In this lesson I'll explain how to tune the guitar. I will discuss three methods, the first being the common method taught in most beginning method books, the second method is more accurate but involves a little more understanding of the instrument, the third method is a variation of the second method which uses harmonics instead of normal pitches. Harmonics are easier to hear because they are "purer" tones, however, they require a little more skill to produce on the guitar. Read the supplement to this lesson: The Acoustics of Music for a complete explanation.
Each of the strings of the guitar are tuned to a particular pitch or frequency of sound. Disregarding constants such as the string diameter, temperature of the instrument, etc., the pitch of each string depends on the tension on the string which is created between the two points on the instrument which support the vibration, and the length of the vibrating portion of the string. The tuning keys control the tension on the string - by tightening the tension on the string, the pitch increases to create a "higher" sounding note - by loosening the tension, the pitch decreases to create a "lower" sounding note. The length of the string is adjusted by using the fingers of the left hand to press a string down until it makes firm contact with a fret.

Beats
Regardless of which method you use to tune the instrument, it is important that you understand the meaning of "beats". I'm not talking about the type of beat played by a percussion instrument, I'm referring to the phenomenon that occurs when two notes that are only slightly different from one another are played together. The actual physics of the phenomenon are very complex but recognizing the auditory effect is critical in order to know when two notes are in or out of tune. A "beat" is a distinct fluctuation in volume which has a "wobbling" sound. If two identical notes are played together it is difficult to tell that there is not just one note being played. If the pitch of one of the notes is very slightly raised or lowered, a "beat" begins to appear. The larger the discrepancy between the two notes, the faster the "beat." Conversely, as an out of tune note is brought closer to the reference pitch, the "beat" slows and finally disappears. The notes are then "in tune." We will tune each string on the guitar by first lowering the string relative to a reference pitch until a beat occurs and then raising the pitch of the string being tuned until the beat slows and finally stops.

The Notes of the Open Guitar Strings
The strings of the guitar are numbered 1 thru 6, where string 1 is the thinnest string and string 6 is the thickest. In standard tuning (all that you will need to know about until you get fairly advanced on the guitar) each string is tuned to a specific pitch. The following list identifies each string and its correct pitch relative to a piano.

Making a sound on the Guitar
Before you can begin to tune the instrument, you must create the proper sound on each string of the guitar. To begin with, assume the "playing position" with the guitar in your hands. Your nails should be properly shaped and you should already know how to correctly move the fingers of both hands. You will not be using the left hand yet so keep it relaxed and don't let your fingers touch the strings. If you want to, you can hold the guitar lightly with your left hand just below where the neck of the instrument meets the body of the instrument. Your right hand should be held above the strings close to the sound hole, with your fingers about a quarter to an eighth of an inch above the strings. We will use the "i" finger to make a sound (I'll just call the fingers by their letter names).

Extension
Begin the stroke by causing the i finger to extend toward the string by straightening the finger while keeping the right hand motionless. This first motion is fairly subtle and should not be exaggerated to where the finger is totally straight or stiff. Most of the motion for this extension occurs in the middle joint of the finger.

Preparation
Lower i to the string so that the string is nestled between the underside of the fingernail and the fleshy part of the tip of the i finger. This position is called the "preparatory position." Despite what some people may tell you, this part of the stroke will always exist, regardless of how well you learn to play or how fast you play. The only difference will be the amount of time you spend in the preparatory position. To do otherwise invites chaos and will result in limited or no control over the sound produced by each stroke.

The Free Stroke
The free stroke is the most commonly used stroke when playing the guitar. It allows you to easily vary the intensity and timbre of the sound and it allows you to play several notes at the same time without having to significantly alter the right hand position. The free stroke is produced by moving the i finger from the preparatory position through an arc produced by flexing the middle joint of the finger. Your finger nail should slide smoothly over the string producing a clear tone as the string is allowed to resonate. Continue with the free stroke by flexing the large knuckle of the i finger until the finger almost touches the palm of your hand. This follow-through will vary in distance depending on the tempo of the music and the volume you want to get from the stroke.

The Rest Stroke
The rest stroke is used when you want to emphasize or put more weight into the sound. Some players use the rest stroke extensively in scale passages, especially when played in the high registers of the instrument. A rest stroke varies from a free stroke in that the initial movement begins with the large knuckle of the finger and the final position is where the soft tip of the finger rests lightly on the next string. In order to prepare for a rest stroke, it is usually necessary to lower the right hand closer to the strings and to extend the fingers a little more than that which is required with a free stroke.
You should practice both of these strokes many times with the i, m, and a fingers, until it feels natural and relaxed. Don't attempt to alternate the fingers yet, that will come shortly - after the guitar is in tune.

Starting to Tune
To properly tune the guitar, begin with a reference pitch that is a universally agreed upon note. In our music culture, that note is called "A 440." Your tuning fork should produce this tone when struck lightly against a hard surface. Be careful - NOT ALL TUNING FORKS ARE A440! Make sure your tuning fork is the correct pitch before continuing. The tone "A 440" is the pitch that is sounded when the high "E" string is played while depressing the 5th fret...or...when you play the harmonic on the fifth fret of the "A" string by touching the string lightly with a finger of your left hand while performing a normal rest or free stroke (do not push the string down with the finger, just touch it lightly). This harmonic is the reference pitch I use when I tune my guitar to a tuning fork. Raise or lower the tension on the "A" string by turning the tuning key while you play the harmonic on the 5th fret of the "A" string while listening at the same time to the reference pitch of the tuning fork. When you begin to notice a "beat", experiment with the effect by causing the "beat" to speed up or slow down as you adjust the tuning. Once you are confident that you are hearing the "beat", adjust the tuning until the "beat" disappears. You have tuned the "A" string and are ready to continue with the other 5 strings.

IMPORTANT NOTE
THE GUITAR IS TUNED ONE OCTAVE
LOWER THAN THE PIANO FOR THE SAME
PITCH NOTATED IN A MUSICAL SCORE.

THE "A" ABOVE MIDDLE "C" ON THE PIANO HAS A FREQUENCY OF 440 CYCLES PER SECOND. THAT NOTE IS NOTATED BY THE SECOND SPACE FROM THE BOTTOM OF THE STANDARD G, OR "TREBLE" CLEF. THAT SAME NOTATION IN GUITAR MUSIC PRODUCES A PITCH OF "A 220", A NOTE EXACTLY ONE OCTIVE LOWER IN PITCH THAN THE PIANO. THE "A" STRING OF THE GUITAR IS ACTUALLY TUNED TO 110 CYCLES PER SECOND, TWO OCTAVES LOWER THAN "A 440". THE VALUE OF TUNING THE REFERENCE STRING TO THE HARMONIC AT THE 5TH FRET OF THE "A" STRING IS THAT THE ACTUAL PITCH IS THE EXACT "A 440" OF YOUR TUNING FORK.

Each of the following methods of tuning assume you have already tuned the "A" string. DO NOT RE-TUNE THE "A" STRING! It is your reference pitch and if it is adjusted you will have to re-tune all of the other notes as well.

Method 1 - Sequential Tuning of Adjacent Strings.
This first method of tuning is simple and easy to learn, however, it is not the best way to tune the instrument. Each time you progress from one string to the next any slight error in tuning is propagated to the next string. By the time you get to the high "E" string you may not even be close to correctly in tune. Once you get to the point where you are playing chords on the guitar this method of tuning will prove inadequate but it is fine for very early beginners on the guitar.

Press the low "E" or 6th string at the fifth fret. Play the "E" string and the open "A" string and adjust the "E" string until there are no beats between the two notes.
Press the "A" or 5th string at the fifth fret. Play the open "D" or 4th string and the "A" string while adjusting the "D" string until there are no beats between the two notes.
Press the "D" or 4th string at the fifth fret. Play the open "G" or 3rd string and the "D" string while adjusting the "G" string until there are no beats between the two notes.
Press the "G" or 3rd string at the fourth fret. Play the open "B" or 2nd string and the "G" string while adjusting the "B" string until there are no beats between the two notes.
Press the "B" or 2nd string at the fifth fret. Play the open "E" or 1st string and the "B" string while adjusting the "E" string until there are no beats between the two notes.

Method 2 - Tuning Relative to One Fixed Pitch
This method of tuning is more accurate than the previous method because it avoids cumulative errors by always tuning each sting to a single reference string. It does require that you learn how to play a harmonic on the "A" string at the 7th fret (you may have already played your first harmonic on the 5th fret of the "A" string to tune the "A" string to the tuning fork). The actual note that will sound when you play the "A" string while touching the string lightly above the 7th fret will be an "E." This "E" harmonic which is played on the "A" string at the 7th fret will be your reference pitch. All other strings will be tuned to this note by finding "E" notes on each other string (yes, there actually are "E's" on every string), and by comparing each "E" with the "E" harmonic on the 7th fret of the "A" string. The only problem with this method of tuning is that it is sometimes difficult to get each "E" to resonate well enough to be able to use it to tune the instrument. This is especially problematic with inexpensive instruments which may not resonate evenly on all notes.

Play the "E" harmonic on the 7th fret of the "A" string and let it ring. Play the low "E" or 6th string while pressing the string against the 12th fret. Adjust the "E" string until there are no beats between the two notes.
Play the "E" harmonic on the 7th fret of the "A" string and let it ring. Play the "D" or 4th string while pressing the string against the 2nd fret. Adjust the "D" string until there are no beats between the two notes.
Play the "E" harmonic on the 7th fret of the "A" string and let it ring. Play the "G" or 3rd string while pressing the string against the 9th fret. Adjust the "G" string until there are no beats between the two notes.
Play the "E" harmonic on the 7th fret of the "A" string and let it ring. Play the "B" or 2nd string while pressing the string against the 5th fret. Adjust the "B" string until there are no beats between the two notes.
Play the "E" harmonic on the 7th fret of the "A" string and let it ring. Play the open high "E" or 1st string. Adjust the "E" string until there are no beats between the two notes.

Method 3 - Harmonic Tuning Relative to One Fixed Pitch
This final method is the best method for tuning the guitar. It is very similar to Method 2 but uses harmonics on all strings except the 2nd instead of using normal notes. The advantage of using harmonics is that they have fewer overtones to confuse the ear so it is easier to hear the beats when two strings are not correctly tuned. This method requires the use of "artificial harmonics." They are a little tricky to produce, but are worth the effort to learn.

Playing Artificial Harmonics
If you have read the supplement to this lesson: The Acoustics of Music, you will have seen how strings vibrate at many frequencies or pitches at the same time. If you excite the string (pluck it, strike it, move it, etc.) directly above a point on the string where a "node" exists for some harmonic frequency, you will be able to clearly hear the pitch of the harmonic, rather than the fundamental frequency of the string. If you press a string against any fret on the neck of the guitar, you effectively shorten the string length. A complete harmonic series will then be accessible relative to the new string length, rather than to the original string length. This opens up some very interesting possibilities, not only for tuning, but for making music on the instrument - more on that later...
In order to produce the harmonic, you must strike the string and touch it lightly at the same time with the fingers of the right hand. This leaves the left hand free to press down at any desired fret. To practice this, choose a string...say, the "D" string. Fully extend the index finger of the right hand (like you're pointing at something) with your other 3 fingers rolled into your palm. Align your right thumb so that it is parallel to the index finger. You should be able to look directly at your right hand and see the top of the thumbnail and the outside edge of the index finger. Lower this entire assembly down to the "D" string. Touch the "D" string lightly at the 12th fret with the soft tip of the index finger, while striking the same string with a lateral movement of the thumb. As soon as the thumb stroke is complete, move the index finger away from the string so that the note will continue to sound. You should hear a bell-like tone, a harmonic, that is actually the octave of the open "D" string. Try the same thing on each of the other strings until you get a feel for how to sound each harmonic. This same technique can be used to get harmonics from each string at the 5th and 7th frets. If you experiment, you will discover that there are other harmonics just waiting to be heard, some of them at points on the string that don't even correspond to fret positions. Anyway, we diverge...
Now try pressing the "D" string at the 2nd fret while producing an artificial harmonic by touching and playing the string at the 14th fret. That note happens to be an "E", exactly the note you will need to continue this lesson on tuning. You can continue experimenting with this technique by pressing any note on any string and counting 5, 7, or 12 frets up from that note to pluck the artificial harmonic. Once again, there will be other harmonics at many other points on the strings, enjoy!

Play the "E" harmonic on the 7th fret of the "A" string and let it ring. Play the harmonic at the 12th fret of the low "E" or 6th string. Adjust the "E" string until there are no beats between the two notes.
Play the "E" harmonic on the 7th fret of the "A" string and let it ring. Play the "E" artificial harmonic on the 14th fret of the "D" or 4th string while pressing the string against the 2nd fret. Adjust the "D" string until there are no beats between the two notes.
Play the "E" harmonic on the 7th fret of the "A" string and let it ring. Play the "G" or 3rd string while pressing the string against the 9th fret. Adjust the "G" string until there are no beats between the two notes. You will adjust this string later to an "A" harmonic, but let it go for now.
Play the "E" harmonic on the 7th fret of the "A" string and let it ring. Play the "B" or 2nd string while pressing the string against the 5th fret. Adjust the "B" string until there are no beats between the two notes. This is the only string where harmonics aren't used in tuning.
Play the "E" harmonic on the 7th fret of the "A" string and let it ring. Play the harmonic at the 12th fret of the open high "E" or 1st string. Adjust the "E" string until there are no beats between the two notes.
Recheck the "G" string by playing the harmonic at the 12th fret of the "A" string while pressing the 2nd fret of the "G" string and playing the artificial harmonic at the 14th fret. Adjust the "G" string until there are no beats between the two notes.

Checking the strings
The final step in tuning the guitar is to check that the strings have not "gone bad". A bad string will be in tune on some points on the neck but way out of tune at other points due to uneven stretching of the string when it is tuned up to pitch. The quickest way to check a string is to play a harmonic at the 12th fret and than compare the pitch to the pitch you get when you actually press the string down on the 12th fret. This should be done for all 6 strings. Because the 12th fret is the half-way point of the string length, the harmonic and the natural tone should be identical. In practice, it is not uncommon that the two pitches will differ slightly so I usually continue to use a string that has only a slight error at the 12th fret. If you get too picky about the correctness of the pitch you might go through many strings before you finally find one that is perfect. Another consideration before you replace strings on the instrument is your own level of playing. If you are a beginner and play mostly on the 1st five frets of the guitar you probably won't be affected too badly by a bad string. On the other hand, if you use the entire neck of the instrument in your playing you will most likely find a bad string to be unacceptable.

Conclusion
Almost all vibrating objects produce harmonics above the fundamental frequency. As a matter of fact the ONLY thing that differentiates the timbre of one instrument from another is the relative mix of harmonic frequencies present in the tone. This is a very important fact with implications that are especially important to the guitar and we will explore this in later lessons.
This concludes the lesson on tuning the guitar. You learned quite a few other things as well, but I believe they were necessary in order to truly understand not only how, buy why. I guess it's on to lesson 6!