My new uke is bitchin' except for one problem, which makes it considerably less bitchin'. The C string doesn't like being fretted. What I mean by that is that I can tune it absolutely, using a tuning box, or I can tune it relatively, by tuning it so the 4th fret on the C string matches an open E string. However, both of these approaches produce different notes. Tuning absolutely makes fretted notes sound too sharp, by about a quarter tone. Tuning relatively makes the open C string audibly too flat. None of the other strings have this problem. I have replaced the strings and found the problem remains unchanged. A visual inspection of screws, nut, bridge, distance of strings from fret board---all of these seem identical for each string.
I can tune a guitar fine and the strings seem to hold their tone well enough. It's just that I need to learn songs that either never require a fretted C string, or always fret it!
Has anyone come across this problem before, and does anyone have advice? Many thanks in advance.