How much does an ultra ideal cut affect percieved Color?

[Jonathan the Jeweler]

I am curious how much color difference there is between a good cut and an ultra ideal if all other factors are controlled? I have heard people say that an ultra ideal cut can mean the difference of one to two perceived color grades, and I understand that color grades are a range. However, to my eye the difference is hardly that noticeable. These "perfectly" cut stones show more brilliance certainly, but people are confusing that with the color of the diamond itself. Hearts and Arrow Ideal cuts are great. The perfect symmetry is impressive, and they do tend to have a superior spread and can show a great amount of fire, but I am just not sure they look whiter. I understand that a deeper diamond will face up with more color because the observer is looking through more diamond, but a shallow diamond will look whiter by the same logic. How much if any effect will the symmetry have on the face-up body color? I am curious what others think on this issue.