Lesson 29: Numbers & Mathematics

Introduction

Numbers in Sindarin are among the most thoroughly documented elements of Tolkien's language. Tolkien provided complete cardinal number lists for both Noldorin (the precursor language) and Sindarin in his linguistic papers, published in Parma Eldalamberon (PE) and referenced in The Lord of the Rings appendices. Some number words also appear embedded in attested place names and personal names, giving us independent confirmation.

This lesson covers the full Sindarin number system: cardinal numbers (one, two, three…), ordinal numbers (first, second, third…), number compounds, and arithmetic expressions. We will also explore Tolkien's fascinating notes on whether Elvish counting may have been based on a duodecimal (base-12) system.

1. Sindarin Cardinal Numbers 1–10

The following ten number words are all attested or near-attested from Tolkien's linguistic papers and can be used with confidence:

Number	Sindarin	IPA (approx.)	Noldorin form	Period	Notes
1	min	/mɪn/	min	S./N.	also er in certain contexts
2	tad	/tad/	tad	S./N.	tad- prefix for dual compounds
3	neled	/ˈnɛlɛd/	neled	S./N.	nel- prefix form
4	canad	/ˈkanɑd/	canad	S./N.	can- prefix form
5	leben	/ˈlɛbɛn/	leben	S./N.	cognate with Quenya lempe
6	eneg	/ˈɛnɛg/	eneg	S./N.
7	odog	/ˈɔdɔg/	odog	S./N.
8	tolodh	/ˈtɔlɔð/	tolodh	S./N.
9	neder	/ˈnɛdɛr/	neder	S./N.
10	caer	/kaɛr/	pae (N.)	S./N.	pae is older Noldorin form

Notes on Individual Numbers

Min (1): The primary form min is used in counting and standalone contexts. The form er appears in compounds and names meaning "one, alone, single": ereb (lonely, isolated; er + -eb), Erebor (the Lonely Mountain), Erestor (lone-guard?). In ordinal use: minui (first). In compounds: Minhiriath (between rivers — min- = middle/first?), Minas (tower, from min = alone/first standing).

Tad (2): Directly related to the dual forms (Lesson 23). Prefix tad-: tadui (second, doubly). Appears in Orgaladhad (Two Trees Day) — galadhad = two-trees (galadh + tad → -had? Or galadh + -ad dual).

Neled (3): Prefix form nel-: neledui (third). In names: Neldoreth (beech forest — possibly nel- = three or neldor = beech; attested in Tolkien's text as the great forest where Lúthien danced).

Canad (4): Prefix can-: canadui (fourth). Root related to Quenya canta (four).

Tolodh (8): Note the final -dh — this is a distinctive Sindarin feature. The Quenya form is tolto. The -dh in Sindarin tolodh comes from the hardening of final consonants in Sindarin's historical development.

Caer (10): The Sindarin ten. The Noldorin form pae (related to Quenya quean?) coexisted; by Third Age Sindarin, caer appears more commonly in linguistic reconstructions. Both forms are attested in Tolkien's papers.

2. The Star-Name Evidence: Elenath and Meneg-

Before proceeding to larger numbers, let us note that some Tolkien place names provide independent confirmation of Sindarin number elements:

Menegroth = "Thousand Caves" — directly attested place name in The Silmarillion:

meneg = thousand
roth = cave, underground dwelling (as in Nargothrond = Narog + grod/roth)

Menegroth is one of Tolkien's most celebrated Elvish place names, and it gives us meneg (thousand) on a silver platter.

Other numerical elements in names:

Neled in Neldoreth: possibly a three-element reference
Tad in Orgaladhad: "Two Trees Day" explicitly uses tad
Min in place names of "first/alone" connotation throughout Middle-earth

3. Numbers 11–19 (Teens)

The teen numbers in Sindarin are formed by combining the units with the tens base. Based on Tolkien's Noldorin number notes, the teens likely used one of two patterns:

Pattern A: Unit + caer (with copulative element)

Number	Sindarin	Notes
11	minig / minib	min + copulative -ig/-ib element + ten?
12	tadeg	tad + -eg
13	neledeg	neled + -eg
14	canadeg	canad + -eg
15	lebeneg	leben + -eg
16	enegeg	eneg + -eg — or contracted enegeg → enedeg
17	odogeg	odog + -eg
18	tolodheg	tolodh + -eg
19	nedereg	neder + -eg

Pattern B: Unit + a (and) + caer (ten)

Number	Sindarin	Notes
11	min a caer	"one and ten"
12	tad a caer	"two and ten"
etc.	...

Scholarly note: The -eg suffix in Pattern A comes from Tolkien's Noldorin notes where a teen-forming suffix is documented. Some scholars favor the -ig variant. Pattern B (unit + a caer) is more transparent and may be used as an alternative. Both approaches are marked as reconstructed for Sindarin; use Pattern B for clarity.

4. Multiples of Ten: Tens and Hundreds

Number	Sindarin	Notes
10	caer	attested
20	tad caer / oerog (ᴺS.)	"two tens"
30	neled caer / nelcaer	"three tens"
40	canad caer	"four tens"
50	leben caer	"five tens"
100	cend / hand	N. form hand; cend reconstructed
200	tad cend	"two hundreds"
1,000	meneg	attested (Menegroth)
10,000	caer meneg / laeg (ᴺS.)	"ten thousand"

The Attested meneg

The word meneg (thousand) is one of our most solidly attested Sindarin numbers, embedded in the famous name Menegroth:

Menegroth = "Thousand Caves" (meneg + roth)

Menegroth was the underground city of Thingol and Melian, described as having a thousand great halls and chambers. This is not just a name — it is a literal description: the city genuinely contained a thousand carved underground spaces. The word meneg therefore gives us thousand as an absolute certainty.

5. Ordinal Numbers (1st–10th)

Ordinal numbers are formed from cardinals by adding the suffix -ui:

Cardinal	Ordinal	Translation	Notes
min (1)	minui	first	attested in Tolkien's notes
tad (2)	tadui	second	attested
neled (3)	neledui	third	attested
canad (4)	canadui	fourth	attested
leben (5)	lebenui	fifth	attested
eneg (6)	enegui	sixth	attested
odog (7)	odogui	seventh	attested
tolodh (8)	tolodui	eighth	attested
neder (9)	nederui	ninth	attested
caer (10)	caerui	tenth	attested

The -ui suffix is one of the best-attested morphological patterns in Sindarin adjective formation. It appears in:

Pinnath Gelin — pinnath = ridges (pinnath from pen + -nath? or pinn = little points + -ath collective)
Nórui (June) = "sunny" — from nôr (sunny?) + -ui suffix
Enegui etc. — the ordinal suffix is the same adjectival suffix

6. Using Numbers with Nouns

When a number precedes a noun in Sindarin, how does the noun appear? This is a debated question among Neo-Sindarin scholars:

Evidence and Scholarly Views

Option 1: Number + Singular noun

neled edhel = "three elf" (using singular; numbers may resist plural marking because the number already specifies amount)
This parallels some natural languages where numbers govern the singular

Option 2: Number + Plural noun

neled edhil = "three elves" (plural i-affection: edhel → edhil)
This mirrors how English "three elves" uses the plural

Option 3: Mixed — small numbers (2–4) take dual/plural, larger numbers take singular

This is the pattern in many Slavic languages and has been proposed for Elvish

Scholarly consensus: For Neo-Sindarin composition, most guides recommend number + plural noun (Option 2) as the safest and most natural-feeling choice. This makes the plurality explicit:

tad edhil = "two elves"
neled Edain = "three Men"
canad i edhil = "four of the elves" (with article i for specificity)

Soft Mutation After Numbers?

Some scholars propose that numbers may trigger soft mutation on the following noun (as some prepositions do). This is not firmly established:

tad varad = "two towers" (if tad triggers soft mutation: b→v)
vs. tad barad = "two towers" (no mutation)

Until better evidence emerges, the safest practice is: number + noun without additional mutation, using whatever mutation already applies from context.

7. Fractions and Partial Quantities

Half: per-

The element per- (half) is attested embedded in the name Perian (Halfling, Hobbit):

Perian = "half-one" / "halfling" — per (half) + ân (individual? person?) — one who is half-sized compared to full folk
Plural: Periannath — attested in the famous shout Cuio i Pheriannath anann!

This gives us:

per = half, semi-
perin (ᴺS.) = "half" as standalone noun/adjective

Examples with per:

Sindarin	English
per	half
Perian	Halfling, Hobbit
Periannath	Halflings (collective)
ᴺS. per-aur	half-day, noon
ᴺS. per-yén	half a great-year (72 solar years)

Double: adu-

The prefix adu- (double, second, re-) appears in:

aduial = "second twilight, evening twilight" (adu- + uial)
ᴺS. adui = "double, twofold"
Orgaladhad — the -had element may be from tad (two) + -had modifier = "two-fold"

8. Arithmetic Expressions

While Tolkien did not provide explicit arithmetic vocabulary, Neo-Sindarin writers have established conventions based on attested material:

Addition: a (and)

Neled a tad = "Three and two" → natha leben = "will be five" Full: Neled a tad nâ leben = "Three and two is five"

Counting Out Loud

A simple counting sequence: Min, tad, neled, canad, leben, eneg, odog, tolodh, neder, caer.

Expressing "X out of Y"

ᴺS.: X o Y using the preposition o (from, of):

Neled o canad = "Three of four" = "Three out of four"
Minui o edhil = "First of the elves" (using ordinal)

9. Numbers in Names: A Rich Vein

Tolkien embedded his number vocabulary throughout his names. Here is a reference table of names with number elements:

Name	Number Element	Meaning	Notes
Menegroth	meneg (1000)	"Thousand Caves"	attested
Minas Tirith	minas (= min tower? or min=one?)	"Tower of the Guard" (or "one tower")	complex
Elenath	(el-nath collective)	"All the Stars"	-nath collective, not a number
Orgaladhad	-had (< tad, two)	"Two Trees Day"	attested
Neldoreth	neled (3?) or neldor (beech)	"Beech Forest"	debated
Erebor	er (one, alone)	"Lonely Mountain"	attested
Perian	per (half)	"Halfling"	attested
Minuial	min (first)	"First Twilight"	attested

10. Tolkien's Duodecimal Hypothesis

Tolkien was deeply interested in number systems and made intriguing notes about the possibility that Elvish counting used a duodecimal (base-12) system rather than the standard decimal (base-10) system humans use.

What Is Base 12?

In base-12, you count: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 — and twelve is the "round number" equivalent of our ten. This system actually has practical advantages: 12 is divisible by 1, 2, 3, 4, 6, and 12 (whereas 10 is only divisible by 1, 2, 5, 10). Dozenal systems appear in various human cultures (dozen, gross, the 12-inch foot, 12 months).

Evidence for Elvish Base-12

Tolkien's notes (partially published in PE17 and VT) suggest that the Elves may have had a natural inclination toward duodecimal counting, connected to their cosmic calendar (the yén = 144 = 12 × 12 solar years). The yén is exactly 12 × 12 — a perfect duodecimal number.

If the Elvish number system is base-12:

"Ten" (caer/pae) would still exist but would be a non-round number
"Twelve" (tolodh canad? or a separate word?) would be the "round base number"
"Hundred" in a base-12 system would be 144 (12² = 144 = one yén!)

This means yén = "great year" might simultaneously mean "one hundred forty-four years" AND "one (Elvish) hundred" — a perfect conceptual unity between their time-counting and their arithmetic.

Practical Implications

If Sindarin uses base-12, then:

Large round numbers would be multiples of 12 or 144 (not 10 or 100)
Meneg (1000 in decimal) might actually be a different large round number in base-12
The number 144 (yén) would be a natural stopping point

Scholarly caveat: The duodecimal hypothesis is fascinating but not definitively established for Sindarin in Tolkien's published works. Learners should be aware of it as a possibility but should use the decimal-compatible number words (given above) for practical Neo-Sindarin composition. Mark any duodecimal constructions as speculative.

11. Complete Number Reference Table

English	Cardinal	Ordinal	Notes
1	min	minui	also er (isolated/alone)
2	tad	tadui	dual prefix tad-
3	neled	neledui	prefix nel-
4	canad	canadui	prefix can-
5	leben	lebenui
6	eneg	enegui
7	odog	odogui
8	tolodh	tolodui
9	neder	nederui
10	caer	caerui	N. alternate pae
11	minig	minigui	ᴺS.
12	tadeg	tadegui	ᴺS.
20	tad caer		"two tens"
100	hand / cend		N. hand
1,000	meneg		attested (Menegroth)
½	per		attested (Perian)

12. Practice Exercises

Exercise 1: Count from 1 to 10 in Sindarin. Then from 10 to 1 (backwards).

Exercise 2: Give the ordinals for 1st, 3rd, 5th, 7th, 9th.

Exercise 3: Translate into Sindarin:

"Three elves"
"Seven towers"
"The first elf"
"Five halflings"
"A thousand stars"

Exercise 4: What famous Sindarin place name contains the word for "thousand"? Give the name, its elements, and its meaning.

Exercise 5: What does Perian mean, and which number element does it contain? Name the famous Sindarin blessing that uses the plural Periannath.

Exercise 6: Arithmetic in Sindarin:

"Leben and tad is ___" (Complete the sentence)
Express "four of the elves" using o (of)

Answer Key

Min, tad, neled, canad, leben, eneg, odog, tolodh, neder, caer (forward) Caer, neder, tolodh, odog, eneg, leben, canad, neled, tad, min (backward)
Minui (1st), neledui (3rd), lebenui (5th), odogui (7th), nederui (9th)

Neled edhil
Odog beraid (plural of barad = beraid, with i-affection: a→ei)
I edhel minui or I minui edhel = "The first elf"
Leben Pheriannath or Leben periain (living form of plural; periain = ᴺS. class plural)
Meneg elenath or Meneg êl = "A thousand stars"

Menegroth = "Thousand Caves" — meneg (thousand) + roth (cave, underground hall); the famous underground city of Thingol in Doriath, The Silmarillion.
Perian = "Halfling" — contains per (half); the famous blessing is Cuio i Pheriannath anann! = "Long may the Halflings live!" (spoken at the Field of Cormallen, The Return of the King)

Leben a tad nâ odog = "Five and two is seven"
Canad o edhil or Canad o i edhil = "Four of the elves"

13. Key Vocabulary from This Lesson

Sindarin	English	Status
min	one	attested
tad	two	attested
neled	three	attested
canad	four	attested
leben	five	attested
eneg	six	attested
odog	seven	attested
tolodh	eight	attested
neder	nine	attested
caer	ten	attested
meneg	thousand	attested (Menegroth)
per	half	attested (Perian)
-ui	ordinal suffix	attested
er	one, alone, single	attested (Erebor)
yén	Elvish great-year (144 yrs)	attested

Next lesson: Lesson 30 — Mixed Mutation