View post (muting unwanted string noise with picking hand)
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I reckon different techniques for different styles of playing is the way to go. If you're playing a palm muted part the obvious way of muting the strings is in the right hand. Other than that I personally prefer to use my left hand to mute the higher strings in most cases when I use a pick. But to me it really does vary depending on what I'm playing. Best is to be versed in as many ways of doing it as possible.