Microtonal Refretting

> Even on quite nice, carefully set up guitars that I might play, I
occasionally
> fine one, or several frets that aren't positioned quite right and the
intonation
> just makes me cringe. Cheap guitars are even worse. So if people who do
> this professionally can't get it right, what are the chances that I'm going to
get
> anywhere close?

It might amaze you (or perhaps it might not!) how little guitar manufacturers
know about tuning. Epiphone guitars, at least while I was in college, I found
to be dreadfully out-of-tune with themselves, for example. Luthiers'
Merchantile sells fretting charts so that makers don't have to do any
calculations. Some of them don't know what the calculations are. A few even
still stick with "the rule of the 18th," which basically estimates the twelfth
root of 2 to be 18/17. That's a pretty good estimate for a half step alone, but
the error really adds up quickly when you apply it repeatedly.

The most common mistake though is not applying a bridge correction - pushing the
bridge slightly away from the nut to compensate for the fact that the bridge is
higher than the nut. That causes higher frets to have higher tension than the
lower frets, and pushing the bridge back makes compensates for that by giving
those higher frets a greater percentage lengthening than the lower ones.