Welsh numerals

The traditional counting system used in the Welsh language is vigesimal, i.e. based on twenties where numbers from 11 to 14 are "x on ten", 16–19 are "x on fifteen" (though 18 is more usually "two nines"); numbers from 21 to 39 are "1–19 on twenty", 40 is "two twenty", 60 is "three twenty", etc.

There is also a decimal counting system, where numbers are "x ten y" unit(s), e.g. thirty-five (35) in decimal is tri deg pump (three ten five) while in vigesimal it is pymtheg ar hugain (fifteen – itself "five-ten" – on twenty).

Numerals

Number Vigesimal system Decimal system
0 sero/dim
1 un
2 dau (m), dwy (f)
3 tri (m), tair (f)
4 pedwar (m), pedair (f)
5 pum(p)
6 chwe(ch)
7 saith
8 wyth
9 naw
10 deg/un deg, deng
11 un ar ddeg
("one on ten")
un deg un
12 deuddeg, deuddeng un deg dau/dwy
13 tri/tair ar ddeg un deg tri/tair
14 pedwar/pedair ar ddeg un deg pedwar/pedair
15 pymtheg, pymtheng un deg pump
16 un ar bymtheg
("one on fifteen")
un deg chwech
17 dau/dwy ar bymtheg un deg saith
18 deunaw/tri/tair ar bymtheg
("two nines"/"three on fifteen")
un deg wyth
19 pedwar/pedair ar bymtheg un deg naw
20 ugain dau ddeg
21 un ar hugain
("one on twenty")
dau ddeg un
22 dau/dwy ar hugain dau ddeg dau/dwy
23 tri/tair ar hugain dau ddeg tri/tair
24 pedwar/pedair ar hugain dau ddeg pedwar/pedair
25 pump ar hugain dau ddeg pump
26 chwech ar hugain dau ddeg chwech
27 saith ar hugain dau ddeg saith
28 wyth ar hugain dau ddeg wyth
29 naw ar hugain dau ddeg naw
30 deg ar hugain
("ten on twenty")
tri deg
31 un ar ddeg ar hugain tri deg un
32 deuddeg ar hugain tri deg dau/dwy
etc.
40 deugain
("two twenty")
pedwar deg
41 deugain ac un
("two twenty and one")
pedwar deg un
50 deg a deugain pum deg
hanner cant ("half a hundred")
51 un ar ddeg a deugain pum deg un
hanner cant ac un
60 trigain
("three twenty")
chwe deg
61 trigain ac un chwe deg un
70 deg a thrigain
("ten and three twenty")
saith deg
71 un ar ddeg a thrigain
("one on ten and three twenty")
saith deg un
80 pedwar ugain
("four twenty")
wyth deg
81 pedwar ugain ac un wyth deg un
90 deg a phedwar ugain
("ten and four twenty")
naw deg
91 un ar ddeg a phedwar ugain
("one on ten and four twenty")
naw deg un
100 can(t)
200 dau gant
300 tri chant
400 pedwar cant
500 pum cant
600 chwe chant
700 saith cant
800 wyth cant
900 naw cant
1000 mil
2000 dau fil/dwy fil
1,000,000 miliwn
1,000,000,000 biliwn
1,000,000,000,000 triliwn

Variation in form

There is some syntactically and phonologically triggered variation in the form of numerals. There are, for example, masculine and feminine forms of the numbers "two" (dau and dwy), "three" (tri and tair) and "four" (pedwar and pedair), which must agree with the grammatical gender of the objects being counted. The numerals for "five", "six" and "hundred" (pump, chwech and cant) also have reduced forms (pum, chwe, can) when they precede the object they are counting. The words for "ten", "twelve", and "fifteen" (deg, un deg dau/deuddeg, un deg pump/pymtheg) have the alternative forms deng, deuddeng, pymtheng used before nasals (which may be the result of mutation) and, occasionally, vowels; these forms are becoming less common.[1] Numerals change as expected according to normal rules of consonant mutation; some also trigger mutation in some following words (see below for details).[2]

Use of the decimal system

The decimal system is widely used, but is rather uncommon for dates and ages. Larger numbers, however, tend to be expressed in this system e.g. 1,965 mil, naw cant chwe deg pump. In referring to years, on the other hand, the number of thousands is stated, followed by the individual digits, e.g. 1965 mil naw chwe(ch) pump. This system appears to have broken down for years after 2000, e.g. whereas 1905 is mil naw dim pump, 2005 is dwy fil a phump.

The Welsh decimal counting system was devised by 19th-century Patagonian Welsh businessmen in Argentina for accountancy purposes. It was recommended to teachers for use in the first Welsh language schools in Patagonia by Richard Jones Berwyn in a book published in 1878. The system was later adopted in Wales in the late 1940s with the beginning of Welsh-medium education.[3]

Use with nouns

The singular form of the noun is used with numbers, but for larger numbers an alternative form is permitted, where o ("of") with the plural noun follows the number. Except where using this plural form, the noun is placed directly after the number but before any parts of the number that are added using ar ("on") in the traditional system.

Nouns are also mutated following many numbers. Un triggers the soft mutation[disambiguation needed] (treiglad meddal) of feminine nouns, other than those beginning with "ll" and "rh", but not masculine nouns. Dau and dwy both trigger the soft mutation (ll and rh included). Tri (but not tair) and chwe trigger the aspirate mutation. Several higher numbers (pum, saith, wyth, deng, deuddeng, and pymtheng) trigger the nasal mutation when used with blynedd ("year(s)"). The part of the number immediately preceding the noun will determine any mutation of the noun. In the plural form with o, the soft mutation is used as is normal after o.

The following example illustrates several of these points:

English Thirty-six dogs .mw-parser-output .interlinear .bold{font-weight:bold}.mw-parser-output .interlinear .smallcaps{text-transform:uppercase;font-size:smaller}UnOnecidogaronbymthegfifteenaronhugaintwentyUn ci ar bymtheg ar hugainOne dog on fifteen on twenty UnOnearonbymthegfifteenaronhugaintwentyoofgŵndogsUn ar bymtheg ar hugain o gŵnOne on fifteen on twenty of dogs TriThreedegtenchwesixchidogTri deg chwe chiThree ten six dog TriThreedegtenchwechsixoofgŵndogsTri deg chwech o gŵnThree ten six of dogs

Notes

1. ^ "Deng". On-line Welsh Grammar Guide. University of Wales, Lampeter. Retrieved 30 July 2009.
2. ^ "Deng". On-line Welsh Grammar Guide. University of Wales, Lampeter. Retrieved 30 July 2009. ,"Pump". On-line Welsh Grammar Guide. University of Wales, Lampeter. Retrieved 30 July 2009.
3. ^ Roberts, Gareth Ffowc (2016). Count Us In: How to Make Maths Real for All of Us. Llandysul, Wales: Gomer Press. ISBN 978-1-78316798-2.