Alan, I cherry-picked Tartini as an example because it is a non-linearity in the human ear. In this regard, while technically subjective, they do exist physically. Maybe not for a tree sloth, but they do exist for humans. In measurement we tend to be very good at isolating individual slices (Chladni, (x, y=0, z=0), etc.), or solving for global systems assuming they are linearized. I see the same issues and measurement arguments in audio engineering. General relativity is probably the best large scale physical example of a system that is easy to solve when linearized but impossible otherwise. In my day job part of what I do is solve PDEs and SDEs via Monte Carlo simulation on very large GPU-grids. 95% of the time I can explain most of what I am seeing and thinking with all the linear first order terms that I calculate. This isn’t disimilar to the calculations that are done in violin, guitar, audio. Where things get interesting are in the higher-order and cross terms. The non-linearities. On most days my d^nY/dX^n terms aren’t very interesting, but on the most interesting days they are. I am not saying anything that hasn’t been said, but I have millions of dollars to spend on my systems and 30 PhD level researchers to code up and tweak my math so I know “why”. Since these resources will never be applied to a guitar, and barring some really clever shortcut, I can only assume that if we think these things are there, and we have our cognitive biases roughly accounted for, then they are probably present. So I agree that it would be possible to measure in some top-down fashion. But, to your point, I like to know why, and this bottom-up analysis probably never happen, so the answer, at least to me, will never be satisfying.