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More tension would be more inclined to overcome any friction in the system.
Shoot me if I'm wrong but that's my tuppenth worth.
It's true that kids' 3/4-size guitars don't stay in tune well usually, but that's at least as much to do with the awful soft nut material and crappy bridges they usually have.
"Take these three items, some WD-40, a vise grip, and a roll of duct tape. Any man worth his salt can fix almost any problem with this stuff alone." - Walt Kowalski
"Only two things are infinite - the universe, and human stupidity. And I'm not sure about the universe." - Albert Einstein
I stand by my statement but no probs if you disagree
If it was correct then a Jaguar wouldn't stay in tune as well as a Gibson, and I can guarantee that it does. I almost never had to tune mine.
So much about how scale length affects guitars is a myth and is actually caused by other factors.
"Take these three items, some WD-40, a vise grip, and a roll of duct tape. Any man worth his salt can fix almost any problem with this stuff alone." - Walt Kowalski
"Only two things are infinite - the universe, and human stupidity. And I'm not sure about the universe." - Albert Einstein
But in terms of open strings staying in tune there’s esentially no difference between Gibson and Fender scale lengths. PRS standard scale is much closer to a Gibson than a Fender but they typically hold tuning excellently. If scale was a factor Fenders would hold tuning better than PRS but there’s pretty much nothing between them as far as I’m concerned with hardtails.
I'm not saying it's the only factor here just that all these points will have an effect.
If you think it's the tension, try this simple experiment - take a Fender-scale guitar and tune it down to Eb, so it now has slightly lower string tension than a Gibson. Does it stay in tune? Yes. (Assuming it's set up well so it does in normal tuning.)
"Take these three items, some WD-40, a vise grip, and a roll of duct tape. Any man worth his salt can fix almost any problem with this stuff alone." - Walt Kowalski
"Only two things are infinite - the universe, and human stupidity. And I'm not sure about the universe." - Albert Einstein
This creates a greater downward and sideways force at the nut and therefore more friction, even with the lower string tension vs say a fender.
And more friction on the nut can't be good for tuning stability as it could lead to uneven tension on either side of the nut.
Unless of course you have essentially infinite friction as is the case with a locking nut/trem.