There is a range of correct action both at the nut and off of the bridge. Too low or too high at either end yields unsatisfactory intonation. Ifnthe regulation of the nut to the first fret is too high, the notes near the nut will be sharp. ''Tis is because the high AC creates higher tension. Tension is what determines pitch. I have exhibited this problem to people on guitars that have been intonated to fret accurately at the 12th fret. In one case, I told the young fellow that his note at the first fret on the G string wto use be quite sharp...even though that string was intonated correctly at the twelfth fret. I told him that that sharpness would incrementally decrease from fret to fret as one moved away from the nut until at some fret the tension would be correct and the intonation would reflect that. The first fret note was 13 cents sharp to a G#. The seventh fret D was the first position to yield accurate intonation. He was a double major....physics and music. He gained some insight into the physical aspects of the machine that he called a guitar...and perhaps his college education will continue to help him understand guitars....now that he has been exposed to that aspect of his musical instrument.