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I know that the A major chord is commonly played by fretting strings 2, 3, and 4, then playing only strings 1 - 5, giving the notes A, E, A, C♯, and E, notes in the A major triad.

If I also add the 6th string, E, that note is also part of the triad. Isn't this still an A major chord? I understand that the 6th string E "roots" the chord at E, but the notes are still the same ones as the triad. Isn't this just a different voicing?

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    You are playing an A major chord as long as what you play consists of the A, C#, and E notes. If A, C#, and/or E appear multiple times in the chord, it is still A major. You can play this combination of notes all over the neck in different octaves and strings. If C# is your bass note then it is called the first inversion. If E is your bass note then it is called a second inversion. – Tarzan Feb 5 at 19:57
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It is a different voicing, but since the lowest note i.e. the bass note is different, it's also a different inversion, and it changes the chord's function a little bit. With the lowest E sounding your chord is an A/E, which is slightly different. It's still an A major, but it's a second inversion A major. (First inversion would have C# as the lowest note. And the regular one with A in the bass is a root position A major chord.)

A/E is commonly used in ending chord sequences like: A/E - E7 - A. When the A/E chord is sounding, I don't feel like being completely home yet, but when the bass moves to A, then I feel completely at home and at rest. Here's a question about the properties of different inversions and the second inversion specifically: Why are second inversion triads considered less consonant than first inversion triads?

Another important thing is that playing both the low A and E at the same time makes the sound a little muddy and unclear. When playing an A/E, you should mute the low A so that there aren't low sounding notes that are too close to each other. Because of the muddiness issue, play either the low A or the E, but not both at the same time. For higher pitches, having notes in a very close voicing is not a problem.

The low E can also be used in alternating bass that's used a lot in country, latin, polka, etc. Play A, A/E, A, A/E ... alternating the bass note between A and E, while keeping the rest of the chord notes the same.

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    Nice answer, alternating bass is a great way to incorporate the low string 5th on this and the C shape too. – John Belzaguy Feb 5 at 17:26
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It is simply a different voicing - but it doesn't really sound very good.

The E underneath might just be the 5th of the A chord, but it's just a bit overpowering that loud when it's below the low A.

You can usually get away with it ringing in sympathy a bit, if you're not fully damping it, but hitting it loud & proud doesn't really work.

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    Well put, I agree. Ralph, try an E shape barre chord at the 5th fret if you want a 6 note A chord. – John Belzaguy Feb 5 at 17:20
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    @JohnBelzaguy - and that alternating (1>5) bass works there too, fretted>open. – Tim Feb 6 at 7:29

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