I've also been having the same problem (no HDMI audio) with a Radeon HD 6670 beginning with the Ubuntu 3.8.0-18 kernel. I can confirm that HDMI audio DOES work in Ubuntu 13.04 with my Radeon HD 6670 in combination with the following mainline kernels: 3.8.0, 3.8.1, 3.8.2, 3.8.6, and 3.8.8.
Interesting to note that HDMI audio works with mainline 3.8.6 and mainline 3.8.8, but not with Ubuntu 3.8.0-18 or Ubuntu 3.8.0-19, which are based on mainline 3.8.6 and mainline 3.8.8, respectively. See http://kernel.ubuntu.com/~kernel-ppa/info/kernel-version-map.html
I'll also add that, at least for me, lots of other problems (including inability to mirror monitors) are present with 3.8.1, 3.8.2, 3.8.6, and 3.8.8. See https://bugs.launchpad.net/ubuntu/+source/xorg-server/+bug/1167301 But most everything seems to be working well with mainline 3.8.0 and Ubuntu 3.8.0-7. So for me, mainline 3.8.0 and Ubuntu 3.8.0-7 are my only current options.
I've also been having the same problem (no HDMI audio) with a Radeon HD 6670 beginning with the Ubuntu 3.8.0-18 kernel. I can confirm that HDMI audio DOES work in Ubuntu 13.04 with my Radeon HD 6670 in combination with the following mainline kernels: 3.8.0, 3.8.1, 3.8.2, 3.8.6, and 3.8.8.
Interesting to note that HDMI audio works with mainline 3.8.6 and mainline 3.8.8, but not with Ubuntu 3.8.0-18 or Ubuntu 3.8.0-19, which are based on mainline 3.8.6 and mainline 3.8.8, respectively. See http:// kernel. ubuntu. com/~kernel- ppa/info/ kernel- version- map.html
I'll also add that, at least for me, lots of other problems (including inability to mirror monitors) are present with 3.8.1, 3.8.2, 3.8.6, and 3.8.8. See https:/ /bugs.launchpad .net/ubuntu/ +source/ xorg-server/ +bug/1167301 But most everything seems to be working well with mainline 3.8.0 and Ubuntu 3.8.0-7. So for me, mainline 3.8.0 and Ubuntu 3.8.0-7 are my only current options.