"Damping is the quieting or abrupt silencing of the strings after they have been sounded..."
This technique can be done on the classical guitar with both the right hand and left hand.
It is a guitar technique of stopping the vibration of a string or strings at an appropriate time in a piece of music.
I say appropriate because sometimes notes can ring on too long, especially bass notes, and this can have the effect of making the music sound very discordant.
The right hand technique can be performed by single fingers or thumb on a string, and is achieved by slightly touching the string. David Braid, in his excellent guitar resource book
Play Classical Guitar
has some excellent photos of how to do this with the thumb. I really recommend this book to anyone whether beginner or advanced. It’s great.
Additionally, if you want to apply this technique to all of the strings at once you can use the "heel" of your hand, much like when you play pizzicato. In this method you place your hand over the strings close to the bridge.
Here is a graphic of what I mean...
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Some people recommend using an open palm when damping the strings but I have found this method to be too sloppy, especially given the different shapes of hands that you encounter when teaching guitar.
Sometimes the note you are trying to stop does not belong to the chord and would create disharmony thus left hand damping is used.
The left hand technique is achieved by placing the fleshy part of a finger adjacent to a string that requires the note to be damped.
By slightly touching the string in this way makes sure the note is cut off whilst the tip of the finger can still be involved in playing the note it is supposed to on another string.
Like any guitar technique it is a little difficult at first but with a little practice and experience over time, becomes easy.
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