"Gibson" 60s-ish parts banjo,
RB-100 + tone ring. Loud, clear sounding, but first string wayyyy sharp when fretted 10th fret and higher. It seemingly has gotten worse, as it didn't have problem at first. I've tried shifting the bridge back, then forward, even slanting it this way or that, to shorten some strings and lengthen others. All to no avail. Hoping there's not something more serious wrong with the banjo like warped neck, etc.
Thanks for any help y'all may send my way!
This has happened to me a couple of times, and it was always solved by putting on fresh strings.
How's your action? Make sure the neck to rim connection isn't loose.
Make sure the bridge is located about double the distance from the nut to the twelfth fret.
DD
The only solution for this is moving the bridge back toward the tailpiece. Don't give up, keep moving it.
Just to understand:
-- The first string goes sharp when you fret 10th fret or higher
-- This didn't happen at first, and it is getting worse.
-- Moving the bridge doesn't help.
Questions:
-- When you move the bridge, do the other strings go out of tune?
-- Can you position the bridge such that the other 4 strings are in tune?
-- How sharp is "sharp"? How sharp is the 1st string sharp at the 12 fret when the bridge is set so that the other 4 strings are in tune?
-- Are you positive that it is getting worse -- that is, that the first string is getting sharper and sharper over time when fretted above the 10th fret?
Advice:
-- Change the first string.
-- Answer these questions. More information is needed.
Thanks to all repliers; I'm a faculty member in a busy closing 2 weeks of college, so I may or may not reply soon. I AM really attempting to get in some playing time every single day, something I've never done since when I started banjo 40 yrs ago...so thank you!
What would make a bad string go sharp? I've had bad strings that went flat a few times over the years but not one that went sharper and sharper... how does this work? Thanks.
I don't know either. Changing the string eliminates the string and any discussion of it as a source of the problem. Anything that can narrow down the BHO discussion to the evidence at hand has a positive effect on getting to a solution. 
I fully agree with Alex that the simple expedient of replacing the string will effectively eliminate one possible source of the problem.
And yes, a bad string can have sections that are sharp. A spot of corrosion or a deformity such as a tiny and nearly invisible kink causes a little added stiffness, but might be compensated for overall, When fretted,however, that stiffness can cause that smaller section to vibrate differently than the full length of wire. (That's a bit of a simplification, as there are also overtones involved, which even in the best of new string circumstances, are never absolutely perfect.)
Tuning is always a bit of a compromise with physics, and a bad string can exacerbate any discrepancies.
Edited by - G Edward Porgie on 12/02/2020 06:29:29
If the string in question used to intonate OK but now doesn't, and all the other strings are OK, then it's 99% certainly some defect in the string.
This is common in nylon strings - one part of the string decides to lose its elasticity and stretch, and so the string ceases to have a uniform diameter - result, it plays out of tune in some places on the fretboard.
AsG Edward Porgie wrote, steel strings can develop flat spots where they are fretted a lot, or corrosion spots, or kinks - I'd suspect all these could lead to the problem.
Don't mess with the bridge, change the string first! If you still have the problem, then it was caused by something else. If it was the string, you then have to reverse everything else you tried to get the banjo back in proper order.
If all the strings go out of tune at once, then it's definitely something else. But just on one string ...?
