Is there a standard nomenclature for bar chord inversions?

It's a bit of a grey area, isn't it?
The most common way, in my experience, is to name the shapes according to their C-A-G-E-D shapes, where the shape takes its name from the "nut position" name of the chord. So that A maj at the 5th fret would be called A major (E shape) or an E shaped A major, not ideal, I know, but its well known enough to be quite useful. It works for chord arrangements rather than chord inversions.
A similar problem could arise with your pianist friend too. If you say "play me a first inversion C", he might play E C G, or he might play E G C, or E C E G. Chord inversions (unlike chord arrangements) are determined only by the bass note.

Nope, there's no standard. You can narrow it down by position (i.e. "fifth position A"), but that doesn't tell a guitarist to do the full barre - he might do 577655, xx7655, x7765x...

There are a couple things that stand in the way of a standard. One Fretsource has already pointed out - even for a pianist, "inversion" only dictates the bass note. The other is the fact that the guitar can play pitches in more than one place - standard notation for x02220 is exactly the same as 57765x. And if you can't differentiate between the two on paper, there's no real point to creating labels for different fingerings.

That hasn't kept people from trying. But since what they create isn't especially useful, none of the naming systems has caught on - and my guess is there will never be a "standard".

Perhaps I'm asking too much.

C-A-G-E-D is fine, but it is still to verbose for quick communications.

I was hoping there was some kind of standard that at least the majority of guitarists and guitar teachers could agree on.

It's nice to know what to do, and even better to have a name for it that everyone will understand.

I guess my open-chord friend and I will have to invent our own system. If it works out, perhaps I'll write a book ;) and perhaps it will become the standard :shock:

Notes

Good luck with the book. But don't just write it for guitarists. Anyone who plays a harmonic instrument must have a similar problem when describing a specific chord arrangement. I mean, how would you ask your pianist friend to play the same chord as the 5th fret 6 string A chord? You'd have to say something like "Play an A major as root, 5th, root, 3rd, 5th, root". You could shorten that to a more snappy "151351", but given the number of possible variations, a book using that system would end up looking more like a phone book. So I hope you find a better system than that one. :D

I'll put on my thinking cap, but since a lot of guitarists have probably also approached this problem, I can't guarantee that I'll find a way. However, sometimes someone who has not been brought up in the world of guitars might have a better chance by being an "outsider looking in". Since I haven't been taught any other method, I can approach it with an open mind and no ingrained habits of thinking to "break". Wish me luck :D (Oh, you already did, THANX).

I started on drums but played sax as my main instrument for many years, and picked up bass, guitar, and keyboards from band-mates. Unlike most guitarists, I didn't start with open stringed chords, and I still find them more difficult than movable chords (although some songs need the open chords and I plod my way through them).

My flat-top friend finds the open chords easier, but can readily see the benefit of movable chords - no capo needed (they put the guitar out of tune and cause you to do mental transpositions). I intend to learn the open chords as well as the bar chords, but it will take some time and practice (I put in 1-2 hours per day).

I find rock/blues/country leads on the guitar to be fairly easy. Thank heavens it's a transposing instrument!!!

Notes

or you can get The Rosetta Stone of Guitar and call the chords Papa, Mama, Younger Brother , etc :)