Q&A for How to Set Your Guitar's Intonation

Take the saddle off. Remove the spring. Put the saddle back in the bridge without the spring. This should give you a bit more room to bring the saddle back and make the string less sharp. If you need more room, take the saddle out again and grind the back side of the saddle, making the saddle shorter. Leave enough threads in the saddle for the screw.

Heavier gauge strings need to be slightly longer to match the intonation of the lighter gauge plain steel strings. The lower tension and larger mass of the wound strings travel slightly more when fretted. This is why acoustic guitars are offset at the bridge like this.

Adjust the saddle so that the string length is longer. If the twelfth fret is sharp, the string is short.

It may be your tuning keys/pegs not keeping proper tension on the string. It could also be an issue with the temperature/humidity levels wherever you are storing the guitar.

The strings are hitting the frets. The truss rod might need to be adjusted, or the bridge raised, or the nut may have been cut poorly. Start with the truss rod and then raise the strings at the bridge if you can.

The string height at the nut is probably too high, and needs to be lowered by deepening the groove in the nut. If too high, you will be forced to bend the string to reach the lower frets. The more the string is bent to reach the fret, the shorter the string length, and the more sharp it will be.

Adjust like the article said. It's common for all strings to need slight adjustment.

This could mean that you have old strings, bad frets, or a truss rod that needs adjustment. If it's an electric, sometimes you may need to flip the saddle on a tune-o-matic style bridge to give you more room for adjustment.

If you're going to keep your guitar tuned to that pitch, it's not a bad idea to set the intonation.

If you have a cheap guitar, it could simply mean that your guitar does not keep its tuning at the 13th fret. Otherwise, check your tuning on the open string again.