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    • Lessons 1-10 >
      • 1 - Pronunciation >
        • Sindarin IPA
      • 2 - Greetings
      • 3 - Origins >
        • Sindarin place names
      • 4 - Questions
      • 5 - Eating & drinking
      • 6 - Plurals (1)
      • 7 - Plurals (2)
      • 8 - Pronouns (nominative)
      • 9 - Pronouns (object & dative)
      • 10 - Colours & Soft mutation introduction
    • Lessons 11-20 >
      • 11 - Soft mutation
      • 12 - Using adjectives & adverbs
      • 13 - Prepositions
      • 14 - Prefixes
      • 15 - 'in' & Nasal mutation
      • 16 - Pronouns (possessive)
      • 17 - Verbs (Present Tense)
      • 18 - Verbs (Past Tense)
      • 19 - Verbs (Intransitive endings and irregulars)
      • 20 - Verbs (Future Tense)
    • Lessons 21-30 >
      • 21 - Verbs (Conditional)
      • 22 - Irregular verbs
      • 23 - Verbs (Dual)
      • 24 - Sentence structure
      • 25 - Negation
      • 26 - 'To be'
      • 27 - Relative pronouns and uncertainty
      • 28 - Timekeeping
      • 29 - Numbers & Mathematics
      • 30 - Mixed mutation and 'En'
    • Lessons 31-40 >
      • 31 - Plurals (3): Class plurals
      • 32 - Possessive, singular and diminutive suffixes
      • 33 - Comparatives & Superlatives
      • 34 - Abstract Suffix
      • 35 - Further suffixes
      • 36 - How to make names (1)
      • 37 - How to make names (2)
      • 38 - Gondorian & Mirkwood Sindarin
      • 39 - Doriathrin Sindarin
      • 40 - Liquid and Stop mutations
    • Lessons 41 onwards >
      • 41 - Elision
  • Resources
    • Mutation chart
    • Pronoun chart
    • (m)b words
    • (n)d words
    • (n)g words
    • -ath
    • Jigsaws
    • Grammatical terms
    • Language of the hands

Lesson 29 - Numbers & Mathematics

There were two different number systems in use in Middle Earth; the duodecimal system (base 12) and the decimal system that we use today. Interestingly Tolkien tells us that although "in Common Eldarin the multiples of three, especially six and twelve, were considered especially important" the decimal system developed first - "and eventually beside the decimal numeration a complete duodecimal system was devised for calculations".

Although he goes on to say that "the special words for 12 (dozen), 18 and 144 (gross) were in general use" we don't have any record of what that special number for 18 might have been in any language. Tolkien further noted that "for general purposes the numeral names were decimal in origin". This is why the numbers for 20, 30 and so on mean 'two tens', 'three tens'.

Cardinals (1-19)

The numbers 13-19 are reconstructed from Quenya.
Sindarin
English
Mîn
1
Tâd (Tad- in compounds)
2
Neledh (Nel- in compounds)
3
Canad (Can- in compounds)
4
Leben (Leb- in compounds)
5
Eneg
6
Odog
7
Tolodh
8
Neder
9
Pae (-paen in compounds)
10
Minib
11
Ýneg
12
Neleb
13
Canab
14
Lebem
15
Eneph
16
Odoph
17
Toloph
18
Nederph
19
The "in compounds" part should make sense when you now look at the numbers from 20 - 90 and see how they are formed. Instead of Neledhchaen for thirty (a long not aesthetically pleasing word) we have the shorter Nelchaen.

Cardinals (20 onwards)

Originally the word for 'ten' was Cae (-caen in compounds), which is why in the King's Letter Aragorn writes
"a Pherhael ar am Meril suilad uin aran o Minas Tirith nelchaenen ned Echuir"
"to Samwise and to Rose greetings from the King of Minas Tirith on the 30th of Spring"
However later (c. 1967 - 1969, long after the Lord of the Rings was published) Tolkien wrote an essay called The Rivers and Beacon-Hills of Gondor (found in Vinyar Tengwar #42) which includes a long section on numbers. In this he clearly gave the Sindarin for 'ten' as pae (-paen in compounds).

These then, are the deduced numbers 20 - 90 using Tolkien's later material. I suggest that these are for Sindarin as spoken by the Elves, and the original forms as written in the King's Letter are Gondorian Sindarin (see Lesson 39).

Sindarin
English
Taphaen
20
Nelphaen
30
Cambaen
40
Lephaen
50
Enephaen
60
Odophaen
70
Tolophaen
80
Nederphaen
90
*Haran
100
Host
144 (a gross, 12*12)
Meneg
1000 (or a great gross of 1728)
*This word is reconstructed.

Numbers like 33, 67, 82 etc. can be formed like this:
Nelphaen a neledh = Thirty and three (33) or Neledh a nelphaen = Three and thirty
Enephaen a odog = Sixty and seven (67) or Odog a enephaen = Seven and sixty
Tolophaen a dâd = Eighty and two (82) or
Tâd a dolophaen = Two and eighty

Ordinals

For any number after 12 you just need to put -ui on the end to form the ordinal, e.g. nederphaenui = 90th
Sindarin
English
Minui
1st
Tadui
2nd
Nelui
3rd
Canthui
4th
Lefnui
5th
Enchui
6th
Othui
7th
Tollui
8th
Nedrui
9th
Paenui
10th
Minibui
11th
Ýnegui
12th
Taphaenui
20th
Haranui
100th
Menegui
1000th

Using numbers

When we use cardinal numbers in a sentence they come before the noun, like so:
Mîn gaud = One machine
Mîn hadhod = One dwarf

If there's more than one of something, we pluralise the noun as we would normally:
Eneg goed = Six machines
Neder hedhyd = Nine dwarves

If we're using ordinals (1st, 2nd etc.) then they are treated like any other adjective (placed after the noun, with soft mutation):
I 'aud vinui = The first machine
I chadhod dollui = The eighth dwarf

Fractions and shapes; a musing on Elven mathematics

Fractions
The attested words we have are Perin = Half and Canath = Quarter
We also have some reconstructions for some of the other fractions:
Nelest = Third
Lebent = Fifth
Enaith = Sixth
Odost = Seventh
Tolost = Eighth
Nederth = Ninth
Paerth = Tenth

Addition
This is not attested anywhere, but I imagine it to be as simple as using the word 'and' in the same way that we can say an addition in English:
M
în a eneg anna odog = One and six gives seven

Multiplication
In Parma Eldalamberon #14, we have the following in Qenya:
Hue yullume i hualqe = Twice nine is eighteen, where -lume is a suffix meaning 'times'. Qenya is the forerunner of Quenya; if we look at the word Lume in Quenya, it means 'time', which led me to the following idea from a reconstructed word of mine - minlû = once (literally, one time).
Perhaps therefore, in Sindarin lû = time (pl. lui = times) could be used as a suffix in the same way:
T
âd tadlui anna canad = Two, two times gives four

Shapes
The attested word we have is Nelthil = Triangle, which literally means 'three points', Nel + Till
Using this as a basis, we can reconstruct the following:
Canthil = Quadrilateral
Lebthil = Pentagon
Enethil = Hexagon
Odothil = Heptagon
Tolothil = Octagon
Nederthil = Nonagon
Paethil = Decagon

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  • Home
    • Donations
    • Contact/About me
  • Words
  • Verbs
  • Phrases
  • Lessons
    • Lessons 1-10 >
      • 1 - Pronunciation >
        • Sindarin IPA
      • 2 - Greetings
      • 3 - Origins >
        • Sindarin place names
      • 4 - Questions
      • 5 - Eating & drinking
      • 6 - Plurals (1)
      • 7 - Plurals (2)
      • 8 - Pronouns (nominative)
      • 9 - Pronouns (object & dative)
      • 10 - Colours & Soft mutation introduction
    • Lessons 11-20 >
      • 11 - Soft mutation
      • 12 - Using adjectives & adverbs
      • 13 - Prepositions
      • 14 - Prefixes
      • 15 - 'in' & Nasal mutation
      • 16 - Pronouns (possessive)
      • 17 - Verbs (Present Tense)
      • 18 - Verbs (Past Tense)
      • 19 - Verbs (Intransitive endings and irregulars)
      • 20 - Verbs (Future Tense)
    • Lessons 21-30 >
      • 21 - Verbs (Conditional)
      • 22 - Irregular verbs
      • 23 - Verbs (Dual)
      • 24 - Sentence structure
      • 25 - Negation
      • 26 - 'To be'
      • 27 - Relative pronouns and uncertainty
      • 28 - Timekeeping
      • 29 - Numbers & Mathematics
      • 30 - Mixed mutation and 'En'
    • Lessons 31-40 >
      • 31 - Plurals (3): Class plurals
      • 32 - Possessive, singular and diminutive suffixes
      • 33 - Comparatives & Superlatives
      • 34 - Abstract Suffix
      • 35 - Further suffixes
      • 36 - How to make names (1)
      • 37 - How to make names (2)
      • 38 - Gondorian & Mirkwood Sindarin
      • 39 - Doriathrin Sindarin
      • 40 - Liquid and Stop mutations
    • Lessons 41 onwards >
      • 41 - Elision
  • Resources
    • Mutation chart
    • Pronoun chart
    • (m)b words
    • (n)d words
    • (n)g words
    • -ath
    • Jigsaws
    • Grammatical terms
    • Language of the hands