What do you call this familial relationship?

Correct.

How about Mom dies, Dad marries her sister and then get a \frac{3}{4} sibling. Then Dad dies, and Aunt-mom marries his brother. I guess that would make a \frac{1}{4} sibling, or a double cousin, though “siblings” would probably be the better term for three kids raised in the same house by the same parents.

My Iranian born wife says there is a specific word in Farsi to describe this half-sibling-also-cousin relationship that results when a widow/widower marries his/her dead spouse’s sibling. It’s common enough that the word is needed.

Her mother and her oldest uncle have this exact relationship, she says.

The first part is true and you would be step child, but the second part is not. Step siblings are your parent’s spouse’s children that were from the spouse’s now-gone spouse – no cosanguinity. In the example above the child she has with your father would be your half-sibling. In this case it is elevated to 3/4 sibling because both of you have the same four grandparents.

I’m going to have to study this.

That makes sense. The more common it is, the more likely a term will evolve or it.

I think the human race is inbred. We did a related thread on this awhile back, asking if you started with 70 (?) people how long would it take to repopulate the planet or something but inbreeding quickly becomes an issue. Draw your family tree back a few generations and see how wide it gets, meaning a big number of people went into making you. The farther back you go, the more likely that big umbrella is going to collide with others, meaning you are (at least distantly) related to everyone else. Mutations help mix that up some, at least.

Of course, some groups push that even harder. The Romani rarely marry outside; in some very sparsely populated areas, the dating pool is mighty thin; of course you’ve got the “blue blood” royals who traditionally married only other royals; plus some religions insist you marry someone else within the fold. Those situations and others amp up the inbreeding beyond what’s already inherent.

Which I suppose supports my point - if you’re in a culture where this happens regularly, you develop the word. Our culture doesn’t do things like this very often (the one almost example presented so far had to go back to the US Civil War), so we don’t have one.

I propose we adopt the Traditional English technique of naming things: Steal the Farsi word.

We can start with “half-brothers and first-cousins”.

In terms of ancestry fractions, they are 3/4th brothers, but I don’t know if there’s a commonly accepted term for that.

Similar to that, there are 2 individuals in my family who are first cousins and second cousins (parallel marriages of pair of siblings to pair of first cousins). That’s exactly how I introduce them, I don’t even attempt to do the math.

SO WHAT IS IT ?!?!

This reminds me of seeing where identical twins married identical twins so while their kids are technically cousins, genetically they are siblings.

I believe the correct term is “brothers from another mother.”

What does she mean by “cold Arkansas” here?

Presumably, she’s referring to the stereotypes of Arkansas hillbillies gettin’ busy with their siblings or other close relatives.

You need to make a distinction between what everybody in the family calls a relationship in nearly every case and what they say if someone insists on a detailed explanation of the relationship. A coworker of mine (A) married one man (B) and they had a daughter (C). B ran off when C was still a baby and A divorced him, so B has no contact with anybody else in this whole thing anymore. She later met another man (D) and married him. They had a daughter (E). A, D, C, and E all go by the last name that D has always had. C never refers to D and E by any name other than “father” and “sister”. D never refers to C by any name except “daughter”. E never refers to C by any name other than “sister”. If pressed, they could explain what the exact relationships are in their family, but that seldom happens.

Many languages other than English have a large number of terms for what we think of as extremely complicated relationships.

What’s wrong with 3/4 sibling? It’s good enough for the International Society of Genetic Genealogy and is perfectly logical.

But if you insist - how about “dotted half sibling”?

Mrs. Martian’s parents (Arkansas born and raised) were first cousins once removed. These weren’t uneducated hicks - he was a PhD chemist who worked for a big east coast chemical company and later was a patent attorney, she was executive secretary to the head of a large insurance company. Just goes to show that you can take the hillbilly out of the hills, but you can’t take the hills out of the hillbilly.

So her mother was the daughter of her father’s first cousin, or

her mother was a first cousin to one of her father’s parents.

Is that right?

The polygamous cults in the American Southwest are highly inbred, and there are some really convoluted family relationships. This is not without consequences……there is a rare genetic condition called fumerase deficiency, at one time there were only 33 known cases in the world. 20 of those cases were in the FLDS cult community located on the Utah/Arizona border.

This.

I’ve heard of second cousins marrying (even know a few), but I don’t think I’ve seen this before.

Unconditionally legal in 43 of 50 states (heck, in 20 states first cousin marriages are unconditionally legal). 44 states if the woman is 55 or older.

I think it’s “there is no such term in English”.

I’d probably call them brothers, unless they preferred another term. That’s what I call kids living in the same household with the same parents.