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Problems with Tuning Guitars

Trying to tune a guitar precisely is an exercise in futility.  It is near impossible to get even a well-set-up, high-end guitar to play in tune with itself and with other instruments on every chord and on every note along the length of the neck.

Have you ever noticed that if you tune your guitar perfectly with a quality headstock tuner and then play a “D” chord, that the octave D that is fretted on fret 3 on the #2 B string is sharp and the chord sounds like crap?  It’s not your imagination, and no the string didn’t slip out of tune after you tuned it perfectly with your tuner.  It is the nature of guitars.  Guitars are very imprecise on pitch.  It is an insolvable problem that is inherent due to their design.

Part of the problem is due to what is called “equal temperament tuning” which is what all fixed pitch instruments are tuned to, and have been since Bach’s day.  In order for 4ths, 5ths, 3rds to be perfectly in tune in a particular key, they will be WAY out of tune in any other key. Here’s the problem: if you tune a piano A and E to be a perfect fifth apart, and then tune the B to the E in a perfect fourth, and then the F# to the B, and so on, and go around the Circle of Fifths, when you finally get back to the next A, if will be WAY out of tune from the original A.  This is an unsolvable mathematical problem.  Way back when keyboard instruments were first invented, they would be tuned for a particular piece of music.  But if there were chords with notes that were not on that scale, or if the music changed key signatures in the middle of the piece, or if there were two pieces of music on the program in different keys, there was no solution except to have two harpsichords tuned differently from each other.  Around Bach’s time, somebody figured out that if you tune all the notes in a way that all intervals are slightly out of tune from each other, you can make every chord in every key equally out of tune, but is barely noticeable.  This was called “equal temperament,” or "well tempered" tuning.

A keyboard instrument that was tuned this way was called a "well tempered clavichord":

Wikipedia has a good article on equal temperament tuning:  Technically, equal temperament means that all 12 notes adjacent to each other in an octave are a mathematically equal distance in pitch from each other.  From a practical standpoint, it means that each interval is more or less “equally out of tune”.  How much is it out of tune?  Each fourth and fifth is approximately 3 beats every 5 seconds out of tune.  So even if our pianos and guitars are tuned exactly with an electronic tuner that is set to equal temperament, every chord is slightly out of tune.  Theoretically, the octaves should be in tune, but that’s all that is perfectly in tune.

The great classical composers loved equal temperament because it gave them complete harmonic freedom in their pieces at the expense of just a little impurity in every interval, which gave all sorts of flexibility on compositions for keyboard instruments.  Equal temperament tuning is what we have heard all our lives, because that’s the only way keyboard instruments have been tuned for the last several hundred years.  We are so conditioned to hearing 3 beats every 5 seconds on 4ths and 5ths (and worse on 3rds) that we don't even notice it. (That’s why when we hear a really good a'cappella choir singing in perfect harmonies without any vibrato it sends chills up our spines, and we wonder why.)

Thus, pretty much all the music we hear is out of tune.  We’re conditioned to it.

In addition to equal temperament, guitars have several other problems that make them out of tune with themselves and with other instruments. Think about the three things that determine pitch on a guitar (or on any stringed instrument): string length, string tension, and string gauge (thickness).  Length changes when we fret the string on different frets on the fretboard.  Tension changes when we turn the tuning machines.  Gauge is what causes the six strings that all are the same length and close to the same tension to sound different pitches from each other (thicker strings have more mass and thus vibrate more slowly than thin strings).  These three things interact to cause tuning problems on guitars, but the biggest problem of the three is tension.

For example, the pitch of any guitar string goes from sharp to flat as it is picked hard and then settles as it vibrates less strongly. You can see this very clearly with a chromatic tuner that has an old fashioned analog meter with a mechanical needle.  When you first hit the string, the needle jumps sharp and then it gradually goes down. This is caused by the change in string tension from the string stretching itself during the wide vibration right after you pluck it. The wider the distance that the middle of the string wobbles, the more it stretches itself and the sharper it goes. How far it wobbles and therefore how sharp it goes varies depending on the gauge and tension of the string, and how hard you pluck it.  That is why if you tune with a tuner, the bottom E will always be sharper than the top E right after you pluck the strings (unless you pluck very softly), then if you let them ring for a second, they will both be in tune.  (Theoretically, pianos also have this problem, but it is very tiny compared to guitars because the length of the strings is so much longer and the tension of the strings is so much higher that the pitch change right after a hard strike is very small even when hit very hard.)

Guitars have the additional problem of stretching the string while we press it to the fret, which also increases the string tension and makes the pitch go sharp.  The farther the string is from the fret, the more the string is stretched to reach the fret.  Guitar makers try to account for this by carefully measuring where the frets are placed on the neck and with the shape of the saddle, but it’s just an estimate and it’s never perfect.  It is inevitable that your guitar will ALWAYS either have a different gauge of strings, or different nut groove height, or different saddle height, or different truss rod adjustment, or your neck will have a slightly different shape than the one they used for their calculations.  This is one of the reasons why set up (nut slot depth, truss rod adjustment, and saddle height) is so important: unless the guitar is set up perfectly, every fretted string is will be sharp or flat (usually sharp) relative to every open string.

Furthermore, the harder you press the string past the fret towards the fret board, the sharper it goes.  This can be a big problem with jumbo/tall frets and a player that presses the string all the way to the fret board.

Anytime we stick a capo on a guitar (unless we take the time to re-tune it with the capo on) we double the problem because the capo bends all the strings all the way to the fretboard, so they are pre-stretched a lot so they're all sharp relative to other instruments.  Then we fret them with our fingers and stretch them even more.

In summary, nut height, saddle height, and truss rod adjustments determine how far a string is stretched when fretted at various places on the neck, and therefore how out of tune the string is when fretted and/or capo’d at different positions on the neck.  And this effect varies with different gauges of strings.  To say a guitar is “not very precise” on tuning is a gross understatement.  Furthermore, even if every single thing is perfect, chords are still slightly out of tune because of equal temperament.

There are things we can do that can help.  For example, many guitarists tune String 2 (B) a couple of cents flat.  The B string is the problem child.  It’s the one that sounds bad more often than the others.  Tuning it a couple of cents flat helps a lot on D chords (but it makes some other chords slightly worse.)

The famous folk guitarist James Taylor recommends the following tuning (this is only possible if you use a chromatic tuner accurate to 1 cent):
E: -12 cents
A: -10 cents
D: -8 cents
G: -4 cents
B: -6 cents
E: -3 cents
As you can see, this compensates for the problem of the thicker strings going more sharp when struck hard.  You’ll also notice that the B string is tuned much lower than it ought to be compared to the G and E strings.  But this is a compromise that only works if you’re constantly strumming.  If you let the strings ring, they will end up quite flat.

The book, “The Acoustic Guitar Bible” describes what is called the Failsafe Tuning Method, that makes all chords sound reasonably in tune, and none of them grate.  Here it is:
Tune the high e string as desired
Tune the 12th fret harmonic of the B string to the high e string fretted at the 7th fret
Tune the 12th fret harmonic of the G string to the high e string fretted at the 3rd fret
Tune the 12th fret harmonic of the D string to the B string fretted at the 3rd fret
Tune the 12th fret harmonic of the A string to the G string fretted at the 2nd fret
Tune the 12th fret harmonic of the low E string to the D string fretted at the 2nd fret
Once you've done that, use the following two chords to test your tuning because, for whatever reason, they are particularly sensitive to inaccuracies:
E5: 079900
A5/E: 002255
People who have trained themselves using this method swear by it.

As for myself, I am a pragmatist.  Because I mostly finger pick and don't hit the strings super hard very often, my overall philosophy has generally been to tune with the tuner and just set the B string a touch flat so that the D chord doesn't sound like crap. With most headstock tuners, each LED has a couple of cents range. (Some of them a lot more than a couple of cents). Using my Planet Waves tuner on my Taylor, I generally put the B so the green LED just barely lights and that makes it just a touch flat.

The truth of the matter is, if you are playing popular music in an ensemble or band, nobody can hear the difference anyway.  When I play with other guitarists and bassists, the various instruments are usually far enough out of tune with each other that nobody can hear the difference of a few cents on one guitar. If I could just get those the other guitarists to always go below the pitch and then tune up to the pitch (you should NEVER tune from sharp down to the pitch!), and then strum the strings hard a few times then check each string again, I'd be happy. A few cents here or there on my guitar will never be heard.

Incidentally, pianos have an additional problem caused by the length and thickness changes of the strings and the huge range in pitch, namely that perfectly tuned octaves sound out of tune to human ears from the top to the bottom of the piano. This is not related to equal temperament, it is a different problem.  I think it has something to do with string harmonics.  Anyway, it requires piano tuners to "stretch tune" at the top and bottom ranges.  An expertly tuned grand piano might be as much as 10-15 cents sharp at the top and flat at the bottom in order to sound in tune to our ears, because we hear pitch differently than mathematical formulas say we should.