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  Written in code: The Long count includes the leap days; 4 ahau and 8 kumku can appear together only if the leap days are included 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 is the same thing: a 360-day cycle 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 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; they are identified by the Tzolkin sign corresponding to the first day of each package. 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, and 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 Limit 13 20 20 18 20 day basic unit 144000 7200 360 20 1 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  ___________________________________ 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 ___________________________________ 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, 6 ... 7, 8, 9, 11 ...  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 148-day short semester) are used to build cumulative 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  Some mayanists have taken the 69 cycles for eclipses; A cycle indicates the distance in days between two eclipses; examples, Hexon: 1033 days; Saros: 6585 days; etc. ____________________________________ 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 YearMaya world Joy Major Stuart Böhm FAMSI Shaw |