Bob-Dubery
Tuning is CGDGBE - IE 5th string down a whole tone and 6th down two whole tones.
Now, this does seem to destabilise things a little. The other strings go a little sharp, I presume that because you take so much tension of 6 and 5. But OK, you can quickly sort that out and the guitar stays in tune.
Sort of.
Consider these chords in that tuning....
G C D
E|--3---0---2-
B|--3---1---3-
G|--0---0---2-
D|--0---2---0-
G|--0---0-----
C|------0---2-
Playing them with no capo things are fine.
Put the capo on at the 2nd fret and things go pear shaped. C & G are OK, but D sounds pretty bad with the 6 string being sharp. I check the tuning of the open strings in case the capo has pulled something out of tune but they're OK.
Move the capo up a fret and things get a lot better. C & G are OK, D is.... well you can get away with it but it's not spot on.
Oddly if, with the Capo at 2, I flatten the 6 string so that the D is in tune the C still doesn't sound that bad - not perfect, but not as bad as the D was.
Snaaks
Bob-Dubery
Thinking of that D shape that I show above, in standard tuning that would be a D with an F# (major 3rd) in the bass.
So that's the same fingering, different tuning and thus different tension on the strings, and I can play that in tune with no problem with capo at 2nd fret.
I don't know if am more or less confused now.