partials as they increase in amplitude with force? Or is it the wire itself? Assuming that there is a steady pattern of some kind, and we can't say that yet...

You cannot say much about something which is non-linear (whatever that may mean in the case of a hammer). There are more curves than lines.

Tried mind-reading to find out what publication it might be, found nothing there. In any case, it has nothing to do with the original question.