So a child of a god and mortal is a demigod. What would a child of two demigods be? Would that be a quarter-god? What about a child of a demigod and a mortal?
So a child of a god and mortal is a demigod. What would a child of two demigods be? Would that be a quarter-god? What about a child of a demigod and a mortal?
According to Rick Riordan's faq page:
Q: If two demigods had a child, would that child be a quarter-blood, a demigod, or what?
A: Most half-bloods at Camp Half-Blood don’t live long enough to have children. Their lives are simply too dangerous. If they did have children, the kids would probably pass for normal mortals, since the godly powers get diluted with each generation. If the parents were extremely strong, the child might be more like a demigod. At Camp Jupiter, things are a bit different, as you know if you've read The Heroes of Olympus.
So the answer is that on the Greek side, they're mostly plain Mortal, but if they do inherit powers strongly enough to need to attend Camp, then they're probably just called Semideuses.
On the Roman side however, descendants of demigods do often inherit powers and even those that don't often live in New Rome. And the books give us the term Legacies of [God/dess X] for these descendants.
Rationale: The word demigod does not mean what is currently the supposition of a being who is "half" god and "half" man. (Unless you are referring to the writer of the Percy Jackson novels, then that is EXACTLY what he means. Anything less than that is likely to be mortal.)
In ancient times:
A demigod (or demi-god) is a divine or supernatural being in classical mythology. The term has been used in various ways at different times and can refer to a figure who has attained divine status after death, a minor deity, or a mortal who is the offspring of a god and a human. (Wikipedia: Demigod)
This implies any being who has through:
their physical prowess, skill at arms, superhuman intelligence could achieve godhood and thus become through apotheosis, a demigod.
Anyone who is the scion of a god, may be called a demigod, but upon their death would achieve their godhood status unless revoked by a higher authority.
In the modern parlance:
The term demigod first appeared in English in the late sixteenth or early seventeenth century when it was used to render the Greek and Roman concepts of semideus and daemon. Since then, it has frequently been applied figuratively to people of extraordinary ability.
John Milton states in Paradise Lost that angels are demigods.
Demigods are important figures in Rick Riordan's Percy Jackson books, where many of the characters, including Percy Jackson himself are demigods. In Riordan's work, a demigod is strictly defined as an individual born of one human and one divine parent.
It is unlikely such a further reduction is necessary or desirable when referring to the offspring of divine beings unless there is a further reduction of their extraordinary capacity in which case there is already a word for them: mortal.
Rick Riordan's FAQ corroborates my suspicions:
"If they did have children, the kids would probably pass for normal mortals, since the godly powers get diluted with each generation. If the parents were extremely strong, the child might be more like a demigod."
In actuallity the term demigod isn't necessarily to describe someone that is merely half god half human, but a moral human with the powers of a god. Hence the fact that Heracles is the son of Zeus and Athena, but being poisoned by Hades caused him to lose most of his godlike abilities. Noting that Phesius, the son of Hermes, was never described as a demigod. Therefore having the lineage of a god doesnt grant you the title of demigod. It's only if your powers manifest, and if not, sorry but you are just a mortal.
They would still be half-bloods. If two half-god, half-human people have a child, the child will still be half-god and half-human (25% God + 25% God + 25% Human + 25% Human).
If not, I would say that "Legacy" is the best term, as that is the term the Roman demi-gods use.
What you seem to be looking for (in spite of the other, quite knowledgeable answers posted) is the correct prefix to denote a quarter. In music you have quarter notes, which the British call crotchets. They call sixteenth notes quavers, and a quarter of that a 64th) a demisemiquaver.
In Astronomy, a synchronous orbit is "an orbit in which an orbiting body (usually a satellite) has a period equal to the average rotational period of the body being orbited (usually a planet), and in the same direction of rotation as that body." A semi-synchronous orbit has half of that period, and if the satellite's period is one quarter of the period of the planet, it is said to have a quarter-synchronous órbita.
From these examples you can see that either demisemigod or quarter-god ought to be appropriate.
I guess if you take it biological it would be like that:
Demi(50% God/50% human) + demi (50% God/50% human)
Possibilidades:
A demigod has half divine and half mortal genes. A child of two demigods has 1/4 chance of being mortal 1/2 demigod or 1/4 completely immortal.
Tags percy-jackson