Department of Science, Math, & Technology

If, OTOH, one keeps track only of those for whom the line of ancestry is all-male or includes at most one female, that is 36 people.
(In other words, one omits any ancestress’s ancestresses.)
(That’s an extension of what the Habesha do.)
in my opinion that’s still too much to remember.
Suppose, instead, one were to keep track just of the patriclan-names of such ancestors.
Then there’d be just eight names to remember.
One would need to memorize one’s own patriclan name, which one inherits from one’s father and all patrilineal ancestors;
And one’s mother’s “maiden” patriclan name, which she inherited from her patrilineal ancestors;
And one’s father’s mother’s “maiden” patriclan-name;
And, in general, the “maiden” patriclan-name of the mother of each of one’s patrilineal ancestors, not further back than seven generations; including one’s FFM, FFFM, (F^4)M, (F^5)M, and (F^6)M.
If H’s list of eight patriclans doesn’t overlap W’s list, they could still be half-cousins, because they could still share a maternal grandmother. HM and WM could still be each other’s uterine half-sisters, as long as HMF and WMF were not only different men, but didn’t even belong to the same patriclan.

That’s the closest blood-relationship permissible between husband and wife in the Habesha system.

If instead one prohibits the couple to share an ancestor seven or fewer generations ago in any line that contains no more than one male ancestor, that’s a different set of 36 ancestors (mostly ancestresses). (This is an extrapolation of Manu’s law, according to at least one interpretation of at least one version of it.)
If everyone belonged to a matriclan, membership in which everyone inherited from their mother, then a person could, instead of memorising the names and/or identities of all 36 of these relatives, just remember the names of eight matriclans.
Namely, one’s own matriclan (shared with one’s mother and all of one’s matrilineal ancestresses),
And one’s father’s “bachelor” matriclan name, inherited by him from his mother and all his matrilineal ancestresses;
And the “bachelor” matriclan-name of one’s mother’s father, one’s MMF, and the father of each of one’s matrilineal ancestresses, as long as one goes back no further than seven generations. That includes one’s MMMF, (M^4)F, (M^5)F, and (M^6)F.

This would still allow H and W to be half-cousins, because they could share their paternal grandfather; HFF and WFF could be the same guy, so HF and WF could be each other’s agnate half-brothers, provided HFM and WFM were not only two different women, but didn’t even belong to the same matriclan.

Suppose a society adopted both restrictions; an extrapolation of what Wikipedia says some Hindu communities do.
Then no great-grandparent of either party can also be a great-grandparent of the other.
HMM, HMMM, HMMF, HMFM, and HFMM, could share a patriclan with WMM, WMMM, WMMF, WMFM, or WFMM; but they couldn’t share a matriclan.
HFF, HFFF, HFFM, HFMF, and HMFF, could share a matriclan with WFF, WFFF, WFFM, WFMF, or WMFF; but they couldn’t share a patriclan.

However:
H and W could still be each other’s sextuple half-third-cousins, in 36 different ways!
Each party has three great-great-grandfathers — their MMFF and MFMF and FMMF — each and any of whom could be the same person as any one (but only one) of those three great-great-grandfathers of the other party.
In fact, there are six ways each such great-great-grandfather of either party could be matched up to also be one such great-great-grandfather of the other party.
Independently and simultaneously, each party has three great-great-grandmothers — their FFMM and FMFM and MFFM — each and any of whom could also fill any one (but only one) of those same great-great-grandmother “slots” in the other party’s family tree.
And there are six ways all of those great^2-grandmas of each party could be one of those GGGMothers of the other party.
Six times six is thirty-six.
So there are 36 ways H and W could be each other’s sextuple-half-third-cousins, if the culture uses only matriclans and patriclans.
If that happened then (provided I’m calculating right) they’d share only 6/(2^7) = 6/128 = 3/64 = 4.69% (about) of their variable autosomal genes. That’s a fraction over 1 chromosome’s worth. [edit:] I forgot that since they are sextuple half-third-cousins, the denominator should be 256=2^8 instead of 128=2^7. So they share 6/256=3/128=2.344%, on average and approximately, of their variable autosomal genes. That’s still between 1.0312 and 1.125 chromosomes, because I did the next calculation wrong, too. [/edit] That might be acceptable; on average only about one in four of their joint offspring together would inherit this chromosome from both parents, and there’s a (57.273%, I think?) probability there isn’t any harmful recessive gene on that chromosome. (The average human carries about 21 harmful recessive genes, so most of us have several (maybe around 25?) chromosomes with no such gene on them.)

But, now might be a good time to consider how using geuns or “Mundugumor ropes” or alterclans might help.
Suppose everyone has an alterclan-name inherited from the parent of the opposite sex.
If we want to keep track of all those ancestors for the past seven generations, along lines in which at most one child-to-parent link was between a child and parent of the same sex, each party would be tracking eight alterclan names.
H would be tracking:
His own alterclan (which includes H himself, and HM, HMF, HMFM, H((MF)^2), HM((FM)^2), H((MF)^3), and HM((FM)^3));
HF’s alterclan (HF, HFM, HFMF, H((FM)^2), HF((MF)^2), H((FM)^3), HF((MF)^3));
HMM’s alterclan (HMM, HMMF, HMMFM, HM((MF)^2), HMM((FM)^2), HM((MF)^3));
HMFF’s alterclan (HMFF, HMFFM, HMFFMF, HMF((FM)^2), HMFF((MF)^2));
HMFMM’s alterclan (HMFMM, HMFMMF, HMFMMFM, HMFM((MF)^2));
H((MF)^2)F’s alterclan (HMFMFF, HMFMFFM, HMFMFFMF);
HMFMFMM’s alterclan (HMFMFMM and HMFMFMMF);
And HMFMFMFF’s alterclan (H((MF)^3)F).

W would track
Her own alterclan;
WM’s alterclan,
WFF’s alterclan;
WFMM’s alterclan;
WFMFF’s alterclan;
WFMFMM’s alterclan;
WFMFMFF’s alterclan; and
WFMFMFMM’s alterclan.

To me this is harder to keep track of eight alterclans than eight patriclans and eight matriclans. But I don’t know whether it’s objectively harder, or it’s just not what I’m used to.

At any rate;
This now means that W has one greatgreatgrandfather, namely WMMFF, who could be either one of two types of H’s greatgreatgrandfather, namely HMMFF or HFMMF.
And H has one GGGrandmother, HFFMM, who could be either WFFMM or WMFFM.
So this lets H and W be each other’s double-half-third cousins in any of four ways.

Let’s consider what kind of burden this puts on young people seeking a spouse.

I’d like to see what it would take to make sure about half the otherwise-eligible members-of-the-opposite-sex are probably not ruled “too consanguineous” by these systems.

If we use only patriclans, or only matriclans, or only alterclans, and require each party to keep track of eight such clans, and not share any of them with the other party;
Then, as long as society has at least 100 clans in total, and they’re all about equally numerous, then on average a bit more than half of the otherwise-eligible members of the opposite sex, will not be considered too consanguineous.

If a society has at least 193 of each type of clan, then assuming they’re all equally numerous and uncorrelated, a bit fewer than five out of seven but a bit more than twelve out of seventeen members of the opposite sex, will not be too consanguineous because of one clan system. So we can expect a bit more than half (less than (5/7)^2 but more than (12/17)^2) of the MOTS to be not ruled too consanguineous by either of two clan systems (assuming each intersection of two clans from different systems — say, a patriclan and a matriclan — have roughly an equal number of eligible bachelors and maidens, and there are at least 193 clans in each of the two systems.)

If society has at least 285 clans of a given kind, and all are equally numerous in each age and each sex, then we can expect (1/2)^(1/3) — a bit less than 80% — of the otherwise-eligible MoTS to not be ruled too consanguineous by any one of these clan-systems.
So if we use all three systems, and have 285 clans in each system, with similar caveats about there being enough marriageable people of each sex in each combination of three clans, and that number being roughly equal, then, still a bit more than half (a bit less than .512 = (.8)^3) the MOTS one encounters won’t be considered too consanguineous by any of the three clan systems.

Note, though, that going back seven generations does not prevent the couple from sharing both a greatgreatgrandfather and a greatgreatgrandmother.
That’s only four generations back. But since we only consider lines containing at most one ancestress; or lines containing at most one male ancestor; or lines containing at most one instance of son-to-father or daughter-to-mother links; we’re considering something fewer than 108 of the 255 people in each party’s seven-generation tree of ancestors. In other words only at most about 42% of each party’s 7-generations-or-closer ancestors must be different from all of at most about 42% of the other party’s 7-generations-or-closer ancestors.
The other about 57% of the ancestors in either party’s 7-generation family tree, can appear anywhere at all in the other party’s family tree; even in the 42% we were just talking about.

This might be alright, though, because double-half-third-cousins share only about 1/64 or 1/128 of their variable autosomal genes inherited from their common shared four-generations-ago ancestors. That’s at most about three-fourths of a chromosome’s worth, if they’re RL humans. There’s only about three chances in sixteen —— less than one in five —— that any given child will inherit any variable autosomal gene from both parents. Unless they plan on having more than five children, they’re probably safe. On the other hand, if one of their children is born with some congenital defect that they suspect is familial, they should probably get genetic counseling to find out whether any of their other shared blood-relatives have or probably have such a defect, and take that advice into consideration when deciding whether or not to beget and conceive a next child by conventional, natural means.