Mesoamerican Long Count calendar
The Mesoamerican Long Count calendar is a non-repeating base-20 and base-18 calendar used by pre-Columbian Mesoamerican cultures, most notably the Maya. For this reason, it is often known as the Maya 'Long Count calendar'. Using a modified vigesimal tally, the Long Count calendar identifies a day by counting the number of days passed since a mythical creation date that corresponds to August 11, 3114 BCE in the proleptic Gregorian calendar. The Long Count calendar was widely used on monuments.
Background
The two most widely used calendars in pre-Columbian Mesoamerica were the 260-day tzolkʼin and the 365-day haabʼ. The equivalent Aztec calendars are known in Nahuatl as the tōnalpōhualli and xiuhpōhualli, respectively.The combination of a haabʼ and a tzolkʼin date identifies a day in a combination which does not occur again for 18,980 days, a period known as the Calendar Round. To identify days over periods longer than this, Mesoamericans used the Long Count calendar.
Long Count periods
The Long Count calendar identifies a date by counting the number of days from a starting date that is generally calculated to be August 11, 3114 BCE in the proleptic Gregorian calendar or September 6 in the Julian calendar. There has been much debate over the precise correlation between the Western calendars and the Long Count calendars. The August 11 date is based on the GMT correlation.The completion of 13 bʼakʼtuns marks the Creation of the world of human beings according to the Maya. On this day, Raised-up-Sky-Lord caused three stones to be set by associated gods at Lying-Down-Sky, First-Three-Stone-Place. Because the sky still lay on the primordial sea, it was black. The setting of the three stones centered the cosmos which allowed the sky to be raised, revealing the
Rather than using a base 10 scheme, the Long Count days were tallied in a modified base-20 scheme. In a pure base 20 scheme, 0.0.0.1.5 is equal to 25 and 0.0.0.2.0 is equal to 40. The Long Count is not pure base-20, however, since the second digit from the right rolls over to zero when it reaches 18. Thus 0.0.1.0.0 does not represent 400 days, but rather only 360 days and 0.0.0.17.19 represents 359 days.
The name bʼakʼtun was invented by modern scholars. The numbered Long Count was no longer in use by the time the Spanish arrived in the Yucatán Peninsula, although unnumbered kʼatuns and tuns were still in use. Instead the Maya were using an abbreviated Short Count.
| Long Count unit | Long Count period | Days | Approximate Solar Years |
| 1 Kʼin | 1 | ||
| 1 Winal | 20 Kʼin | 20 | |
| 1 Tun | 18 Winal | 360 | |
| 1 Kʼatun | 20 Tun | 7,200 | |
| 1 Bʼakʼtun | 20 Kʼatun | 144,000 | |
| 1 Piktun | 20 Bʼakʼtun | 2,880,000 | |
| 1 Kalabtun | 20 Piktun | 57,600,000 | |
| 1 Kʼinchiltun | 20 Kalabtun | 1,152,000,000 | |
| 1 Alautun | 20 Kʼinchiltun | 23,040,000,000 | |
| 1 Hablatun | 20 Alautun | 460,800,000,000 |
Mesoamerican numerals
Long Count dates are written with Mesoamerican numerals, as shown on this table. A dot represents 1 while a bar equals 5. The shell glyph was used to represent the zero concept. The Long Count calendar required the use of zero as a place-holder and presents one of the earliest uses of the zero concept in history.On Maya monuments, the Long Count syntax is more complex. The date sequence is given once, at the beginning of the inscription and opens with the so-called ISIG which reads tzik-a habʼ . Next come the 5 digits of the Long Count, followed by the Calendar Round and supplementary series. The supplementary series is optional and contains lunar data, for example, the age of the Moon on the day and the calculated length of current lunation. The text then continues with whatever activity occurred on that date.
A drawing of a full Maya Long Count inscription is shown [|below].
Earliest Long Counts
The earliest contemporaneous Long Count inscription yet discovered is on Stela 2 at Chiapa de Corzo, Chiapas, Mexico, showing a date of 36 BCE, although Stela 2 from Takalik Abaj, Guatemala might be earlier. Takalik Abaj Stela 2's highly battered Long Count inscription shows 7 bak'tuns, followed by k'atuns with a tentative 6 coefficient, but that could also be 11 or 16, giving the range of possible dates to fall between 236 and 19 BCE.Although Takalik Abaj Stela 2 remains controversial, this table includes it, as well as six other artifacts with the eight oldest Long Count inscriptions according to Dartmouth professor Vincent H. Malmström. Interpretations of inscriptions on some artifacts differ.
| Archaeological site | Name | Gregorian date GMT correlation | Long Count | Location |
| Takalik Abaj | Stela 2 | 236 – 19 BCE | 7..?.?.? | Retalhuleu, Guatemala |
| Chiapa de Corzo | Stela 2 | December 6, 36 BCE or October 9, 182 CE | 7.16.3.2.13 or 8.7.3.2.13 | Chiapas, Mexico |
| Tres Zapotes | Stela C | September 1, 32 BCE | 7.16.6.16.18 | Veracruz, Mexico |
| El Baúl | Stela 1 | 11 – 37 CE | 7.18.9.7.12, 7.18.14.8.12, 7.19.7.8.12, or 7.19.15.7.12 | Escuintla, Guatemala |
| Takalik Abaj | Stela 5 | August 31, 83 CE or May 19, 103 CE | 8.2.2.10.15 or 8.3.2.10.15 | Retalhuleu, Guatemala |
| Takalik Abaj | Stela 5 | June 3, 126 CE | 8.4.5.17.11 | Retalhuleu, Guatemala |
| La Mojarra | Stela 1 | May 19, 143 CE | 8.5.3.3.5 | Veracruz, Mexico |
| La Mojarra | Stela 1 | July 11, 156 CE | 8.5.16.9.7 | Veracruz, Mexico |
| Near La Mojarra | Tuxtla Statuette | March 12, 162 CE | 8.6.2.4.17 | Veracruz, Mexico |
Of the six sites, three are on the western edge of the Maya homeland and three are several hundred kilometers further west, leading some researchers to believe that the Long Count calendar predates the Maya. La Mojarra Stela 1, the Tuxtla Statuette, Tres Zapotes Stela C and Chiapa Stela 2 are all inscribed in an Epi-Olmec, not Maya, style. El Baúl Stela 2, on the other hand, was created in the Izapan style.
The first unequivocally Maya artifact is Stela 29 from Tikal, with the Long Count date of 292 CE, more than 300 years after Stela 2 from Chiapa de Corzo.
More recently, with the discovery in Guatemala of the San Bartolo stone block text, it has been argued that this text celebrates an upcoming time period ending celebration. This time period may have been projected to end sometime between 7.3.0.0.0 and 7.5.0.0.0. Besides being the earliest Maya hieroglyphic text so far uncovered, this would arguably be the earliest evidence to date of Long Count notation in Mesoamerica.
Latest Long Counts
The Xultun Stela 10 at the site of Xultun in Guatemala, excavations in 1915 found an inscription with a Long Count date of "10.3.0.0.0 1 Ajaw 3 Yaxk’in ", at that time the latest. Monument inscriptions at Seibal and Uaxactun in Guatemala had the same date. For context, the latest known long count date from Palenque is "9.18.9.4.4, corresponding to A.D. November 15, 799", on pottery. Inscriptions from Toniná and Tzibanche in Mexico had a long count date of "10.4.0.0.0". The Dresden Codex has a long count date of 10.19.6.1.8" though this may not be historical.Correlations between Western calendars and the Long Count
The Maya and Western calendars are correlated by using a Julian day number of the starting date of the current creation — 13.0.0.0.0, 4 Ajaw, 8 Kumkʼu. This is referred to as a "correlation constant". The generally accepted correlation constant is the Modified Thompson 2, "Goodman–Martinez–Thompson", or GMT correlation of 584,283 days. Using the GMT correlation, the current creation started on September 6, −3113 – August 11, 3114 BCE in the Proleptic Gregorian calendar. The study of correlating the Maya and western calendar is referred to as the correlation question. The GMT correlation is also called the 11.16 correlation.In Breaking the Maya Code, Michael D. Coe writes: "In spite of oceans of ink that have been spilled on the subject, there now is not the slightest chance that these three scholars were not right ..." The evidence for the GMT correlation is historical, astronomical and archaeological:
Historical: Calendar Round dates with a corresponding Julian date are recorded in Diego de Landa's Relación de las cosas de Yucatán, the Chronicle of Oxcutzkab and the books of Chilam Balam. De Landa records a date that is a Tun ending in the Short Count. Oxkutzcab contains 12 Tun endings. Bricker and Bricker find that only the GMT correlation is consistent with these dates. The Book of Chilam Balam of Chumayel contains the only colonial reference to classic long-count dates. The Julian calendar date of 11.16.0.0.0 confirms the GMT correlation.
The Annals of the Cakchiquels contains numerous Tzolkʼin dates correlated with European dates. These confirm the GMT correlation. Weeks, Sachse and Prager transcribed three divinatory calendars from highland Guatemala. They found that the 1772 calendar confirms the GMT correlation. The fall of the capital city of the Aztec Empire, Tenochtitlan, occurred on August 13, 1521. A number of different chroniclers wrote that the Tzolkʼin date of the event was 1 Snake.
Post-conquest scholars such as Sahagún and Durán recorded Tonalpohualli dates with a calendar date. Many indigenous communities in the Mexican states of Veracruz, Oaxaca and Chiapas and in Guatemala, principally those speaking the Mayan languages Ixil, Mam, Pokomchí and Quiché, keep the Tzolkʼin and in many cases the Haabʼ. These are all consistent with the GMT correlation. Munro Edmonsen studied 60 Mesoamerican calendars, 20 of which have known correlations to European calendars, and found remarkable consistency among them and that only the GMT correlation fits the historical, ethnographic and astronomical evidence.
Astronomical: Any correct correlation must match the astronomical content of classic inscriptions. The GMT correlation does an excellent job of matching lunar data in the supplementary series. For example: An inscription at the Temple of the Sun at Palenque records that on Long Count 9.16.4.10.8 there were 26 days completed in a 30-day lunation. This Long Count is also the entry date for the eclipse table of the Dresden Codex.
Using the third method, the Palenque system, the new moon would have been the first evening when one could look to the west after sunset and see the thin crescent moon. Given our modern ability to know exactly where to look, when the crescent Moon is favorably located, from an excellent site, on rare occasions, using binoculars or a telescope, observers can see and photograph the crescent moon less than one day after conjunction. Generally, most observers cannot see the new Moon with the naked eye until the first evening when the lunar phase day is at least 1.5. If one assumes that the new moon is the first day when the lunar phase day is at least 1.5 at six in the evening in time zone UTC−6, the GMT correlation will match many lunar inscriptions exactly. In this example the lunar phase day was 27.7 at 6 pm after a conjunction at 1:25 am and a new Moon when the lunar phase day was 1.7 at 6 pm on . This works well for many but not all lunar inscriptions.
Modern astronomers refer to the conjunction of the Sun and Moon as the new moon. But Mesoamerican astronomy was observational, not theoretical. The people of Mesoamerica did not know about the Copernican nature of the Solar System — they had no theoretical understanding of the orbital nature of the heavenly bodies. Some authors analyze the lunar inscriptions based on this modern understanding of the motions of the Moon but there is no evidence that the Mesoamericans shared it.
The first method seems to have been used for other inscriptions such as Quirgua stela E. By the third method, that stela should show a moon age of 26 days, but in fact it records a new moon. Using the GMT correlation at six AM in the time zone UTC−6, this would be 2.25 days before conjunction, so it could record the first day when one could not see the waning moon.
Fuls analysed these inscriptions and found strong evidence for the Palenque system and the GMT correlation; however, he cautioned: "Analysis of the Lunar Series shows that at least two different methods and formulas were used to calculate the moon's age and position in the six-month cycle ..." which gives eclipse seasons when the Moon is near its ascending or descending node and an eclipse is likely to occur. Dates converted using the GMT correlation agree closely with the Dresden Codex eclipse tables. The Dresden Codex contains a Venus table which records the heliacal risings of Venus. Using the GMT correlation these agree closely with modern astronomical calculations.
Archaeological: Various items that can be associated with specific Long Count dates have been isotope dated. In 1959 the University of Pennsylvania carbon dated samples from ten wood lintels from Tikal. These were carved with a date equivalent to 741 AD, using the GMT correlation. The average carbon date was 746±34 years. Recently one of these, Lintel 3 from Temple I, was analyzed again using more accurate methods and found to agree closely with the GMT correlation. In 2012,
using modern AMS radiocarbon dating, a single beam from Tikal was dated, also strongly supporting
the GMT.
If a proposed correlation only has to agree with one of these lines of evidence there could be numerous other possibilities. Astronomers have proposed many correlations, for example: Lounsbury, Fuls, et al., Böhm and Böhm and Stock.
Today, , in the Long Count is .
| Name | Correlation |
| Bowditch | 394,483 |
| Willson | 438,906 |
| Smiley | 482,699 |
| Makemson | 489,138 |
| Modified Spinden | 489,383 |
| Spinden | 489,384 |
| Teeple | 492,622 |
| Dinsmoor | 497,879 |
| −4CR | 508,363 |
| −2CR | 546,323 |
| Stock | 556,408 |
| Goodman | 584,280 |
| Martinez–Hernandez | 584,281 |
| GMT | 584,283 |
| Modified Thompson 1 | 584,284 |
| Thompson | 584,285 |
| Pogo | 588,626 |
| 622,243 | |
| Böhm & Böhm | 622,261 |
| Kreichgauer | 626,927 |
| 660,203 | |
| Fuls, et al. | 660,208 |
| Hochleitner | 674,265 |
| Schultz | 677,723 |
| Escalona–Ramos | 679,108 |
| Vaillant | 679,183 |
| Weitzel | 774,078 |
| Long Count | Gregorian date GMT correlation | Julian day number |
| 0.0.0.0.0 | Mon, Aug 11, 3114 BCE | 584,283 |
| 1.0.0.0.0 | Thu, Nov 13, 2720 BCE | 728,283 |
| 2.0.0.0.0 | Sun, Feb 16, 2325 BCE | 872,283 |
| 3.0.0.0.0 | Wed, May 21, 1931 BCE | 1,016,283 |
| 4.0.0.0.0 | Sat, Aug 23, 1537 BCE | 1,160,283 |
| 5.0.0.0.0 | Tue, Nov 26, 1143 BCE | 1,304,283 |
| 6.0.0.0.0 | Fri, Feb 28, 748 BCE | 1,448,283 |
| 7.0.0.0.0 | Mon, Jun 3, 354 BCE | 1,592,283 |
| 8.0.0.0.0 | Thu, Sep 5, 41 CE | 1,736,283 |
| 9.0.0.0.0 | Sun, Dec 9, 435 | 1,880,283 |
| 10.0.0.0.0 | Wed, Mar 13, 830 | 2,024,283 |
| 11.0.0.0.0 | Sat, Jun 15, 1224 | 2,168,283 |
| 12.0.0.0.0 | Tue, Sep 18, 1618 | 2,312,283 |
| 13.0.0.0.0 | Fri, Dec 21, 2012 | 2,456,283 |
| 14.0.0.0.0 | Mon, Mar 26, 2407 | 2,600,283 |
| 15.0.0.0.0 | Thu, Jun 28, 2801 | 2,744,283 |
| 16.0.0.0.0 | Sun, Oct 1, 3195 | 2,888,283 |
| 17.0.0.0.0 | Wed, Jan 3, 3590 | 3,032,283 |
| 18.0.0.0.0 | Sat, Apr 7, 3984 | 3,176,283 |
| 19.0.0.0.0 | Tue, Jul 11, 4378 | 3,320,283 |
| 1.0.0.0.0.0 | Fri, Oct 13, 4772 | 3,464,283 |