So I had a parking lot conversation the other day about intonation, and it really occurs to me that many players look upon the concept like it’s some sort of mystery and are sometimes intimidated by it. This is my attempt to simplify without over simplifying the concept.
Scale Length = the distance between the nut and the bridge
The 12th fret in a western chromatic scale is exactly half the distance of the scale.
Example: Fender Guitars use a 25.5 inch scale, therefore the 12th fret is 12.75 inches from either the nut or the bridge.
The halfway point in any given scale length will produce an octave (the same note only higher) of the open note. However by pushing down the string against a fret, you will cause the note to go slightly sharp. The amount the note goes sharp depends on the tension the string is under. the higher the tension the sharper the note. The tension is a factor of pitch (the note) and the gauge (thickness) of the string.
The process of intonation is to compensate for the note going sharp by slightly changing the scale of that individual string. With an instrument that has individually adjustable saddles, this typically means lengthening the string by moving that saddle farther towards the tail of the instrument. You will need to measure how much to move the saddle with a tuner. Tune the string to the desired pitch, then fret the 12th and play. If the note is sharp, move the saddle back and repeat. If it is flat, you’ve gone too far.
When all of your strings are properly compensated, your chords will be in tune all the way up the neck and your guitar will be adjusted for intonation properly. However, if your guitar is adjusted properly and notes are sharp in the first 3 or 4 frets, then your string height is too high at the nut. But that’s a topic for another day!