Have any of you put a locking nut on your American strat, and did it affect sound at all? There is no way to stay in tune using tremolo so I just don't use it, which sucks.

If you have put a locking nut on, which kind have you used?

There are two different types of locking nut, the Floyd Rose nut, which uses 3 or 4 screwing bolts to lock the strings at the neck and the LSR, which employs low-friction roller bearing balls.

I opt for the LSR. which is an essential element (with the Schaller locking tuners) of the Deluxe Locking Tremolo Assembly, which has been taken out of production 3 years ago.

I've never put just a locking nut on a guitar - actually I've only owned one Floyd-equipped guitar in my life, and that was over 12 years ago - so I can't comment on that. It just seems odd to me that you would only put on a locking nut and not go all the way and install a Floyd bridge as well (or some other trem system) if you're going to do that kind of surgery to your Strat. Of course, if you're doing radical whammy work then it would be best to just bite the bullet and install the entire Floyd system - even with a locking nut you could have strings go out of tune due to slippage on the bridge. Plus, with only a locking nut you have no way to fine-tune the guitar without unlocking the strings (which was why they wound up adding fine tuners to the Floyd bridge back in 1983).

What about putting locking tuners on your Strat? That would be less invasive than the locking nut. I'm sure you're already doing this but putting some kind of lubricant on the nut should help a bit (like Big Bends Nut Sauce, or even the graphite from a pencil lead). You could also consider a Graphtech nut or an LSR roller nut (which is not a locking nut contrary to what chromeface posted) - either one would be less invasive than installing a locking nut.

You are right on the tuning if I just put the Floyd Rose locking nut on the strat. Maybe I should go all the way with the full-on Floyd Rose. That would be pretty sweet on the strat.

You can get a standard strat trem to stay in tune, all mine do, even with moderate to heavy trem use.
A LSR is not a locking nut.
Putting a locking nut on a strat requires some timber to be cut from the neck and will cause trussrod adjuster nut access problems.

All in all your far better off with just getting the guitar set up properly.

Saying that these people make a retrofit system that you may like.
http://www.super-vee.com/

Just dont care for the look of it myself.

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No no and no

My American Special has the LSR roller nut and locking tuners. Even after a good string stretching session it still won't stay in tune if I dive more than 1/2 step with the trem.