Iridescence color in blacks is either the result of different melanizing genes that can cause the chicken to be black, or because of a nutritional imbalance when the feathers are growing from my understanding, nothing to do with the blue gene. Nutritional issues lead to 'banding' in the sheen, while genetics cause a more even sheen from what I've read. I've seen black birds with purple sheen called 'over-melanized'. I do not know what the genetic components are there; my assumption has been that those with both purple and green sheen are somewhere between appropriate melanizing and being 'over-melanized'.
I know that it's not definitive proof, but I have plenty of Blacks bred out of Blues that have beetle green sheen just like my Blacks out of Blacks. It's really hard to capture in pictures because my birds are silkied, but you can kinda see the green sheen around the edge of this hen's face in this picture. She's a Black out of a Blue x Black crossing if I remember correctly, but might have been from a Blue x Blue breeding. I have several more silkied Black Cochins that have green sheen and none of them have shown purple sheen, regardless of whether they're from Black x Black, Blue x Blue, or Blue x Black crossings.
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I also have Chocolates who have no connection whatsoever to Blues in their background and they have both green and purple sheen. This is the best picture I have that sort of shows it:
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I've never seen anything claiming purple sheen is related to Blue breedings in all my reading.
Remarkable how hard it is to actually photograph the sheen, isn't it?
I wonder if the "over-melanized" thing is related to the extra genes that put the lacing on blues?