Naming this chord

Here's a chord I use for fingerpicking. I've never heard any other guitarist use it because I made it up myself (I know, dangerous thing to do). It doesn't sound the best, but it has its uses.

e-2 (index)
b-0
g-4 (ring)
d-4 (flipper)
a-6 (pinky)
e-4 (thumb)

I've been wondering, what is it called?

Lets see.. it's [Ab, Eb, F#, B], B, F#.
Abm7 is [Ab, Eb, F#, B], Eb, Ab,
B is F#, B, F#, B, Eb, F#,

So..B/Ab(m7)? I dunno if it would just be written B/Ab because the C in Ab major doesn't fit. Or is it just an alternate voicing of Abm7? Any other ideas?

Check out my response to your other thread where you mentioned this chord. I came up with Abm7 or G#m7 depending on how you want to look at it.

Oh, and Hammurabi, Abm7 = Ab, Cb, Eb, Gb. The reason I'd rather call it G#m7 is because who the hell wants to play in Abm which uses Cb?

That chord kicked my a$$...I hate having to use my thumb.

I should probably explain my use of sharps and flats..

In concert band key signatures have either only naturals and sharps or naturals and flats. What happens is some notes are only used as one or the other commonly. With a concert C instrument, like the flute or piano or guitar, you will see Bb or Ab millions of times more than A# or G#, whereas you'll see F# commonly but I've never seen Gb. That's the way it goes for concert music. In order for those exceptions to occur it requires playing in completely queer keys like Db (which is not C#, becuase that note is most commonly seen in the key of Ab. It's the fourth flat of the scale after Bb, Eb, and Ab).