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Getting a Grip on Hammers and Pulls
The pull-off occurs when you pluck a particular note and then, by using the finger holding the note and using another finger to fret another note below it on the fretboard while the first one rings, you pull your original finger off the first note with enough force such that the second fretted note rings. The attack of the second note (i.e. the "pull-off") is more subtle since you aren't plucking it. This also allows your picking hand to do less work, since the work of the second note is being achieved solely by your fretting hand.
Measure 1 shows the basic pull-off, and the subsequent measures show different variations of it. In general, you'll hear more of the pulled note on an electric and even more if you're using distortion or compression. For acoustic guitars, it requires a bit more effort to really get it to ring.