Dvi-hdmi1.4

Yes, the DVI port supports HDMI 1.4a 3D video formats.

There is no "HDMI 1.4a cable" (or adapter). Either "Standard" HDMI cable or "High Speed" HDMI cable. This page. Buy a High Speed HDMI cable. Any DVI-HDMI adapter will work.

Video is always necessary to transmit audio over HDMI. Use extended desktop mode and send the unused desktop to AVR.

Any DVD-HDMI adapter will work. Like this.

No it is not... I have a DVDO DUO with an audio only HDMI out going to my receiver. They also exist on some Panasonic and other Blu-Ray players. I have read though not tried to do it that some folks have used the onboard iGPU HDMI device to play audio while using a discrete card for HDMI video.

My DUO has 3 HDMI outs 1 for audio only. It can be used with our without a Video HDMI in use. It will also trascode optical onto to the HDMI audio. It is not even required that Audio and Video have any correlation. I could have channel 13.1 play video from input HDM1 on HDMI Display 1 out and have music music from DVD player on HDMI2 in playing on HDMI audio out.

In a general sense audio and video over HDMI are part of the same signal so perhaps you are right there. Your own suggested work around pretty much is an exception that disproves your rule.

Speculation is OK. But first try to send audio to a HDMI 1.3 AVR and 3D video to a HDMI 1.4a 3D display from a *PC*. See what happens and come back here. Extended desktop mode is the only solution, whether you use Intel, NVIDIA or dual GPU (whatever combination of AMD, NVIDIA and Intel), a well-known method originally dated back to my post in 2008. If you find a better workaround, let us know.

"I have read that some folks have used the onboard iGPU HDMI device to play audio while using a discrete card for HDMI video": Yes, they are all using extended desktop mode: sending the unused desktop portion to AVR along with audio. You just didn't read enough what they are actually doing.

HDMI signal (TMDS) is basically video in Video Data Period + audio in Data Island Period, an extenison of DVI TMDS (video in Video Data Period, no audio in Data Island Period). DUO must be sending some kind of video pixels (can be any, e.g. black screen) along with audio data over HDMI. Because you don't have to feed video to DUO does not necessarily mean that output HDMI does not contain video data. Discussing here how DUO handles audio in HDMI is pretty useless anyway. That does not help the op at all.

Why clone mode does not work.

So the extended desktop mode does not work either? Does 3D work if your 3D TV is connected to the HDMI port, with the DVI port unused (then perhaps audio is limited to stereo)?

I don't 3D, but use extend mode all the time. Hdmi to AVR and dvi to desktop or other display. Set your correct resolutions. Audio in playback devices set default to hdmi. Set or drag your video player to the dvi display.

Oh, it's working. Glad to hear that.