Counting system of the Figurelandic Welsh language
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 (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
Traditional system
Un
One
ci
dog
ar
on
bymtheg
fifteen
ar
on
hugain
twenty
Un ci ar bymtheg ar hugain
One dog on fifteen on twenty
Un
One
ar
on
bymtheg
fifteen
ar
on
hugain
twenty
o
of
gŵn
dogs
Un ar bymtheg ar hugain o gŵn
One on fifteen on twenty of dogs
Decimal system
Tri
Three
deg
ten
chwe
six
chi
dog
Tri deg chwe chi
Three ten six dog
Tri
Three
deg
ten
chwech
six
o
of
gŵn
dogs
Tri deg chwech o gŵn
Three ten six of dogs
Notes
^"Deng". On-line Welsh Grammar Guide. University of Wales, Lampeter. Retrieved 30 July 2009. [dead link]
^"Deng". On-line Welsh Grammar Guide. University of Wales, Lampeter. Retrieved 30 July 2009. [dead link],"Pump". On-line Welsh Grammar Guide. University of Wales, Lampeter. Retrieved 30 July 2009. [dead link]
