Artificial Harmonics
Artificial Harmonics are a way to get harmonic resonance from a string while it is fretted. Like natural (open string) harmonics, artificial harmonics involve dividing the string into an integer multiple of separate resonating pieces, by placing a finger on one of the pivot points or "dead spots" and sounding the string. The big difference is that since our left-hand is busy fretting the note, we have to use the right hand to do so.
Artificial harmonics are usually indicated by a * before or after the fret number. Sometimes the actual pitch of the sounded note is written above the tab. And sometimes the * is simply above the tab.
E * e--<5>--*12--12--
The above is a natural harmonic created by using the left-hand as a pivot above the 5th fret. The next note involve actually fretting the 12th fret, but using an artificial harmonic to get that same note. We are given the actual pitch that should be sounded's note name, but we don't know exactly which harmonic this is. It could be the 2nd, 4th, or higher. The final note is an ambiguous artifical harmonic - we know we are getting a harmonic of the 12th fret E note, but we don't have any information about which harmonic to sound.
The way artificial harmonics are executed using the right hand thumb usually means the harmonic sounded is the 4th, 5th, or 6th harmonic, which is going to be very high-pitched compared to non-harmonic notes played at the same location on the left-hand. For this reason, they are often called squeals or squealies.
Picking Technique
This is what is most commonly referred to when saying "artificial harmonic". This technique uses a slighted tilted picking hand to allow the thumb to touch the string as the pick plucks it. The thumb acts as a pivot point to create the harmonic, just like the left-hand finger for a natural harmonic. And again like natural harmonics, you want to lift the thumb off the string as soon as the harmonic is sounded. Usually its just a normal picking motion, but you add the thumb.
It is possible to use your right hand index finger (or another finger) as the pivot point; however, I find this is more difficult. For my pick grip, my index finger's nail would likely touch the string, which doesn't work as well as the flesh of the side of my thumb.
For this technique to work correctly, you must focus on pressure, timing, and accuracy. You must use enough right hand thumb pressure on the string to deaden that point on the string but not so much that you end up muting the string instead of simply deadening the pivot point. Your thumb must touch the string at the appropriate time - right before the pick plucks the string or right after (basically at the exact same time), and it must be pulled off the string as soon as possible after plucking the string with the pick. Finally, the location of your right thumb (the pivot point) must be correct. This will depend both on which harmonic you are trying to sound, as well as what fret your left hand is fretting.
