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I watched a guitarist on YouTube, and he fingerstyles and arranges his music for covers. I was watching one of his videos, and he was playing, then he took his index finger and tapped the string above the soundhole up along the neck and it made a really cool sound. I don't know how he did it.
He didn't "tap" the string with his index finger. He placed his index finger on the string at a specific location and plucked it with the other finger(s) of his right hand. This uses the principle of harmonics as Tim pointed out. There are several places (in theory an infinite number) where you can excite a harmonic. On the open string the most common ones are at the 12th, 7th, 5th and between the 3rd and 4th frets. When you fret a note these same harmonics can be excited by touching the string at some fraction of the length between the bridge and fret, 1/2, 1/3, 1/4, 1/5, 1/6, etc. These can be excited by touching the string and plucking it or gently tapping at these nodal locations.
It's all down to harmonics. By touching (gently) the string being plucked exactly half way along its speaking length, it produces a note an octave higher.
You can sample this by touching an open string above its 12th fretwire. Then play that string.The note will come out an octave higher. Two hands will help initially, but this guy is using a finger to touch, and another to play. That's because his other hand is occupied fretting the note concerned. Watch how each note played is touched at its halfway point.
