Ifrit tempers (nearly indiscriminately), Garuda tempers everything, leviathan drowns (non sahagin), ramuh touches (few), titan does not seem to temper anyone. Thordan, shiva, king mog, Bismarck, and ravana don't temper anyone either (though iirc the possibility is mentioned with ravana, even though he is similar to titan in seeming to care for his children; and similar to ramuh in his reasoning with the WoL).
Remember that shiva, thordan, and moogle are different kinds of primals.
I'm taking 'artistic' to mean something along the lines of the thordan story mode or similar to the fight with the grand companies with plenty of dialogue.