The Mesoamerican 260-day calendar consists of a cycle of 260 days, each day signified by a combination of a number from 1 to 13, 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 Reed, the cycle of numbers would restart (though the twenty day signs had not yet been exhausted), resulting in 1 Jaguar, 2 Eagle, and so on, as the days immediately following 13 Reed. This cycle of number and day signs would continue similarly until the 20th week, which would start on 1 Rabbit, and end on 13 Flower. 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 sequence back to 1 Crocodile.
Day signs of the Mesoamerican calendar:
| N | Day sign | Day sign (Mayan) | Day sign (Aztec) | Secalli Life Cycle |
| 1 | Crocodile |  Imix |  Cipactli |  Creation |
| 2 | Wind |  Ik |  Ehecatl |  Quickening |
| 3 | House |  Akbal |  Calli |  Birth |
| 4 | Lizard |  Kan |  Cuetzpalin |  Adult |
| 5 | Serpent |  Chikchan |  Coatl |  Rebirth |
| 6 | Death |  Kimi |  Miquiztli |  Death |
| 7 | Deer |  Manik |  Mazatl |  Spirit World |
| 8 | Rabbit |  Lamat |  Tochtli |  Materialism |
| 9 | Water |  Muluk |  Atl |  Triumph |
| 10 | Dog |  Ok |  Itzcuintli |  Anguish |
| 11 | Monkey |  Chuwen |  Ozomahtli |  First Rung |
| 12 | Grass |  Eb |  Malinalli |  Rising |
| 13 | Reed |  Ben |  Acatl |  Resurrection |
| 14 | Jaguar |  Ix |  Ocelotl |  Sanctify |
| 15 | Eagle |  Men |  Cuauhtli |  Fulness |
| 16 | Vulture |  Kib |  Cozcacuauhtli |  Awareness |
| 17 | Movement |  Kaban |  Ollin |  Motion, Life |
| 18 | Flint |  Etznab |  Tecpatl |  Perfection |
| 19 | Rain |  Kawak |  Quiahuitl |  Lightning |
| 20 | Flower |  Ajaw |  Xochitl |  Lord |
The sacred calendar is laid out as follows:
1 Crocodile
2 Wind
3 House
4 Lizard
5 Serpent
6 Death
7 Deer
8 Rabbit
9 Water
10 Dog
11 Monkey
12 Grass
13 Reed
1 Jaguar
2 Eagle
3 Vulture
4 Movement
5 Flint
6 Rain
7 Flower
8 Crocodile
9 Wind
10 House
11 Lizard
12 Serpent
13 Death
1 Deer
2 Rabbit
3 Water
4 Dog
5 Monkey
6 Grass
7 Reed
8 Jaguar
9 Eagle
10 Vulture
11 Movement
12 Flint
13 Rain
1 Flower
2 Crocodile
3 Wind
4 House
5 Lizard
6 Serpent
7 Death
8 Deer
9 Rabbit
10 Water
11 Dog
12 Monkey
13 Grass
1 Reed
2 Jaguar
3 Eagle
4 Vulture
5 Movement
6 Flint
7 Rain
8 Flower
9 Crocodile
10 Wind
11 House
12 Lizard
13 Serpent
1 Death
2 Deer
3 Rabbit
4 Water
5 Dog
6 Monkey
7 Grass
8 Reed
9 Jaguar
10 Eagle
11 Vulture
12 Movement
13 Flint
1 Rain
2 Flower
3 Crocodile
4 Wind
5 House
6 Lizard
7 Serpent
8 Death
9 Deer
10 Rabbit
11 Water
12 Dog
13 Monkey
1 Grass
2 Reed
3 Jaguar
4 Eagle
5 Vulture
6 Movement
7 Flint
8 Rain
9 Flower
10 Crocodile
11 Wind
12 House
13 Lizard
1 Serpent
2 Death
3 Deer
4 Rabbit
5 Water
6 Dog
7 Monkey
8 Grass
9 Reed
10 Jaguar
11 Eagle
12 Vulture
13 Movement
1 Flint
2 Rain
3 Flower
4 Crocodile
5 Wind
6 House
7 Lizard
8 Serpent
9 Death
10 Deer
11 Rabbit
12 Water
13 Dog
1 Monkey
2 Grass
3 Reed
4 Jaguar
5 Eagle
6 Vulture
7 Movement
8 Flint
9 Rain
10 Flower
11 Crocodile
12 Wind
13 House
1 Lizard
2 Serpent
3 Death
4 Deer
5 Rabbit
6 Water
7 Dog
8 Monkey
9 Grass
10 Reed
11 Jaguar
12 Eagle
13 Vulture
1 Movement
2 Flint
3 Rain
4 Flower
5 Crocodile
6 Wind
7 House
8 Lizard
9 Serpent
10 Death
11 Deer
12 Rabbit
13 Water
1 Dog
2 Monkey
3 Grass
4 Reed
5 Jaguar
6 Eagle
7 Vulture
8 Movement
9 Flint
10 Rain
11 Flower
12 Crocodile
13 Wind
1 House
2 Lizard
3 Serpent
4 Death
5 Deer
6 Rabbit
7 Water
8 Dog
9 Monkey
10 Grass
11 Reed
12 Jaguar
13 Eagle
1 Vulture
2 Movement
3 Flint
4 Rain
5 Flower
6 Crocodile
7 Wind
8 House
9 Lizard
10 Serpent
11 Death
12 Deer
13 Rabbit
1 Water
2 Dog
3 Monkey
4 Grass
5 Reed
6 Jaguar
7 Eagle
8 Vulture
9 Movement
10 Flint
11 Rain
12 Flower
13 Crocodile
1 Wind
2 House
3 Lizard
4 Serpent
5 Death
6 Deer
7 Rabbit
8 Water
9 Dog
10 Monkey
11 Grass
12 Reed
13 Jaguar
1 Eagle
2 Vulture
3 Movement
4 Flint
5 Rain
6 Flower
7 Crocodile
8 Wind
9 House
10 Lizard
11 Serpent
12 Death
13 Deer
1 Rabbit
2 Water
3 Dog
4 Monkey
5 Grass
6 Reed
7 Jaguar
8 Eagle
9 Vulture
10 Movement
11 Flint
12 Rain
13 Flower
Correlations between Western calendars and the Long Count
The Maya and Western calendars are correlated by using a Julian day number (JDN) of the starting date of the current creation — 13.0.0.0.0, 4 Ajaw, 8 Kumkʼu.[d] 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 (Julian astronomical) – 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.[16][17][18][19][20] 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 (conflated to G-M-T when talking about the correlation) were not right …”.[21] 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 (written circa 1566), 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 in consistent with these dates.[22] The Book of Chilam Balam of Chumayel[23] contains the only colonial reference to classic long-count dates. The Julian calendar date of 11.16.0.0.0 (November 2, 1539) confirms the GMT correlation.[24]
The Annals of the Cakchiquels contains numerous Tzolkʼin dates correlated with European dates. These confirm the GMT correlation.[25] Weeks, Sachse and Prager transcribed three divinatory calendars from highland Guatemala. They found that the 1772 calendar confirms the GMT correlation.[26] The fall of the capital city of the Aztec Empire, Tenochtitlan, occurred on August 13, 1521.[27] A number of different chroniclers wrote that the Tzolkʼin (Tonalpohualli) date of the event was 1 Snake.[28]
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[29] and in Guatemala, principally those speaking the Mayan languages Ixil, Mam, Pokomchí and Quiché, keep the Tzolkʼin and in many cases the Haabʼ.[30] 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.[31]
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.[32] 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.[33] This Long Count is also the entry date for the eclipse table of the Dresden Codex.[34][e]
Using the third method, the Palenque system,[36] 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.[37][38][39][40][41][42] 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 time zone of the Maya area), the GMT correlation will match many lunar inscriptions exactly. In this example the lunar phase day was 27.7 (26 days counting from zero) at 6 pm after a conjunction at 1:25 am October 10, 755 and a new Moon when the lunar phase day was 1.7 at 6 pm on October 11, 755 (Julian calendar). This works well for many but not all lunar inscriptions.
Modern astronomers refer to the conjunction of the Sun and Moon (the time when the Sun and Moon have the same ecliptic longitude) as the new moon. But Mesoamerican astronomy was observational, not theoretical. The people of Mesoamerica didn’t 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 (9.17.0.0.0). By the third method, that stela should show a moon age of 26 days, but in fact it records a new moon.[43] 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[44] 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.[45] 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.[46]
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.[47] 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.[48]
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,[49] Fuls, et al.,[50] Böhm and Böhm[51][52] and Stock.[53]