by Konrad Schwingenstein
Position of the saddle.
On condition that the distances between the frets are correct (normally they are correct) all fretted tones from the 1st at least up to the 12th fret can be made in tune choosing the right position of the saddle. That means:
If, --once in tune the 1st fret--, the other frets result increasingly sharp the greater distance has to be between the frets and the saddle ... and the other way round if the frets result increasingly flat.
Some work of filing...
You will notice, that the saddle results not parallel to the frets; That´s because the thick strings will need a larger scale than the thin ones.
The reason why, is the different stiffness of the strings and sufficiently known and does not need any further discussion.
But notice: To find the right position of the saddle we have to consider only the fretted tones and ignore the open strings.
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!
So what´s about the open strings?
They are not touched.
The pitch of the open string is not raised at all!!
Having in tune the 1st fret the pitch of the open string will be flat.
That´s why until now the open strings have to be deliberately ignored. That´s why they have to be treated separately.
It is therefore necessary to compensate the open strings.
The only way to tune the open string separately is to shift the position of the nut (not touching the bridge and the frets any more, nor changing the tension of the string).
And the right position will not be a 0 fret but a nut moved forward to shorten the open string length and so to raise its pitch.
But how much do I really have to move foreward the nut ??
Having in tune the 1st fret I can see on the electronic tuner how many cent the open string is flat.
That indicates the amount of the compensation!
So let`s saw a wedge dedicated to be stuck in front of the nut. That´s the other work to do.
Why is it a wedge?
The amount of the nut compensation for a thin string will be less (about ½mm) than for the bigger ones (about 1-3mm sometimes more) cause they have a different elasticity.