The usual method of tuning a guitar involves tuning each high string by matching the pitch played at the fifth or forth fret of the next lower string. Another method uses harmonics produced between the fifth fret of the lower string and the seventh fret of the next higher. I have seen this method used by tuning the harmonics until the beats disappear, but I found when I tried to do this, the tuning never came out quite right. It turns out, that as a consequence of the equal tempered scale , these harmonics must be mistuned very slightly for this to work out. I have found that I can get a suitable tuning by this method, but that the beat rates required are not always the same.

The need to tune the harmonics produced by each string slightly flat is a result of the difference between the natural harmonic series and the equal tempered scale. Consider the frequency of the first three natural harmonics of each of the guitar strings:

Harmonic:	Fund	2nd	3rd	4th
Fret:		12th fret	7th fret	5th fret
E	82.407	164.814	247.221	329.628
A	110.000	220.000	330.000	440.000
D	146.832	293.665	440.497	587.330
G	195.998	391.995	587.993	783.991
B	246.942	493.883	740.825	987.767
E	329.628	659.255	988.883	1318.510

Notice that the difference between the 3rd harmonic of the A string and the 4th harmonic of the low E string is .372 Hz. This means you can tune these strings open, without fretting, by listening to and adjusting the beat rate of .372 Hz, or about one beat every 3 seconds. To tune the whole guitar, start by ringing the 3rd harmonic on the A string (7 th fret) and the 4th harmonic of the low E string (5th fret), and adjusting the A string sharp to a beat rate of .372 beats per second ( 2.7 seconds per beat). Next, ring the 3rd harmonic on the D string (7th fret) and the 4th harmonic on the A string, adjusting the D string sharp to a beat rate of .497 beats per second. Ring the 3rd harmonic on the G string (7th fret) and the 4th harmonic of the D string and adjust the G string sharp to a beat rate of .664 beats per second. The high and low E strings can be tuned directly by ringing the 4th harmonic of the low E string (5th fret) and the open high E string and tuning until the beats stop. Then ring the 3rd harmonic of the high E string (7th fret) and the 4th harmonic of the B string and adjust the B string flat to a beat rate of 1.116 beats per second. The guitar should now sound reasonably well in tune, but on close inspection, it may not actually be so. This is because beat rates used in the above procedure were based on ideal harmonics, the partials actually produced by the string are somewhat different.

A precision strobe tuner can be used to measure how much the partials produced vary from the harmonic series. This is done by ringing each harmonic separately while adjusting the calibration control to stop the pattern rotation. Then the error is read from the calibration setting. These measurements must be setup and made very carefully, since many things can minutely change the fundamental tuning during the measurements. The neck should be supported at a point around the 12th fret and the temperature must be stable. A furnace turning on can vary the string pitch by several cents or more! The following table shows the results of such a set of measurements, along with the resultant frequency of each harmonic, for a new set of Ernie Ball Super Slinky strings on a Gibson Les Paul Special:

Harmonic:		1	2	3	4	5	6
Fret:		Open	12th	7th	5th	9th	3 1/2
E	Cents	0	-1.4	0.4	-0.2	1	2.6
	f	82.407	164.681	247.278	329.589	412.273	495.184
A	Cents	0	-0.2	1.4	0.8	2.6	2.2
	f	110.000	219.975	330.267	440.203	550.827	660.839
D	Cents	0	1.6	1.8	2.4	3	3.4
	f	146.832	293.936	440.955	588.144	735.435	882.726
G	Cents	0	1	1.6	2.2	3	2.4
	f	195.998	392.222	588.537	784.988	981.688	1177.618
B	Cents	0	0.2	0.8	1	0.4	0.4
	f	246.942	493.940	741.167	988.337	1234.994	1481.992
E	Cents	0	0	0.2	0	-0.2	-0.4
	f	329.628	659.255	988.997	1318.510	1647.947	1977.308

A careful measurement of the partials produced by a set of guitar strings shows that not only do the partials vary considerably from the harmonic series, but that how much inharmonicity exists depends on the type of string, and how worn and dirty it is. One could use the information from such a set of measurements, and figure the precise beat rate to use for each set of string pair harmonics for a perfect tuning. From the table of actual measurements of guitar strings above, the beat rate required between the 3rd and 4th harmonics of the B and high E string would be .66 beats per second, rather than 1.116 beats per second if the harmonics were ideal. This method would then work until you changed string types, let the strings rust for a while, or stretched the living crap out of them. Worn and dirty strings can produce partials which are off by more than 10 cents from the ideal harmonic series. The best method for finding the correct beat rates to use for each sting is probably to tune the six strings perfectly by some other method and listen for the beat rates actually produced by each string pair harmonic. This information could then be used as a basis of a quick tuning check using string harmonics. But whatever you do, don't try to tune by zero beating the harmonics, it just won't end up sounding right.