Insulate sound between wooden beams?

You need to explain that in more detail, what you are planning. An old cellar, a wooden beam ceiling, and a new building on top of that??

We have purchased an old holiday cottage, where there is a solid basement built on a rock below. Currently, there is a wooden beam ceiling on this basement, and a house in timber frame construction has been built on top of it. This will now be demolished, and the basement gutted. We would now pour a concrete ring around it, then renew the basement ceiling, then build up one floor, then the intermediate ceiling, and build up again, then a shed roof with [Aufsparrendämmung]. That is the plan. Why no [HBD] on an old basement? Because practically only the load-bearing elements would remain…..

Here is the floor plan, maybe it is helpful. In the two upper floors, the ceilings rest only on the exterior walls.

Interesting project. Honestly, I would hold back on tips here, since it is quite a special case. If it were my project, I would definitely - no matter which variant it ends up being - consult with the structural engineer again. This is something different from just applying a bit of dry screed with screed on a wooden beam ceiling somewhere in a normal intermediate ceiling of an old house. But I can advise you to check with Fermacell; they also have good customer service and detailed product descriptions with concrete examples for improving soundproofing with their products in wooden beam ceilings. Personally, I wouldn’t install HBD anymore, but always go with concrete. We have HBD in our old building and that’s fine, but if you’re building new...?

Yes, concrete was also the plan at first, but on the one hand the concrete work in the location accounted for about 70% of the shell construction costs and the company insisted on a crane. But since the crane builder then said he couldn't get there, actually only the HBD remains, which also looks nice, well, impact sound is annoying, but I also hope the construction costs will go down significantly... I'm still waiting for offers....