A pinch harmonic is produced by lightly touching the thumb of the picking hand against the string immediately after it is picked. This action is sufficient to silence the fundamental and all overtones except those which have a node at that location. This is generally accomplished by holding the guitar pick so that very little of its tip protrudes between the thumb and forefinger (roughly 3-5mm), allowing the thumb to brush the string immediately after it is picked.
The technique must be performed at one of the appropriate harmonic nodes for the note to sound. For example, to produce a pinch harmonic which is one octave higher than the fundamental of a string which is stopped at the third fret of a guitar, the string must be plucked halfway between the third fret and the bridge (i.e. 15th fret as the neck is logarithmic). Other overtones of the same fundamental note may be produced in the same way at other nodes along the string. The point at which the string is plucked therefore varies depending on the desired note. Most harmonics have several accessible nodes evenly spaced on the string; so it is no surprise that the nodes used in practice are normally those around where the string is normally picked (around the pickups on an electric guitar), rather than those above the neck as these are the easiest to access with the picking hand from normal playing.
Overtones with a frequency of a multiple of the intended overtone (i.e. the same note in a higher octave) will share the nodes of the lower overtones, so won't be muted. They will, however, be at a much lower volume and since they are the same note in a higher octave, don't detract from the sound of the note. If the string is pinched at the antinode of the intended overtone, no higher overtones will sound.
A single harmonic overtone is far quieter than a normal note which contains many overtones. For this reason, the gain of an amplified instrument is often increased to make it more easily audible. Thicker strings, stronger pickups and adjustment to amplifier settings (increasing gain) are some ways of doing this. It is important to note that as there is only one fundamental sounding, it will have a different volume through different pickups, depending on the proximity of nodes or antinodes to the pickup. The different volumes of overtones are the reason pickups sound different. The outcome of this is that if a node is directly over a pickup, it won't sound through that pickup.
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