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In the Harry Potter books, there is a small bit in the story where the currency of the society is described. The names are a bit weird, but ultimately, it's a parody of the old pounds, shillings and pence where there is a medium unit in between and none of them are powers of ten.
The creator of this system clearly hasn't really appreciated how the system works, because the numbers are not really chosen particularly intelligently. The system in particular is that there is 29 *shillings to the *pound, and then also 17 *pence to the *shilling. I think it's utterly remarkable how the creator of this system managed to stumble on not one but two intensely jagged prime numbers, making this a system completely impossible to occur in any realistic manner.
Of course, in a sense this is to be expected. It is a fictional story after all, and there's no need to think about any significant backstory – certainly, other parts of the story and ancillary details given by the team have given ample evidence that they certainly have not. And second, there is value in saying "ha-ha, pounds shillings and pence are stupid because they don't use metric numbers. Also maths is hard and I want to make sure everyone knows, even the people who are otherwise good at maths."
For the latter point, I think the idea is solid but this execution has missed the plot somewhat. Consider a related observation that has also bedevilled many: "it is intolerable how many words in English have completely opaque orthography." This point is true, but this system would analogise to making a language where what is spelt has absolutely no relationship to how the word is pronounced whatsoever, and you don't get any hints like a picture component or punning. And this has the additional benefit that some civilisations have actually did this. (Most notably, there's Book Pahlavi, where the alphabet inherited from the Phoenicians have been made so cursive that individual letters lose their identity and they can only be found on a word-by-word basis, /and/ the words typically don't spell words written in the Iranian languages that the script is writing but instead the ancient Aramaic words that the languages descend from, which frequently use completely different lemmata.)
So I think there is a bit of a missed opportunity here, because a "no-twos" three-tier currency system is certainly something that could have organically arisen with humans. It will still fulfil the "look at this obtuse maths" bit that I have the feeling is the intent, which while I think is a bit oafish I will preserve anyway.
Let me introduce you to this particular one that I think is worth discussing. Now the idea is that we have a system that looks like pounds shillings and pence, but we want to omit even numbers because it is funny. Fortunately, two is not the only number that is important, and we also have three, five and seven as reasonably good numbers to use when making a coinage system. Therefore let's consider a system of:
That makes 1 *shilling equal to 15 *pence.
Notice that 21 = 3 × 7 and 15 = 3 × 5. The numbers are therefore all 7-smooth and therefore one can be reasonably comfortable with handling them and these can even be useful in daily life when dividing things up.
Despite its obvious inferiority to even the real £sd system, there's plenty to love about it. For example, it has a 7 in it which means that turning weekly divisions into daily ones is given a lot of help. And also, that 315 can be seen on a compass mark (it's the northwest bearing) should make it fairly obvious to any user that it's 7 lots of 45, so this helps with understanding the system.
Certainly someone having undergone enculturation with any system would find all manners of excuses to show how the system they have lived on makes total sense and doesn't need change, but here the system at least doesn't actively resist any such justification and it has some things that are simply defensible even to an enemy. It may not be a /good/ system, and writing a story doesn't mean that you have to make a /good/ system, but just a /good enough/ system, and there can be reasonable justifications for them.
The takeaway to all this is that it would be nice after all, if you are creating a system for a story, that the system does not obviously have signs of "oh I just chose that without thinking". It's obviously not tolerated when it's about writing characters in stories, and this is well known to the point where there's actual writing advice about how to "write characters deeply", but once again there's a bit of a deficiency in the aesthetic sense when it comes to complex systems that are not easily packaged into a single thing called "a character" so this happens all the time, even in (mostly) widely respected children's fiction.
A lemma is a word that is "its own thing" in the context of its own language. For instance, the words "fire" and "pyre" are two different lemmata, because within English you cannot find a direct relationship between them that you can also find in other English words within English. "Fire" and "pyre", however, do come from the same /etym/, in that they come from the same word which ultimately is the a single /proto-Indo-European/ lemma: "fire" through Germanic, and "pyre" through Greek.