Conditional formatting gradient based on frequency of text entries

I'd like to apply a color gradient to a range of cells based on the number of times a text value appears in that range. For example:

Burn
Burn
Sprain
Laceration
Burn
Sprain

'Burn' appears the most, so it would appear red in the standard gradient pattern. Laceration only appears once, so it would be green. Values that appear more or less frequently would appear in varying shades from green through yellow to red.

Right now I have a separate table under my data with a COUNTIF function used to apply the colors, but I'd like to put the formatting into the main table using a conditional formula that does the math and applies the color gradient. I've viewed another thread where individual colors were assigned based on discrete frequencies, but that seems a little awkward when I'd have to add another formula every time an entry appears more frequently than the previous maximum number.

Can Excel do this?

Thanks. Is that as close as I can get to what I want to do?

What I want is basically what you showed, but with the colors applied to the text column, not the numbers. So in the screenshot below, the colors would appear in column A, with no need to have column B.
Excel frequency formatting.jpg