# “Score”, “dozen” and other “odd” numbers

#### Apollodorus

##### Senior Member
“Score”, “dozen” and other “odd” numbers.

Some languages, e.g. Basque, Celtic, Albanian, show evidence of a vigesimal (base 20) number-system that seems to have passed into other languages like French.

Irish:

fiche, “twenty” = 20 (cf. Proto-Celtic *wikantī, Latin vīgintī, French vingt)

deich ar fiche, “ten and twenty” 10 + 20 = 30

da fiche, “two twenties” = 2 x 20 = 40

deich ar da fiche, “ten and two twenties” 10 + 40 (2 x 20) = 50

This seems to have originated in some substrate language, perhaps Pre-Indo-European. Could “score” and “dozen” be in any way related and what would have been the original language/culture?

• 'Traditional' Welsh (= 'Celtic') is still based on base 20 (ugain), and you can't tell the time nor use ordinals without using this system. In this system 21 is 'one on twenty', 22 'two on twenty' ... 40 'two twenty', ... 50 'ten and two twenty'*, ... 60 'three twenty', 80 'four twenty'.

*Or 'half a hundred'.

This can lead to strange cases using the pre-decimal (1971) currency of the UK.

A 'new' 50 pence coin is interpreted as a 'six twenty piece' (120 old pence) - there being 240 pence (d) in an 'old' pound.

But even within this traditional system, you get strange concepts:

12 is 'twoten', 13 is 'three on ten', 14 is 'four on ten', 15 is 'fiveten', 16 is 'one on fiveten', 17 is 'two on fiveten', 18 is 'twonine* and 19 'four on ten'

*More rarely, 'three on fiveten'.

Base 9 is also extant. 27 is 'threenine' as well as 'seven on twenty'.

You can also count backwards 99* is 'a hundred less one', 98 is 'a hundred less two' ...

*My personal favourite in the Welsh vigesimal system: 'four on fiveten and four times twenty'. (And don't forget to mutate appropriately and correctly as well as according the number to the gender of the noun!)

And did I also say that the preference from say 2 to 12 (or so) is to use the noun counted in the singular and thereafter (with exceptions) to use the 'of + plural' structure? X + plural is an erroneous construction in Welsh ...

'Dwsin' for 12 we borrowed from French.

Could “score” and “dozen” be in any way related and what would have been the original language/culture?

Dozen comes from Latin duodecim (“twelve”)

Etymology: 13th Century: from Old French douzaine, from douze twelve, from Latin duodecim, from duo two + decem ten

(Collins Concise English Dictionary)

*My personal favourite in the Welsh vigesimal system: 'four on fiveten and four times twenty'. (And don't forget to mutate appropriately and correctly as well as according the number to the gender of the noun!)

And did I also say that the preference from say 2 to 12 (or so) is to use the noun counted in the singular and thereafter (with exceptions) to use the 'of + plural' structure? X + plural is an erroneous construction in Welsh ...

'Dwsin' for 12 we borrowed from French.
Yes, it does sound like Celtic languages have certain features that set them apart from other European languages.

Presumably, the vigesimal system comes from counting two times ten fingers? But why duodecimal (base twelve)? And why France, a formerly Celtic-speaking area?

Presumably, the vigesimal system comes from counting two times ten fingers?
- or fingers + toes ...

Duodecimal base
- not a Celtic system, but 12 is useful in having so many factors: 1, 2, 3, 4, 6 and 12. Further, multiply it by 5 and you get 60 - an ancient number base in the middle east (60 seconds in a minute, 60 minutes in an hour - and yet another factorial: 24 hours in a day (12 x 2). The British pre-decimal currency was essentially base 12 (12d = 1s), and the coinage reflected this: 1d, (2d), 3d, 4d, 6d, 12d (= 1s), 24d (= 2s), 30d (= 2/6s), 60d (= 5s).

why France, a formerly Celtic-speaking area?
- I think you are asking how/why we acquired dwsin. It's likely that this followed the Norman Conquest of 1284, but it may also come from Middle English as the first reference to dwsin is in the 15C. (GPC 'dwsin').

. Further, multiply it by 5 and you get 60 - an ancient number base in the middle east (60 seconds in a minute, 60 minutes in an hour

Add to that 360 (degrees in a circle), plenty of factors to play with there!

Yes, it does sound like Celtic languages have certain features that set them apart from other European languages.
This would be a thread to itself. (Unless it already exists ...)

This seems to have originated in some substrate language, perhaps Pre-Indo-European. Could “score” and “dozen” be in any way related and what would have been the original language/culture?
The words have decent IE etymologies, so no, they do not from a substrate language. But the concepts of 20 based counting may be borrowed from a culture before the IE expansion into Europe. 12 based counting in European culture seems to be from Mesopotamian origin but it is not excluded the possibility that there also was a pre IE culture in Europe with 12 based counting. All European number words except score are from a 10 based system of number words. And the word score seems to come from a counting process where you count to 20 in your head and than make a cut, a "score", with a knife in a piece of wood.

Presumably, the vigesimal system comes from counting two times ten fingers?
- or fingers + toes ...

Good point. Especially if the original speakers or counters wore open-toe sandals or boots! 😀
Duodecimal base
- not a Celtic system, but 12 is useful in having so many factors: 1, 2, 3, 4, 6 and 12. Further, multiply it by 5 and you get 60 - an ancient number base in the middle east (60 seconds in a minute, 60 minutes in an hour - and yet another factorial: 24 hours in a day (12 x 2). The British pre-decimal currency was essentially base 12 (12d = 1s), and the coinage reflected this: 1d, (2d), 3d, 4d, 6d, 12d (= 1s), 24d (= 2s), 30d (= 2/6s), 60d (= 5s).

why France, a formerly Celtic-speaking area?
- I think you are asking how/why we acquired dwsin. It's likely that this followed the Norman Conquest of 1284, but it may also come from Middle English as the first reference to dwsin is in the 15C. (GPC 'dwsin').
Well, base-twelve currency seems to suggest a bit more than just coincidence. And duodecimal counting probably goes much further back than the division of the day into twelve hours, etc.

If anything, it may have to do with the division of the year into twelve months based on the phases of the moon, which must have preceded the concept of "hour" by millennia. So, it may have an autochthonous European origin.

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Dozen comes from Latin duodecim (“twelve”)
Yes, the existence of the “odd” numeral “dozen” suggests that many people find or found it easy to count in twelves. (Like they used to count pennies, and still count eggs). But the word “dozen” has a clear origin in a decimal system.

Swedish:
Dussin - dozen (12)
Gross - from French douzaine grosse (grand dozen) (12 x12 = 144)
Tjog - 20
Skock - either 3 tjog or 5 dussin = 60
Storhundra - (long hundred, twelfty), either 6 tjog or 10 dussin = 120
See: Long hundred - Wikipedia

Dozen comes from Latin duodecim (“twelve”)

Etymology: 13th Century: from Old French douzaine, from douze twelve, from Latin duodecim, from duo two + decem ten

(Collins Concise English Dictionary)
In both Swedish (elva, tolv) and English (eleven, twelve) the words for 11 and 12 that doesn't build on the x + 10 as there are in 13 - 19.

In both Swedish (elva, tolv) and English (eleven, twelve) the words for 11 and 12 that doesn't build on the x + 10 as there are in 13 - 19.
Good point. Another thing that might be worth considering is that vigesimal and duodecimal systems are not necessarily mutually exclusive or incompatible.

It looks like in some ancient cultures people were happy to use ten-month calendars alongside twelve-month ones and the same applies to number-systems.

Of course, ultimately, even the vigesimal system is based on 10.

In both Swedish (elva, tolv) and English (eleven, twelve) the words for 11 and 12 that doesn't build on the x + 10 as there are in 13 - 19.
All Germanic languages share the same etymology of numbers 11-19 and all are constructed from a 10 based system though in different ways for 11-12 and for 13-19 which suggest the lack of elementary words for 11 and 12 where felt as a kind of defect in the language which had base words only for 1-10. While 13-19 are constructed based on the logic x+10, as you correctly pointed out and as is still transparent to modern speakers, the Germanic words for 11 and 12 derive from *ainlif-? and *twalif-? (both forms except for possible endings can be considered safe reconstructions because they are attested in Gothic), which means one left/remaining and two left/remaining, respectively with the apparent meanings one/two left [to count beyond ten].

This suggest that the Germanic for 11-12 were constructed in a different context, possibly at a different time, than the words for the numbers 13-19. It would be quite plausible to assume that these two words may be has evolved as a result of contact with cultures or traditions of 12 based counting complementing an older stage of PGm that had only the inherited IE 10 based numbers.

In Finnish the numbers 11 - 19 are constructed as "x of/into the second decade", 11 was in the beginning yksi toista kymmentä, today shorted to yksitoista.
See: -toista - Wiktionary

In Finnish the numbers 11 - 19 are constructed as "x of/into the second decade", 11 was in the beginning yksi toista kymmentä, today shorted to yksitoista.
See: -toista - Wiktionary
This suggests that different number- or counting-systems existed.

What is interesting is that English actually has a word for twenty ("score") that emerged in a previously Celtic-speaking (vigesimal) area. While the word "score" itself may be derived from the action of marking numbers on wood, etc. the concept of "twenty" must have already existed.

And while 20 as a unit probably represents two times 10 fingers, it is more difficult to see why 12 became a unit - unless it is connected with the division of the year into 12 lunations/months.

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The numb12 could well have to do with astronomy/astrology, and religion. There are two equinoxes and two solstices, a knowledge humans have had for a long time (think Stonehenge and solstices). That makes it possible to divide the year into four parts. Then you can divide each season onto three parts, for example to honour different deities, as triple deities were common in many religions (and still are today). Both the Western and the Chinese zodiac is divided into 12 signs.

Twelve can be tied to mechanical counting too: if you keep a tally with your thumb against your fingers and count your phalanges starting from the index, you'll arrive at 12 by the time your reach the last phalanx of your pinky.

The numb12 could well have to do with astronomy/astrology, and religion. There are two equinoxes and two solstices, a knowledge humans have had for a long time (think Stonehenge and solstices). That makes it possible to divide the year into four parts. Then you can divide each season onto three parts, for example to honour different deities, as triple deities were common in many religions (and still are today). Both the Western and the Chinese zodiac is divided into 12 signs.

I agree that equinoxes and solstices may have played a role. However, I think the twelve lunations/months making up one year are a matter of simple observation.

If 20 originated in finger-counting (2 x 10 fingers), 12 likely has the same origin, one hand having 4 fingers with 3 joints each: 4 x 3 = 12, as @Swatters says. This also seems to have been the origin of the sexagesimal system (12 x 5 = 60).

Georges Ifrah, The Universal History of Numbers, pp. 94-95

If 12 acquired a special significance through association with the 12 lunations/months, this must have occurred fairly early after which the significance was gradually lost but the use of 12 was preserved in some cultures (alongside finger-counting) with or without a specific name attached to it.

I don't wish to side-track over-much, but I notice you cite Ifrah.

I just want to mention that his account of the Welsh numbers (I have both French and English versions of his book) are absolutely appalling and have often wondered as to his source(s). It is tempting to think that much else of the work is suspect as a result, but as I read in only three languages, I can't vouch/refute any suggestions in languages outwith those.

Yeah, Ifrah is a historian of mathematics, not a linguist. I only cited him re. finger-counting but it might be worth checking his sources. Ta for pointing that out.

In any case, what is clear is that a shift occurs in the numerals at 20 in other European languages. Latin, for example, has decem for 10 but changes to -ginti/ginta (< Proto-Italic *wīgentī?) from 20 to 90. Greek has δέκα déka, “ten” and είκοσι eíkosi “twenty”, etc.

But evidence of a vigesimal number-system is most prominent in Celtic languages, Basque and Albanian.

Albanian:

një 1

dy 2

tre 3

...

dhjetë (“ten”) 10

një-zet (“one-score”) 1 x 20 = 20

dy-zet (“two-score”) 2 x 20 = 40

tri-zetë (dialect, “three-score”) 3 x 20 = 60

Basque:

bat 1

bi 2

hiru 3

lau 4

hamar 10

hogei 20

hogei-ta hamar 20 + 10 = 30

ber(r)-ogei 2 x 20 = 40

ber(r)-ogei-ta hamar 2 x 20 + 10 = 50

hiru(r)-ogei 3 x 20 = 60

hiru(r)-ogei-ta hamar 3 x 20 + 10 = 70

lau(r)-ogei 4 x 20 = 80

lau(r)-ogei-ta hamar 4 x 20 + 10 = 90

It follows that French is identical with Celtic and Basque, e.g., quatre-vingt-dix, “four-score-ten” (90) = Irish ceithre fichid a deic/deich agus ceithre fichid, “four-score and ten/ten and four-score” = Basque laurogeita hamar, “four-score and ten”(90). If Celtic borrowed from Basque, which seems to have a special name for 20, then the system could go even further back in European history.

As regards the dozen, in the monetary system introduced by Charlemagne, one pound of silver (livre) was used to make 12 denarii of 20 solidi each, which shows that the score was used alongside the dozen (Carolingian monetary system - Wikipedia). Additionally, English also has “shock” (a lot of sixty pieces). Selling merchandise by dozens (12s), scores (20s) and shocks (60s) seems to have been common in the Middle Ages.

French douzaine could be formed after vingtaine.

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If Celtic borrowed from Basque, which seems to have a special name for 20, ...

________

There are those who aver that Basque borrowed '20' from Brythonic Celtic. Cf. Welsh ugain which in certain circumstances becomes hugain. The fact that it has this initial h- form irregularly after the prep. ar 'on' may indicate some connection to some pre-Indo-European sourcing. This I can't prove.

I agree that equinoxes and solstices may have played a role. However, I think the twelve lunations/months making up one year are a matter of simple observation.

If 20 originated in finger-counting (2 x 10 fingers), 12 likely has the same origin, one hand having 4 fingers with 3 joints each: 4 x 3 = 12, as @Swatters says. This also seems to have been the origin of the sexagesimal system (12 x 5 = 60).

Georges Ifrah, The Universal History of Numbers, pp. 94-95

If 12 acquired a special significance through association with the 12 lunations/months, this must have occurred fairly early after which the significance was gradually lost but the use of 12 was preserved in some cultures (alongside finger-counting) with or without a specific name attached to it.
If you by "year" mean the solar year of 365/366 days, then there are 12.368 lunations in the solar year, so there are a 13th lunation about once every third year. If the solstices were important, for example for celebrations at Stonehenge, then just counting lunar months would quickly get things out of sync with the solar year.

But evidence of a vigesimal number-system is most prominent in Celtic languages, Basque and Albanian.
Georgian (Caucasus) also uses a vigesimal system.

But even within this traditional system, you get strange concepts:
18 is 'twonine*
...and Breton '18' is 'threesix' (triwec'h)!

There are those who aver that Basque borrowed '20' from Brythonic Celtic. Cf. Welsh ugain which in certain circumstances becomes hugain. The fact that it has this initial h- form irregularly after the prep. ar 'on' may indicate some connection to some pre-Indo-European sourcing. This I can't prove.
It is true that Basque was surrounded by a vast Celtic-speaking area extending from the Atlantic to Anatolia (Galatia) prior to the expansion of Latin and other languages. So, some Celtic borrowing into Basque would be predictable.

On the other hand, Basque seems to be connected with the Pre-Indo-European populations that migrated to Europe from the Near East during the Neolithic. Celtic may have borrowed the vigesimal system from this earlier language family of which Basque was a member.

Interestingly, archaeological and DNA data shows that insular Celtic populations were formed about 2,000 BC when groups from Eastern Europe mixed with others from the Middle East, while traditional accounts (Historia Brittonum, The Book of Invasions) seem to suggest links with Spain or Greece.

Neolithic and Bronze Age migration to Ireland and establishment of the insular Atlantic genome

Are the Irish Descendants of the Ancient Greeks?

In any case, the evidence indicates that different methods have been used to count different types of items since ancient times (e.g., Sumer), so the vigesimal and duodecimal systems should not be regarded as mutually exclusive.

As “twenty/score” has been used extensively in counting livestock, especially sheep (Yan tan tethera - Wikipedia), this means that the vigesimal system may have emerged among pastoralist populations with which the Celts were in contact.

By the way, another “odd” number is the “gross” (12 x 12) = 144. Also “great gross” (12 x 12 x 12) = 1728:

1411 [To export from England to Ireland] unum groos de poyntes. Close Roll, 12 Henry IV 26 April

1480 A groos pointes of sylk of divers colours. Wardrobe Accts. Edward IV in N. H. Nicolas, Privy Purse Expenses of Elizabeth of York (1830) 150

1495–7 Bowes—cc; Strynges—v groce; Arowes—cccc sheffes. in M. Oppenheim, Naval Accounts & Inventories Henry VII (1896) 265

gross, n.³ meanings, etymology and more | Oxford English Dictionary (oed.com)

If you by "year" mean the solar year of 365/366 days, then there are 12.368 lunations in the solar year, so there are a 13th lunation about once every third year. If the solstices were important, for example for celebrations at Stonehenge, then just counting lunar months would quickly get things out of sync with the solar year.
Correct. But the original calendar seems to have been lunar and was based on 12 lunations or lunar cycles. See Old English mōnaþ, “month” < Proto-Germanic *mēnōþs “month” < PIE *mḗh₁n̥s, “moon, month”; Old Irish (pl. míonna) < Proto-Celtic *mīns < PIE *mḗh₁n̥s.

The alignment with the solar year was done by the addition of an intercalary period at intervals of several years, as in Ancient Egypt, Greece, etc.

Again, as with counting, multiple calendars were in use for religious, agricultural or administrative purposes. But 12 remained the basic number of months, though ten-month years also existed - hence December (< decem, “ten”) as the last month of the year in the Roman calendar.

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Twelve is divisible by 2, 3, 4, 6, while 10 is just divisible just by 2, 5. So twelve, a dozen, is quite useful to distribute food item at home, for example.