How do you perform artificial harmonics on a classical guitar?
The mixed exercise I have been given for my exam is "artificial harmonics in thirds".
First of all, how do you play artificial harmonics but with a chord underneath to create the third?
Thanks in advance 
Artificial harmonics are simply harmonics played on a fretted note, and there are a lot of methods for playing them.
It sounds like you are supposed to be playing the 5th harmonic, which produces a tone an octave and a third above the fundamental.
I suggest you watch these videos I made about harmonics for the guitar. They will not only give you a better understanding of what harmonics are and how they work, but several different ways to play them.
http://www.youtube.com/playlist?list=PLED4AAB6B0E11BF3E
EDIT: I can’t believe I didn’t include this in the video, but one other technique is to reach you little finger out above the 4th fret from whatever note you’re fretting. You can use the first method I show in the video to find exactly where to place your finger.
Artificial harmonics are simply harmonics played on a fretted note, and there are a lot of methods for playing them.
It sounds like you are supposed to be playing the 5th harmonic, which produces a tone an octave and a third above the fundamental.
I suggest you watch these videos I made about harmonics for the guitar. They will not only give you a better understanding of what harmonics are and how they work, but several different ways to play them.
http://www.youtube.com/playlist?list=PLED4AAB6B0E11BF3E
EDIT: I can’t believe I didn’t include this in the video, but one other technique is to reach you little finger out above the 4th fret from whatever note you’re fretting. You can use the first method I show in the video to find exactly where to place your finger.
References :