Luthier

Inspiration

 * FMIT tuner gives you a table of the distribution of tunings of all the notes you play.
 * Calibration of guitars are basically done by moving the bridge pieces

Method

 * By the same method as FMIT measures tuning and distribution of tuning per note, playing notes in just one string you measure the de-tuning of each note there.
 * Making a simple string model, we fit the distributions of tunings to the behaviour it would be for the string to be shorten (but frets in the same place)
 * We give the distance to move the bridge piece in mm to have most of the notes played in tune.
 * We repeat the process, for further precission.

Formula of misplaced bridge pieces
$$

x/l_0=(2^(-C_t/1200)-1)/(2^(t/12)-1)

$$

Where x is the distance to shorten the string (move the bridge saddle towards the headstock), l_0 is the open string distance from the initial bridge saddle up to the nut ; t is the fret number ; and C_t is the amount of cents it is off in the Tth fret.