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Watch the Typical Chord Forms: 2 online guitar lesson by Muriel Anderson from 1-2-3 Fingerstyle Guitar

The minor barre can also be played leaving the pinky free when alternating back and forth between the 6th and 4th strings.

When you're playing an A minor barre chord on the 5th fret, you can play the 5th string open, instead of the 6th string.