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1.
On the guitar, finger tapping is the act of plucking a string with your right hand middle finger (the most common "tapping finger"), either open or fretted, and then hammering on the fretboard with the same finger. Usually you will do hammer-ons/pull-offs with your left hand in between the time that your right hand is tapping.

Tapping can be very simple, e.g. 2 finger tapping where you are simply playing a fast trill (like Toccata and Feuge in D Minor), or it can be very complicated like Buckethead's 10 finger tapping.

Many people claim that Eddie Van Halen invented multiple finger tapping, others say it was Billy Sheehan or Randy Rhoads, etc. But it was definitely Van Halen who brought it to the main stream audience in the 80's.

Finger tapping can add a lot to a guitar solo.
by bryan18 September 17, 2005
 
2.
Or just known as tapping, is a guitar technique popularized, but not invented, by Eddie Van Halen and is usually used in Hard Rock and Heavy Metal. This technique easy to some extent and beginners often use it to impress other people since it is so easy yet so hard-looking. This technique is essentially hammering-on and pulling-off through use of both hands, tapping can range from 2 fingers (Surfing With The Alien) all the way to 10 fingers (Buckethead live). The first song to use tapping that I know of is Dirty Deeds Done Dirt Cheap by AC/DC in 1976, even though Angus Young doesn't tap it live, he originally tapped the solo in the studio to make it a lot easier to play correctly without a lot of extra string noise, but over the years he definitely mastered it with just hammer-ons and pull-offs. Others have claimed that 50's blues and jazz musicians have used tapping as well.
Holy shit! Look at Joe! He's tapping so fast you can't even see his fingers! Finger tapping looks so cool!
by SGROCKS October 10, 2009