The traditional counting system used in the Welsh language

Welsh language

Welsh is a member of the Brythonic branch of the Celtic languages spoken natively in Wales, by some along the Welsh border in England, and in Y Wladfa...

is vigesimal

Vigesimal

The vigesimal or base 20 numeral system is based on twenty .- Places :...

, i.e. based on twenties, as in the French numerals for 60-99, where numbers from 11–14 are "x on ten", 16–19 are "x on fifteen" (though 18 is more usually "two nines"); numbers from 21–39 are "1–19 on twenty", 40 is "two twenty", 60 is "three twenty", etc.

There is also a decimal counting system, which is widely used, especially in Patagonian Welsh, where numbers are "x ten y" unit(s), e.g. thirty-five in decimal is (three ten five) while in vigesimal it is (fifteen – itself "five-ten" – on twenty).

Numerals

Number	Vigesimal system	Decimal system
0
1
2	(m), (f)
3	(m), (f)
4	(m), (f)
5
6
7
8
9
10	,
11	("one on ten")
12	,
13
14
15	,
16	("one on five-ten")
17
18	("two nine")
19
20
21	("one on twenty")
22
23
24
25
26
27
28
29
30	("ten on twenty")
31
32
etc.
40	("two twenty")
41	("two twenty and one")
50	("half a hundred")
51
60	("three twenty")
61
70	("ten on three twenty")	saith deg
71	("one on ten on three twenty")
80	("four twenty")
81
90	("ten and four twenty")
91	(" one on ten and four twenty")
100
200
300
400
500
600
1000
2000
1,000,000
1,000,000,000

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" ( and ), "three" ( and ) and "four" ( and ), which must agree with the grammatical gender

Grammatical gender

Grammatical gender is defined linguistically as a system of classes of nouns which trigger specific types of inflections in associated words, such as adjectives, verbs and others. For a system of noun classes to be a gender system, every noun must belong to one of the classes and there should be...

 of the objects being counted. The numerals for "five", "six" and "hundred" (, and ) also have reduced forms (, , ) when they precede the object they are counting. The words for "ten", "twelve", and "fifteen" (, , ) have the alternative forms , , used before nasals (which may be the result of mutation) and, occasionally, vowels; these forms are becoming less common. Numerals change as expected according to normal rules of consonant mutation

Consonant mutation

Consonant mutation is when a consonant in a word changes according to its morphological and/or syntactic environment.Mutation phenomena occur in languages around the world. A prototypical example of consonant mutation is the initial consonant mutation of all modern Celtic languages...

; some also trigger mutation in some following words (see below for details).

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 . In referring to years, on the other hand, the number of thousands is stated, followed by the individual digits, e.g. 1965 . This system appears to have broken down for years after 2000, e.g. 2005 is .

Use with nouns

The singular form of the noun is used with numbers, but for larger numbers an alternative form is permitted, where ("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 ("on") in the traditional system.

Nouns are also mutated following many numbers. triggers the soft mutation

Welsh morphology

The morphology of the Welsh language shows many characteristics perhaps unfamiliar to speakers of English or continental European languages like French or German, but has much in common with the other modern Insular Celtic languages: Irish, Scottish Gaelic, Manx, Cornish, and Breton. Welsh is a...

(treiglad meddal) of feminine nouns, other than those beginning with "ll" and "rh", but not masculine nouns. and both trigger the soft mutation (ll and rh included). (but not ) and trigger the aspirate mutation. Several higher numbers (, , , , and ) trigger the nasal mutation when used with ("year(s)"). The part of the number immediately preceding the noun will determine any mutation of the noun. In the plural form with , the soft mutation is used as is normal after .

The following example illustrates several of these points:

English	Thirty-six dogs
Traditional system	Un ci ar bymtheg ar hugain One dog on fifteen on twenty
	Un ar bymtheg ar hugain o gŵn One on fifteen on twenty of dogs
Decimal system	Tri deg chwe chi Three ten six dog
	Tri deg chwech o gŵn Three ten six of dogs