Appendix III: Method for Calculating Tzolkin Dates

 

With  this simple table, one can easily calculate the  tzolkin designation for any Julian or Gregorian date for some 8000 years, 3114 B.C to 4800 A.D.

 

1) Add up the century year, year and month numbers for the date you wish to convert to the tzolkin, using tables a, b and c. Then add the day of your birth. *Notes: 1) In table c, the months marked (B) should be used if your year is a leap year (see “The Julian and Gregorian Calendars” in Chapter Two for an explanation). 2) Negative years should be divided in such a way that the last two figures are positive (e.g., -464 becomes -500 and +36. Table a is consulted for -500 and Table b is consulted for 36). 3) In Table a, two values are given for 1500, one for the Julian calendar (J) and one for the Gregorian (G). You now have a number that indicates the number of days elapsed since August 11th, 3114 B.C. Long Count 0.0.0.0.0. This number is called the Mayan Day Number, or M.D.N.

 

2) To find the number coefficient of your tzolkin date, divide your M.D.N. by 13. Multiply the decimal remainder by 13 to arrive at a  whole number remainder. Take this remainder and  count forward beginning with the number 5, using base 13 (13  is followed by 1). For example, if your remainder was 12: 4 + 12 = 16; 16 - 13 = 3. 3 is the number coefficient of your date. Next, to find your day-sign, divide that same M.D.N. by 20 and figure the whole number remainder (this can be easily done since the multiples of 20 are obvious). Take that remainder and count off the consecutive day-signs, beginning with Imix. Here is a day-sign list:

 

     1) Imix        6) Cimi       11) Chuen     16) Cib     

     2) Ik          7) Manik      12) Eb        17) Caban

     3) Akbal       8) Lamat      13) Ben       18) Eznab    

     4) Kan         9) Muluc      14) Ix        19) Cauac

     5) Chicchan    10) Oc        15) Men       20) Ahau

 

            Together with the number coefficient previously arrived at, this is the universal Sacred Calendar Day for your date. Considering the potential  difficulties  in calculating tzolkin conversions  for  western dates, this is an extremely simple method.

 

3) To find the haab date, divide the same M.D.N by 365. Multiply the decimal remainder by 365 to arrive at a whole  number remainder. Count of haab days with this number, beginning with 9 Cumhu. Since we are figuring from the base date 4 Ahau 8 Cumhu, and 0 counting was used in designating the first haab day as 8 Cumhu in the Tikal system, you will need to count the haab month days from 0 - 19. Consult the haab month-name list in Chapter Two if necessary. Consult Chapter Four to convert any Tikal haab date to the Quiché haab.   

 

4) Long  Count dates can also be calculated, using  the  same M.D.N. arrived at in Step 1. The process is almost self-explanatory. Divide accordingly:

 

            1st Long Count place value = Baktuns of 144,000 days

            2nd Long Count place value = Katuns of 7200 days

            3rd Long Count place value = Tuns of 360 days

            4th Long Count place value = Uinals of 20 days

            5th Long Count place value = Kin (days remaining)

 

            Example: M.D.N. = 1,803,296 (5 Cib):

 

1,803,296 = 12 baktuns, 10 katuns, 9 tuns, 2 uinals and 16 kin or days. Thus: 12.10.9.2.16.

 

            In the event that you are converting archeological Long Count dates to Western dates, the process is reversed. First, add up the place values of your Long Count date to arrive at a M.D.N. Then, add 584283 to this number to find the Julian Day Number of your date. You will need to consult some kind of table to discover which Gregorian or Julian date corresponds with that J.D.N.  

 

            Converting tzolkin/haab dates to Western dates is a bit more tricky, since any tzolkin/haab date repeats every 52 haab. You would need to know the general time frame of your date.

 

     Table a: Century Year

 _______________________________

 Year   number   Year   number 

--------------------------------

 -3200   -32025      0  1136775

 -3100     4500   +100  1173300

 -3000    41025    200  1209825

 -2900    77550    300  1246350

 -2800   114075    400  1282875

 -2700   150600    500  1319400

 -2600   187125    600  1355925

 -2500   223650    700  1392450

 -2400   260175    800  1428975

 -2300   296700    900  1465500

 -2200   333225   1000  1502025

 -2100   369750   1100  1538550

 -2000   406275   1200  1575075

 -1900   442800   1300  1611600

 -1800   479325   1400  1648125

 -1700   515850(J)1500  1684650

 -1600   552375(G)1500  1684640

 -1500   588900   1600  1721165

 -1400   625425   1700  1757689

 -1300   661950   1800  1794213

 -1200   698475   1900  1830737

 -1100   735000   2000  1867262

 -1000   771525   2100  1903786

  -900   808050   2200  1940310

  -800   844575   2300  1976834

  -700   881100   2400  2013359

  -600   917625   2500  2049883

  -500   954150   2600  2086407

  -400   990675   2700  2122931

  -300  1027200   2800  2159456

  -200  1063725   2900  2195980

  -100  1100250                

--------------------------------

 

      Table b: Additional Year

__________________________________________

 Year  number  Year  number  Year  number

------------------------------------------    

   0        0   34    12418   68    24837     

   1      365   35    12783   69    25202    

   2      730   36    13149   70    25567         

   3     1095   37    13514   71    25932    

   4     1461   38    13879   72    26298    

   5     1826   39    14244   73    26663    

   6     2191   40    14610   74    27028      

   7     2556   41    14975   75    27393    

   8     2922   42    15340   76    27759    

   9     3287   43    15705   77    28124        

  10     3652   44    16071   78    28489    

  11     4017   45    16436   79    28854    

  12     4383   46    16801   80    29220     

  13     4748   47    17166   81    29585    

  14     5113   48    17532   82    29950

  15     5478   49    17897   83    30315       Table c: Month

  16     5844   50    18262   84    30681      -----------------

  17     6209   51    18627   85    31046       month    number

  18     6574   52    18993   86    31411      -----------------

  19     6939   53    19358   87    31776       Jan         0

  20     7305   54    19723   88    32142       Jan (B)    -1

  21     7670   55    20088   89    32507       Feb        31

  22     8035   56    20454   90    32872       Feb (B)    30

  23     8400   57    20819   91    33237       Mar        59

  24     8766   58    21184   92    33603       Apr        90

  25     9131   59    21549   93    33968       May       120

  26     9496   60    21915   94    34333       Jun       151

  27     9861   61    22280   95    34698       Jul       181

  28    10227   62    22645   96    35064       Aug       212

  29    10592   63    23010   97    35429       Sep       243

  30    10957   64    23376   98    35794       Oct       273

  31    11322   65    23741   99    36159       Nov       304

  32    11688   66    24106                     Dec       334

  33    12053   67    24471                    -----------------

------------------------------------------      

 

Table d. Additional Century Years for 3000 to 4800  A.D., effectively extending the Tzolkin Calendar to a full 20 baktun cycle:

 

Table d:

-----------------------------------

 Year    number     Year   number

-----------------------------------

 3000    2232504    4000   2597747     

 3100    2269028    4100   2634271

 3200    2305553    4200   2670795

 3300    2342077    4300   2707319

 3400    2378601    4400   2743844

 3500    2415125    4500   2780368

 3600    2451650    4600   2816892

 3700    2488174    4700   2853416

 3800    2524698    4800   2889941

 3900    2561222

-----------------------------------

 

            Table e: Century numbers to use if Gregorian dates are used for the years -3200 to 1500 (supplement to Table a).

 

 

Year       number               Year       number

----------------------------------------------------------

-3200      -31999               -800       844583

-3100      4525                 -700       881107

-3000      41049                -600       917631

-2900      77573                -500       954155

-2800      114098               -400       990680

-2700      150622               -300       1027204

-2600      187146               -200       1063728

-2500      223670               -100       1100252

-2400      260195                 0        1136777

-2300      296719               100       1173301

-2200      333243               200       1209825

-2100      369767               300       1246349

-2000      406292               400       1282874

-1900      442816               500       1319398

-1800      479340               600       1355922

-1700      515864               700       1392446

-1600      552389               800       1428971

-1500      588913               900       1465494

-1400      625437               1000       1502019

-1300      661961               1100       1538543

-1200      698486               1200       1575068

-1100      735010               1300       1611592

-1000      771534               1400       1648116

-900       808058               1500       1684640

-------------------------------------------------------------------

 

Note. June 2007. These tables were laboriously collated, figured out, and distilled in 1991, at the stat lab at the University of Colorado. It was a room with early computers for engineering students and, although I was not a student, I often snuck in to run my astronomy software. The engineering library had encyclopedic books with Julian day numbers and Gregorian dates. I realized that tables could be compiled to allow for a calculation method of tzolkin dates. By 1991, Peter Meyer had come out with his ingenius Mayan Calendrics computer software that could calculated Maya calendar dates, and a lot more. But I wanted to have something for my book Tzolkin, which I was writing at the time, that could be done by hand. Charts on a page that could be consulted. (Tzolkin was published privately in the summer of 1992 and with Borderland Sciences Research Foundation in 1994, in an edition of 1000 copies.) The tables above became an appendix in Tzolkin. I distilled the tables into an even more concise method, so that it would fit on one side of a half-piece of standard paper. I sent these out in my Four Ahau Press catalog mailings from 1991 up to 1996 or so.

The career of these charts is rather interesting. In 1998 I was contacted by Ian Lungold, who devised a calculation method that he wanted to install on restaurant placemats. It was a marketing plan, designed to make money, some of which would be filtered back to Maya communities. He sent me a copy and I noted that they used an approach similar to mine in converting Julian day numbers to the tzolkin calendar, but had collapsed or reduced some of the numbers by common factors (this was a simplification by reducing the extraneous factors). He said he had reached the method in a flash of insight, in a vision. Later, Erick Gonzalez told me that Ian had stayed with him in his house in California in 1996, and was there introduced to my book Tzolkin. He revised my tables at that time and derived his placemat version. Ian's simplified version of my charts have spawned many products in the marketplace. Most notably, Carl Calleman used them in his books, which he admitted in our debate of 2001, and Barbara Clow repeated them in her 2007 book. Various Maya calendar books and charts can be found in New Age bookstores that adopted Ian's derivation, which were sold as placemats or wall charts through his Mayan Majix website. These things take on a life of their own and if you are at the very inception of something, and it passes through one or more derivations, it is unlikely that your original work — in this case, laborious number crunching by hand late at night in CUs stat lab in 1991 — will be credited. It's the way that an initial lightning strike of inspiration disperses as the thunder rolls through the air and over the land, being absorbed by all it encounters. By the final rumble the lightning has been forgotten.

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