I don't think it these terms are used or even relevant any more in the U.S. either, bilby. (though I'm sure you knew that) These terms are about a century old, at least (not the made-up ones, obviously), and are quite frankly a relic of slavery. (In the U.S.)
The idea of calculating "how black" or "how white" someone is reminds me of an excellent book I read a few years ago called Modern Medea, which, by virtue of the story (microhistory) it told, exposed the seamy underbelly of slavery as being a generational series of rapes that produced children who were increasingly white. People don't often think of this aspect of American slavery.
("Seamy underbelly" may not sound surprising, but I've met a shocking number of apologists for lack of a better term who insist that slavery "wasn't that bad" or that "good masters took care of their slaves." Yes, and they also took care of their livestock. And then there were those masters such as the one in Modern Medea. The system quite simply turned men, women, and children into petty tyrants who were quite free to abuse, torture, and even kill other men, women, and children without repercussion.)
Sorry to get off on a tear there. My point is that these words were developed in the nineteenth century, at least in the U.S., in order to describe "how white" a person was, in a system and culture in which it was terribly important. The words are less used today just because nobody cares as much anymore "how white" a person is (though watching this presidential campaign, I have to wonder).
Still a great word. Kind of like arthropleura--great word, meaning makes you go "eugh!"
I believe that in times past various Australian agencies made such calculations with regard to Aborigines. It's certainly a no-no now. The current definition of Aboriginal would be something like 'identifies as being of Aboriginal descent, and is recognised by the Aboriginal community as being so'. This test is used by government departments spending money that is earmarked for Aboriginal and Torres Strait Islanders. Fractions of ancestry or indeed colour don't come into it.
Or, we could 1. accept that those are awesome words and don't necessarily have to mean anything, and then 2. dork out on some other page. ;)
The other thing is that the -oon doesn't HAVE to mean "a given fraction of black ancestry." I read somewhere a long time ago that someone once asked the president of Haiti (was it?) what percentage of people in his country were white. "Ninety-five percent," he said. Questioner was surprised--what do you mean? Your country's people are mostly black! The answer was that in that country (which may or may not be Haiti, now that I think about it.... Dominican Republic?), if you have any white blood, you're white. That turns "octoroon" on its head, and certainly is different from what we in the United States normally think of as "black" or "white."
So... if I want to call my new invented type of cookie a hexadodecaroon, I'ma gonna. Plthththth.
All measures of ancestry are of the form c / 2^n. Therefore, ancestries of 1/12 are impossible. If you go back enough generations, you can asymptotically approach 1/12, but eventually you'll reach apes, and at some point you have to stop.
Exactly 1/16? I'm not sure that race can be calculated that specifically. Besides, I'd expect that most people have some small portion of every race in their blood. That is, providing race even exists at all.