HDMI output with kodi plugin

I am not a specialist. But I can say that for the sound to travel via HDMI, it has to be interlaced with a video signal. The TV must be completely synced with the Raspi, otherwise you would not hear anything. Can you display what kind of video the TV receives, like 640 lines 60 hz or else?
You can google hdmi setting for Raspi in the configuration file, and you could see if there is something worth trying.