I was going to mention something along these lines but had decided to not... but since you bring this in.... It is of course interesting to delve into as much as you can. I have my own project going with explaining pitch changes due to string deflections at the bridge and and with the help of PhD Alexander Galembo arrived at a set of math formulas for calculating change in pitch for change in length. This employs Hookes law and is a different approach then using elongation formulas... which I have yet to see a sensible explanation for in this context. Regardless of approach... one is immediately confronted with a host of friction moments and it gets very iffy for more then very general querries right away. In the end... as related to the present issue... about all you can model with maths here is how much increase in tension a free standing string will experience for any given amount of movement for a pin of a given diameter. Once you start adding termination and other friction points as in a real piano you are not going to get much of anything meaningful with math models... only hints of what <<should be>> under uniform and ideal conditions... which of course never are in existence. In the end... a techs job is from a practical perspective a matter of feeling, touch, listening... and putting these together to arrive at a sensation of <<knowing>> what the string and pin are doing for whatever kind of stress you are exerting on them. That takes experience... lots of it. The rest is academic... interesting... perhaps useful.. perhaps as much a goose trail as anything else depending on the tech pursuing the trail. Cheers RicB Theory and Practice of Piano Tuning by Brian Capleton has a 40 page chapter on Setting the Pin. www.amarilli-books.co.uk Ed Sutton
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