If your banjo develops a string rattle what's the first thing you try? I've already checked all the hardware and nothing is loose, and the strings are not so low they are hitting the fretboard or anything else. I'm thinking the string rattle is a sign that the head has become a bit loose. Am I on the right track?
Regarding head tension. If the head is losing tension, it will cause the action to get lower and you run the chance of having the strings buzzing against the frets when you play. So that could be a possibility.
I would check head tension first, as the buzz may go away by itself when you increase the head tension the action will rise a tiny bit.
If that doesn't alleviate the buzz, I would put a capo on the 1st fret and play the instrument a little bit louder/more aggressively than usual and proceed to the 2nd fret, 3rd fret and so on until the rattle went away.
If it's coming from string buzz you'll then be able to locate at which fret it's buzzing, then make a truss rod adjustment accordingly.
Also, what type tailpiece do you have? Sometimes on Presto style tailpieces, the folding 'door' is the culprit.
Most likely not enough relief in the neck if you find the head tension is good and the action is dialed in. However, I did have a loose 5th string tuner button one time that was causing a buzz...
Check the 4th string winding. Sometimes it breaks and will cause a distinct buzz.
Is it one string or all strings? Does it rattle when the string(s) is open, when it's fretted, or both? Has the action changed since the last time you played? Has the weather changed lately? Have you recently changed strings or changed anything else?
There are many things that can cause rattles, so you need to answer these questions before blindly proceeding to adjust this, that, and the other thing.
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