F1 means first generation.
Okay, first lets talk about barring. Barring and cuckoo are the same genetically, the terms are basically interchangeable for breeding purposes.
In pure bred barred birds, the male has two barring genes. The barred gene is responsible for the white "bars" on an otherwise black bird. So, a pure bred male has a double dose of white. This makes him lighter overall in color. Females, even pure bred, can only carry one copy of the gene. So, they have more black than white and are darker overall.
A double barred male gives one copy of his barring gene to each offspring, regardless of gender of the chick and who the momma is.
A barred female only passes a barring gene to her male offspring.
A single barred male passes his gene to 50% of his offspring, no matter the gender of the chick.
Now, for the silkie gene. The gene responsible for the silkie feathers is recessive. That means both parents have to have it and pass is on to the chick for the chick to have silkie feathers.
If you breed a silkie to a non-silkie, the chick won't have silkie feathers. But, it will carry that recessive gene for silkie feathers and can pass it on to it's offspring. This is what we mean when we say "split" for a specific gene--it means the bird doesn't express/show the characteristic, but carries it and can pass it on if bred to an appropriate mate. Split can be thought of as a carrier, if you will.
So, if you start with a barred Cochin rooster, he's pure bred and double barred. That means all his offspring (F1) will be barred. But, since you're putting him over a hen with no barring (your black silkie), she doesn't have any barring gene to pass to her sons. So, the males will only have one copy of the barring gene and be single barred (as will the females). That first generation won't have silkie feathers, but they'll all be split (carriers) of the silkie gene. The chicks will all be black barred (one copy of the barring gene).
Probably the quickest way after that would be to take a cockerel from that hatch that has the most silkie traits (comb, five toes, etc) and put him back over another black silkie hen. Since he's not pure bred, he only has one copy of the barring gene, so only half his babies will be barred, regardless of gender. He's also a carrier for the silkie gene, even though he doesn't have silkie feathers himself, so breeding him to a silkie feathered hen will give you (I think) 50% silkie feathered birds and 50% that are split or carriers. You'll have 50% barred and 50% solid, so it will just be a matter of how many chicks you have to hatch to get some that are both silkie feathered and barred. You might luck out the first time, or you might have to hatch several batches.
Trying to get the silkie feathers and the barring makes things a bit more complicated than if you were only trying to get one of those traits.
The color of the silkie hen really doesn't matter. If you used a splash silkie under a black barred Cochin, all your chicks' base color would be blue instead of black. The base color doesn't effect either the barring or the silkie genes. Blue barred birds are very pretty, but on silkies I think the barring might get washed out and hard to see, and you might not really be able to tell they were barred unless you looked closely. You can also add barring on top of other colors like buff or partridge, but again with the silkie feathers it may get blurry and difficult to see. It might be a lot of work for a not-very-visible result is all.
did that clear things up at all? Or just create more confusion
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Where are you located? If you put your state/general area in your profile, and are looking for specific birds, you might run into someone local here. Never know!