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Natural harmonics
When you strike a guitar string, the note that you hear is called the 'fundamental'. It's by far the loudest note created, but along with it you are also hearing 'harmonics'. These are subsidiary tones that accompany the fundamental, and are responsible for making each instrument sound the way it does.
Guitar 'harmonics' are created when you lightly touch the string with your finger at specific positions and then pluck the string. This causes both sections of the string, to the right and left of the spot you're touching, to vibrate simultaneously, giving a bell like quality to the note. It's best to quickly remove your finger as you pluck. What you are doing is removing the fundamental and only hearing the harmonics.
There are three points along the string points this: the fifth, seventh and twelfth frets ... directly above the fret-wire. At these points, the string is divided exactly into fourths, thirds and halves respectively. The purity of sound comes from these perfect fractions of string ringing together. If you try it anywhere else on the string, you hear a dead sound without any ring.
You never push down on the string, all you need is to very lightly touch it and as soon as you've plucked it with the other hand, stop touching it. It takes a little while to master, a bit like rubbing a note out of the rim of a wine glass, but once you get it, you've got it forever.
The notes created are not always the same notes as the fretted note.
At the 12th fret, they are the same note, and in fact playing one after the other is a good way to see if the intonation on your instrument is right: both fretted note and harmonic should be identical in pitch. If they're not, your bridge needs adjusting.
At the 7th fret, the harmonic is one octave higher than the fretted note.
At the 5th fret, the harmonic is the 'fifth' of the fretted note, but 2 octaves higher. In other words, on the E string, the fretted note at the 5th fret is an A note, but the harmonic played at the 5th fret is an E note two octaves higher.
These open string harmonics are the 'natural harmonics'.
Artificial harmonics
Artificial harmonics are those created on a string that's already fretted by the left hand. The right hand must do the light touch AND the pluck at the same time, AND the position of the light touch must be five, seven or (usually) twelve frets away from the fretting hand ... a lot to think about.
Harmonics are usually used as embellishment, rarely as any main guitar part.
Fenderbender
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