The Theory
The pitch of a vibrating string is determined by it's length, diameter, mass and tension. When you fret a note you are effectively reducing the length of the string (scale) - thus raising it's pitch. Unfortunately, when you push the string down to the fret, the string is stretched - which raises the tension and sharpens the note slightly. This effect increases as you fret closer to the bridge (as shorter scale lengths are more sensitive to variations in tension). To compensate for this, the scale length is increased by moving the saddle further away from the nut.

Checking the intonation
Tune the guitar to pitch and check the intonation of each string separately. First play the note on the 12th fret (one octave above the open string). then play the 12th fret harmonic (the same note). A digital tuner is likely more accurate than your ear, so use one if you have it.

• If both notes have exactly the same pitch, the intonation is correct.
• If the pitch of the fretted note is sharper of the two notes, the saddle should be moved away from the nut (increasing scale length).
• If the pitch of the fretted note is the flatter of the two notes, the saddle must be moved towards the nut (decreasing scale length).

Adjusting the Saddle
	Acoustic guitars - do not allow adjustment of the scale length - although most steel-string saddles are angled to improve intonation. If an adjustment is necessary, it may be possible to compensate by re-shaping the top of the saddle. If this is the case, you should probably take the guitar to a luthier.
	Arch-top Bridges - often have a floating bridge which can be moved freely backwards and forwards.  They will often need to be angled slightly towards the nut on the treble side of the bridge.
	Floating bridges - Set the treble E string first. Push and hold the bar down, loosen the Allen bolt at the very front of the saddle, Move the saddle in the desired direction and tighten the bolt. Release the bar and retune (i.e. loosen the lock nut, retune all the strings, and tighten the locks again). Check the intonation again and repeat. Then move to the second saddle and repeat. Repeat. Repeat. Repeat. Maybe by now you are beginning to understand why I hate these devices....
	"Gibson" style bridges - Each string sits on a small metal insert that acts as it's own saddle. These can be moved backwards and forwards individually by means of small screws located at the back of the bridge. It makes no difference which string you do first. Just remember to retune between each and every adjustment.
	"Strat" style bridges - Small screws mounted at the back of base plate control the position of the saddle for each string.  It makes no difference which string you do first. Just remember to retune between each and every adjustment.
	"Telecaster" style bridges - These allow the strings to be adjusted in pairs, the intonation settings are always a compromise. Consider upgrading the bridge to one which has six separate saddles. The setting method for these is the same as for a "Strat" style bridge.

General Points

• The theory and method of adjustment  is the same for basses as for guitars.
• Retune between each and every single adjustment. By moving the saddle you change the pitch and tension of the entire string - and this will affect the intonation readings.
• If you change gauge of strings, or change to an altered tuning, your intonation will probably need adjustment.
• Sometimes, a different type or make of string will change the adjustment needs. This is due to different compounds having different masses and tensions.