I notice that in the Absolute Beginner Lesson, Mr. Hodge shows that the 5th and 6th string are not played for the D-Chord. I have had real trouble with this chord because it always sounds so thin, like it is lacking a little bass. Now, since the notes that belong in a D-Major chord are D, F#, and A, and since the 5th string is the A-String, I wonder why so many chord charts show that string should not be played. When I think about it, it seems reasonable that the note belongs in that chord, or at least is not out of place in it. When I then play it with the open 5th string, my ear tells me I am right.
So, my question is this: Why does most teaching not show that note in the D-Major chord?
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Most books will try to show a fingering with the root as the bass note - it makes it easier to teach other things (like altered bass notes) later on.
The 5th string can be played with the D chord, and it's still a D. There are a few chords like that... the C can be played with the open 6th string, and the F with the open 5th, etc.
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Another way to phrase that D chord is to play the F# at the second fret - sixth string instead of the first. You'll find it smooth to move to either a G or E chord from there as well. And you get that bass note.
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Remember however that you still do play an A when you fret only the top four strings -- the third string fretted on the 2nd fret is an A.
But I think typically most songs that show an open D intend for that chord to have a brighter sound (you've called it "thin" but I prefer to think of it as bright). That's why the other variations discussed here (open 5th string and 2nd fret on the 6th string) are typically listed as slash chords -- either D/A or D/F# -- to indicate the altered bass note.
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