Muting is a technique that allows you to keep notes from ringing out, to choke them off, to muffle them. Piano players have a pedal that they can press to bring felt pads down on the strings; we guitarists use the blade of our hand or finger tips to mute. The most common way is called 'palm-muting'. Mostly used when playing rhythm, the technique involves gently bringing the edge of the right hand down on the strings just in front of the bridge (pictured). This allows the note(s) to be heard, but without ringing out. It keeps the sound very compact and bubbly rather than jangly and spread out. A great example is the opening guitar of the tune 'Every breath you take' by The Police. The other way to mute is to choke off strings you're not playing so that you can eliminate stray harmonics.
You can get strings to ring out just by singing or humming loudly into the soundhole, so long as the note you sing is in tune with one of the open string notes. Try it and hear for yourself. When you're playing melodically, the same thing can happen and not always to good effect. I got into the habit a long time ago of using the side of my thumb and my fingertips to choke off any string I'm not actually playing to solve that problem. This comes in very handy when playing slide guitar, too, as the biggest challenge with that style is to keep notes you don't want to hear from ringing out under the slide. Another way to stop notes from ringing is to simply take the pressure off the string. As soon as the string loses contact with the fret wire, it stops ringing out. You can do that with whole chords; it's especially effective with barre chords.
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