black fibrous board (4X8 sheets) that I have seen installed under drywall
that seems to help sound transmission.

Would that fibrous board be called "buffalo board"?

Or homasote soundboard.

I remember meeting someone who saved all his drywall scraps and cut them
into pieces 3 1/2" wide. He laid them down inside the wall cavity as a
sound proofing method. I never did find out how that worked. I was

Pure weight is a significant part of stopping sound, as is chopping up
any empty space into random-sized volumes.

wondering if something similar would work inside the joist cavities. I
would never try anything this silly but I'm visualizing lining the joists
and bottom of the upper subflooring with drywall.

Ivan