Lately, I've been watching a bit of
Paul Robinson on Youtube. While most of it is pertinent to geodesic domes, this one is about the acoustics of a hemispherical space:
While I agree with what he says, the way I would express it is the central zone is 'live', while sound travels along the walls without going through the center. The one I lived in had a lower level and an upper loft with no line of sight. One could sit in a couch in the loft with one's head a foot from a ceiling angled at 30° and hear someone whisper, sitting in a chair by the window downstairs.
The wing walls he shows should be effective for moderating sound, but I would consider an inverted cone in the center top. Either acoustic absorbing material or an active noise-canceling speaker box.
Even though the sound originating by the wall isn't heard in the center, the sound waves are passing through there, as he shows.