The state of being rotten or decayed.
Rottennesses are usually bad because they mean something is old and not good anymore.
Examples:
The rottennesses of the fruit made it smell bad.
The house was full of rottennesses.
I don't like the rottennesses of the old wood.
The rottennesses of the cheese made everyone leave the room.
The rottennesses of the ancient book made it fall apart.
The rottennesses of the banana were so bad, I had to throw it away.