[Aztlan] List of Maya terminal long-count dates sought

Thu Mar 13 17:45:09 CDT 2008

Prof. Thomas:

I am unsure of whether you wanted a list of the Calendar Round dates of Period Endings or a comprehensive list of all P.E. dates in all sites. As far as the latter goes, I do not know of one. There are several lists in various books for different sites, but not a comprehensive list that I know of. 

As for the former, my copy of "Appendix C: Table of tun-endings between 8.1.15.0.0 and 10.9.3.0.0" is from (Ian Graham) Corpus of Maya Hieroglyphic Inscriptions, Vol. 1, Appendix C.

These are so easy to calculate, however, that I rarely have to look up a Period Ending.
(NOTE: A Long Count Date is just a big Distance Number (DN) counted from zero.)

To calculate the Calendar Round Date resulting from adding a DN to a known date:

To find the Tzolk'in:
1. Count -1 for each Baktun, -2 for each K'atun, -4 for each Tun, and -6 for each Winal, casting out 13s.
2. Add the result to the starting date Tzolk'in number, and cast out 13s again, if necessary.
3. The Day Name is Day of the Remainder of division by 20 (that is, the Day that corresponds to the number of Days in the K'ins place). In a Period Ending, the Day Name is always Ajaw (0 K'ins).
4. If necessary, add in K'ins, casting out 13s from the number and putting the Day Name which corresponds to the number of K'ins. (For example, 12 in the K'ins place is the 12th Day, Eb' in Maya, Dying Grass in Mixtec and Aztec).

For example, P.E. 8.14.3.0.0 is [8 x -1 (Baktuns)] + [(14-13)] = 1 x -2 (K'atuns)] + [3 x -4 (Tuns)] = -8 -2 -12 = -22 + 26 (2x13) = 4; Add 4 [0 Days] to [4 Ajaw] = 8 Ajaw. So the Tzolk'in of 8.14.3.0.0 is 8 Ajaw and 9.0.0.0.0 is also 8 Ajaw, because DN 117 Tuns is an even multiple of 13 Tuns away from 8.14.3.0.0.

To find the haab' date,
1. First use a similar procedure to the one before, but in this case, cast out 73s from the number of Tuns (not total days). (This works because 72 x 365 = 73 x 360.)

For example, 
8.14.3.0.0 is (8 x 20) = 160 + 14 = 174 K'atuns - 146 (2 x 73) = 28 K'atuns.
28 K'atuns x 20 = 560 Tuns + 3 Tuns = 563 Tuns - 511 (7 x 73) = 52 Tuns.

2. Then multiply the result by -5 (because 365 is 5 more than 360), add to the previous haab' date, and cast out 365s, if necessary.

In this case, 52 x -5 = -260 + 348 (because 8 Kumk'u = (17 Winals x 20) + 8 = 348). 
The result is 8 Tzek (88 = 4 Winals + 8).

So the Period Ending date of 8.14.3.0.0 is 8 Ajaw 8 Tzek.

Note that this is even easier if you memorize lock dates so you don't have to start counting at zero.

For example, 
P.E. Baktun 9 is 8 Ajaw 13 Keh (233); 
P.E. Baktun 8 is 9 Ajaw 3 Tzip (43); and
P.E. 8.4.0.0.0 is 1 Ajaw 8 Pohp (8)

Also note that:
11 K'atuns increases the Tzolk'in number by 4 and decreases the haab' by 5 K'ins.
So 8.16.0.0.0 is 3 Ajaw [Day 0] 8 Kank'in (13.8) because
Tolk'in: 176/11 = 16 x 4 = 64 - 52 = 12; 12 + 4 [Ajaw] = 16 - 13 = 3 Ajaw.
Haab': 16 x -5 K'in = -80 + 348 [8 Kumk'u] = 268 = 8 Kank'in (268). 

One last trick I find useful is
For a decimal number, you can find the MOD (remainders) of division by 9, 11, 7, and 13 easily.

For example, 8.14.3.1.12 (Leiden plaque Long Count) totals 1,253,912 K'in.
1. MOD9: Add the digits together, casting out 9s: cast out 1 + 5 + 3 = 9; cast out 9; so Lord of the Night (Remainder division by 9) = 2 +1 +2 = G5. [Or (1 Winal x 20) = 20 +1 +2 = +2 +1 +2 = 5 because Tuns and higher periods are evenly divisible by 9 and are therefore cast out.]
2. For MOD7, MOD11, and MOD13: Start at the decimal point and mark out numbers in threes, counting plus, minus, plus (dividing at the commas) until you run out of numbers. Add the pluses and minuses together to get a number that is the remainder of division by 1001 (because 1001 is an even multiple of 7, 11, and 13). Then find the remainders of 7, 11, and 13 using the new, smaller number.

So, for 1,253,912, count +912 -253 +1 = +913 -253 = 660, which is an even multiple of 11 (MOD11 remainder 0); with remainder 10 for MOD13, and remainder 2 for MOD7.

So our Tzolk'in for 8.14.3.1.12 is [10 (MOD13) +4 (from 4 Ajaw) = (14 -13)] = 1 Eb' (Day 12), and our date is evenly divisible by 11; with a remainder of 2 when divided by 7.
The haab' date is 32 K'in more than 8 Tzek (88) = 0 Yaxk'in (120 = 6.0) or
8.14.3.1.12 1 Eb' 0 Yaxk'in G5

The above procedure also works for casting Tzolk'in out of our Period Endings. (This works because 13 Tuns = 18 Tzolk'in.)

For example,
9.0.0.0.0 = 9 x 400 = 3,600 Tuns; 600 - 3 = 597 Tuns -598 (46 x 13) = (-1 x -4) (remember that adding one Tun decreases the Tzolk'in number by 4) = +4 +(4 Ajaw) = 8 Ajaw. 

Lynda Manning-Schwartz

-----Original Message-----
>From T. R. Thomas

I am trying to find a comprehensive list of Maya
terminal long-count
 dates.    I have searched a number of online
databases (British Library,
 ISI Web of Science, JSTOR), but the only published
list I have been
 able to find is in a paper by Premo (Journal of
Archaeological Science 31
 (2004) 855â€“866).  This is itself an update of an
earlier list by Bove
 (American Antiquity 46 (1981) 93â€“112), who
apparently compiled it
 himself from primary sources.  Both these lists apply
only to the Maya
 lowlands.  

As a non-Mayanist I would find it surprising if no
more definitive list
 of terminal dates existed, and I conclude that I am
looking in the
 wrong places.  If anyone can refer me to a more
comprehensive list than
 the ones cited above, I should be very grateful. 
Please respond to my
 email address directly, not to the list.

Many thanks,

Tom Thomas

Professor T. R. Thomas
Sektionen fÃ¶r Ekonomi och Teknik  
Halmstad University
Box 823, Kristian IV's vÃ¤g 3
SE-301 18 Halmstad 
Sweden 

email: tr.thomas at set.hh.se