Recently, I was talking to my parents about how I was confused about the way numbers are named in Danish. I’ve been actively studying Danish for the past month and I’m constantly baffled by the numbers, specifically the 10s.
When you first start counting up to 40, they make sense:
- 1 (one): en
- 2 (two): to
- 3 (three): tre
- 4 (four): fire
- 5 (five): fem
- 6 (six): seks
- 7 (seven): syv
- 8 (eight): otte
- 9 (nine): ni
- 10 (ten): ti
- 20 (twenty): tyve
- 30 (thirty): tredive
- 40 (fourty): fyrre
Ok, so far pretty straightforward, and you can even see the connection to the same numbers in English.
Until you get into the 50s, 60s, 70s, and so on:
- 50 (fifty): halvtres
- 60 (sixty): tres
- 70 (seventy): halvfjerds
- 80 (eighty): firs
- 90 (ninety): halvfems
This is where it gets confusing.
Ok, so halv = ‘half’. But, say I’m looking at halvtres and tres, 50 is not half of 60. And similarly, 70 is not half of 80 (assuming the –fjers in halvfjerds is equivalent to firs). And then halvfems (90) is alone – there is no number called fems. Instead, halvfems is followed by et hundrede (100).
And then the second half of these words clearly refer back to single digit numbers: the tres in 50 and 60 comes from tre (3), the -fjerds/firs in 70 and 80 comes from fire (4), and -fems comes from fem (5).
There must be some sort of math-related reason for how these number words are arranged.
I pulled out my Complete Danish grammar and workbook that I was using for my studies and pulled up the chapter which goes over the numbers of Danish. In there, it explained that the numbers for 50 through to 90 were shortened older forms which included an ending meaning “times 20”:
- halvtreds (50) used to be halvtredsindstyve (“two and a half times twenty” which equals 50)
- halvtedje = two and a half (2.5)
- sinds = times
- tyve = twenty (20)
- tres (60) used to be tresindstyve (“three times twenty” which equals 60)
- tre = three (3)
- sinds = times
- tyve = twenty (20)
- halvfjers (70) used to be halvfjersindstyve (“three and a half times twenty” which equals 70)
- halvfjerde = three and a half (3.5)
- sinds = times
- tyve = twenty (20)
- firs (80) used to be firsindstyve (“four times twenty” which equals 80)
- fire = four (4)
- sinds = times
- tyve = twenty (20)
- halvfems (90) used to be halvfemsindstyve (“four and a half times twenty” which equals 90)
- halvfemte = four and a half (4.5)
- sinds = times
- tyve = twenty (20)
That got me thinking about the number 20 specifically. I thought back to learning French in school and, like many other, being baffled by the construction of the French names for 80 and 90: quatre-vingt (four-twenty) and quatre-vingt-dix (four-twenty-ten), respectively. Similarly to Danish, the final name for a number features a mathematical equation totalling the number in question. For instance, with the number 80, the name ‘quatre-vingt’ or ‘four-twenty’ stems from how multiplying 4 by 20 equals 80.
Then I recalled the now-outdated term ‘score’ to refer to twenty of something (“Four score and seven years ago…”), and that got me wondering what the obsession with the number 20 was. So, why did multiple number systems feature it?
After some digging, I learned about the base-20 (also called vigesimal) number system. This is where numbers are counted in sequences of 20, instead of sequences of 10 like they would in a base-10 (or decimal) number system. A base-10 system is what exists in English, where you count from 0 to 9 between each ten and then go back to zero:
| Number | Gloss |
| 20 | twenty |
| 21 | twenty-one |
| 22 | twenty-two |
| 23 | twenty-three |
| 24 | twenty-four |
| 30 | thirty |
| 31 | thirty-one |
| 32 | thirty-two |
| 40 | forty |
| 41 | forty-one |
| 42 | forty-two |
A base-20 system like what French has, meanwhile, counts from 0 to 19 before going back to zero:
| Cardinal number | French name | Gloss |
| 60 | soixante | sixty |
| 61 | soixante-et-un | sixty-and-one |
| 62 | soixante-deux | sixty-two |
| 63 | soixante-trois | sixty-three |
| 64 | soixante-quatre | sixty-four |
| 65 | soixante-cinq | sixty-five |
| 70 | soixante-dix | sixty-ten |
| 71 | soixante-et-onze | sixty-and-eleven |
| 72 | soixante-douze | sixty-twelve |
| 73 | soixante-treize | sixty-thirteen |
| 80 | quatre-vingts | four-twenties |
| 90 | quatre-vingt-dix | four-twenty-ten |
| 91 | quatre-vingt-onze | four-twenty-eleven |
In the case of French specifically, this base-20 numbering system is borrowed from the Celtic languages, specifically Gaulish, an extinct language that was spoken in what is now France until the 6th century CE. However, the base-20 counting system is still founding in Celtic languages spoken today, including Breton, Welsh, Scottish Gaelic, and Manx Gaelic:
| Breton | Welsh | Scottish Gaelic | Manx Gaelic | |
| 20 | ugent | ugain | fichead | feed |
| 30 | deich ar fhichead ‘ten over twenty’ fichead ‘s a deich ‘twenty and ten’ | jeih as feed ‘ten and twenty’ | ||
| 40 | daou-ugent ‘two times twenty’ | deugain ‘two twenties’ | dà fhichead ‘two twenties’ | daeed ‘two twenties’ |
| 50 | dà fhichead ‘s a deich ‘two twenty and ten’ | jeih as daeed ‘ten and two twenties’ | ||
| 60 | trigain ‘three twenties’ | trì fichead ‘three twenties’ | tree feed ‘three twenties’ | |
| 180 | naoidh fichead ‘nine twenties’ |
While Danish also includes ‘tyve’ as a (hidden) base number for 50 to 90, like I showed earlier, unlike the Celtic languages and French, this is just in name alone. Danish numbers still follow a base-10 counting system (i.e. 70 is ‘halvfjers’ instead of ‘ti-og-tres’ [sixty-and-ten]).
Other languages that use their word for 20 as a base in the words for other numbers include Albanian (40 is dyzet or ‘2 times 20’), Basque (40: berrogei ‘two-score’, 60: hirurogei ‘three-score’, 80: laurogei ‘four-score’), Georgian (40: ormotsi ‘2 times 20’, 31: otsdatertmeti ‘twenty and eleven’), and Aini (40: tu hotnep ‘two twenties’, 30: wanpe etu hotnep ‘ten more until two twenties’).
I could keep going on, but hopefully you get the picture with this.
Unfortunately for myself, none of this helps me to remember the 10s in Danish. For now, I may have to accept defeat.
Have your own language question you want answered? Leave a comment below!
References:
- Complete Danish Beginner to Intermediate Course
- Vigesimal – Wikipedia, the Free Encyclopedia
- Why does French have that eccentric number system for seventy, eighty and ninety? – The Guardian
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