strings of one note vertical and.and weird overtones

....and? Pianos would sound like crap if all strings of a note would be set to exactly the same pitch.

Evil, yes, unison is extremely important in pianoforte. The tool can be flat, electric, glass, melodic, juicy .. and all the difference thanks to the tuning of unison. And also enjoyable for the game or not. I hope in the future to look into these moments more ..

jcfelice88keys,of course I know the notion of non-harmony. If the strings diverge in a disharmony the situation would be such-one overtone for example would stand still, some would lower, and some would overstate. But then there was a situation where the overtone was moving away in different directions.

Yes, in principle, it is. Too clean unison sounds dry, glassy, boring.
But the example from the first post is not about that. Also, this is not about the disharmony of the string. If the tuner assumes some frequencies with some string harmony, but he hears a string with other properties, then it will look like strobe rings rotating at different speeds. With different brevity, but in one direction. For example, the first ring - stands still, and the next - rotating at an ever-increasing speed. The example from the first post is a little about another. The tuner is tuned in harmony parameters to the string that he hears. But it is clear that some frequencies are biased. And this is a manifestation of the interaction of the string with the deck. In Pianoteq there are instruments in which a sound such as if its strings are pulled over a perfectly rigid frame. Such a tool, for example, YC5. And due to the fact that one end of the string dangles and sways in all three planes, this shift of some frequencies occurs. I used to want to find clear research about this. And recently an article came out:

https://asa.scitation.org/doi/abs/10.1121/1.5132940

But, unfortunately, so far I can’t read it (

Apparently there everything is described quantitatively..

First a short comment: the coupling of the three strings of each choir via the soundboard has indeed the consequence that "pure" unisons almost never exist: even if the three strings have exactly the same tension and same other physical parameters (length, diameter, etc.), the resulting frequencies of the three fundamental modes (or any given overtone modes) are usually slightly different. It does not imply a beat because those modes have usually very different decays, and hence, being most of the time at a different loudness, the beating is not perceptible, apart a possible strong attenuation during the transition from fast to slow decay.

This coupling is already modelled in Pianoteq, and it depends essentially on the soundboard impedance: the higher the soundboard impedance, the smaller the coupling (and infinite impedance means perfect rigid soundboard and no coupling), and vice versa. So the new control slider you are seeking is already there in the design panel of Pianoteq (Standard and Pro)

From my experiments, I think I have found that to a greater extent (than with any other parameter) I am able to match up slight velocity inconsistencies  between notes using impedance parameter note for note adjustments. Am I right in thinking so?