Recently, I was having a perplexing problem of a double locking guitar going out of tune on certain strings after a bend.
If I bent, it would be flat on the return. If I tuned it back up, as soon as I hit the tremolo, it would go sharp. This tremolo was locked to “dive only” so it really had me scratching my head! Then I had a look at the lock nut. If you have a Floyd or a Kahler or some other lock nut and are having weird tuning issues, have a look here:
This is a seven string, so the strings are, from left to right: Low A, low E, high A, D, G, B, high E. Have a look at the low E and D strings compared to the high A or G. The string is not centered in the lock nut, which can change the strings length on bends or dives. You would think that the act of clamping would force the strings into the center, but the size difference between the strings can create a lever effect, so check them carefully next time you lock them!