If I'm reading the numbers right, on Emperor a barb spawns every 20 turns for each 35 tiles of unowned land. See http://forums.civfanatics.com/showthread.php?t=161282 Handicaps table at iUnownedTilesperBarbarianUnit and iBarbarianCreationTurns Elapsed. By comparison, on Monarch a barb spawns every 25 turns for each 40 tiles of unowned land. For Prince it its every 30 turns for each 50 unowned tiles. I'm sure there are other factors which affect the number of barbarians, the type and where they appear, but those look like the main two.