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Harmonics
When a guitarist plays a harmonic, for example the harmonic at the 12th fret, what he or she is doing is lightly touching the string at the exact mid-point while plucking the string. This deadens the main vibration, which has a swell at the midpoint, but leaves any overtones that are vibrating around the midpoint, such as the 1/2 vibration, the 1/4 vibration, etc. And with the main tone being cancelled out, the predominant tone becomes the 1/2 vibration, which is one octave higher than the open string. Similarly, if you play the harmonic at the 7th fret, this deadens the main tone and the octave overtone (since both vibrations produce swells where your finger is touching the string), but it leaves the one third vibration as the dominant tone. Since this is 3 times the frequency of the open string, it produces a tone that is one octave plus a fifth above the tone of the open string. Similarly, the harmonic at the 5th fret emphasizes the one quarter overtone of the string which is 4 times the open tone or two octaves higher.