What happens is this:
As you tighten the string, being wound with a coiled metal of some kind, it "grabs and holds on" to the nut. So as you try to tune the string up (tighten the string) it only tightens from the machine head to where the winding is holding on to the nut.
This means that you won't hear the pitch change as you tighten the string because the vibrating area of the string (when it is played) hasn't changed. Even though you are turning the tuning key the string is only tightening in that small area between the tuning (machine head) peg and where the string is hanging up.
You need to lubricate the slot in the nut where the string passes through so the string won't hang up. The issue here is that you don't want to use an oil lubricant for obvious reasons.
- Get an old fashion no.2 pencil and sharpen it. Pencil lead is graphite, for the most part, which is a DRY lubricant.
- Loosen the string and lift it out of the slot in the nut.
- Mark in the slot with the pencil so that you create a powder out of the pencil lead leaving it in the slot (you may have to sharpen the pencil several times if you have more than one string hanging up.)
- Slip the string back into the slot and tune it back up.
That should do it! If you have any trouble with it slipping again just add more lead to the slot. Remember to use a soft lead pencil like a number 2.