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Step 1
First we must determine what the problems actually are. If the strings don't have the correct clearance over the first fret, the guitar won't play in tune. If the string action is too high to compensate at the bridge, it won't play in tune. String compensation must be adjusted correctly or the guitar cannot play in tune. Let's take it one step at a time.
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Step 2
Think about how the guitar works. Each string is under exactly the right tension to vibrate at a particular pitch. It has to have some clearance over the finger board or it will strike the frets and buzz and rattle. When you push the string down to the fret with your finger, you actually tighten the string a little bit. That makes it go sharp. You must compensate for that at the bridge. Before the intonation can be correctly compensated, however, you must make certain that the string has the right clearance over the first fret.
The most common problem on factory made guitars (sometimes even quite expensive ones) is that the strings are too high at the nut. Solve this by cutting the grooves in the nut so that the strings have the same clearance from the nut over the FIRST fret as they do over the SECOND fret, when fretted at the FIRST fret. (For detailed instruction on how to do this, see "How to Correctly Cut the Nut on Your Guitar".) -
Step 3
When the string clearance over the nut is right, then we deal with the intonation. When the open string is at the right pitch and you push it down to the fret, it will get tighter and go sharp. You fix that by making the string a little bit LONGER. Most electric guitars have individual saddles at the bridge and each saddle has a screw mechanism so that you can move it back and forth. Move the saddle so that it is a little bit farther from the twelfth fret than the twelfth fret is from the nut. How much? Remember that the twelfth fret is the mid point of the string and that a note on that fret is an octave higher than on the open string. Play the harmonic at the twelfth fret by lightly touching the string over the fret as you pluck it. (If you need help with this, see "How to Play Harmonics and Chimes on your Guitar".) You will hear the true harmonic octave of the open string. Then, fret the string at the twelfth fret and adjust the string compensating saddle so that the fretted note is the same as the harmonic note.
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Step 4
So far as acoustic guitars go, the procedure is the same regarding the string height over the nut, but acoustic instruments don't have much individual string adjustment to work with. You will notice on a round-hole, flat-top, acoustic guitar, that the bridge saddle is mounted at an angle. The little string is about a quarter of an inch shorter than the big string. That is about the right amount of compensation but you must use the same gauge strings for which the guitar was designed. Arched top f-hole guitars often have a moveable bridge. You just slide it back and forth as needed. Again, use octave harmonics and fretted notes on the twelfth fret to correctly position the moveable bridge.







