We get a bunch of music channels. If I turn to one of this the screen is "black", no picture. Is this no picture at all or is it "black" that might cause burn in?
I assume you mean via satellite or cable, yeah these are usually just black screens with music, or they have a text display of the song info of what's playing.
A full-black screen should cause no wear at all, and certainly no burn-in. It is bright portions of the picture that causes phosphor wear on a CRT TV. Consult the Burn in thread at the top of this forum for more info.
IF there is a fixed text display or other logos on the screen for long periods of time, you may suffer froom burn in. Again, consult the thread.
On my cable system, some channels have zero text, some give the text only when the song changes then it goes black again, some channels give text all the time in different formats for each song as to avoid burn in.
I have music channels from cable and mine does shows pictures, like album covers and the history of the group. I have everything going through an amp. I flip to the music channel and turn my tv off and listen through my 5.1.