Neo Sindarin - Reconstructed duodecimal system
Reconstructed duodecimal system
Imagine that converting from the decimal system to duodecimal works like converting from kilometres to miles. A certain distance is the same, but it's represented by different numbers.
The system of base 12 is called the duodecimal system. In that system, instead of using 10 digits, we use 12. That means that we need two missing algarisms. So, after the algarism nine (9), we use, in English, two new algarisms we will call dek and el.
In a duodecimal place system, based on the standards laid out by the Dozenal Societies of America and Great Britain (organisations promoting the use of duodecimal), ten (or dek) is written as A (or ᘔ), eleven (or el) is written as B (or Ɛ), twelve is written as 10, meaning "1 dozen and 0 units", instead of "1 ten and 0 units", whereas 12 means "1 dozen and 2 units" (i.e. the same number that in decimal is written as "14"). According to this notation, 50 means sixty (= five times twelve), 60 means seventy two or "half a gross" (= six times twelve), 100 means one hundred forty-four (= twelve times twelve) or "1 gross", 1000 means one thousand seven hundred twenty eight or "1 great gross", and 0.1 means "1 twelfth" instead of "1 tenth".
These are reconstructed names of the numbers in duodecimal:
0 lad 10 rast 1 min 11 rasdmin 2 tâd 12 rastas 20 tadrast 3 neledh 13 rasneledh 30 neledhrast 4 canad 14 raschanad 40 canadarast 5 leben 15 rathleben 50 leberast 6 eneg 16 rasteneg 60 enegrast 7 odog 17 rastodo 70 odôrast 8 tolodh 18 rastsol 80 tolodhrast 9 neder 19 rasneder 90 nederrast A pae 1A rasche A0 paerast 100 host (gross) B minib 1B rasdmib B0 mibrast 1000 hû (great-gross)
The words in red are reconstructions based on other terms we have available. These are not widely used and very hypothetical.
Some prefer to describe duodecimal numbers using the known terms, like for example 13 as neledh rast ("three dozen" or "a dozen and three".) In my opinion, if the terms in decimal are compound words, they should also be compound words in duodecimal. I will lay out both approaches here and the reader decides which one s/he prefers.
The same way it works with decimals, the words for gross and great gross are pluralised. So 200 is "hyst dâd" and 2000 is "hui dâd".
Writing cardinal numbers
As explained in the main page, in Sindarin, we break down number terms in reverse order.
In duodecimal system, things get confusing even in English.
The examples below mirror the decimal examples in the main page.
It's important to stress here the equivalences:
70012 in duodecimal is exactly the same amount of a thing as 100810 in decimal.
"70012" means 7 gross, and a gross is 14410. 14410 × 7 = 100810.
The number is named differently, it has different algarisms, but it's the same amount.
Ordinal numbers
Just like decimal numbers, duodecimal ordinal numbers use the suffix -ui:
0 -- 10 rastui 1 minui 11 rasdminui 2 tadui 12 rastasui 20 tadrastui 3 nelui 13 rasneledhui 30 neledhrastui 4 canthui 14 raschanadui 40 canadarastui 5 levnui 15 rathlebenui 50 leberastui 6 enchui 16 rastenegui 60 enegrastui 7 othui 17 rastodoui 70 odarastui 8 tolthui 18 rastsolui 80 tolodhrastui 9 nedrui 19 rasnederui 90 nederrastui A paenui 1A rascheui A0 paerastui 100 hostui B mibui 1B rasdmibui B0 mibrastui 1000 hûthui ?