By the way, the 12th fret should not be exactly halfway between the nut and the bridge. There should be some extra length on the bridge side for compensation. I.E. when you fret a string, you are stretching it, thus raising the pitch slightly more than just decreasing the scale length that much. Therefore a bit of extra compensation length is added to the string at the bridge end, generally a bit more than 1/8 inch (slightly less on classicals), increasing for bass strings on steel string guitars. That's why the bridge is installed on a slant.