I have a bunch of (potentially relevant) thoughts.
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Over the years, I've played a range of guitars -- & by "range" I mean that I'm a gear addict.

Anyway, a very common problem, IME, is that the nut is worn, ever so slightly, & particularly under the wound strings; if an electric guitar has seen lots of vibrato use, this wear can extend all across. As a result, it's impossible to properly tune such a guitar relying on the open-string tone: to do so would make all fretted notes sharp, however slightly, & adjusting the bridge based on the open note would screw up ALL fretted notes.
When I adjust a bridge, I put a capo at Fret #1 (though, as I'll get to, maybe #3 would be better). And when I tune a guitar, I tend to adjust for where I'm playing, so an acoustic will be tuned to sound best on first-position chords, a rhythm guitar for accuracy around frets 5-7, & an electric for soloing work around fret 10.
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Though I have been critical of the Buzz Feiten Tuning System, I should make clear that it is an
excellent fix for an inherent problem of the guitar, namely the "break angle" over the nut. See, in a mechanically ideal system, the edge of the nut ought to be as close as possible to the exact center of the string. Instead, not only do strings vary in diameter, but some of them have further wraps that push the string up from its proper break point (not unlike the mounting end of strings in an autoharp or piano). As a result, when fretting the thicker strings, pressing down stretches the string, raising its pitch. The BFTS is a very simple & smart way of compensating for this.
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However, this is NOT some miraculous cure-all. Feiten's own literature states that this compensation is intended to make up for problems
in the first two or three frets. Anything higher on the fretboard is probably imaginary.
This eliminates sharp notes at the first three frets.
[url]http://www.buzzfeiten.com/howitworks/howitworks.htm[/quote]
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Ultimately, though, it's a game of "close enough for jazz" (or whatever). It is impossible to tune ANY guitar
perfectly, because
even temperament is a compromise... but that's another discussion for another day.
