Tengwar Numerals

This is an explanation of the tengwar numerals.

Above is a single line of the tengwar numerals with variations, which I wrote out myself. It shows the relationships between the letters, and how they are spaced, that is, which have ascenders which go above the line of writing and which have descenders which go below it.

There are two main systems of using the numerals, one is a duodecimal system (Base 12) used by the Elves and the other is a decimal system (Base 10) used by mortals.

.The number zero is the same in both systems.
But this should only have a dot over it if it is being used in the Mortal (Base 10)
system. For the Elvish (Base 12) it should have a dot under it (see further
down for an example).

Decimal System used by Mortals

Here is a table that shows how the numbers are used when writing in the decimal system (Base 10). The numerals here have a dot over them. This is just to indicate that they are numerals, and it also indicates that they are in the base 10 system. I could have left them off, because properly speaking, the dots are not an essential part of the numeral, but I thought it best to leave them there so that you could see where they go on each numeral. The number for 10 or "full" should have a dot over like the others here.

1	2	3	4	5	6	7	8	9	10 (full)

Here is a little graphic to show you how to write the number 24 in the decimal system. Instead of putting dots over each numeral, you can just draw a line across the top of the numeral, as I have done here, in order to mark the numerals off if they should appear in a body of text. The number is written with the small number first so this reads 4-2 (four ones and two tens).
This is my example, Tolkien had a much longer one.

Duodecimal System used by Elves

Here is a table for the duodecimal system (in Base 12), according to the usage of the Elves. The dots should appear below the numerals in this system (as they do on the numerals 10, 11 and "full"). But please forgive me, it took me several hours to form this artwork and upload it and I hope that you can get the idea without me having to produce a separate set of numerals with the dots below just to show you.

1	2	3	4	5	6	7	8	9	10	11	12 (full)

Notice that the number which is used for 12 here, and which I have called "full" is the same as the numeral for 10 in the Base 10 system. That numeral would be used for the full amount in whatever base you are counting in. By the way, Tolkien doesn't use the word "full", I do, and I would call it quanta in Quenya.

In the duodecimal system the number 24 would be written like this:
This also has the small number to the left, and it is zero, and the larger number to the right, which is 2. In the duodecimal system, 24 is 2 twelves. Also, you can see that the dots are very different. The zero has a single dot under it, and the number in the duodecades (the twelves column) has a little circle under it. In the Quettar text, it appears as a larger blob, (larger than the dot), but in my copy of the Marquette notes, I copied it as a small circle.

The other numbers that you will see are an alternative for "full" which appears like this, shown with a dot under it:
I don't know why we have or need an alternative to the
first "full", but I'll go back and see if it is in the notes.

Tolkien also says that an alternative numbering system was used in which the first 24 letters of the tengwar alphabet (meaning the chart, as it appears in LotR), were used as numbers. They could be marked with either a line or a dot to distinguish them from letters (although both lines and dots are used as tehtar on tengwar letters, so this can't have been such a great system). Anyway the examples are the letter tinco, shown with a line (and standing for the number 1),

and the letter tinco with a dot, also standing for the number 1.

I hope this makes it possible for you to see how the numerals were written, and you should be able to use them now. If this explanation isn't clear, please let me know and I will try to rewrite it.

References: This analysis is based on a description of the tengwar numerals which was published in Quettar and on information at Marquette which has not yet been published. The Quettar article is described on the List of Unpublished and Slightly Published Manuscripts Page, and although Quettar is no longer available, here is a a link to an image of the pages from the Unpubs webpage.

And following is a set of all the numerals, which I am just going to leave at the bottom of the page for convenience.

Return Home.

This page hosted by Get your own Free Home Page