Wait you actually wear headphones with nothing playing? That's genius but seems so weird to me. I could never pull that off without looking crazy at my desk. My coworkers would definitely tap my shoulder to ask what I'm listening to. Still, if it keeps the drama away, maybe looking a little odd is worth it.
Totally do the silent headphone thing when our accounting team gets loud. They argue about spreadsheet formulas like it's the end of the world. My boss just assumes I'm on a call and leaves me alone. It's the only way to stop Karen from HR coming over to tell me about her cat's new diet. Looks a little odd, but it beats having to hear another debate on tax codes.