Has done several oversadon intonations and measured each individual guitar. My experience tells me that there is no mathematical equation that applies to all guitars, each intonation is a little different. Therefore, you have to measure again every time.
One thing that is disturbing is that the measured measurements to the intonation point on the stable leg did not match as well as one might wish. Have used the stoboscope tuner as a result and the measurements only as a suggestion. Sometimes it has happened that the stable leg was not enough to reach the intonation point for the two thickest strings and a wider stable leg was made. Something was wrong in the Kingdom of Denmark…
Began to suspect that there is a difference between the tone of the stable leg with a floating stable and a stable with string sticks. I have used a string holder to measure the intonation on fixed stalls. I did a jig to be able to use a string instead, just like on the finished guitar. Here is the prototype jig during measurement.
A brass string peg had a hole drilled and tapped. Two nuts are attached to each other, the nuts are stuck in the screw when it is turned. An aluminum rod has two screws that attach a "clip", the rod can be adjusted with the screw in the string pin and the "clip" with it. Using my drills with steps of 0.1 mm thickness to together with the "clip" give the string the right height at the 12th fret. The intonation point is in the middle of the "paperclip". The jig works very well, the drill is included when adjusting the "clip" as it is clamped between the "clip" and the string.
Made three separate intonation measurements on the same guitar and with the same strings. First as in the picture with one string at a time with the new jig (the second string is only needed to hold the control of the strings for the zero bands), one with the same jig but with all strings aligned and one with the old method with string holders.
The tables show string, distance from the back of the 1st band to the intonation point upper part (mm), distance from the back of the 1st band to the intonation point stable leg (cm).
1 New jig one string at a time
E 35.00 58.85
A 35.18 58.70
D 36.77 58.65
G 35.48 58.60
b 36.16 58.50
e 35.79 58.40
2 New jig all strings aligned
E 34.96 58.85
A 34.70 58.65
D 36.56 58.65
G 35.41 58.60
b 36.20 58.55
e 35.86 58.40
3 Old method with string holder
E 34.29 58.60
A 34.83 58.50
D 36.50 58.50
G 35.31 58.50
b 35.89 58.50
e 35.77 58.40
The difference is a bit shocking to say the least. With a stick stall, the intonation point of the thick E string is 2.5 mm further down the stall than with a floating stall! In contrast, the thinnest e-string sounds the same. The difference in the two measurements with the new jig is the most measurement error (had trouble reading the stroboscope tuner for the A string), most because it was so difficult to measure with three strings simultaneously on the drill. The method with one string at a time is the one I will use.
The finished jig was made entirely of brass.
A complete intonation was made with the measurements from the new jig and individual strings on the guitar. For the first time, the dimensions of the stable leg were to be trusted and the intonation was also very good immediately without time-consuming adjustments as before. One advantage is that I do not need to make the stable leg as thick as before to find the right intonation, the dimensions can be trusted.