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Thanks for asking. Regarding EyeTV, I recommend to contact Elgato 
support about this or ask for help in the EyeTV Lounge forums.
With regards to toggling audio and the screensaver: since both are not 
directly scriptable on an OS level, such solutions will always be a 
bit hackish. You'll also waste precious energy that way.
I'd personally recommend to get a special "master-slave" multiple 
socket outlet (not sure, whether I used the right translation. You can 
see a picture of what I'm meaning at http://www.amazon.de/dp/ 
B000HZ3GM2 ). These have a master socket, in which you'd plug your 
Mac. If more than, say, 10 Watts are consumed on that master socket, 
the slave sockets get powered on. If the energy consumption of that 
master socket drops below 10 Watts (=> most modern Macs consume only 
around 1-2 Watts when asleep), power of the slave sockets is turned 
off. So, if you plug your Mac in the master socket and your TV and 
other equipment in the slave socket, your TV and other equipment is 
automatically powered off when your Mac is turned off or put asleep 
and automatically powered on again when your Mac wakes from sleep or 
is powered on. You'll save energy and money and get convenience at the 
same time.
Best regards, 
Felix Schwarz