Infinite Dungeon-Info please help

So I have beaten the game and unlocked the infinite dungeon but haven’t gone past the second floor.  Is there any benefit other than musical scores for going deep into the dungeon?

If so, what and what floor do you receive said item/monster on?

Musical scores are a good enough benefit! But yes, there are also gold eggs you can get on each floor. 

Eggs = every 10th floor starting on 9. You must beat the boss on these floors to get the egg. 

Musical score = every 10th floor starting on 10.