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Quenya Grammar P93: Numerals

Tolkien wrote a series of essays on Elvish numbers in the late 1960s. One of those essays, Eldarinwe Leperi are Notessi (ELN), gave a set of numbers that many Neo-Quenya writers now use (VT48/6):

¹ ELN actually gave lemen as the word for “five”. Elsewhere in those 1960s essays (as well in earlier writings from the 1930s) the word for “five” was consistently given as lempe, and that word is used more broadly in Neo-Quenya.

Most of these numbers were very well established. Almost all of the above appeared in The Etymologies from the 1930s, except for (a) toldo “eight” and quean “ten” which were late 1960s replacements for 1920-50s tolto and kainen, and (b) yunque “twelve” which does not appear in The Etymologies itself but does appear the Early Qenya Grammar (EQG) of the 1920s. Indeed, many of these numbers (er/min, nelde, kanta, enqe, otso, tolto, kainen, minqe) have the same or similar forms in EQG as well. So it seems Tolkien largely retained the same basic numbering systems from the 1920s to the 1960s.

The late 1960s change of kainen > quean did have a significant impact on numbers above twelve, however, whose forms were given as (VT48/21):

The words for “thirteen”, “fourteen” and “eighteen” were given only in their primitive forms ✶nelekwe, ✶kanakwe and ✶tolokwe. After the Quenya syncope, their Quenya forms would be nelque, canque and tolque, which is supported by the Telerin forms nelpe, kampe and tolpe (VT48/21 note #22), as well as the ordinal form nelquea. The form tolokwe appears in the middle of a set of Quenya forms (spelt with -que), leading Patrick Wynne to suggest that it was a Quenya form with abnormal spelling. I think it is likelier that Tolkien put this primitive form in the middle of the Quenya list for reasons unclear, otherwise the lack of syncope is hard to explain.

Helge Fauskanger drew the opposite conclusions in his Quettaparma Quenyallo, suggesting that the proper form for “fourteen” might also be canaque without syncope, making canaque and toloque popular Neo-Quenya alternatives for 14 and 18. Indeed, it is possible that these variations represent vacillations on Tolkien’s part on whether or not syncope was possible before kw, which may have been considered a cluster [kw] or pronounced as more unitary [kʷ]. But Tolkien had syncope apply in the etymology of minque “eleven” < ✶minikwē (VT48/7-8), so I think the syncopated forms are more appropriate.

There were also variant forms quainel, quaican, quailepen, quainque for 13 to 16, where the “ten” element is prefixed rather than suffixed, but these are less used in Neo-Quenya writing. Another alternate word for 13, yunquenta “12 and one more” appeared elsewhere in these essays (VT47/15); this is probably a specialized word similar to a “baker’s dozen” (12 plus one).

min vs. er, atta vs. yúyo: In the chart in ELN, Tolkien gave two Elvish words for “one”: er and min. Describing the origins of these words Tolkien said that the root √ER meant “single, alone” whereas √MIN meant “first of a series” (VT42/24; VT47/17). From √ER we get words like erinqua “single, alone”, eressea “lonely” and [ᴹQ.] eresse “solitude”, whereas from √MIN we get minya “first”, [ᴹQ.] minda “prominent”, as well as mindon “tower” from the sense “stands alone, sticks out”. It seems min = “one” for purposes of counting and quantities but er = “one” is used to refer to unique things: á anta ni min ohte “give me one egg” vs. er oron tare Rhovaniondesse “one mountain stands in Rhovanion”. Compare:

  • rehtielva mauya er atan “our saving needs one man (a specific unique man)”.
  • rehtielva mauya min atan “our saving needs one man (total, but any one man will do)”.

There is a similar pair of words for two: atta “two” and yúyo “both”, the latter an adjective rather than a number. The first is used for basic counting and quantities and the second for pairs of things: elda atta tuluvat síra “two elves will come today” vs. yúyo eldat melit lye “both elves love you” (see below for a discussion of the use of dual with atta “two”). yu- is an element in some other numbers, such as yunque which is etymologically “a pair of sixes” (VT47/41; VT48/10). It is also (probably) connected to the dual suffix -u.

Ordinal Numbers: The ordinal numbers appear in an appendix to Tolkien’s notes on The Rivers and Beacon-hills of Gondor, also from the late 1960s. They are (VT42/25):

The ordinal nelya is not explicitly marked as archaic, but it probably is given similar archaic forms tatya and lepenya. Another (possible) ordinal nelquea < nelkwăya also appeared in ELN (VT48/21); according to Patrick Wynne it was glossed “13” but given its form I think it is likelier to be “13th”. In any case, the pattern for forming ordinals is clear: add -ea with the number, replacing the last vowel, with abnormal variations for minya and quainea (see above for minya and below for quainea).

Fractions: Quenya fractions appear in some notes associated with The Shibboleth of Fëanor, again from the late 1960s. Most of the fractions appear in both long and short forms (VT48/11):

The pattern for the long fraction name is to take the first part of the number’s root, omitting the last consonant but including a second base vowel, oto-, tolo-, nere-, etc. + sta. The short fraction names are further reduced to the initial consonant (if any) and the first vowel, o-, to-, ne- etc., + sta, with abnormal short variants perta and nelta. The suffix -sta is derived from the root √SAT “part”, and the fraction “one half” is based on the root √PER “half” instead of atta “two”. There is a third set of variants for “1/3” through “1/9”: nelsat, cansat, lepsat, otsat, tolsat, nersat, using an alternate suffix -sat; these variants are probably less used in Neo-Quenya.

The fraction name caista for “one tenth” indicates these fractions were coined before cainen “ten” >> quean. In the later paradigm, “one tenth” is probably *quaista. The names for “one eleventh” and “one twelfth” are simply the number + -sta, and the same is probably true for fractions with higher numbers.

Larger Numbers: In Tolkien’s later writing, the largest Quenya number is neterque “19”. For numbers bigger than this we need to look at the Early Qenya Grammar from the 1920s (PE14/49-50, 82-83). That document used the earlier name kainen for “ten”, and the numbers for 20, 30, 40 were ᴱQ. yukainen = yu + kainen, nel(de)kainen = nel(de) + kainen, kan(ta)kainen = kan(ta) + kainen, etc. After kainen >> quean (quain), these forms might become:

There is no general consensus on these forms for Neo-Quenya. For example, Helge Fauskanger used neterquean for “ninety” in his Neo-Quenya New Testament (NQNT) with suffixal -quean. The above are just my best guesses, but I believe that quean (< CE ✶kwayam) would be the independent word for “ten” and the reduced form quain (< CE *✶kway’m) would be preferred in compounds. See the examples above for the words quainea “tenth” or the variant quainel “thirteen”. For these multiples of ten, I think the shorter forms (nelquain) are preferable to longer forms (neldequain), especially in combination with other numbers: otso nelquain “37” (see below).

For numbers 100 and above, we have only Early Qenya words to work from:

  • ᴱQ. tuksa “hundred”, plural tukse (see below).
  • ᴱQ. húme or maite “thousand” (the latter is unsuitable for Neo-Quenya because it clashes with maite “handy, skilled”).
  • ᴱQ. mindóre “million”.
  • ᴱQ. yundóre “billion”.
  • ᴱQ. neldóre “trillion”.
  • ᴱQ. kantóre “quadrillion”.
  • ᴱQ. lemindóre “quintillion” (which might be revised to *lependóre).
  • ᴱQ. enqendóre “sextillion”.
  • ᴱQ. otsondóre “septillion”.

I personally prefer to use these for larger numbers in Neo-Quenya. However, there is the word haranye “century” which might contain a later word for “hundred” (?haran), and a Sindarin word meneg “thousand” which some people used to produce a neologism ᴺQ. mence “thousand”.

Combining Numbers: In English, number words are combined by putting larger numbers first followed by smaller numbers: “twenty one”. Quenya seems to put smaller numbers first instead: ᴱQ. min yukainen “21 = one [and] twenty”, ᴱQ. yukainen tuksa “120 = twenty [and] hundred”. In Neo-Quenya these might become *min yuquain “21”, *yuquain tuxa “120”.

In the EQG, 200, 300, etc. placed the multiplier before the 100: ᴱQ. yúyo tuksa “200 = two hundred”, ᴱQ. nelde tukse “300 = three hundreds”. Somewhat interestingly, while the Early Qenya number for “200” uses singular tuksa, the number for “300” uses the plural declined as if it were an adjective: nelde tukse. Perhaps larger numbers would be similarly pluralized: otso húmi “seven thousands”, enqe mindóri “six millions” but ᴱQ. yúyo yundóre “two billion”. This is identical to how numbers modify nouns in EQG (and in Tolkien’s later writing): with “two” the noun remains in the singular, but with three or more it is in the plural (see Numbers modifying noun below).

In EQG, numbers were placed before the noun they modify, but in later writing they are placed after. So it is probable that the Early Qenya ordering yúyo tuxa, nelde tuxe would need to become tuxa atta, tuxe nelde “200, 300” to be compatible with Tolkien’s later ideas.

Multiples: English has specialized words for indicating the number of times something occurred: “once, twice, thrice”, as well as prefixes like “uni-, bi-, tri-”. In the Early Qenya Grammar these were ᴱQ. eru “once”, “twice”, nel “thrice”, kan “four times”, especially as prefixal forms (PE14/51, 84). There are signs of these prefixes in Tolkien’s later writings, such as [ᴹQ.] neltil “triangle” (Ety/NEL), Nelólamaite “triconsonantal” (PE18/33, 84), and cantil “fourth finger” (VT47/26).

Given Tolkien’s later use of Eru as the name of God, it seems unlikely that it still meant “once” in the 1950s and 60s. Perhaps er “one” could be used adverbially for that purpose: carin sa er “I did that once”. In later writings er- did appear as a prefixal form, as in: Erólamaite “uniconsonantal” (PE18/33, 84). Similarly, in Early Qenya yúyo meant “two” but in later writings it meant “both”, so the later prefixal form was at(a)- or att- as in Attólamaite “biconsonantal” (PE18/33, 84), attalya [at-tal-ya] “biped (lit. two footed)” (WJ/389), ataformaite “ambidextrous” (VT49/9). Compare this with “twilight” = ᴹQ. yúkale or Q. úyale (< ✶yuy(u)ŋal).

In Tolkien’s later writing there was also the prefix per- “half, semi-” as in Pereldar “Half-elven” or Pereldar “Half-elven” (Let/386, PM/348) or [ᴹQ.] perómanda “semivocalic” (PE18/30).

In EQG there were also long forms produced using the suffix ᴱQ. -llume “times” related to ᴱQ. lúme “time”. Since lúme remained the word for time in Tolkien’s later writing, the suffix -llume may remain valid as well. From this we get (PE14/51):

Other examples make it clear this pattern extrapolates to larger numbers: minqelume “eleven times”, tuksallume “hundred times” (PE14/51, 84). This longer form was used in multiplicative expressions: ᴱQ. hue yullume i hualqe “twice nine is eighteen” (PE14/51), which might be revised to nerte yullume (ná) tolque “nine twice is eighteen”.

Note that in Tolkien’s later writings he changed [ᴹQ.] ullume “forever” >> úlume “ever, at all times” and sillume >> silume “at this time, now”, so it is possible the multiple suffix should be -lume instead of -llume. The reason for the l-doubling isn’t clear, but my guess is its function is similar to prosodic lengthening to emphasize the boundary between the morphemes; it also appears in the names Avallónë and (maybe) Lórellin. For now, I’d stick with -llume in Neo-Quenya writing, since the phenomenon isn’t really understood.

Numbers modifying nouns: In Quenya numbers generally follow the noun they modify, as mentioned by Tolkien in several places:

Adjectives normally preceded the qualified noun … A standing exception was made by numerals which usually immediately followed the noun (Common Eldarin: Noun Structure, early 1950s, PE21/77).

Note numerals follow the noun, except er (1) which is indeclinable. The noun is indeclinable in that case before atta, which takes sg. inflexion. (Only in O[ld] Q[uenya] is dual inflexion preserved.) “Of 2 stars” would be elen atto. From nelde 3 onwards: (a) Noun is in gen. pl. and numerals inflect as sg. noun or [(b)] later noun is declined and numeral indeclinable. [(a)] elenion nelde or [(b)] eleni nelde. “Of 3 stars” = [(a)] elenion neldeo or [(b)] elenion nelde (linguistic notes from 1969, VT49/45).

Thus with the exception of er “one, alone” a number follows its noun. One peculiarity is that nouns qualified by atta “two” take the singular form: elen atta “two stars”. This is probably an artifact of how the ancient dual nouns were formed: u-duals were originally used only for natural pairs (both) and would not be qualified by atta “two”, whereas t-duals were the reduction of the following atta “two”, so that **auret atta “two days [dual]” would (incorrectly) be a double “two”. However, the verb would be inflected into the dual to agree with the duality of the subject: nai elen atta siluvat aurenna veryanwesto “*may two stars shine upon the day of your wedding” (VT49/43). For numbers bigger than two, the qualified nouns (and presumably also the verbs) are put into the plural as in: eleni nelde silir “three stars shine”, eldar otso oryar “seven elves rise”, and so forth.

Tolkien’s notes on the interaction of numbers and noun cases is a bit unclear. He said that with atta “two”, the noun was indeclinable and atta was declined as if it were a singular noun, as in genitive elen atto. This is consistent with the “last declinable word” rule for noun cases. For numbers bigger than two, in older Quenya the noun was put into the genitive plural and the case ending was apply to the number as if it was a singular noun: elenion neldeo “of three (of) stars” and presumably eldaron otsollo “from seven (of) elves”. However, it seems in “modern” Quenya the number is indeclinable and only the noun is declined if there is a noun case: eleni nelde “three stars”, elenion nelde “of three stars” and presumably eldallor otso “from seven elves”; exactly when this change occurred isn’t clear. Assuming this is correct, numbers bigger than two do not obey the “last declinable word” rule.

It is not clear how min would behave. It is possible that, like er, it is indeclinable and placed before the noun: min eldallo “from one elf”. It is also possible that, like atta, it follows the noun and is declined for case: elda minello “from one elf (of many possible elves)” vs. er eldallo “from one (distinct) elf”. For purposes of Neo-Quenya, I’d treat min like er and assume the more unique placement rules are limited to larger numbers.

Numbers and body parts: Some special rules apply to numbers with body parts. In particular, body parts are counted for each individual rather than collectively, as Tolkien described in several places:

Since by Quenya idiom in describing the parts of body of several persons the number proper to each individual is used, the plural of parts existing in pairs (as hands, eyes, ears, feet) is seldom required. Thus mánta “their hand” would be used = (they raised) their hands (one each), mántat = (they raised) their hands (each both), and mánte could not occur. In such cases as “many hands were raised” the normal Quenya expression would [be:] they many raised hand (or hands dual) (Quenya notes from 1957, PE17/161).

remained in use in Quenya, with pair-dual mát; but the only plural in use (at any recorded period) was máli. … General statements, such as “hands are cleverer than feet”, were more often expressed in the singular: “hand is cleverer than foot”. In cases such as “they raised their hands” hand was in Eldarin syntax always singular, if each (which need not be expressed) raised one hand, and always dual if each raised both hands; the plural was impossible (Eldarin Hands, Fingers and Numerals, 1968, VT47/6).

Thus “the men shut their lips (both each)” = i atani holyaner péntat (dual) and “the elves kicked their leg (one each)” = i eldar lacce telconta (singular). Proverbial expressions would likewise tend to use the singular. The partitive plural (máli “some hands”) might be used for an amorphous collection of body parts, as in: i orcor hostaner aucirina máli et rondonta “the orcs collected chopped-off hands outside their cave”.

Duodecimal Numbering: The elves used ordinary decimal numbers (maquanotie = “hand counting”) for most day to day purpose, but they a separate duodecimal (base 12) numbering system as well. Tolkien mentioned this in several places:

The Eldar preferred to reckon in sixes and twelves as far as possible (LotR/1107).

The Eldar used two systems of numerals, one of sixes (or twelves) and one of fives (or tens) (description of tengwar numerals, date unknown, Quettar #14 p. 5-6).

But already in Common Eldarin the multiples of three, especially sixes and twelve, were considered specially important, for general arithmetical reasons; and eventually beside the decimal numeration a complete duodecimal system was devised for calculations, some of which, such as the special words for 12 (dozen), 18, and 144 (gross), were in general use. But since this appears to have been a relatively late development (only begun after the Common Eldarin [?Period] except for the word for 12), the vague similarity of nel(ed), e-nek-we, net-er are probably not significant (notes on The Rivers and Beacon-hills of Gondor, late 1960s, VT42/24).

Much later, but before the end of the Common Eldarin period, the Eldar leaving behind the primitive beginnings with the hand devised a counting in sixes and twelves which they used in all more elaborate reckonings; but in daily and colloquial use many of the decimal terms remained in use (Eldarin Hands, Fingers and Numerals, late 1960s, VT47/14).

At a (probably) later period the Eldar now provided with a numeral system firmly based on the manual decimals 5, 10 (Note 4) became interested in sixes, and a word for 6 x 2 (12) was already devised before the end of the Common Eldarin period (since it occurs in Quenya, Telerin and Sindarin) … Note 4: So it remained. In spite of their later predominant (?and theoretical) interest in and use of six-twelve (as group units) they did not develop a complete duodecimal nomenclature, though they invented (after the Common Eldarin period for numbers above 12) special names for the multiples of six x six. Of these, 18 and 24 were also in daily use, as well as the “gross” 144 (12 x 12), and 72 half-gross (notes on neter, canat, enek, late 1960s, VT47/16-17).

… but was after the (centre) of a non-mutual duodecimal system much later but still up to 12 already devised in Common Eldarin. Since 6 and 11, 12 have evidently connected in formation, it is possible that enek was later invented than 4, 7 and belongs to duodecimals (or deliberate invention on en-et). If so, old word for 6 has been lost (rough notes associated with Eldarinwe Leperi are Notessi, late 1960s, VT48/9).

The precise dating of many of the above notes is uncertain. It is clear that Tolkien imagined the Elves as have some sort of duodecimal counting, but he kept changing his mind on when it was devised and how extensively it was used. His ideas ranged from a complete (and possibly ancient) system of mathematics using base 12 to only a small number of 12-based words like English “dozen” or “gross” (144) as well as the use of such numbers in the reckoning of time (e.g. yén = 144 solar years).

In his description of tengwar numerals Tolkien said that the Elves used the same symbols for duodecimal numerals with additional symbols for 10 and 11; duodecimals had an underdot to distinguish them for decimal numbers, which used an overdot (Quettar #14 p. 5-6). Thus it is possible that the duodecimal system used the same number names, at least for 1 to 11.

Other than 6 and 12, we don’t know of any special names for duodecimal numbers from Tolkien’s later writings, but a few appear in earlier documents, notably custom words for “eighteen” ᴱQ. hualqe (PE14/50) or ᴹQ. nahta, the latter of which appeared beside a special word for “twenty-four” ᴹQ. yurasta (VT41/17 note #6). This word for 24 is of special interest, since it seems to be the duodecimal equivalent of yukainen or *yuquain “20”. Thus -rasta may fulfill the same role as -cainen or *-quain from the decimal system: *nellasta “36 = 3 x 12”, *carnasta “48 = 4 x 12” etc. In fact, the root ᴹ√RASAT “12” appears in The Etymologies of the 1930s (Ety/RÁSAT), and seems to be specialized for use with duodecimals as opposed to more ordinary yunque “twelve”.

Assuming the Elves had a complete system of duodecimal mathematics, they almost certainly had specialized words for “144 = 12 x 12” and “1728 = 12 x 12 x 12”, as well as duodecimal equivalents of million, billion, trillion, etc. If so, we don’t know what such words might be.

Conceptual Development: The conceptual evolution Qenya numerals can be traced through five major number lists: 1910s Qenya Lexicon (QL), 1920s Early Qenya Grammar (EQG), 1930s Etymologies (Ety), 1950s (?) notes associated with Galadriel’s song (PE17/95) and 1960s Eldarinwe Leperi are Notessi (ELN, VT48/6). A couple of the number words were introduced in QL and basically remained the same thereafter: ᴱQ. er “one”, otso “seven”, minqe “eleven”. Others gradually changed over the years:

  • one: min introduced in the 1920s and retained thereafter.
  • two: 1920s yúyo >> 1930s+ atta.
  • three: 1910s ole >> 1920s+ nelde.
  • four: 1910s nelde >> 1920s+ canta.
  • five: 1910-20s lemin >> 1930s+ lempe (with a brief restoration of lemen “five” in ELN).
  • six: 1910s ende >> 1920s+ enque.
  • seven: 1910s+ otso (with occasional alternate forms like 1950s otos on PE17/95 and 1960s osko on VT47/42).
  • eight: 1910s umna >> 1920s-50s tolto >> 1960s toldo.
  • nine: 1910s olme(t) >> 1920s hue >> 1930s+ nerte.
  • ten: 1910s lempe >> 1920s-50s kainen or kea(n) >> 1960 quëan or quain.
  • eleven: 1910s+ minqe.
  • twelve: 1920s+ yunqe.

Tolkien gave an elaborately detailed numbering system in the Early Qenya Grammar (EQG) of the 1920s, though there were some minor differences between the manuscript (PE14/49-51) and typescript (PE14/82-85) versions. Many features of the EQG system are discussed in the main entry, since it is the last time Tolkien mentioned certain features of Quenya numbering. There are also earlier versions of ordinals (ᴱQ. minya, potsina, nelya, kanya vs. later minya, attea, neldea, cantea) and fractions (ᴱQ. lempe, neldesto, kantasto, leminto vs. later peresta, neldesta, canasta, lepesta).

In EQG, numbers appeared before the nouns they modified, as in yúyo elda “two elves” and minqe eldali “eleven elves” (PE14/50), where later on they would appear after (elda atta, eldar minque). The notion that a noun modified by “two” would remain singular already appeared in EQG, but in EGQ noun pluralization was sometimes optional for other numbers, notably 3, 9, 11, 12 and 18 (probably due to their connection to duodecimal counting).

More information about duodecimals from the 1930s is known to exist (VT41/17 note #6) but is currently only partially unpublished.

Neo-Quenya: To summarize the above, I recommend the following use of numbers for Neo-Quenya writing:

Multiples of 100, 1000 behave as if they are nouns modified by a number which means the numeric multiple comes after, as with tuxa atta, húme atta “200, 2000” or tuxe nelde, húmi atta “300, 3000”. The base number is declined into the plural when the multiple is three or more (but not for two, see below), with an abnormal plural form tuxe for “hundred”. An unqualified 100, 1000, etc. is simply tuxa, húme, not preceded by min, however.

Combined numbers put the smaller numbers before the larger ones: nelde otoquain “three [and] seventy = 73”, yuquain tuxa “twenty [and] hundred = 120”, canta canquain tuxe canta “444 = four [and] forty [and] four hundred”. 9004 can be distinguished from 4009 by word order: nerte húmi canta “4009” vs. canta húmi nerte “9004”, as is the case of English “four thousand nine” vs. “nine hundred four”. This also means that number words in Quenya are the reverse of the order used by English: “three hundred seventy eight” becomes toldo otoquain tuxe nelde [eight seventy hundreds three].

Ordinals are formed by taking the number and changing its last vowel to -ea as in attea “second”, neldea “third” and cantea “fourth”, with special words for minya “first” and quainea “tenth”. Fractions are formed by adding -sta to larger numbers as in minquesta “one eleventh”, but smaller numbers have specialized fraction words:

Multiples are formed with the suffix -llume as in otsollume “seven times” or tuxallume “one hundred times”, including in equations like canta otsollume (ná) toldo yuquain “four times seven is 28”. There are a few specialized multiples for smaller numbers:

With the exception of er and min, numbers follow the noun they modify, as elda atta “two elves” and atani canta “four men”. The behavior of atta is a bit unusual; the noun it modifies is left in the singular, whereas for larger numbers the noun is put into the plural. With atta the verb is put into the dual, whereas with larger number it is put into the plural: elda atta tulit ar atani canta autar “two elves come and four men leave”.

The number atta follows the “last declinable word” rules and receives the noun case ending for the phrase, if any, but larger numbers are an exception to this rule and the noun is declined instead: nás anna elda attallo “it is a gift from two elves” vs. nás anna atanellor canta “it is a gift from four men”.

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