An average set of strings put about 150 pounds of force on a guitar but you expect me to believe that gravity will pull your headstock down 1/16"??
Nope I don't believe it
the laws of physics will not support that conclusion
What does your headstock weigh? less than a pound ... how does that counteract 150 pounds of force, plus the stiffness of the wood, plus the stiffness of the truss rods ...
It doesn't
So if I'm playing guitar in my bedroom & check the tuning sitting upright & then decide to lay on my back & check the intonation again & find the strings have uniformly gone a few cents sharp, then what is occuring?
