Knowledge base · Part VIII — Pronouns, Demonstratives, Postpositions, and Numerals · this topic as a network
54. The Vigesimal Numeral System
How does the language structure its numeral system, and what are the grammatical categories of numerals?
Numeral determiners require the bound noun pe/p, reanalyzed as a non-human classifier suffix, to form an independent nominal meaning 'N things'. (Bugaeva 2012: 470–471) Human numerals are formed by suffixing -n after a vowel or -iw after a consonant to numeral stems. (Bugaeva 2012: 470–471) Ainu has a vigesimal numeral system based on ten and twenty. (Bugaeva 2012) Ainu has non-composite numerals from 'one' to 'six' as well as for 'ten' and 'twenty', but lacks a native non-composite word for 'hundred'. (Bugaeva 2012) Numerals from 'six' to 'nine' are composed by their distance from 'ten'. (Bugaeva 2012) All numerals over twenty are constructed on a base of twenty through multiplicative, subtractive, and additive combinations. (Bugaeva 2012) In Karafuto dialects, numerals above ten are formed decimally, using kunkutu for tens units and tanku for hundreds units. (Tangiku 2022: 9.3)
Overview
What are the grammatical categories of numerals and how do they differ in syntax?
Numerals above 11 rarely occur in recorded texts, and among numbers 10 and below, sine '1', tu '2', re '3', and iwan '6' are used much more frequently than the others. (Nakagawa 2024: 468)
The numeral roots 1–10 and the three form classes
What are the three paradigmatic shapes for each numeral value from 1 to 10 and 20?
The basic numeral morphemes in Ainu are used exclusively in adnominal position. (Refsing 1986: 111, 112) In Hokkaido Ainu, only the numerals 1 to 5 and 10 are basic morphemes, while 6 to 9 are derived subtractively from 10. (Refsing 1986: 111, 112) The simple cardinal numerals from 1 to 10 are shine, tu, re, ine, ashikne, iwan, arwan, tupesan, shinepesan, and wan. (Kindaichi & Chiri 1936) The numerals from 6 to 9 are formed subtractively relative to 10 (wan): iwan (10-4), arwan (10-3), tupesan (10-2, 'two lacking'), and shinepesan (10-1, 'one lacking'). (Kindaichi & Chiri 1936) The numeral adnominals from 1 to 10 are sine (1), tu (2), re (3), 'iine (4), 'asne (5), 'iwan (6), 'arawan (7), tupesan (8), sinepisan (9), and wan (10). (Murasaki 2025: 101) For non-human numeral nouns, the suffix is identical to the formal noun p ~ pe 'thing', taking -p after vowel-final stems (1-5) and -pe after consonant-final stems (6-10). (Nakagawa 2024: 464) For human numeral nouns, the suffix is -n for 1-5 and -iw for 6-10, an element that otherwise appears only in very limited words like ne-n 'who' and hempak-iw 'how many'. (Nakagawa 2024: 464) In counting, the numbers from 1 to 10 in the Saru dialect are sinep, tup, rep, inep, asik, iwan, arwan, tupes, sinepes, wan. (Nakagawa 2024: 466) The basic numeral is always used adnominally. (Refsing 1986: 45) The subclass of quantity nouns comprises numerals and quantity expressions. (Refsing 1986: 75) The numeral iwan 'six' is historically composed of i- (< ine 'four') and wan 'ten' (i.e. 'four deducted from ten'). (Refsing 1986: 111) According to Chiri, the numeral arwan 'seven' represents 'three deducted from ten', where ar- derives from re 'three'. (reported in Refsing 1986: 111) Tupesan 'eight' and sinepesan 'nine' are traditionally analyzed as tu/sine + p + e + san ('two/one - thing - thereby - ten'), with san originating from wan. (reported in Refsing 1986: 111) Patrie reconstructs tupesan and sinepesan as originating from tu-upis and sine-upis, based on the Kuril Ainu numeral upis 'ten'. (reported in Refsing 1986: 111) The final -an in tupesan and sinepesan may possibly be related to the existential verb an. (proposed in Refsing 1986: 111) Chiri proposes that the element -ne in sine 'one', ine 'four', and asikne 'five' is an adjectivizing suffix deriving adjectives from nouns. (reported in Refsing 1986: 111) Refsing suggests that if -ne in the numerals sine, ine, and asikne is an independent morpheme, it should be analyzed as the copula in adnominal position. (proposed in Refsing 1986: 111) Chiri derives sine 'one' from simompet 'thumb' and re 'three' from rimompet 'middle (third) finger'. (reported in Refsing 1986: 111) On the basis of comparative evidence, ar may be an older morpheme for 'one'. (reported in Refsing 1986) Ainu numerals distinguish between counting forms used when reciting numbers ('one, two') and numeral nominal forms used nominally in sentences, differing from five through nine. (Satō 2008: 256) The numeral counting forms from 1 to 10 are sinep (1), tup (2), rep (3), ínep (4), asik (5), iwan (6), arwan (7), tupes (8), sinepes (9), and wanpe (10). (Satō 2008: 257) Numeral nouns distinguish inanimate/non-human forms (usable also for humans) and human-specific forms from 1 to 10: non-human sinep, tup, rep, ínep, asiknep, iwanpe, arwanpe, tupesanpe, sinepesanpe, wanpe; human sinen, tun, ren, ínen, asiknen, iwaniw, arwaniw, tupesaniw, sinepesaniw, waniw. (Satō 2008: 257) The numeral adnominals from 1 to 10 are sine (1), tu (2), re (3), íne (4), asikne (5), iwan (6), arwan (7), tupesan (8), sinepesan (9), and wan (10). (Satō 2008: 258) Numerals can be nominalized by suffixing the nominalizer -p(e) or -n. (Shibatani 1990: 42)
The vigesimal counting architecture
How are numbers above 10 formed using additive, multiplicative, and subtractive strategies?
In Shizunai Ainu, numerals from 11 to 19 are formed by adding 1 to 9 to ten using the verb ikasma 'to be in excess'. (Refsing 1986: 113) In Shizunai Ainu, numerals from 21 to 29 are formed by adding 1 to 9 to hotne 'twenty' using ikasma. (Refsing 1986: 113) In Shizunai Ainu, decades from 30 to 100 are counted vigesimally, with even decades as multiples of hotne and odd decades formed subtractively with wan e 'ten less than'. (Refsing 1986: 113) The numerals from 11 to 19 are constructed by placing the smaller number first, followed by the particle ikashma 'remainder/plus', and then wan 'ten' (e.g. shine ikashma wan 'eleven'). (Kindaichi & Chiri 1936) The numeral hotne 'twenty' is based on the noun hot 'a set' (concrete form hochihi), originally referring to all twenty fingers and toes of a person. (Kindaichi & Chiri 1936) The numerals 30, 50, 70, and 90 are formed subtractively from the even twenties using the affix -e- 'with', as in wan-e-tu-hotne 'thirty' (20 × 2 - 10). (Kindaichi & Chiri 1936) The numeral suffix -pish originates from a root meaning 'to count', which is also reflected in kotan pishno shirkush, upish iwan-sui, and pishki. (Kindaichi & Chiri 1936) The prefix e- is used in fractional numeral expressions such as emko-e-tup 'one and a half' (lit. 'two with half') and wampe-e-tu-hot 'thirty' (lit. 'forty with ten'). (Kindaichi & Chiri 1936) In older usage, the numeral for 20 is hohne. (Murasaki 2025: 44) The numeral hot means '20'. (Murasaki 2025: 44) The numeral prenominal hotne '20' is derived from the root hot. (Nakagawa 2024: 461) In the Saru dialect, numeral prenominal expressions for 11 to 19 have the structure: units numeral + ikasma 'surpass/exceed' + wan '10'. (Nakagawa 2024: 462) In the Saru dialect, numeral prenominals for 21 to 29 follow the structure: units numeral + ikasma + hotne '20'. (Nakagawa 2024: 462) Multiples of 20 such as 40, 60, 80, and 100 are expressed as numeral prenominal + hotne (e.g., tuhotne, rehotne, inehotne, asiknehotne). (Nakagawa 2024: 463) Odd tens like 30, 50, 70, and 90 are constructed subtractively from 40, 60, 80, and 100 using wan e-[multiple of 20] (wan etuhotne, wan erehotne, wan einehotne, wan easiknehotne), meaning 'with 10 (less) towards the multiple'. (proposed in Nakagawa 2024: 463) In counting, '20' is represented neither by the numeral prenominal hotne nor by the numeral noun hotnep, but by the bare root hot. (Nakagawa 2024: 467) The numeral for 'twenty', hot, is a basic morpheme meaning 'a set', suggesting a complete set of fingers and toes in a human being. (Refsing 1986: 111) The numeral for 'twenty', hot, is a basic morpheme meaning 'a set', suggesting a full set of fingers and toes. (Refsing 1986: 112) When counting with -p(e), twenty is expressed as hot with -pe dropped. (Refsing 1986: 113) Multiples of twenty are expressed using hot: sine hot (20), tu hot (40), re hot (60), íne hot (80), and asikne hot (100). (Satō 2008: 258) 'Twenty-two' is expressed as tup ikasma sine hot ('two excess twenty'). (reported in Satō 2008: 258)
Numeral syntax
What are the syntactic positions of prenominals, numeral nouns, and counting-off forms?
Numerals are divided into simple forms (adjectival forms), which are placed attributively before nouns, and complex forms, which carry numeral classifiers and function as verb complements or postnominal adverbial modifiers. (Kindaichi & Chiri 1936) All compound (nominal) forms of numerals are used adverbially. (Kindaichi & Chiri 1936) Numerals take the suffix -ne to form adverbs such as shinenne 'alone' or tunne 'two people together'. (Kindaichi & Chiri 1936) Numerals in Ainu span multiple parts of speech and are classified into three word classes: numeral prenominals (prenominals/adnominals), numeral nouns (nouns), and counting numerals (interjections). (Nakagawa 2024: 461) The stem of a numeral is grammatically a prenominal (adnominal), and the numeral prenominals for 1 to 10 are shared across many dialects as sine '1', tu '2', re '3', ine '4', asikne '5', iwan '6', arwan '7', tupesan '8', sinepesan '9', and wan '10'. (Nakagawa 2024: 461) Depending on the following noun, the numeral '1' can be expressed by ar- (or assuy before suy 'time'). (Nakagawa 2024: 461) Because numeral prenominals are prenominals (adnominals), they are placed before a noun to modify it. (Nakagawa 2024: 462) Numeral nouns are divided into two types: those used for counting non-human things and those used for counting human beings. (Nakagawa 2024: 463) Unlike numeral prenominals, numeral nouns can form a noun phrase on their own. (Nakagawa 2024: 464) When a numeral noun is used together with a noun, it is placed after the noun (e.g., tuki sinep 'one cup'). (Nakagawa 2024: 464) In compound numerals such as '31' (sinep ikasma wanpe etuhotnep), each constituent element must appear in the form of a numeral noun. (Nakagawa 2024: 466) When combining a complex numeral with a noun, as in '31 dogs', the noun must be repeated after each numeral prenominal (e.g. sine seta ikasma wan seta etuhotne seta). (Nakagawa 2024: 466) A complex numeral modifying a noun can partially replace numeral prenominals with numeral nouns, as in sinep ikasma wan sike '11 bundles' or sinen ikasma wan poyson '11 children'. (reported in Nakagawa 2024: 466) Repetition of the noun across numeral elements can be avoided by preposing the noun to the complex numeral, as in seta, sinep ikasma wanpe etuhotnep 'dogs, 31'. (Nakagawa 2024: 466) Because counting numerals are used independently of clauses, their part of speech is interjection. (Nakagawa 2024: 467) Numerals precede the nouns that they quantify. (Shibatani 1990: 42) Nominalized numerals occur after the nominals that they quantify or alone. (Shibatani 1990: 42)
Numerals with the copula ne
How do numeral nouns combine with the copula to predicate a count or form an adverbial?
Special number uses and lexicalized expressions
What extended or bleached meanings do numeral roots carry in fixed expressions?
The numeral iwan 'six' is the sacred number of the Ainu and very often expresses the meaning 'many'. (Kindaichi & Chiri 1936) When prefixed with no- as no-iwan, the meaning of iwan 'many' is further intensified (e.g., no-iwan-sui 'many times over'). (Kindaichi & Chiri 1936) The numerals tu 'two' and re 'three' are often used correlatively to express the meaning 'many'. (Kindaichi & Chiri 1936) The combinations tu-wan and re-wan mean not 'twenty' or 'thirty', but 'many tens'. (Kindaichi & Chiri 1936) The forms o-tu and o-re have the same indefinite plural meaning ('many') as tu and re. (Kindaichi & Chiri 1936) For counting days, Ainu has tutko 'two days' and rerko 'three days'; for 'four days' and above, rerko has lost the meaning '3' and functions merely as 'day' in forms like ine rerko 'four days' and asikne rerko 'five days'. (Nakagawa 2024: 465) The form iwan rerko corresponding to 'six days' is normally used to mean 'a long time' as an idiomatic usage of iwan 'six'. (Nakagawa 2024: 465) The combination of tu '2' and re '3' produces expressions meaning 'many / a lot', rather than 'a few / a small amount' as in Japanese 'two or three'. (Nakagawa 2024: 468) The expression tutko rerko means 'two or three days', denoting a relatively short period of time. (Nakagawa 2024: 468) The numeral iwan ('6') can be used alone to mean 'many', and often occurs with the emphatic prefix no- in the form noiwan. (Nakagawa 2024: 469) When counting a number of times or occasions, the special term arsuy (< suy 'time') expresses 'once'. (Refsing 1986) The numeral iwan 'six' is occasionally used in the meaning of 'many', especially in oral literature and fixed sayings such as riddles. (Refsing 1986) The combination of tu and re can mean 'many', and in this meaning they are often reinforced by the prefix o-. (Refsing 1986)
The counter and classifier question
Does the language have numeral classifiers, and what is the evidence?
In actual usage, non-human numeral nouns in -p/-pe can also be used to count human beings, without a clear, consistent distinction in politeness from human numeral nouns in -n/-iw. (Nakagawa 2024: 464) Numerals (the basic digit morphemes) belong to the class of adnouns, whereas numbers (the basic morpheme plus a counter) belong to the class of nouns. (Refsing 1986) Numbers rarely function as adnouns, and otherwise appear as pure nouns or appositional to pure nouns. (Refsing 1986) The term 'numeral' refers to the basic numerical morphemes, while 'number' designates expressions consisting of a numeral combined with a counter. (Refsing 1986: 111)
Dialect variation and the vigesimal-to-decimal shift
How does the numeral system vary across dialects, particularly regarding the base?
The Asahikawa dialect possesses a decimal numeral system where hot functions as a base for ten (e.g., sine hot '10', tu hot '20'). (reported in Nakagawa 2024: 467, Refsing 1986: 113) The Raychishka dialect of Sakhalin has a decimal numeral system using the morpheme kunkutu for 'ten'. (reported in Refsing 1986: 113) Apart from the Asahikawa dialect, Hokkaido dialects possess a vigesimal numeral system based on the morpheme hot. (Refsing 1986: 113) In Sakhalin Ainu, a decimal numeral system was adopted through loanwords for higher numerals, replacing the vigesimal base for twenty and above. (Murasaki 2025: 25, 85) According to Dobrotvorsky's dictionary, the Sakhalin Ainu numeral terms kunkutu, tanku, and wantanku entered via Tungusic languages in connection with the trade of large quantities of sable pelts. (reported in Murasaki 2025: 25) The Rayciska dialect preserves hohne 'twenty' in elderly speech as an archaic remnant of ancient Ainu hot 'twenty'. (reported in Murasaki 2025: 25) 'asnetanku is the numeral for 500. (Murasaki 2025: 68) kunkutu is a numeral element expressing tens (-ty). (Murasaki 2025: 70) In the Chitose dialect, '10' in counting is expressed by wanpe instead of wan. (Nakagawa 2024: 466) The word atuyta means '100' in Asahikawa, but in Saru and Chitose it is used only for counting animals, designating '10 animals' in Saru and '20 animals' in Chitose. (Nakagawa 2024: 467) The word for '100' is sineik in Yakumo and Obihiro, asiknehot in Horobetsu, Saru, and Nayoro, ik and asiknehot in Bihoro, wanhot in Soya, and sinetanku in Sakhalin. (reported in Nakagawa 2024: 468) Numerals show little variation across Hokkaido dialects, whereas the dialects of Sakhalin and the Kuril Islands exhibit differences, particularly in numerals exceeding twenty. (Refsing 1986: 111) Krasheninnikov's data indicate a decimal numeral system for the Kurile dialect(s) based on the morpheme wan. (reported in Refsing 1986: 113)