2012: Aztec and Mayan Calendars

BY CLARK ROBERT KEATING

Historically, the Aztec name for the huge basaltic monolith is Cuauhxicalli Eagle Bowl, but it is universally known as the Aztec Calendar or Sun Stone.

 

It was during the reign of the 6th Aztec monarch in 1479 that this stone was carved and dedicated to the principal Aztec deity: the sun. The stone has both mythological and astronomical significance. It weighs almost 25 tons, has a diameter of just under 12 feet, and a thickness of 3 feet.

On December 17th, 1760 the stone was discovered, buried in the "Zocalo" (the main square) of Mexico City. The viceroy of New Spain at the time was don Joaquin de Monserrat, Marquis of Cruillas. Afterwards it was embedded in the wall of the Western tower of the metropolitan Cathedral, where it remained until 1885. At that time it was transferred to the national Museum of Archaeology and History by order of the then President of the Republic, General Porfirio Diaz.

Mesoamerican calendars are the calendrical systems devised and used by the pre-Columbian cultures of Mesoamerica. In addition to the basic function of a calendar—defining and organizing periods of time in a way that allows events to be fixed, ordered and noted relative to each other and some absolute progression—Mesoamerican calendars were also used in religious observances and social rituals, such as for divination.

Among the various calendar systems in use, two were particularly central and widespread across Mesoamerica. Common to all recorded Mesoamerican cultures, and the most important, was the 260-day calendar, a ritual calendar with no confirmed correlation to astronomical or agricultural cycles. Apparently the earliest Mesoamerican calendar to be developed, it was known by a variety of local terms, and its named components and the glyphs used to depict them were similarly culture-specific. However, it is clear that this calendar functioned in essentially the same way across cultures, and down through the chronological periods it was maintained. The second of the major calendars was one representing a 365-day period approximating the tropical year, known sometimes as the "vague year". Because it was an approximation, over time the seasons and the true tropical year gradually "wandered" with respect to this calendar, owing to the accumulation of the differences in length. There is little hard evidence to suggest that the ancient Mesoamericans used any intercalary days to bring their calendar back into alignment. However there is evidence to show Mesoamericans were aware of this gradual shifting, which they accounted for in other ways without amending the calendar itself.

These two 260- and 365-day calendars could also be synchronised to generate the Calendar Round, a period of 18980 days or approximately 52 years. The completion and observance of this Calendar Round sequence was of ritual significance to a number of Mesoamerican cultures.

A third major calendar form known as the Long Count is found in the inscriptions of several Mesoamerican cultures, most famously those of the Maya civilization who developed it to its fullest extent during the Classic period (ca. 200–900 CE). The Long Count provided the ability to uniquely identify days over a much longer period of time, by combining a sequence of day-counts or cycles of increasing length, calculated or set from a particular date in the mythical past. Most commonly, five such higher-order cycles in a modified vigesimal (base-20) count were used, generating a linear progression of days to span a period of roughly 5125 solar years.

The use of Mesoamerican calendrics is one of the cultural traits that Paul Kirchoff used in his original formulation to define Mesoamerica as a culture area. Therefore the use of Mesoamerican calendars is specific to Mesoamerica and is not found outside its boundaries.

The existence of Mesoamerican calendars is attested as early as ca. 500 BCE, with the essentials already appearing by then as fully defined and functional. Mesoamerican calendar usage—of one form or another, some (such as the Long Count) fell into disuse earlier—continued throughout the pre-Columbian era until the arrival of the Spanish conquistadores in the early 16th century. Even after the subsequent colonialisation of Mesoamerican territory by Europeans and the consequent adoption of the Julian Calendar, some indigenous communities continue to use aspects of Mesoamerican calendars in parallel with the Western system, such as among K'iche' Maya communities of the Guatemalan highlands and the Mixe of Oaxaca.

The Aztec calendar is the calendar system that was used by the Aztecs as well as other Pre-Columbian peoples of central Mexico. It is one of the Mesoamerican calendars, sharing the basic structure of calendars from throughout ancient Mesoamerica.

The calendar consisted of a 365-day calendar cycle called xiuhpohualli (year count) and a 260-day ritual cycle called tonalpohualli (day count). These two cycles together formed a 52 year "century," sometimes called the "calendar round." The xiuhpohualli is considered to be the agricultural calendar, since it is based on the sun, and the tonalpohualli is considered to be the sacred calendar.

The calendric year may have begun at some point in the distant past with the first appearance of the Pleiades (Tianquiztli) asterism in the east immediately before the dawn light. But due to the precession of the Earth's axis, it fell out of favor to a more constant reference point such as a solstice or equinox. Early Spanish chroniclers recorded it being celebrated in proximity with the Spring equinox.

The heliacal rising of a star (or other body such as the moon, a planet or a constellation) occurs when it first becomes visible above the eastern horizon at dawn, after a period when it was hidden below the horizon or when it was just above the horizon but hidden by the brightness of the sun.

Each day after the heliacal rising, the star will appear to rise slightly earlier and remain in the sky longer before it is hidden by the sun (the sun appears to drift eastward relative to the stars along a path called the ecliptic). Eventually the star will no longer be visible in the sky at dawn because it has already set below the western horizon. This is called the heliacal setting. A star will reappear in the eastern sky at dawn approximately one year after its previous heliacal rising. Because the heliacal rising depends on the observation of the object, its exact timing can be dependent on weather conditions.

Not all stars have heliacal risings: some may (depending on the latitude of observation on the earth) remain permanently above the horizon, making them always visible in the sky at dawn, before they are hidden by the brightness of the sun; others may never be visible at all (like the North Star in Australia).

Constellations containing stars that rise and set were incorporated into early calendars or zodiacs. The ancient Egyptians based their calendar on the heliacal rising of Sirius and devised a method of telling the time at night based on the heliacal risings of 36 stars called decan stars (one for each 10° segment of the 360° circle of the zodiac/calendar). The Sumerians, the Babylonians, and the ancient Greeks also used the heliacal risings of various stars for the timing of agricultural activities. To the Māori of New Zealand, the Pleiades are called Matariki and their heliacal rising signifies the beginning of the new year (around June).

The corresponding rising of a celestial body above the eastern horizon at nightfall is called its acronychal rising.

The tonalpohualli ("day count") consists of a cycle of 260 days, each day signified by a combination of a number from one to thirteen, and one of the twenty day signs. With each new day, both the number and day sign would be incremented: 1 Crocodile is followed by 2 Wind, 3 House, 4 Lizard, and so forth up to 13 Reed, after which the cycle of numbers would restart (though the twenty day signs had not yet been exhausted) giving 1 Jaguar. The cycle of day signs would continue until 7 Flower, after which it would restart and give 8 Crocodile. It would take a full 260 days (13×20) for the two cycles of twenty day signs and thirteen numbers to realign and repeat the combination 1 Crocodile.

Trecenas

A set of thirteen numbered days is known by the Spanish term trecena (from trece "thirteen"). Each of the twenty trecenas in the 260-day cycle was associated with a particular deity:
Trecena Deity
1 Crocodile – 13 Reed Ometeotl
1 Jaguar – 13 Death Quetzalcoatl
1 Deer – 13 Rain Tepeyollotl
1 Flower – 13 Grass Huehuecoyotl
1 Reed – 13 Snake Chalchiuhtlicue
1 Death – 13 Flint Tonatiuh
1 Rain – 13 Monkey Tlaloc
1 Grass – 13 Lizard Mayahuel
1 Snake – 13 Quake Xiuhtecuhtli
1 Flint – 13 Dog Mictlantecuhtli

Trecena Deity
1 Monkey – 13 House Patecatl
1 Lizard – 13 Vulture Itztlacoliuhqui
1 Quake – 13 Water Tlazolteotl
1 Dog – 13 Wind Xipe Totec
1 House – 13 Eagle Itzpapalotl
1 Vulture – 13 Rabbit Xolotl
1 Water – 13 Crocodile Chalchiuhtotolin
1 Wind – 13 Jaguar Chantico
1 Eagle – 13 Deer Xochiquetzal
1 Rabbit – 13 Flower Xiuhtecuhtli

THE MAYAN CALENDAR

The Classic Mayan civilization was unique and left us a way to incorporate higher dimensional knowledge of time and creation. By tracking the movements of the Moon, Venus, and other heavenly bodies, the Mayans realized that there were cycles in the Cosmos. From this came their reckoning of time, and a calendar that accurately measures the solar year to within minutes.

For the Maya there was a time for everything and everything had it's place in time. The priests could interpret the heavens and calendar. As the result they could control the daily activities of the populace. Knowing when to plant, when to harvest, the rainy and dry seasons, etc. gave them total power and control. Their comprehension of time, seasons, and cycles was immense.

The Maya understood 17 different Calendars based on the Cosmos. Some of these calendars go back as far as ten million years and are so difficult that you would need an astronomer, astrologer, geologist, and a mathematician just to work out the calculations. They also made tables predicting eclipses and the orbit of the planet Venus.

The calendars that are most important to beings of earth are the Haab, the Tun-Uc and the Tzolk'in. The Tzolk'in is the most important and the one with the most influence.

Archaeologists claim that the Maya began counting time as of year 3114 B.C. 
This is called the zero year and is likened to January 1, 1 AD. All dates in the Long Count begin there, so the date of the beginning of this time cycle is written 0-0-0-0-0. 13 cycles of 394 years will have passed before the next cycle begins, which is in year 2012 A.D. (13-0-0-0-0).

Mayan Calendar Basics

The Mayas used three different calendar systems (and some variations within the systems). The three systems are known as the tzolkin (the sacred calendar), the haab (the civil calendar) and the long count system.

The tzolkin is a cycle of 260 days and the haab is a cycle of 365 days.
The tzolkin cycle and the haab cycle were combined to produce a cycle of 18,980 days, known as the calendar round. 18,980 days is a little less than 52 solar years.

The "Calendar Round" is like two gears that inter-mesh, one smaller than the other. One of the 'gears' is called the tzolkin, or Sacred Round. The other is the haab, or Calendar Round. The smaller wheels together represent the 260-day Sacred Round; the inner wheel, with the numbers one to thirteen, meshes with the glyphs for the 20 day names on the outer wheel. A section of a large wheel represents part of the 365-day year - 18 months of 20 days each (numbered 0-19). The five days remaining at year's end were considered evil. In the diagram, the day shown is read 4 Ahua 8 Cumka. As the wheels turn in the direction of the arrows, in four days it will read 8 Kan 12 Cumku. Any day calculated on these cycles would not repeat for 18,980 days - 52 years.

Thus the Mayas could not simply use a tzolkin/haab date to identify a day within a period of several hundred years because there would be several days within this period with the same tzolkin/haab date.

The Mayas overcame this problem by using a third dating system which enabled them to identify a day uniquely within a period of 1,872,000 days - approximately 5,125.36 solar years. To do this they used a vigesimal (i.e. based on 20) place-value number system, analogous to our decimal place-value number system.

The Mayas used a pure vigesimal system for counting objects but modified this when counting days. In a pure vigesimal system each place in a number is occupied by a number from 0 to 19, and that number is understood as being multiplied by a power of 20. Thus in such a system:

    2.3.4 = 2*20*20 + 3*20 + 4*1 = 864
  11.12.13 = 11*20*20 + 12*20 + 13*1 = 4653 and 
    1.3.5.7 = 1*20*20*20 + 3*20*20 + 5*20 + 7*1 = 9307

When counting days, however, the Mayas used a system in which the first place (as usual) had a value of 1, the second place had a value of 20, but the third place had a value not of 400 (20*20) but of 360 (18*20). (This may have been due to the fact that 360 is close to the length of the year in days.) The value of higher places continued regularly with 7,200 (20*18*20), 144,000 (20*20*18*20), etc. In such a system:

                  1.3.5.7 = 1*20*18*20 + 3*18*20 + 5*20 + 7*1 = 8,387
and 11.12.13.14.15 = 11*20*20*18*20 + 12*20*18*20 + 13*18*20 + 14*20 + 15*1
                            = 11*144,000 + 12*7,200 + 13*360 + 14*20 + 15
                            = 1,675,375.

A Maya long count date is a modified vigesimal number (as described above) composed of five places, e.g. 9.11.16.0.0, and interpreted as a count of days from some base date. There are many long count dates inscribed in the stellae and written in the codices. Calculation of the decimal equivalent of a long count yields a number of days. This is regarded as a number of days counted forward from a certain day in the past. It is the number of days since the day 0.0.0.0.0. The obvious question is: What day was used as the base date? This question has two aspects: (1) What day was used by the Mayas as the base date? (2)  What day was that in terms of the Western calendar? We shall return to these questions below.

Just as we have names (such as week) for certain periods of time, the Mayas had names for periods consisting of 20 days, 360 days, 7,200 days, etc., in accord with their modified vigesimal system of counting days. A day is known as a kin. Twenty kins make a uinal, 18 uinals a tun, 20 tuns a katun and 20 katuns a baktun. Thus we have:

             1 kin    =  1 day
            1 uinal  = 20 kins   = 20 days
            1 tun    = 18 uinals = 360 days
            1 katun  = 20 tuns   = 7,200 days
            1 baktun = 20 katuns = 144,000 days

The numbers at the five places in the long count are thus counts of baktuns, etc., as follows:

baktuns . katuns . tuns . uninals . kin

Thus, for example, 9.15.9.0.1 denotes a count of 9 baktuns, 15 katuns, 9 tuns, no uinals and 1 kin, or in other words, 9*144,000 + 15*7,200 + 9*360 + 0*20 + 1*1 days, or 1,407,201 days. It is a count of days from the Maya base date of 0.0.0.0.0.

Most of the long count dates which occur in the stone inscriptions have a baktun count of 9. The period 9.0.0.0.0 through 10.0.0.0.0, the period of the Classic Maya, is now thought by scholars to coincide with the period (approximately) 436 A.D. through 829 A.D. There are, however, some strange anomalies. Morley  deciphers two long count dates (found at Palenque) as 1.18.5.4.0 and 1.18.5.3.6 (14 days apart) which are some 2,794 solar years prior to 9.0.0.0.0. Since there is no evidence that the Mayas existed before about 500 B.C., what could these early long count dates possibly be referring to?

We would expect that the next higher unit after the baktun would consist of 20 baktuns, and it appears there was such a unit, called a pictun. However, no long count date occurs with a baktun count of more than 12, except that 13.0.0.0.0 occurs. A widely-accepted school of thought holds that in the Maya long count system 13.0.0.0.0 marks the beginning of a new cycle, and so is equivalent to 0.0.0.0.0. In this view, 13 baktuns make up a great cycle or, Maya era, of 13*144,000 = 1,872,000 days (approximately 5125.37 solar years).

The date 0.0.0.0.0 is equal to year 3113 B.C..
The date 13.0.0.0.0 is equal to year 2012 A.D..

Sacred Calendar - Tzolkin dates

The tzolkin, sometimes known as the sacred calendar, is a cycle of 260 days. Each tzolkin day is denoted by a combination of a number from 1 through 13 and a name from the set of twenty (in the order: Imix, Ik, Akbal, Kan ....):

   Imix       Cimi    Chuen  Cib

   Ik         Manik   Eb     Caban

   Akbal      Lamat   Ben    Edznab

   Kan        Muluc   Ix     Cauac

   Chicchan   Oc      Men    Ahau

The days cycle through the numbers and through the names independently. The sequence of tzolkin days thus runs:

            1 Imix

            2 Ik

            3 Akbal

            4 Kan

              . . .

            13 Ben

            1 Ix        (here we repeat the cycle of numbers)

            2 Men

            3 Cib

            4 Caban

            5 Edznab

            6 Cauac

            7 Ahau

            8 Imix      (here we repeat the cycle of names)

            9 Ik

            10 Akbal

              . . .

There are 260 elements in this sequence. That is because 260 is the least common multiple of 13 and 20. Thus the cycle of (13) tzolkin day numbers combined with (20) tzolkin day names repeats each 260 days.

In order to explain this 260-day calendrical cycle some have speculated that the Mayas chose this number of days because their allegedly advanced astronomical knowledge revealed to them that a period of 260 days fits well with certain astronomical periods, such as the eclipse-year. A more prosaic explanation is that there were originally two branches of Maya society, one of which used a 13-day cycle of numbered days and the other a 20-day cycle of named days. (There is a set of thirteen Maya gods, which may be the origin of the 13 numbered days, similar to our week.) Then at some point in early Maya history the two groups merged, combining the two calendars so that neither group would lose their method of day-reckoning, resulting in the 260-day cycle as described above.

Mayan Civil Calendar - Haab dates

The Mayas also maintained a so-called "civil" calendar, called the "haab". This was similar to our calendar in that it consisted of months, and within months, of days numbered consecutively. However, unlike our calendar, the haab cycle is made up of eighteen months of twenty days each, plus five days at the end of the year. The eighteen names for the months (in the order: Pop, Uo, Zip ...) are:

    Pop    Xul     Zac   Pax

    Uo     Yaxkin  Ceh   Kayab

    Zip    Mol     Mac   Cumku

    Zodz   Chen    Kankin

    Zec    Yax     Muan

The five extra days formed the "month" of Uayeb, meaning "nameless". The five "nameless" days were considered unlucky. One did not get married in Uayeb. The haab cycle thus consisted of 18*20 + 5 = 365 days, the integral number of days closest to the mean solar year of 365.2422 mean solar days.

The sequence of days from the first day of the year to the last thus runs as follows:

    0   Pop

    1   Pop

    ...

    19  Pop

    0   Zip

    1   Zip

    ...

    19  Zip

    0   Zodz

    ...

    19  Cumku

    0   Uayeb

    ...

    4   Uayeb

For most of Maya history the first day of Pop was denoted by 0 Pop and the last by 19 Pop. However, on the eve of the Spanish conquest the first day of Pop began to be numbered 1, and the last day 20 (except for Uayeb), so that the year began with 1 Pop and ended with 5 Uayeb.

There is some uncertainty as to whether (what has usually been taken to be) the first day of each haab month (e.g., 0 Zip) is really the last (i.e., the 20th, or the 5th) day of the preceding month (Pop in this case), or in other words, whether the last day of each month was actually written as "the day before the beginning of (the next) month", where the glyph translated as "the seating of" was used with the meaning of "the day before the beginning of the next month, namely ...". 0 Zip can be interpreted either as the first day of Zip or as the last day of Pop, but unfortunately the classic Maya are no longer here to tell us how they understood this date.

The Maya calendar round

The tzolkin and the haab are each cycles of days; the former is a cycle of 260 days and the latter is a cycle of 365 days. When specifying a day the Maya usually used both the tzolkin date and the haab date, as in 4 Ahau 3 Kankin. For the Mayas these two cycles ran together and concurrently, as shown by the following sequence of days:

 
Since 260 = 4*5*13 and 365 = 5*73, the earliest that a tzolkin/haab date combination can repeat is after 4*5*13*73 = 18,980 days, or just short of 52 solar years. This cycle of 18,980 days is called the Maya calendar round.

Maya long count dates are often given in association with the corresponding tzolkin/haab date, as in: 

            8.11.7.13.5     3  Chicchan 8 Kankin
        10.1.19.15.17    12  Caban     0 Yax
           10.3.8.14.4      6  Kan       0 Pop
             10.6.2.0.9      9  Muluc      7 Yax
        10.6.10.12.16      3  Cib        9 Uo

A particular tzolkin/haab date recurs every 18,980 days, whereas a long count date (assuming that the long count starts over at 0.0.0.0.0 on reaching 13.0.0.0.0) recurs every 1,872,000 days (once in 5,125.37 years). The combination of a long count date and a tzolkin/haab date occurs only once every 136,656,000 days (approximately 374,152 years or 73 Maya eras).

DECEMBER 12, 2012 THE TRUTH

The world is coming to an end on December 21, 2012! At least, that's the date predicted by the Mayans more than two thousand years old. DECODING THE PAST peels back the layers of mystery and examines in detail how the Maya calculated the exact date of doomsday. Journey back to the ancient city of Chichen Itza, the hub of Maya civilization deep in the heart of Mexico's Yucatan Peninsula. The Maya were legendary astronomers and timekeepers--their calendar is more accurate than our own. By tracking the stars and planets they assigned great meaning to astronomical phenomena and made extraordinary predictions based on them--many of which have come true. Could their doomsday prophecy be one of them? In insightful interviews archaeologists, astrologers, and historians speculate on the meaning of the 2012 prophecy. Their answers are as intriguing as the questions.