Hmm, i am kind of taking a shot in the dark here but in Final Fantasy IV Bahamut was the eidolon that was on the moon (also i read somewhere that the moon Bahamut lived was called red moon but i dont really remember that detail from when i played it) and since in XIV his prison was an artificial red moon, maybe our primal is Asura, the Queen of eidolons in Final Fantasy IV. She could be the one singing as well :P