Tuning your Guitar...
Tuning the guitar can be a frustrating experience because the guitar is not tuned to pure intervals but rather to tempered intervals. Fourths and fifths can be + or – 2 cents while thirds can be off by 14cents from pure. Because we have 12 frets equally spaced for all 6 strings you will never get pure equal intervals on all chord forms. The answer is to get no pure intervals on anything except unison and octaves and train your ear to accept tempered intervals for everything else.
You are going to want to adjust certain strings because they sound out of tune with a chord only to find that now a different chord is out of tune. That troublesome second string: Play an open position A major chord. Listen to the C# on the second string and you may want to lower it slightly. Play a first position C chord and listen to the E on the first string and fourth string at 2. These tones are slightly higher than your ear would like. Now play an open position G chord. Listen to B on the second string. Yes, it would sound a little better if lowered ever so slightly. Why not try it? Slack off the second string a couple of vibrations and notice what beautiful G chord results. Now play the C chord and with that lowered second string, and you are going to dislike the rough C and E a lot more than before. Take the open B, second string back up to equal temperament so that it will be equally acceptable on all forms. Learn to expect and accept the slight sharpness of the major third in each chord (and oppositely, the flatness of the minor third in each minor chord). Train your ear to accept tempered intervals and you will be much happier with your guitar.
Scholarly articles exist if you really want to get into this but we are going to get to the point of getting our guitar tuned the best way possible.
My first suggestion is to buy an electronic tuner. This has been a Godsend for guitarists of all levels. Electronic tuners are very affordable and can be used for just about any stringed instrument. I particularly like the clip on variety. But, even with these tuners you may need to make some minor adjustments so it is essential that you learn to tune your guitar without the help of a tuner as well. Batteries go dead and you don’t want to get caught out of tune.
I am going to start with the Best method. Not necessarily the easiest but the one that will give you the best results.
Tuning the 1st and 6th strings: The E, open 1st string, must be in pure unison with the harmonic of the E, 6th string at the fifth fret. When these two strings have been properly tuned with each other, continue as follows. Tuning the 4th string: Play a harmonic on the (in tune) 6th string at twelve, and as this harmonic sounds, adjust the 4th string until the tone E on the second fret is in pure unison. Now you have the E, open 1st string, 1st on the 4th string at two, and E, open 6th string tuned pure (permissible because they are octaves).
Tuning the 2nd string: Play a harmonic on the (in tune) 4th string at twelve. As this sounds, adjust the 2nd string until D at the third fret is in pure unison. As you have used two fretted tones for references and as the frets are positioned for tempered intervals, you now have the open 1st, 2nd 4th and 6th strings in tempered tuning.
Tuning the 3rd string: As it is easier to adjust a string while listening to a continuous reference tone, you may first try the following: Play a harmonic on the (in tune) 4th string at twelve and as this sounds, adjust the 3rd string until D at the 7th fret is in pure unison.
Double check: Now make this check to see if you have been accurate or if the instrument plays tune when fretted at seven. Play a harmonic on the (now tuned) G string at twelve, and as this tone sounds, play G on the 1st string at three. The two tones should be in pure unison. If they are not, either you are at fault or the instrument doesn't fret tune at seven. Go back to the beginning and carefully check each step up to this point. If the tones are still faulty, then readjust the 3rd string until the harmonic at twelve is in unison with the 1st at three. Do not tamper with the 1st and 4th strings because it is the 3rd string you are trying to bring in tune. When you have the 1st, 6th, 4th, 2nd and 3rd strings in tune, in that order, continue with the remaining 5th string.
Tuning the 5th string: Play the tone A on the (in tune) 3rd string, at the second fret. Listen to this pitch carefully and now adjust the 5th string until the harmonic at twelve is in pure unison. When the foregoing steps are followed correctly, the strings will be tuned perfectly to equal temperament. No further tuning adjustments
The 5/4 method:
The old faithful "5/4" method is perfectly
correct in principle, since unison intervals are
used. The method is as follows: one string
(usually high E) is tuned to a reference
The 5th fret E on the B string is tuned to match the open E,
the 4th fret B on the G string is tuned to match the open B,
the 5th fret G on the D string is tuned to match the open G,
the 5th fret D on the A string is tuned to match the open D,
finally the 5th fret A on the low E string is tuned to match the open A.
If you have tuned accurately the interval between the two E strings will be exactly two octaves - the 5th fret double octave harmonic on the low E should sound at the same pitch as the open high E. The problem with this method is that if you get one string wrong, the following strings will also be out. But if you have a well-adjusted guitar and a good ear, it can work well.
Octave Method: Any tuning method using octaves is correct in principle. There are many variations - one way is to tune the open B string one octave below the 7th fret B on the high E string, the open G string one octave below the 8th fret G on the B string, the open D string one octave below the 7th fret D on the G string, the open A string one octave below the 7th fret A on the D string, and - you guessed it - the open low E one octave below the 7th fret E on the A string.
But we're back to small errors affecting the following strings again. To avoid this, and because tuning errors become more obvious further up the fingerboard, make your comparisons using only fretted octaves between the 7th and 12th frets, and try tuning in this order:
1. Tune low E two octaves below high E.
2. Compare high E and D - tune D.
3. Compare high E and G - tune G.
4. Compare D and B - tune B.
5. Compare G and A - tune A.