When I started thinking about audio I didn’t realise that Linux already had good support for audio with HDMI. I checked the playback options of my system with the command aplay -l .
$ aplay -l
**** List of PLAYBACK Hardware Devices ****
card 0: NVidia [HDA NVidia], device 0: ALC662 rev1 Analog [ALC662 rev1 Analog]
Subdevices: 1/1
Subdevice #0: subdevice #0
card 0: NVidia [HDA NVidia], device 1: ALC662 rev1 Digital [ALC662 rev1 Digital]
Subdevices: 1/1
Subdevice #0: subdevice #0
card 0: NVidia [HDA NVidia], device 3: NVIDIA HDMI [NVIDIA HDMI]
Subdevices: 1/1
Subdevice #0: subdevice #0
Looking at the options in the MythTV setup screens for audio playback one of the available options for device was ALSA:hdmi, choosing this just worked! Now playing back of recordings sends audio over the one HDMI cable to the TV which is perfect for me.
For some reason I couldn’t use the same for MythMusic so what I ended up doing was choosing /dev/dsp in the Music setup section for the audio device. This means I can use the normal audio output (the 3.5mm green audio jack) to connect to my Amplifier so music playback goes through my stereo speakers but TV audio goes through the TV speakers.