I have all but finished my first guitar, and I am quite pleased with the results. However, the intonation is not quite correct. I'm afraid I'm going to have to make a new bridge in order to move the saddle back enough. But I can believe just how far it has to move, according to my calculations - nearly 3/16"!
To confirm this, I removed the saddle a placed a piece of fret wire back of the saddle slot to simulate the new saddle position. The intonation measures correctly in this position with the 12 fret, open and harmonic reading pretty close to the same on my tuning device. But it doesn't make mathematical sense to me.
I understand that the 12th fret should theoretically be half way between the nut and the saddle. I also understand that because a string stretches when you fret it, that compensation is needed and increases with the thickness of the string. That is why the saddle angles, giving greater length to the fatter strings. If I measure the distance from my high E string (1:E), the distance from the nut to the 12th fret is 12 - 11/16", while the 12th fret to the saddle is 12 - 3/4". The low E string (6:E) is 12 - 7/8". That is a full 3/16" of compensation, which seems like a lot to me.
The action is admittedly a little high in this temporary setup (4/32" at the 12th fret), but is it possible to require this much compensation, or am I missing something?