Calendar and Cycles


                              Maya Calendars

Calendar and Cycles
NAHUATL VARIANT
The CORRELATION

                                
Calendario y ciclos
LA CORRELACION
Variante NAHUATL


Calendrier et Cycles
LA CORRELATION
Variante NAHUATL





                                                                                                                                              Research:  1998 - 2012


                                                                                                                    Contents:


                                                             Introduction                     Maya Calendar System                     Natural Cycles of Time



 

There are many truths about the Maya Calendar System (MCS):   it is also Quiche, Zapotec, Olmec, Toltec, Aztec;  all peoples from Honduras to Mexico have adapted it to their geography and culture.   Each author gives a correct version depending on what region is talking about.


         There are two great cultural federations in Mesoamerica:  Nahuatl and Maya.



                                   Where they agree:

 There are 2 calendars:  260-day,  365-day  and  the Long count (both combined)

 The MCS is exact because it records real past days -opposed to calculated-

 Buildings and monuments are used as alignment tools with stars and planets

 Light wells mark the zenith (center of the sky) passages of the sun

 It is not evident how the Maya and the Nahuatl managed the leap days

 The Dresden Codex is supposed to show eclipses and Venus cycles

 Goodman, Martinez, Thompson (GMT):  correlation of Maya and Gregorian dates

 The Gregorian calendar is often unsynchronized with the solar cycle

 It is impossible to situate astronomical events in the GMT and Gregorian frame of time;  that is why they do not correlate with the Mayan records (Dresden codex);   yet many "experts" prefer to believe that the Mesoamerican astronomers have made errors.






                     Written in code:

 The Long count adds the leap days;  4 ahau and 8 kumku can appear together only if the  leap days are added

 Tropical year (365.24218967 days):  mean distance between equinoxes, solstices or zeniths

 4 years is not enough to complete the first leap day of the tropical solar cycle

 The Maya/Nahuatl precession of the equinoxes is not 25626 years but 25769 years long

 Dresden Codex: 236-90-250-8 is not a Venus cycle and there are not eclipses but eclipse cycles

 GMT believed that  Haab or Tun were the same thing  - Haab is 365 days  -  Tun 360 days

 The Julian year (365.25 days), created 25 nonexistent days every 3200 years

 The Gregorian year (365.2425 days), creates 1 nonexistent day every 3200 years

 The exact measure of the Solar cycle is the Tropical year:   128-year cycle (31 leap days)

 The MCS records the exact number of days created by the solar cycle:  46720 normal and 31 leap days (46751 days) every 128 years


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                                             THE MAYA CALENDAR SYSTEM (MCS)

  

    How they track and record the passage of time:

The corners and center of some pyramids mark the 2 solstices and 2 equinoxes (the 4 seasons).  On a leap year, the alignment of each one of these points with the sun, arrives 1 day later than usual;  the first day of the Maya year coincides with the spring equinox (march 20 or 21).





                                                                      The calendars:


      For administration and agriculture:

 Unrecorded 365 day Haab (366 the leap years);  always synchronized with the solar cycle.


      For the permanent records:


 The Tzolkin records all normal and leap days by packages of 260 and never stops.  It cumulates the total of days since the beginning of the calendar.


 The Haab records all normal and leap days by packages of 365 and never stops;


 The leap days are also recorded in a separated count. A special version of the Tzolkin shows the evolution of normal and leap years in real time.


       Since both calendars record all past days, no adjustment is ever needed.


              How they work:


      Tzolkin (260 days):  20 day-signs counted from 1 to 13, again and again, until the day 260.  And starts again





      Haab (365 days):  18 month-signs, the 20 days of each month numbered from 0 to 19;  plus 1 month of 5 days, from 0 to 4.



For the permanent records, both calendars run together by packages of 365 days called haabs;  each package is identified by  the Tzolkin sign corresponding to its first day


                                   Evolution of the Tzolkin signs relative to the Haab first and last month

                                            The same 4 signs alternate to start with each haab;  they are called year bearers






The Haabs are organized by groups of 13:

13 Haabs imix, 13 Haabs Kimi, 13 Haabs Chuen, 13 Haabs Kib, etc....

                                                                The same 4 year bearers are also "trizen" (13-haab) bearers


Calendar Round:  both calendars reset to zero, every  73 tzolkins  (52 haabs)






Auto-adjusting Haab


  1508 years  =  1509 Haabs

 
Solar cycle and Haab count reset to zero at 1508 tropical years, when 365 leap days are accumulated (1 extra Haab).  The Haab count restarts to the first day of the solar year on  0 Pop.

                                                                        Accumulated leap days:

  Every leap year the Haab ends 1 day before the solar year;  Examples from year 0:

  At the end of year 9 there are 9 Haabs and a new one with only 2 days (accumulated leap days).   The year 1508 ends at the same time than the  Haab 1509


                          Year                                       9     29      62     128     256      512     1024      1508
     
                   Accumulated leap days               2      7      15       31       62      124       248        365








 Long Count:

It combines both calendars in order to record cyclic or historical dates, ; its a vigesimal (base 20) record of days past since a chosen day zero:  4 ahau - 8 kumku, for a 13 baktun (some 5125 years) cycle ending on 4 ahau - 3 kankin, which becomes day zero for the next 13 baktuns, and so on.

Its unit is the 360 day Tun:

                                                                        Baktuns           Katuns        Tuns         Months        Days

                                                                                                                                            1               20

                                                                                                                          1               18                                     360 days

                                                                                                         1              20                                                    7 200 days

                                                                                 1                     20                                                                 144 000 days


  Great cycle:         5125 years, 133 days           13                     0               0                 0                0         1872 000 days


 

According to GMT correlation, the Christian dates for the current cycle go from  -3113/08/11  to  2012/12/21

 

   Examples for 2010:           march 20                        june 21               september 22             december 21

                                 (11 ben - 11 kumku)        (13 kimi - 19 zotz)    (2 cauac - 12 chen)    (1 muluc - 2 kankin)

                                    12.19.17. 3.13                12.19.17. 8. 6           12.19.17.12.19          12.19.17.17. 9



 Months, Tuns and Katuns always end on the last sign Ahau, and are identified by their last day number:

                  Months, Ahau                                                     Tuns, Ahau                                                    Katuns, Ahau                          

 7  1  8  2   9   3   10   4   11   5   12   6   13       9   5  1  10   6   2   11   7   3   12   8   4   13       11   9   7  5   3  1   12   10   8   6   4   2   13

 7 1   8  2   9                                                    9   5  1  10   6   2   11









 The Maya used a 20 Katun round;  the Nahuatl, a 13 Katun round;  their Tzolkin dates are different.





                        MAYA/NAHUATL variant, the Short Count                        (see  The Nahuatl variant in this site)


  
                                                            Long and short counts include normal and bissextile days








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          Gregorian and Meso-american dates can not be correlated


                                                                                                         (see The correlation in this site)


    In the Tropical solar cycle, the leap days not always happen every 4 years;


                      number of years needed to complete each leap day:

5  4  4  4  4  4  4        5  4  4  4  4  4  4  4       5  4  4  4  4  4  4  4        5  4  4  4  4  4  4  4


Meso-american dates can only correlate with the Tropical solar cycle;  example:  Dresden Codex



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                                           THE NATURAL CYCLES OF TIME:     Solar, Sidereal, Lunar 

 

                            TROPICAL Solar cycle    -128 years formed by 4 groups

                   It takes 5 years to complete the first leap day of each group 

 

  128 years:              29         +              33           +             33            +             33

    Leap

    years:          5-4-4-4-4-4-4         5-4-4-4-4-4-4-4         5-4-4-4-4-4-4-4          5-4-4-4-4-4-4-4


 31 leap days:          7                           8                              8                            8




      Leap year Tzolkin

  Leap year bearers in green  -the first sign of each group in blue appears twice;  ex:  1 imix, 5 imix




 

             Tropical solar cycle, evolution of normal and leap years in real time: 


               1 Imix  to  1 Chikchan                                                   4 Kib to 4 Ahau  

               2 Kimi  to  2 Oc                                                          5 Imix to  6 Kimi

               3 Chuen to 3 Men                                                         7 Manik to 7 Chuen...  etc.


 

                                      A  tropical solar cycle (128 years):

                                         Vertically, and left to right     - last day of each year:

                                            1rst year: 1 Chichan;  second: 2 Oc;  3 Men;  4 Ahau;  shift to 6 Kimi (leap), ...



                                            The natural sequence changes at each leap year:  1, 2, 3, 4,  ... 7, 8, 9, 11 ...


                                                                   Each year takes the name of its first day;  The first year 1 imix goes from  1 imix   to   1 chichan








                   NEW FIRE   -the Maya/Nahuatl  precession of the equinoxes: 

             Average year;  tropical: 365.24218967 days       sidereal: 365.256363051 days

         Difference:  (20.3586444684 minutes a year)  =  1 day in 70 years and 203 days.


 Because the sidereal year is longer, every  70 tropical years and 203 days (25769 days), the last one is 1 extra day taken by a sidereal object (star, constellation) or event in order to be again in line with an observation point on earth.

 The midday-midnight, sun and pleiades at the zenith  "conjunction"  is celebrated in Mesoamerica in may.  The last one recorded by the Aztecs was in may 13, 1507 (Gregorian).   In 2009, the same event happens in may 20 in the mayan latitude.   The new fire is also celebrated in november 20, but without a conjunction.






                                         SIDEREAL CYCLE  (cycle of the constellations)

                        A group of                                4 years                  1 leap day

  13 groups of 39 years                                    507 years

  Each group 10 leap days   (13  *  10)                                          130 leap days

                                      Total                      511 years              131 leap days


   Groups of 39 years: 1 leap day every 4 years, except the last one, the third year. 

  511 * 365 +  131  =  186646 days.



                                                Comparison:

                    Haabs:       9 times  51  =  459  +  52  =  511         =  186515  normal days

                     Leap days:   9 times  13  =  117  +  14                           131  Leap days

                                                                             Total            =   186646  Days


 

                              Sidereal cycle, evolution of normal and leap years on real time:

                                 1 Imix  to  1 Chikchan                                         3 Chuen  to  3 Men

                                 2 Kimi  to  2 Oc                                                    4 Kib  to  5 imix

                                                                              etc.,

                                        1st year(last day):  count 5 signs  = 1 Chikchan on first line

                                        Vertically:  1 Chikchan, 2 Oc, 3 Men, 5 Imix (leap), 6 Kimi, 7 Chuen, 8 Kib, 10 Ik...









   LUNAR CYCLE:

    4 phases  =  1 lunation  =  29.530589 days;    2 lunations  =  29 days  +  (29  + 1 extra day)

The lunations counted by pairs:  29 and 30 days.    An additional extra day is completed on lunation 17 and  every (17, 17 and 15),  (17, 17 and 15) .... lunations.


                                                                    Complete cycle,  850 lunations  =  25101 days.


 

                  Lunar year:  354.36706 days             Lunar semester:  177.18353 days


                                                   The full moon starts before the first day of the solar year:

                                     Year:                    1        2        3         4        5         6         7        8        9        10            etc.,

                             Days before:                 -       11      22         3      13       25        6       17       27       10

 

 


                                                                                              Eclipses





                              A catalogue of 69 Eclipse cycles                   pedagogical table -not about actual eclipses


         Eclipse seasons (177-day semester and/or 148-day short semester) are added to calculate eclipse cycles

The shortest lunations are about 29d-6h-30m, and the longuest about 29d-20h;  the synodic month could vary on a scale of about 13h-30m; So the length of the semesters can also vary.

                Not all eclipses are visible from a given observation point, and some cycles have "empty" spaces where there are no eclipses.


                                           FAMSI codex Dresdensis                                    Eclipse Cycles 

  
                         

A cycle indicates the distance in days between two same type eclipses;   examples:
distance between 2 Hexon eclipses = 1033 days .... and between 2 Saros eclipses = 6585 days








      For the calendar, the multiples for each level are:   1   20   360   7200


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                                    COMMENTS AND REFERENCES:



         Venus tables  ? ?

    

 The constant:  236-90-250-8 (584 days) on pp. 46 to 50 Dresden Codex, is not a venus serie.  The venus cycle is variable and different:

259-54-256-13 (582 days);     257-57-265-5 (584 days);     260-54-255-14 (583 days);    265-48-265-9 (587 days);

and the second period (behind the sun), is never 90 days.



 

 


          ABOUT 2012

May 20, 2009  Start of my research for a new correlation...  please check every 3 or 6  months.



 

                                                 NOTES:

        Floating versions of the Tzolkin are used for human gestation (9 months), divination and for the agriculture, in places where the haab is not used. 

From 1520 on, mesoamerican calendars were studied by european astronomers.  In 1582, the Gregorian reform adjusted the Julian Calendar, taking off 10 days.


 


          REFERENCES - in Spanish or English:

Calendar        Report        2012       Bearers      LeapYear       Methods        Year

Maya world       Joy          Major        Stuart         Böhm           FAMSI          Shaw




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