Maybe a strange title, but you'll understand what I mean.

How do I play this with down AND up strokes without hitting the E-strings (6th string)?

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I tried putting my index finger muting it, but the I mute the A-string also because I lower the pressure there.
Anyone got a idea?

ThX anyway!
Try to mute it with your palm, also adjust where you hit with the pick so you avoid hitting the E string

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Adjust where you hit the pick? I'm not that good in English, I don't understand...
when you play them just let your index finger touch the string a little, so when you hit the string it doesnt have anywhere to go, cause it just bumps into your finger. dont put your finger on the E string just put it a little past the A so that it touches it a little bit. its kind of a hard thing to explain haha.
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sorry english is not my first language, try to hit with the pick lower on the guitar so you dont touch the E string

Guitar :
Supreme Black Devil (LP copy)
Jackson RR3
Levin Lg-4 Acoustic
Peavey Vypyr 60 Tube

TL-2 Metal Distortion - Hardwire
Crybaby GCB-95 - Dunlop
Just dont play the e string? You arent supposed to have to mute it you know...
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Yea, but I want to play it with up- and downstrokes so I know I'm not supposed to play the E-string, but I can't avoid it...

So, muting it with the index finger is a good thing...Okay, thanks!
I guess there are 3 things you could try:

1. Practice muting the E string with your index until you get the hang of it. It's actually fairly easy, just touch the E string with the tip of your finger, while still keeping the A string pressed

2. Don't pick the E string

3. Use your thumb to mute it. I don't really recommend this, because it could feel uncomfortable and it could turn into a bad habit, but it's up to you, after all.
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When your holding down a half chord(thats what I call them) you should mute the middle string with you index finger, like angle it so it mutes the string while holding down the upper sting. To mute the rest you use your index finger again to mute the rest of the strings by having it at an angle. Almost like baring the entire fret board, except your just left hand muting it so the string dont ring out. your index finger should be holding down the 5 while left hand muting the rest of the strings and your pinky, ring finger, which ever one you use to bar chords should be holding down the 7 sting.

If you mute all the stings on the 5th fret with one finger except the one you want to ring out then you can have any other string past the 5th fret ring out if you hold it down as well.
Just practice. Get more control over your picking hand.
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Besides that, he's right this time. As usual.
It's like barre chords except you don't fully press down with your index so it's muting the strings. As for not being able to put enough pressure on the A string, you just need to practice playing the chords. Develop more finger strength.
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One way is to mute it with the tip of your index finger, another I'd use is to mute it with the middle finger, the last is do the right thing and not play it at all, I'd use a combination of muting and not playing it to avoid messing up