Every time a string is fretted it is also stretched. To touch the strings means always to increase their tension. And as you stretch the string it will rise in pitch for a few cent!

That´s the problem and here´s the solution.

With a lower tension of the string than you normally do, you can get in pefect tune the 1st fret.

Once in tune the 1st fret (F;B;Dis;gis;c;f) ,  you can see on the tuner two exact  values:

1. How much out of tune  the 12th fret.

2. How much out of tune  the open string.

The first you can compensate on the saddle, the second on the nut.

That´s all!