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Mar 12 at 23:00 comment added Edward @ojs The part you're missing is that pitch increases with the square root of tension. So, increasing a 20lb string to 21lb will have a larger effect on pitch than increasing a 30lb string to 31lb.
Mar 12 at 17:05 comment added ojs It works the other way round. The required stretch depends on the geometry but thicker string needs more force to stretch, increasing the tension and pitch more.
Mar 12 at 16:53 history answered Tom Williams CC BY-SA 4.0