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Locking Tuners
What's the best way to improve the tuning stability of my 1995 Epiphone Sheraton?

I am going to replace the tuning machines with grover locking ones. The original tuners are probably pretty worn. I keep reading about the nut playing a role in how well the guitar holds its pitch. Is that true? Is there any other thing I should consider? Thank you!!!

I went to check out some specs and pix of your guitar before answering, I'm nothing if not thorough lol. NIce git, I had a similar type hollow-body years ago so I'm aware of the problems you might be having.
Your first instinct was probably the right one. The guitar is only 13 years old and unless you've been dragging heavy gauge strings through the string slots in the nut, it shouldn't be the root of the problem. Do check that the strings aren't sitting in grooves much wider than they are. Each slot should be just wider than the string it's cut for. I wish I knew what kind of tuning problems you're having, it makes diagnosis easier. Can you get the git tuned but it won't stay in? That's usually the machine heads and new Grovers should fix it. If the problem is that you can't get the git in tune with itself, harmonics all weird etc, it could be the floating bridge having wandered from it's correct spot. The stop-bar piece (the big bit of the bridge pairing) is fixed to secure the strings to. Next, they pass over the adjustable saddles in the floating bridge. The position of the bridge itself AND each of the saddles has to be right or the intonation of the guitar will be off, I don't know how much you know so scuse me if I'm overexplaining. I'd rather answer fully than leave something out.
If you're getting the new machine heads fitted at a store, ask them to set up the intonation while they're at it. Can be a fiddly task, but at least you don'y own a Floyd Rose trem, they're a nightmare. You ask if there's any other stuff you should consider and yes there is. Is your guitar kept in its case when not used? In a pretty constant temp and humidity? Wood shrinks and swells according to heat and humidity and strings can slacken unevenly as temp changes. Are your strings very old or very new. If old, change 'em. If new, make surn they're properly stretched and run in. Sight down the neck and check if it's warped or out of true. If so, you'll need the truss rod adjusting at a store. I think that's pretty much it as regards guitar hardware , so if you do all that and still have probs, its yer ears!

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