Well if your finger brushes the string just right, directly after picking it, a harmonic will ring out at any fret or open string. I do it by accident alot.
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You could do a pinch harmonic, with some difficulty.

You can't do a natural harmonic on an open string, for obvious reasons. But then you can't do them on most frets, can you?
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a natural harmonic is a harmonic on an open string isn't it?

by that i mean you don't really "fret" a natural harmonic, you just put the strings main frequency out of phase.
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Ummm, yeah I think technically the natural harmonic is an open string. Blompcube seemed to make a lot of sense.

Other than that, I would just pinch harmonic it...you still get a cool noise.
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Pinch harmonic, with the fretting hand. You could play the open string then tap the twelth fret but then I guess it is not an open string harmonic.

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