Calendar used by several pre-Columbian Mesoamerican cultures
East side of stela C, Quirigua with the mythical creation date of 13 baktuns, 0 katuns, 0 tuns, 0 winals, 0 kins, 4 Ahau 8 Cumku – August 11, 3114BCE in the proleptic Gregorian calendar.
The Mesoamerican Long Count calendar is a non-repeating base-20 and base-18 calendar used by pre-ColumbianMesoamerican cultures, most notably the Maya. For this reason, it is often known as the MayaLong 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.[lower-alpha 1] The Long Count calendar was widely used on monuments.
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 Tonalpohualli and Xiuhpohualli, respectively.
The combination of a Haabʼ and a Tzolkʼin date identifies a day in a combination which does not occur again for 18,980days (52Haabʼ cycles of 365days equals 73Tzolkʼin cycles of 260days, approximately 52years), a period known as the Calendar Round. To identify days over periods longer than this, Mesoamericans used the Long Count calendar.
Detail showing columns of glyphs from a portion of the 2nd centuryCE La Mojarra Stela 1. The left column gives a Long Count date of 8.5.16.9.7, or 156CE. The other columns visible are glyphs from the Epi-Olmec script.
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, 3114BCE in the proleptic Gregorian calendar or September 6 in the Julian calendar (or −3113 in astronomical year numbering). 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 (August 11, 3114BCE) 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 sun.[1]
Rather than using a base10 scheme, the Long Count days were tallied in a modified base-20 scheme. In a pure base20 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 (and only that digit) rolls over to zero when it reaches 18.[citation needed] Thus 0.0.1.0.0 does not represent 400days, 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 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 (Introductory Series Initial Glyph) which reads tzik-a(h) habʼ [patron of Haabʼ month] ("revered was the year-count with the patron [of the month]").[2] Next come the 5 digits of the Long Count, followed by the Calendar Round (tzolkʼin and Haabʼ) 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.[lower-alpha 2] 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 Stela2 at Chiapa de Corzo, Chiapas, Mexico, showing a date of 36BCE, although Stela 2 from Takalik Abaj, Guatemala might be earlier.[3] Takalik Abaj Stela 2's highly battered Long Count inscription shows 7bak'tuns, followed by k'atuns with a tentative 6coefficient, but that could also be 11 or 16, giving the range of possible dates to fall between 236 and 19BCE.[lower-alpha 3][citation needed]
Although Takalik Abaj Stela2 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 (two of the artifacts contain two dates and Malmström does not include Takalik Abaj Stela2).[4][5] Interpretations of inscriptions on some artifacts differ.[4][6][7]
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.[11] La Mojarra Stela1, the Tuxtla Statuette, Tres Zapotes StelaC and Chiapa Stela2 are all inscribed in an Epi-Olmec, not Maya, style.[12] El Baúl Stela2, on the other hand, was created in the Izapan style.
The first unequivocally Maya artifact is Stela29 from Tikal, with the Long Count date of 292CE (8.12.14.8.15), more than 300years after Stela2 from Chiapa de Corzo.[13]
More recently, with the discovery in Guatemala of the San Bartolo (Maya site) stone block text (c. 300BCE),[14] 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 (295BCE) and 7.5.0.0.0 (256BCE).[15] 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.
Correlations between Western calendars and the Long Count
The back of StelaC from Tres Zapotes, an Olmec archaeological site. This is the second oldest Long Count date yet discovered. The numerals 7.16.6.16.18 translate to September 1, 32BCE (Gregorian). The glyphs surrounding the date are what is thought to be one of the few surviving examples of Epi-Olmec script.
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.[lower-alpha 4] This is referred to as a "correlation constant". The generally accepted correlation constant is the Modified Thompson2, "Goodman–Martinez–Thompson", or GMT correlation of 584,283days. Using the GMT correlation, the current creation started on September 6, −3113 (Julian astronomical) – August 11, 3114BCE 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 12Tun endings. Bricker and Bricker find that only the GMT correlation is 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][lower-alpha 5]
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 (26days counting from zero) at 6pm after a conjunction at 1:25am October 10, 755 and a new Moon when the lunar phase day was 1.7 at 6pm 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 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 (9.17.0.0.0). By the third method, that stela should show a moon age of 26days, 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 2.25days 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 Pennsylvaniacarbon dated samples from ten wood lintels from Tikal.[47] These were carved with a date equivalent to 741AD, 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] In 2012, using modern AMS radiocarbon dating, a single beam from Tikal was dated, also strongly supporting the GMT.[49]
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,[50] Fuls, et al.,[51] Böhm and Böhm[52][53] and Stock.[54]
Today, 1 November 2024 (UTC), in the Long Count is 13.0.12.0.13 (using GMT correlation).
JDN correlations to the Maya creation date (after Thompson 1971, et al. and Aveni 1980)
According to the Popol Vuh, a book compiling details of creation accounts known to the Kʼicheʼ Maya of the Colonial-era highlands, humankind lives in the fourth world.[55] The Popol Vuh describes the first three creations that the gods failed in making and the creation of the successful fourth world where men were placed. In the Maya Long Count, the previous creation ended at the end of a 13th bʼakʼtun.
The previous creation ended on a Long Count of 12.19.19.17.19. Another 12.19.19.17.19 occurred on December 20, 2012 (Gregorian Calendar), followed by the start of the 14th bʼakʼtun, 13.0.0.0.0, on December 21, 2012.[lower-alpha 6] There are only two references to the current creation's 13thbʼakʼtun in the fragmentary Mayan corpus: Tortuguero Monument6, part of a ruler's inscription and the recently discovered La Corona Hieroglyphic Stairway2, BlockV.[57]
Maya inscriptions occasionally reference future predicted events or commemorations that would occur on dates that lie beyond 2012 (that is, beyond the completion of the 13thbʼakʼtun of the current era). Most of these are in the form of "distance dates" where some Long Count date is given, together with a Distance Number that is to be added to the Long Count date to arrive at this future date.
For example, on the west panel at the Temple of Inscriptions in Palenque, a section of the text projects into the future to the 80thCalendar Round (CR) 'anniversary' of the famous Palenque ruler Kʼinich Janaabʼ Pakal's accession to the throne (Pakal's accession occurred on a Calendar Round date 5Lamat 1Mol, at Long Count 9.9.2.4.8 equivalent to 27July 615CE in the proleptic Gregorian calendar).[lower-alpha 7] It does this by commencing with Pakal's birthdate 9.8.9.13.0 8Ajaw 13Pop (24March 603 CE Gregorian) and adding to it the Distance Number 10.11.10.5.8.[58]
This calculation arrives at the 80th Calendar Round since his accession, a day that also has a CR date of 5 Lamat 1 Mol, but which lies over 4,000years in the future from Pakal's time—the day 21October in the year4772. The inscription notes[citation needed] that this day would fall eight days after the completion of the 1st piktun (since the creation or zero date of the Long Count system), where the piktun is the next-highest order above the bʼakʼtun in the Long Count. If the completion date of that piktun—13October 4772—were to be written out in Long Count notation, it could be represented as 1.0.0.0.0.0. The 80thCR anniversary date, eight days later, would be 1.0.0.0.0.8 5Lamat 1Mol.[58][59]
Despite the publicity generated by the 2012 date, Susan Milbrath, curator of Latin American Art and Archaeology at the Florida Museum of Natural History, stated that "We have no record or knowledge that [the Maya] would think the world would come to an end" in 2012.[60]USA Today writes "'For the ancient Maya, it was a huge celebration to make it to the end of a whole cycle,' says Sandra Noble, executive director of the Foundation for the Advancement of Mesoamerican Studies in Crystal River, Florida. To render December 21, 2012, as a doomsday event or moment of cosmic shifting, she says, is 'a complete fabrication and a chance for a lot of people to cash in.'"[60] "There will be another cycle," says E. Wyllys Andrews V, director of the Tulane University Middle American Research Institute (MARI). "We know the Maya thought there was one before this, and that implies they were comfortable with the idea of another one after this."[61]
Converting between the Long Count and western calendars
Calculating a Western calendar date from a Long Count
It is important to know the difference between the Julian and Gregorian calendars when calculating a Western calendar date from a Long Count date.[lower-alpha 8]
Using as an example the Long Count date of 9.10.11.17.0 (Long Count date mentioned on the Palenque Palace Tablet), first calculate the number of days that have passed since the zero date (August 11, 3114 BCE; GMT correlation, in the Proleptic Gregorian calendar, September 6, −3113 Julian astronomical).
9
× 144,000
= 1,296,000
10
× 7,200
= 72,000
11
× 360
= 3,960
17
× 20
= 340
0
× 1
= 0
Total days
= 1,372,300
Then add the GMT correlation to the total number of days.
From this number, subtract the nearest smaller Julian Day Number (in the table below), in this case 1,940,206, which corresponds to the year 600CE.
year
JDN:
year
JDN:
1
1,721,060
1100
2,122,827
100
1,757,585
1200
2,159,351
200
1,794,109
1300
2,195,876
300
1,830,633
1400
2,232,400
400
1,867,157
1500
2,268,924
500
1,903,682
1600
2,305,448
600
1,940,206
1700
2,341,973
700
1,976,730
1800
2,378,497
800
2,013,254
1900
2,415,021
900
2,049,779
2000
2,451,545
1000
2,086,303
1,956,583 – 1,940,206 = 16,377
Next, divide this number by 365days (vague year).
16,377 / 365 = 44.86849
The remainder is 44.86849years, which is 44years and 317days. The full year date is 644CE. Now calculate the month and day number, taking into account leap days over the 44years. In the Gregorian Calendar, every fourth year is a leap year with the exception of centuries not evenly divisible by 400 (e.g. 100, 200, 300). When the year is divisible by 400 (e.g. 400, 800, etc.), do not add an extra day. The calculated year is 644CE. The number of leap days, keeping in mind that the year 600 is not a leap year, is 10. Subtracting that from 317 remainder days is 307; in other words, the 307th day of the year 644CE, which is November3. To summarize: the Long Count date 9.10.11.17.0 corresponds to November3, 644CE, in the Proleptic Gregorian calendar.
Use an astronomical algorithm such as the Method of Meeus[63] to convert the Julian day to a Julian/Gregorian date with astronomical dating of negative years:[lower-alpha 9]
In this example:
input: Julian day JJ = J + 0.5 // 1,956,583.5Z = integer part of J// 1,956,583F = fraction part of J// 0.5ifZ < 2,299,161 then// Julian?A = Zelsealpha = floor((Z - 1,867,216.25) / 36,524.25) // 15A = Z + 1 + alpha - floor(alpha / 4.0) // 2,436,129// The floor operation rounds a decimal number down to the next lowest integer.// For example, floor(1.5) = 1 and floor(−1.5) = -2end ifB = A + 1524 // 1,958,107C = floor((B - 122.1) / 365.25) // 5,360D = floor(365.25 × C) // 1,957,740E = floor((B - D) / 30.6001) // 11day = B - D - floor(30.6001 × E) + F// 31.5ifE < 14 thenmonth = E - 1 // 10elsemonth = E - 13 end ififmonth > 2 thenyear = C - 4716 // 644elseyear = C - 4715 end ifreturn (year, month, day)
In this example the Julian date is noon October 31, 644. The Method of Meeus is not valid for negative year numbers (astronomical), so another method such as the method of Peter Baum[64] should be used.
Calculating a full Long Count date
Chichen Itza Initial Series inscription. This date (glyphs A2, B2, ..., A5) is 10.2.9.1.9 9Muluk 7Sak, equivalent to July 28, 878 (GMT Gregorian).
A full Long Count date not only includes the five digits of the Long Count, but the 2character Tzolkʼin and the two-character Haabʼ dates as well. The five digit Long Count can therefore be confirmed with the other four characters (the "calendar round date").
Taking as an example a Calendar Round date of 9.12.2.0.16 (Long Count) 5Kibʼ (Tzolkʼin) 14Yaxkʼin (Haabʼ). One can check whether this date is correct by the following calculation.
It is perhaps easier to find out how many days there are since 4Ajaw 8Kumkʼu and show how the date 5Kibʼ 14Yaxkʼin is derived.
9
× 144000
= 1296000
12
× 7200
= 86400
2
× 360
= 720
0
× 20
= 0
16
× 1
= 16
Total days
= 1383136
Calculating the Tzolkʼin date portion
The Tzolkʼin date is counted forward from 4Ajaw. To calculate the numerical portion of the Tzolkʼin date, add 4 to the total number of days given by the date and then divide total number of days by 13.
(4 + 1,383,136) / 13 = 106,395 (and 5/13)
This means that 106,395 whole 13day cycles have been completed and the numerical portion of the Tzolkʼin date is 5.
To calculate the day, divide the total number of days in the long count by 20 since there are twenty day names.
1,383,136 / 20 = 69,156 (and 16/20)
This means 16day names must be counted from Ajaw. This gives Kibʼ. Therefore, the Tzolkʼin date is 5Kibʼ.
Calculating the Haabʼ date portion
The Haabʼ date 8Kumkʼu is the ninth day of the eighteenth month. There are 17days to the start of the next year.
Subtract 17days from the total, to find how many complete Haabʼ years are contained.
1,383,136 − 17 = 1,383,119
by 365
1,383,119 / 365 = 3,789 and (134/365)
Therefore, 3,789complete Haabʼ have passed and the remainder 134 is the 135thday in the new Haabʼ, since a remainder of 0 would indicate the first day.
Find which month the day is in. Dividing the remainder 134 by 20, is six complete months and a remainder of 14, indicating the 15thday. So, the date in the Haabʼ lies in the seventh month, which is Yaxkʼin. The fifteenth day of Yaxkʼin is 14, thus the Haabʼ date is 14Yaxkʼin.
So the date of the long count date 9.12.2.0.16 5Kibʼ 14Yaxkʼin is confirmed.
Piktuns and higher orders
There are also four rarely used higher-order periods above the bʼakʼtun: piktun, kalabtun, kʼinchiltun and alautun. All of these words are inventions of Mayanists. Each one consists of 20 of the lesser units.[65][66][lower-alpha 10][67]
Many inscriptions give the date of the current creation as a large number of 13s preceding 13.0.0.0.0 4Ahau 8Kumkʼu. For example, a Late Classic monument from Coba, Stela1. The date of creation is expressed as 13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.0.0.0.0, where the units are 13s in the nineteen places larger than the bʼakʼtun.[68][69][70][71] Some authors think that the 13s were symbolic of a completion and did not represent an actual number.[72]
Most inscriptions that use these are in the form of distance dates and Long Reckonings – they give a base date, a distance number that is added or subtracted and the resulting Long Count.
The first example below is from Schele (1987). The second is from Stuart (2005 pp.60, 77)[73]
Palenque Temple of the Cross, tablet, Schele (1987 p.) 12.19.13.4.0 8Ajaw 18Tzek in the prior era 6.14.0 Distance number linking to the "era date" 13.0.0.0.0 4Ajaw 8Kumkʼu
Palenque TempleXIX, South Panel G2-H6 Stuart (2005 pp.60, 77) 12.10.1.13.2 9Ikʼ 5Mol (seating of GI in the prior era) 2.8.3.8.0 1.18.5.3.2 9Ikʼ 15Keh (rebirth of GI, this date also in Temple of the Cross)
The tablet of the inscriptions contains this inscription:[72] 9.8.9.13.0 8Ajaw 13Pop 10.11.10.5.8 1.0.0.0.0.8
The Dresden codex contains another method for writing distance numbers. These are Ring Numbers. Specific dates within the Dresden codex are often given by calculations involving Ring Numbers. Förstemann[74] identified these, but Wilson (1924):24–25 later clarified the way in which they operate. Ring Numbers are intervals of days between the Era Base date 4Ajaw 8Kumkʼu and an earlier Ring Base date, where the place-holder for the numeral of days in the interval is circled by an image of a tied red band. Added to this earlier Ring Base date is another count of days forward, which Thompson[75] refers to as a Long Round, leading to a final date within the Long Count that is given as an entry date to be used within a specific table in the codex.[76]
Ring number(12) 12.12.17.3.1 13Imix 9Wo (7.2.14.19 before (13) 13.0.0.0.0) distance number (0) 10.13.13.3.2 Long Count10.6.10.6.3 13Akʼbal 1Kankʼin
Ring number (portion of the DN preceding era date) 7.2.14.19 Add Ring number to the ring number date to reach 13.0.0.0.0
Thompson[77] contains a table of typical long reckonings after Satterwaite.[73]
The "Serpent Numbers" in the Dresden codex pp.61–69 is a table of dates using a base date of 1.18.1.8.0.16 in the prior era (5,482,096 days).[78][79][80]
↑ The correlation between the Long Count and Western calendars is calculated according to the one used by a majority of Maya researchers, known as the (modified) GMT or Goodman-Martinez-Thompson correlation. An alternate correlation sometimes used puts the starting date two days later. August 11, 3114BCE is a date in the proleptic Gregorian calendar, which is to September 6, −3113 Julianastronomical.
↑ Notable in this sequence is the glyph with nine variant forms labeled G by early epigraphers. It has been connected with the cycle of Lords of the Night known from colonial era sources in Central Mexico but alternate explanations have also been offered. See Thompson.
↑ To clarify, there are Long Count inscriptions which refer to dates earlier than the 1st century BCE, but these were carved much later in a retrospective fashion.
↑ All extant Maya inscriptions that represent this base date wrote it with a "13" bakʼtuns, not "0". But when using "13.0.0.0.0" as a base date in calculations, the "13" bakʼtuns has the numerical value 0, as if it were written as "0.0.0.0.0". This is easily confused when the "13" bakʼtuns has the actual value 13 in the current baktʼun, as in the Maya date for today: 13.0.12.0.13 (=23:21, Friday, November 1, 2024 (UTC)).
↑ According to Thompson[35] "The point from which the moon age is counted is not surely known. The possibilities are disappearance of the old moon, conjunction, or appearance of the new moon ... Beyer (1973a) believed that the calculation was made from the disappearance of the old moon. The latter method of counting (disappearance of the old moon) is still current in some Tzeltal, Chol, and Tzotzil villages in Chiapas..."
↑ Various sources place this on other dates, notably on December 23.[56]
↑ In 46 BC Julius Caesar adopted the convention of having three years of twelve months of approximately 30days each to make a year of 365days and a leap year of 366days. This made the length of the civil year 365.25days, close to the length of the solar year of 365.2422days. This is the Julian calendar. By 1582 there was an appreciable discrepancy between the winter solstice and Christmas and the spring equinox and Easter. Pope Gregory XIII, with the help of Italian astronomer Aloysius Lilius (Luigi Lilio), reformed this system by abolishing the days October 5 through October 14, 1582. This brought the civil and tropical years closer together. He also missed three days every four centuries by decreeing that centuries are only leap years if they are evenly divisible by 400. So for example 1700, 1800 and 1900 are not leap years but 1600 and 2000 are. This is the Gregorian calendar. Astronomical calculations will return a year zero and years before that are negative numbers. This is astronomical dating. Years before 46BC are calculated as proleptic Julian dates. There is no year zero in historical dating. In historical dating the year 1BCE is followed by the year 1CE For example, the year −3113 (astronomical dating) is the same as 3114BCE (historical dating). Many books about the Maya and many computer programs to do Maya calendar conversions use the Proleptic Gregorian calendar. In this calendar all dates before the start of the Gregorian calendar are revised as if the Gregorian calendar had been in use before its adoption in October1582. Although this system is popular among Mayanists, it is rarely used by anyone else, so for example, dates converted using this system are useless for the study of Maya Astronomy.
↑ Astronomical algorithms calculate a day as a decimal number equal to a day and a fraction of a day. The Julian date starts at noon. Astronomical dating has a year0. In historical dating the year 1BCE is followed by the year 1CE. Astronomical years before 0 are written with a negative sign. For example, the year 3114BCE is the year −3113 astronomical.
↑ "...we have clear evidence that the current Bakʼtun cycle does not conclude at 13, as the last one did, but advances to 20. In other words, 13.0.0.0.0 will be followed by 14.0.0.0.0, 15.0.0.0.0, and so on to 19.0.0.0.0. A text at the site of Palenque, Mexico, makes this very plain when it records the completion of 1Piktun, the next unit above the Bakʼtun, in 4772CE.
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↑ Graham (1992, p. 331, see Fig. 5 for a line drawing of the monument)
1 2 Malmström, Vincent Herschel (1997). "Chapter6". Cycles of the Sun, Mysteries of the Moon. University of Texas Press. ISBN978-0-292-75197-2. Archived from the original on 24 August 2011. Retrieved 22 August 2010. Note: Malmström's Gregorian dates are three or four days later than a correlation of 584283 would give (the Wikipedia table has been corrected).
↑ Mora-Marín, David F. (2005). "Kaminaljuyu stela10: Script classification and linguistic affiliation". Ancient Mesoamerica. 16 (1). Cambridge University Press: 63–87. doi:10.1017/S0956536105050029. ISSN0956-5361. S2CID162510333. The parallel *oo Ͼ *uu Ͼ *u shift in Chʼolan is attested indirectly in the use of the T548 TUN/ HABʼ logogram with the Initial Series Introductory Glyph on Takalik Abaj Stela 2 (236–19b.c.; Justeson and Mathews 1983; MoraMarín 2001:253).
↑ Bricker, Harvey M.; Bricker, Victoria Reifler (1 August 2011). Astronomy in the Maya Codices. Memoirs of the American Philosophical Society. American Philosophical Society. p.85. ISBN978-0871692658. if the 12 tun endings in the Chronicle of Oxkutzcab are accepted as referring to the 12 consecutive years and if the calendar-round dates (except that containing the month of Ceh) are correct when translated to a common calendar, the "11.16" correlation is the only possible one.
↑ The Book of Chilam Balam of Chumayel Ralph L. Roys, Washington D.C.; Carnegie Institution 1933, pp. 79, 83
↑ Recinos 1953, p.33 Recinos gives 2Tihax (Etzʼnabʼ) is September 10, 1541(Julian). The date which marked the destruction of the city of Guatemala founded at the foot of the Volcano of Agua. "After a period of heavy rain there was an earthquake and then a flood of water (a lahar) that destroyed the old city of Guatemala".
↑ Weeks, John M.; Sachse, Frauke; Prager, Christian M. (15 May 2013). Maya Daykeeping: Three Calendars from Highland Guatemala (Mesoamerican Worlds). University Press of Colorado. pp.176–84. ISBN978-1607322467. In Appendix2, Notes on the Correlation of Maya and Gregorian Calendars, the authors give the examples of December 9, 1722 = 8Kej 20Ukabʼ Siʼj (8Manikʼ 0Yax) and December 9, 1723 = 9 E 20 Ukabʼ Siʼj (9 Ebʼ 0 Yax). "Using Thompson's correlation constant of A = 584,283, all values from the calendar round correspond with the information in the 1722Kʼicheʼ calendar."
↑ Miles, Susanna W, "An Analysis of the Modern Middle American Calendars: A Study in Conservation." In Acculturation in the Americas. Edited by Sol Tax, p. 273. Chicago: University of Chicago Press, 1952.
↑ Barbara Tedlock, Time and the Highland Maya Revised edition (1992 p. 1)
↑ Edmonson, Munro S. (1988). The Book of the Year Middle American Calendrical Systems. Salt Lake City: University of Utah Press. ISBN0-87480-288-1.
↑ Ralph, Elizabeth K. (1965). "Review of radiocarbon dates from Tikal and the Maya calendar correlation problem". American Antiquity. 30 (4): 421–427. doi:10.2307/277941. JSTOR277941. S2CID163676704.
↑ Kennett, Douglas J., et al., "Correlating the ancient Maya and modern European calendars with high-precision AMS 14C dating", Scientific reports 3.1, 2013
↑ A Derivation of the Maya-to-Julian Calendar Correlation From the Dresden Codex Venus Chronology, in The Sky In Mayan Literature (1992)
↑ Kettunen, Harri; Helmke, Christophe (2014). "Introduction to Maya Hieroglyphs"(PDF). The Slovak Archaeological and Historical Institute. Wayeb. Bratislava: Comenius University.
↑ Meeus, Jean (2009) [1991]. "Chapter7: Julian Day". Astronomical Algorithms (Seconded.). Willman-Bell. p.63. ISBN978-0-943396-61-3. with corrections as of 10 August 2009
↑ Thompson 1960, pp.314, 316, 148–49 harvnb error: no target: CITEREFThompson1960 (help) Appendix IV: "I have throughout assumed that the baktuns were grouped, not in 13's, but in 20's, for the evidence supporting a vigesimal count of baktuns in Dresden and at Palenque and Copan is too strong to be overridden."
↑ Grofe, Michael John (2007). The Serpent Series: Precession in the Maya Dresden Codex. p.55. On occasion, the Maya also recorded intervals of time even greater than 13Bʼakʼtuns, such as one Piktun, composed of 20Bʼakʼtuns. This is relevant to the current discussion concerning the Serpent Series.
↑ Förstemann, Ernst. Commentary on the Maya Manuscript in the Royal Public Library of Dresden. Vol.IV. No. 2. Peabody Museum of American Archaeology and Archaeology and Ethnography, Harvard University. pp.222–264.
↑ Thompson 1972, pp.20–21 harvnb error: no target: CITEREFThompson1972 (help)
↑ Grofe, Michael John (2007). The Serpent Series: Precession in the Maya Dresden Codex. p.55.
↑ Thompson 1972, pp.20–22 harvnb error: no target: CITEREFThompson1972 (help)
↑ Beyer, Hermann (1933). "Emendations of the 'Serpent Numbers' of the Dresden Maya Codex". Anthropos (St. Gabriel Mödling bei Wien). 28: 1–7.
↑ The Long Count Position of the Serpent Number Dates. Vol.I. Mexico: Proc. 27th Int. Cong. Of Amer., Mexico, 1939. 1943. pp.401–05.
↑ Grofe, Michael John (2007). The Serpent Series: Precession in the Maya Dresden Codex. p.63.
Graham, John A. (1992). J.P. Laporte; H. Escobedo; S. Brady (eds.). "Escultura en bulto Olmeca y Maya en Takʼalik Abʼaj: Su desarrollo y portento"(PDF). IV Simposio de Investigaciones Arqueológicas en Guatemala, 1990 (in Spanish). Guatemala: Museo Nacional de Arqueología y Etnología: 325–334. Archived from the original(PDF) on 11 December 2009. Retrieved 16 March 2013.
Recinos, Adrián (1953). The Annals of the Cakchiquels Translated from the Cakchiquel Maya by Adrián Recinos and Delia Goetz. Translated by Goetz, Delia (1sted.). Norman: University of Oklahoma Press. pp.3–165.
Schele, Linda (1992). "A New Look at the Dynastic History of Palenque". In Victoria R. Bricker (Volume), with Patricia A. Andrews (ed.). Supplement to the Handbook of Middle American Indians, Vol. 5: Epigraphy. Victoria Reifler Bricker (general editor). Austin: University of Texas Press. pp.82–109. ISBN0-292-77650-0. OCLC23693597.
Wagner, Elizabeth (2006). "Maya Creation Myths and Cosmology". In Nikolai Grube (ed.). Maya: Divine Kings of the Rain Forest. Eva Eggebrecht and Matthias Seidel (assistant eds.). Cologne: Könemann. pp.280–293. ISBN3-8331-1957-8. OCLC71165439.
External links
Coba Stela 1 (Schele #4087), partial illustration from the Linda Schele Drawings Collection of the monument from Coba with an expanded Long Count date
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