Your starting chord...
X 3 2 0 3 0
X C E G D E
re-arrange the letters by thirds...
C E G (no B) D
That give us
Cadd9, no minor seventh so it's just an
That chord is open so we can sort of think of it as barred at fret zero.
Next, barre the first fret and you get...
X 3 2 1 3 1
X C E G# D F
re-arrange the letters in thirds...
C E G# (no B) D F
That gives us
C#5add9add11 or maybe it should be
C11#5add9. I would not spend time trying to give it a sensible label, because the barre was just arbitrarily added. That's not how functional chords are constructed. Is this really a 9th or 11th chord? Where is the dominant 7th then? Without the 7th we have to resort to using
add labels. But do you really mean to construct a chord based on the ^1,^2,^3,^4 scale degrees then a #^5? This is more like non-tertial harmony or tone-clusters. You can do it if you want, but trying to figure out a label for the result doesn't make much sense. I don't mean to sound chiding, I just want to 'unpack' what's going on in the example.
Maybe if this chord was followed by sliding all the non-barre fingers up one fret the "chord" could be considered a type of suspension/retardation between a
Cadd9 and a
Dbadd9. If so, formally it should not be called a chord.
But I'm not sure I you meant to switch fingers 2,1,3 to 3,2,4 and move them up one fret to match the change of the barre from open (fret zero if you will) to fret 1. Personally, my hand can't make the stretch to do that, but it would be...
X 4 3 1 4 1
X Db F Ab Eb F
Notice I made the enharmonic change of
Re-arrange the letters in thirds...
Db F Ab (no C) Eb
That gives us
Notice that I came up with a
Db root whereas @Tim came up with a
C# root. Neither choice is right or wrong. Certainly guitar seems to "favor" keys with sharps so
C# is a natural choice.
Db because of the change of the
E. If we sharp the
C then we should sharp the
E and get
E#. Personally I think it's easier to read
F natural. So I started by changing the pitch class - meaning the letters. So,
E goes up to
C goes up to a
D that is a half step above which is
Db. My root is
Sorry if that's a bit long winded! But I thought it might be helpful to explain. When you get used to making enharmonic changes you kind of do all that stuff without much thinking.
But the important point is theoretically you could take any open chord shift the fingered tones up X frets and then barre at fret X to get a chord of the same quality but with the root shifted by X semi-tones. Some of the resulting chords may be impossible or difficult to play especially the ones based on open