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It is a widely recognized fact that equal temperament gives inaccurate intervals (particularly, the major third). People usually ignore it, but some people try to actually fix this.

I have heard that one easy way to improve your sound is flattening your B-string - this is claimed to improve how the "cowboy" chords (Am, C, D, E, G) sound.

Why does it work?

What other adjustments to string tension could I do? How does it depend on the key(s) I am going to play in?

(I am talking about the regular 6-string guitar with 12 frets per octave, without altering the frets themselves in any way).

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    Mathematicians (and some musician) have been trying to square this circle for at least 1000 years already. Reading about the history is interesting, but you are unlikely to invent a "magic solution" that is better that those that are already known! – user19146 May 10 '17 at 17:41
  • So, there are known solutions, which are in a sense optimal. This would be a good place to describe them. I know one solution (probably too weak to be of use), and I'd be happy to know why it works, and how it can be improved. – anatolyg May 11 '17 at 8:09
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It's not exactly equal temperment that is to blame. It's the fact that a modern steel string guitar is the result of a design history that is not completely compatible with equal temperment.

There are two main factors at work. First, the way a guitar works is based on the idea that one fret position can create the right fundamental frequency for six different strings. Now this is true enough that people make and enjoy all kinds of music with guitars all the time, and have done so for over 100 years. But it's not actually 100% accurate. As our ears develop as musicians we can start to detect the inaccuracies of the fret positions and it can annoy us more and more, no matter how much we adjust the intonation set at the bridge or play around with different string gauges.

The second factor is that a long time ago, acoustic guitars were strung with gut, not steel, and jigs and templates for necks, bridge position, and most importantly fret positions were created for gut strings. Then when steel string guitars were developed, those jigs and templates were not always adjusted to match the radically different string thickness and stiffness of steel strings. Some of those fret position calculations, jigs, and templates have persisted to this day. That means a lot of nuts are positioned too far from the first fret, even on guitars from major manufacturers.

Combine that with the desire to make sure a new guitar doesn't buzz no matter how hard it's played, which means you need to cut the nut slots pretty shallow, and you create major intonation problems for the open chords (including the cowboy chords) on many steel string guitars that are fresh from the factory.

Some "quick" fixes are to cut the nut slots down a bit (at least for players who have a more appropriate touch) and even to move the nut about 1/32" to 1/16" closer to the first fret, which has the heart-stopping requirement of permanently removing a sliver of the fingerboard.

A more sophisticated fix is to have a compensated nut (e.g., Earvana, Buzz Feiten, etc.) professionally installed.

All of these things help (and there are many other options out there instead of or in addition to these!), but there is no solution to the problem. The guitar will always be an approximation of equal temperment. One thing that I believe makes the guitar a compelling instrument for people to play and hear is the very fact that it's "wrong". It has a subtle rebellious quality. It sometimes sounds a little close to just intonation, other times it's an approximation of equal temperment, and most of the time it's just a bit inharmonic everywhere. I think people have learned to like it that way.

  • Yet another reason to make guitars with a zero fret. Although most of the major manufacturers don't. – Tim May 10 '17 at 14:45
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    @Tim Also probably part of the reason why Ian Anderson from Jethro Tull pretty much always used a capo. – Todd Wilcox May 10 '17 at 14:48
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    I shall now look upon players who insist on capoing, in a different light! – Tim May 10 '17 at 15:06
  • Is this part of the reason why you can't just tune a guitar by open/5th[4th] fret? I absolutely cannot get happy tuning that way. I've discovered I do it best by simply playing open strings from the top E down, one second or so apart. I can get it right pretty much first time like that. – Tetsujin May 10 '17 at 16:44
  • @Tetsujin Probably. I use an electronic tuner to make sure the open strings are in tune with the other band members. I also use an electronic tuner (instead of harmonics) to set the intonation myself, but I do it in a weird way. I adjust intonation to make it so the best intonation is at the 8th fret, because most of the notes I play are usually at the 5th through 11th frets. Intonating at the 12th fret is standard, but I don't play those notes often enough to care about that area. I used to tune using the 10th fret compared to two strings up, (not the next string), so you might try that. – Todd Wilcox May 10 '17 at 22:05
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There is no easy fix (other than compensated nut or "true" temperament frets). You can flatten B or (alternatively G string), which makes G open chord shape sound more natural, but it will result in bad sounding C or E chord (or others).

You can also try to add an overdrive (even small amount), which will cover the the imperfection (of course it is not a perfect solution). There are a lot of players, which heavily rely on open G even they use equal temperament using crunch or overdrive.

As to the flattening the B string, if you do that you will have to avoid a lot of chord shapes (especially typical open C).

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