Scheherazade left, Black Beauty right. The edge on Scheherazade can vary in color depending on temperature, here this one has more of a yellow edge and you can see it is a lot bigger than Black Beauty. Note that the petals on Black Beauty roll back into a form more like a ball and just the petal tips roll back on Scheherazade making it more of a flat-faced lily. Can you post a photo of your bigger lily? A wider white band might mean a different lily altogether.
