The rules around using music in video or film are Byzantine. As noted already, in this specific case it’s not the music, it’s the performance that’s copyrighted. But, IIRC, there are also considerations WRT who published the music. So while Beethoven’s music is in the public domain, the sheets it’s printed on that the orchestra is using might not be. I think lyrics can be copyrighted separate from music, and (I think) you need an additional license if you’re broadcasting the music in a commercial setting.
It’s so complicated I’m pretty sure I’m getting some of it wrong.
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