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When adjusting a string saddle and moving it back, making the string effectively longer, does that decrease the sharpness or increase it??

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I assume you're talking about adjusting a guitar's intonation. You need to compare the pitch of the fretted note on the 12th fret with the harmonic on the 12th fret. If the fretted note is higher than the harmonic, this means that the distance between the saddle and the 12th fret of that string is too short, i.e. you need to move the saddle back such that that distance is increased. If the fretted note is too low, you obviously do the opposite.

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    Note that the 12th fret isn't some magical intonation fret. I usually check intonation on frets 2 through 7 and 12 through 15 and find that I can't get the whole guitar intonated correctly, so I compromise. Depending on the guitar I might favor the lower frets or the higher frets for best intonation, but usually I try to split the difference. – Todd Wilcox Jan 7 '16 at 15:40
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    @ToddWilcox: I agree, but for beginners the 12th fret and its harmonic is usually the easiest way to check intonation. Also, I've noticed that with a decent guitar that is set up well, it's often sufficient to adjust the intonation in the way I've described. If you want to avoid all those intonation issues (once you've set it up correctly), you have to go for True Temperament. – Matt L. Jan 7 '16 at 16:38
  • Good point about beginners starting with the 12th fret only for intonation. On that note, I would suggest that, especially for beginners, using an automatic chromatic tuner to check the intonation at the 12th fret will be easier than comparing it to the 12th fret harmonic. I never use the harmonics any more (it would be hard to do that at any fret other than the 12th). – Todd Wilcox Jan 7 '16 at 16:45
  • It should be pointed out that the amount of pressure applied to the string when fretting a note (especially with jumbo frets) can change the pitch by quite a bit. So it is important to use a normal amount of pressure on the string when comparing the harmonic (unfretted) to the fretted note. "Normal" amount of pressure will vary from one guitarist to the next. It's not an exact science unfortunately. – Rockin Cowboy Jan 7 '16 at 19:16
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For a given tension and thickness of string, making the string longer lowers the pitch. If your open string was in tune, but your 12th fret was flat, you would want to shorten the string or lengthen if the 12th fret was sharp.

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