{{Short description|Calendar used by Mesoamerican cultures}} {{Use American English|date=June 2018}} {{use mdy dates|date=July 2025}} {{Infobox calendar date today|default_calendar=Maya}} [[File:East side of stela C, Quirigua.PNG|thumb|200px|right|East side of stela C, Quirigua with the mythical creation date of 13 [[baktun]]s, 0 katuns, 0 tuns, 0 winals, 0 kins, 4 Ahau 8 Cumku – August 11, 3114 BCE in the [[proleptic Gregorian calendar]].]] The '''Mesoamerican Long Count calendar''' is a non-repeating [[vigesimal|base-20]] and base-18 calendar used by [[pre-Columbian]] [[Mesoamerica]]n cultures, most notably the [[Maya civilization|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 [[Mesoamerican creation myths|mythical creation date]] that corresponds to August 11, 3114 [[Common Era|BCE]] in the [[proleptic Gregorian calendar]].{{efn|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, 3114 BCE is a date in the [[proleptic Gregorian calendar]], which is to September 6, −3113 [[Julian calendar|Julian]] [[astronomical year numbering|astronomical]].}} The Long Count calendar was widely used on monuments. ==Background== The two most widely used calendars in pre-Columbian Mesoamerica were the 260-day {{lang|myn|[[tzolkʼin]]}} and the 365-day {{lang|myn|[[haabʼ]]}}. The equivalent Aztec calendars are known in [[Nahuatl]] as the {{lang|nah|[[tōnalpōhualli]]}} and {{lang|nah|[[xiuhpōhualli]]}}, respectively. The combination of a {{lang|myn|haabʼ}} and a {{lang|myn|tzolkʼin}} date identifies a day in a combination which does not occur again for 18,980 days (52 {{lang|myn|haabʼ}} cycles of 365 days equals 73 {{lang|myn|tzolkʼin}} cycles of 260 days, approximately 52 years), a period known as the [[Calendar Round]]. To identify days over periods longer than this, Mesoamericans used the Long Count calendar. ==Long Count periods== {{more citations needed section|date=August 2017}} [[File:La Mojarra Estela 1 (Escritura superior).jpg|thumb|266x266px|Detail showing columns of glyphs from a portion of the 2nd century CE [[La Mojarra Stela 1]]. The left column gives a Long Count date of 8.5.16.9.7, or 156 CE. 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, 3114 BCE 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 [[Baktun|bʼakʼtuns]] (August 11, 3114 BCE) 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 {{nowrap|Sun.Freidel, Schele & Parker (1993, pp. 59–75).}} 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 (and only that digit) rolls over to zero when it reaches 18.{{Citation needed|date=May 2018}} 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 [[kʼatun]]s and tuns were still in use. Instead the Maya were using an abbreviated [[Maya calendar#Short count|Short Count]]. {|class="wikitable" style="margin: 1em auto;" |+ '''Table of Long Count units''' ! Long Count
unit !! Long Count
period !! Days !! Approximate
[[Tropical year|Solar Years]] |- |1 Kʼin ||  ||style="text-align:right;"| 1 ||style="text-align:right;"|  |- |1 Winal ||20 Kʼin ||style="text-align:right;"| 20 ||style="text-align:right;"|  |- |1 Tun ||18 Winal ||style="text-align:right;"| 360 ||style="text-align:right;"|{{val|fmt=commas|{{Rnd|360/365.2422|0}}}} |- |1 Kʼatun ||20 Tun ||style="text-align:right;"| 7,200 ||style="text-align:right;"|{{val|fmt=commas|{{Rnd|7200/365.2422|0}}}} |- |1 Bʼakʼtun ||20 Kʼatun ||style="text-align:right;"| 144,000 ||style="text-align:right;"|{{val|fmt=commas|{{Rnd|144000/365.2422|0}}}} |- |1 Piktun ||20 Bʼakʼtun ||style="text-align:right;"| 2,880,000 ||style="text-align:right;"|{{val|fmt=commas|{{Rnd|2880000/365.2422|0}}}} |- |1 Kalabtun ||20 Piktun ||style="text-align:right;"|57,600,000 ||style="text-align:right;"|{{val|fmt=commas|{{Rnd|57600000/365.2422|0}}}} |- |1 Kʼinchiltun ||20 Kalabtun ||style="text-align:right;"|1,152,000,000 ||style="text-align:right;"|{{val|fmt=commas|{{Rnd|1152000000/365.2422|0}}}} |- |1 Alautun ||20 Kʼinchiltun ||style="text-align:right;"|23,040,000,000 ||style="text-align:right;"|{{val|fmt=commas|{{Rnd|23040000000/365.2422|0}}}} |- |1 Hablatun ||20 Alautun ||style="text-align:right;"|460,800,000,000||style="text-align:right;"|{{val|fmt=commas|1,261,628,585}} |} ==Mesoamerican numerals== [[File:maya.svg|thumb|Maya 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 [[0 (number)#History|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]").Boot, p. 2. Next come the 5 digits of the Long Count, followed by the Calendar Round (tzolkʼin and Haabʼ) and [[Maya calendar#Supplementary Series|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 [[wikt:lunation|lunation]].{{efn|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.}} The text then continues with whatever activity occurred on that date. A drawing of a full Maya Long Count inscription is shown [[#Calculating a full Long Count date|below]]. ==Earliest Long Counts== The earliest contemporaneous Long Count inscription yet discovered is on Stela 2 at [[Chiapa de Corzo (Mesoamerican site)|Chiapa de Corzo]], [[Chiapas]], Mexico, showing a date of 36 BCE (although this date is not certain, see table), although Stela 2 from [[Takalik Abaj]], [[Guatemala]] might be earlier.Graham (1992, p. 331, see Fig. 5 for a line drawing of the monument) (See [[:File:Abaj Takalik Stela2.jpg|illustration]].) 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.{{efn|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.}}{{citation needed|reason=Some sources identify just Baktun 7, though Katun 6–16 is at least consistent with Mora-Marín (2005)'s 236–19 BCE|date=February 2014}} 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 (two of the artifacts contain two dates and Malmström does not include Takalik Abaj Stela 2).{{cite book | first=Vincent Herschel | last=Malmström | chapter-url=http://www.dartmouth.edu/~izapa/CS-MM-Chap.%206.htm | title=Cycles of the Sun, Mysteries of the Moon | chapter=Chapter 6 | date=1997 | publisher=[[University of Texas Press]] | isbn=978-0-292-75197-2 | access-date=22 August 2010 | archive-date=24 August 2011 | archive-url=https://web.archive.org/web/20110824101110/http://www.dartmouth.edu/~izapa/CS-MM-Chap.%206.htm | url-status=dead }} Note: Malmström's Gregorian dates are three or four days later than a correlation of 584283 would give (the Wikipedia table has been corrected).{{cite web | title=Vincent H. Mahlstrom | work=Department of Geography, Faculty & Staff | publisher=[[Dartmouth College]] | url=http://www.dartmouth.edu/~geog/facstaff/mahlstrom.html | access-date=2014-02-17 }} Interpretations of inscriptions on some artifacts differ. {| class="wikitable" style="margin:auto;" !Archaeological site !Name !Gregorian date GMT (584283) correlation !Long Count !Location |- |[[Takalik Abaj]] |Stela 2 |236 – 19 BCE{{cite journal |last1=Mora-Marín |first1=David F. |title=Kaminaljuyu stela 10: Script classification and linguistic affiliation |journal=Ancient Mesoamerica |publisher=[[Cambridge University Press]] |volume=16 |issue=1 |date=2005 |pages=63–87 |issn=0956-5361 |doi=10.1017/S0956536105050029 |s2cid=162510333 |quote=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 (236–19 b.c.; Justeson and Mathews 1983; MoraMarín 2001:253). }} |7.(6,11,16).?.?.? |[[Retalhuleu Department|Retalhuleu]], Guatemala |- |[[Chiapa de Corzo (Mesoamerican site)|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{{cite book |last=Stuart |first=David |chapter=Chapter 11: The beginnings of the Copan dynasty: A review of the hieroglyphic and historical evidence |editor1-last=Bell |editor1-first=Ellen E. |editor2-last=Canuto |editor2-first=Marcello A. |editor3-last=Sharer |editor3-first=Robert J. |title=Understanding Early Classic Copan |chapter-url=https://books.google.com/books?id=C7O-GHuLAfIC&pg=PA219 |date=2004 |publisher=[[University of Pennsylvania Museum of Archaeology and Anthropology|University of Pennsylvania Museum of Archaeology]] |location=Philadelphia, PA |isbn=978-1-931707-51-0 |page=219 }} |Chiapas, Mexico |- |[[Tres Zapotes]] |Stela C |September 1, 32 BCE |7.16.6.16.18{{cite journal | last=Marcus | first=Joyce | title=The origins of Mesoamerican writing | journal=Annual Review of Anthropology | date=1976 | volume=5 | publisher=[[Annual Reviews (publisher)|Annual Reviews Inc.]] | pages=49–54 | url=http://www.latinamericanstudies.org/ancient/writing-origins.pdf | doi=10.1146/annurev.an.05.100176.000343}} |[[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 Department|Escuintla]], Guatemala |- |Takalik Abaj |Stela 5 |August 31, 83 CE or
May 19, 103 CE |8.2.2.10.15{{cite book |last=Riese |first=Berthold |chapter=Epigraphy of the southeast zone in relation to other parts of the Maya realm |editor-last1=Boone |editor-first1=Elizabeth Hill |editor-last2=Willey |editor-first2=Gordon Randolph |title=The Southeast Classic Maya Zone: Papers from the Dumbarton Oaks Symposium, 6th and 7th October, 1984 |chapter-url=https://books.google.com/books?id=XOA0e8FcAhoC&pg=PA68 |date=1988 |publisher=Dumbarton Oaks, Trustees for Harvard University |location=Washington, D.C. |isbn=978-0-88402-170-4 |page=68}} or
8.3.2.10.15{{cite book |editor-last1=Ochoa |editor-first1=Lorenzo |editor-last2=Lee |editor-first2= Thomas A. |title=Antropología e historia de los mixe-zoques y mayas |url=https://books.google.com/books?id=Qd4WAAAAYAAJ |pages=191, 194 |date=1983 |publisher=[[National Autonomous University of Mexico|Universidad Nacional Autónoma de México]], Instituto de Investigaciones Filológicas, Centro de Estudios Mayas |location=Mexico |language=es |isbn=978-968-5804-97-4}} |Retalhuleu, Guatemala |- |Takalik Abaj |Stela 5 |June 3, 126 CE |8.4.5.17.11 |Retalhuleu, Guatemala |- |[[La Mojarra]] |[[La Mojarra Stela 1|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.Diehl (2004, p. 186). La Mojarra Stela 1, the Tuxtla Statuette, Tres Zapotes Stela C and Chiapa Stela 2 are all inscribed in an [[Epi-Olmec script|Epi-Olmec]], not Maya, style."A sketch of prior documentation of epi-Olmec texts", Section 5 in Peréz de Lara & Justeson (2005). El Baúl Stela 2, on the other hand, was created in the [[Izapa]]n style. The first unequivocally Maya artifact is Stela 29 from [[Tikal]], with the Long Count date of 292 CE (8.12.14.8.15), more than 300 years after Stela 2 from Chiapa de Corzo.Coe & Koontz (2002), p. 87 More recently, with the discovery in Guatemala of the [[San Bartolo (Maya site)|San Bartolo]] stone block text ({{circa}} 300 BCE),Saturno et al. 2006 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 (295 BCE) and 7.5.0.0.0 (256 BCE).Giron-Abrego 2012 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. Recently at the site of [[El Palmar (Maya site)|El Palmar]] in Mexico three stelae (stelae 20, 45 and 46) were analyzed and said to hold the earliest long count date of a lowland Mayan site. The date of Stelae 46 was 8.7.1.0.0 4 Ajaw 8 Sotz (Aug. 31, AD 180 Julian). The stelae were examined combining photogrammetry and the Artec Spider II high-resolution 3D scanner. [https://www.cambridge.org/core/journals/ancient-mesoamerica/article/emergence-of-kingship-and-early-long-counts-in-the-maya-kingdom-of-el-palmar-campeche-mexico/72DECC08F19B6FC30B39065C1F26F7A5]Tsukamoto K, Esparza Olguín OQ, Salazar Lama D, Campaña Valenzuela LE, Velázquez Morlet A, López Camacho J, "The Emergence of Kingship and Early Long Counts in the Maya Kingdom of El Palmar, Campeche, Mexico", Ancient Mesoamerica, pp.1-21, 2026 ==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 (ad 889)", at that time the latest. Monument inscriptions at [[Seibal]] and [[Uaxactun]] in Guatemala had the same date.Zender, Marc, and Joel Skidmore. "Unearthing the Heavens: Classic Maya Murals and Astronomical Tables at Xultun, Guatemala." Mesoweb Reports, 2012 For context, the latest known long count date from [[Palenque]] is "9.18.9.4.4, corresponding to A.D. November 15, 799" (November 11 Julian GMT), on pottery.Strawinska-Zanko, Urszula, et al., "Capital in the first century: The evolution of inequality in Ancient Maya Society", Mathematical modeling of social relationships: What mathematics can tell us about people. Cham: Springer International Publishing, pp. 161-192, 2018 Inscriptions from [[Toniná]] (on a jade stone) and Tzibanche in Mexico had a long count date of "10.4.0.0.0" (January 18, 909 AD - January 13 Julian GMT).Lowe, John W. G., "The Dynamics of Apocalypse: A Systems Simulation of the Classic Maya Collapse", Albuquerque: University of New Mexico Press, 1985 The [[Dresden Codex]] has a long count date of 10.19.6.1.8" (September 25, 1210 AD - September 18 Julian GMT) though this may not be historical.Pharo, L. K., "I The Ritual Practice of Time of the Long Count Calendar of the Classic Maya Civilisation", in The Ritual Practice of Time. Leiden, The Netherlands: Brill, pp. 17–150, 2014 ==Correlations between Western calendars and the Long Count== [[File:Estela C de Tres Zapotes.jpg|thumb|250px|The back of Stela C 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, 32 BCE (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.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: {{Maya date}} (={{CURRENTDATE}}). This is referred to as a "correlation constant". The generally accepted correlation constant is the Modified Thompson 2, "[[Joseph T. Goodman|Goodman]]–Martinez–[[J. Eric S. Thompson|Thompson]]", or GMT correlation of 584,283 days. Using the GMT correlation, the current creation started on September 6, −3113 ([[Julian calendar|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.{{cite web |url=http://www.mesoweb.com/publications/CAA_14/Thompson1935.pdf |title= Maya chronology: The correlation question |first=J. Eric |last=Thompson |website=mesoweb.com |access-date=2015-09-06}}{{cite book|title=Maya hieroglyphic writing |author=Thompson, J.E.S. |publisher=Forgotten Books |isbn=978-1-60506-860-2 |url=https://books.google.com/books?id=VrSVFTyTOegC&pg=PA73 |page=73}}{{cite web |url=http://alignment2012.com/fap3.html |title=Clarifications: The Correlation Debate |website=alignment2012.com |access-date=2015-09-06}}{{cite web |url=http://www.hermetic.ch/cal_stud/maya/chap2.htm |title=Maya Calendar: The Correlation Problem |website=hermetic.ch |access-date=2015-09-06}}{{cite web |url=http://www.famsi.org/research/vanstone/2012/faq.html#correlation |title=FAMSI – FAQ's about 2012: The end of the World? – FAQ's – What is this correlation constant? |website=famsi.org |access-date=2015-09-06}} 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 ..."''Breaking the Maya Code'', 1992, p. 114. The evidence for the GMT correlation is historical, astronomical and archaeological: '''Historical''': Calendar Round dates with a corresponding [[Julian calendar|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 [[Maya calendar#Short Count|Short Count]]. Oxkutzcab contains 12 Tun endings. Bricker and Bricker find that only the GMT correlation is consistent with these dates.{{cite book |last1=Bricker |first1=Harvey M. |last2=Bricker |first2=Victoria Reifler |date=August 1, 2011 |title=Astronomy in the Maya Codices |series=Memoirs of the American Philosophical Society |publisher=American Philosophical Society |page=85 |isbn=978-0871692658 |quote=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 ChumayelThe Book of Chilam Balam of Chumayel Ralph L. Roys, Washington D.C.; Carnegie Institution 1933, pp. 79, 83 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.{{cite journal |last1=Edmonson |first1=Munro S. |date=December 1976 |title=The Mayan Calendar Reform of 11.16.0.0.0 |journal=Current Anthropology |volume=17 |issue= 4 |pages=713–17 |jstor=2741269 |doi=10.1086/201806|s2cid=145181714 }} The [[Annals of the Cakchiquels]] contains numerous Tzolkʼin dates correlated with European dates. These confirm the GMT correlation.{{sfn|Recinos|1953|p=33 Recinos gives 2 Tihax (Etzʼnabʼ) is September 10, 1541([[Julian calendar|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, Sachse and Prager transcribed three divinatory calendars from highland Guatemala. They found that the 1772 calendar confirms the GMT correlation.{{cite book |last1=Weeks |first1=John M. |last2=Sachse |first2=Frauke |last3=Prager |first3=Christian M.|date=May 15, 2013 |title=Maya Daykeeping: Three Calendars from Highland Guatemala (Mesoamerican Worlds) |publisher=University Press of Colorado |pages=176–84 |isbn=978-1607322467}} In Appendix 2, ''Notes on the Correlation of Maya and Gregorian Calendars'', the authors give the examples of December 9, 1722 = 8 Kej 20 Ukabʼ Siʼj (8 Manikʼ 0 Yax) 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 1722 Kʼicheʼ calendar." The fall of the capital city of the Aztec Empire, [[Tenochtitlan]], occurred on August 13, 1521.(Díaz 1904: 2:129) A number of different chroniclers wrote that the [[Tzolkʼin]] ([[Tonalpohualli]]) date of the event was 1 Snake.(Sahagún 1975: 12:122) Post-conquest scholars such as [[Bernardino de Sahagún|Sahagún]] and [[Diego Durán|Durán]] recorded [[Tonalpohualli]] dates with a calendar date. Many indigenous communities in the Mexican states of Veracruz, Oaxaca and ChiapasMiles, 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. and in Guatemala, principally those speaking the Mayan languages Ixil, Mam, Pokomchí and Quiché, keep the Tzolkʼin and in many cases the Haabʼ.Barbara Tedlock, Time and the Highland Maya Revised edition (1992 p. 1) 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.{{cite book |last=Edmonson |first=Munro S. |date=1988 |title=The Book of the Year Middle American Calendrical Systems |location=Salt Lake City |publisher=University of Utah Press |isbn=0-87480-288-1 }} '''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 [[Maya calendar#Supplementary Series|supplementary series]].{{cite web |url=http://www.astras-stargate.com/lunarglyphs.html |title=Lunar Glyphs in the Maya Calendrics – The Lunar Series – The Supplementary and Lunar Glyphs |website=astras-stargate.com |access-date=2015-09-06}} 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.Fuls (2007) ''Ancient Mesoamerica'', 18, 273–282 Cambridge University Press. after Robertson 1991: Vol. 4 : p. 95. This Long Count is also the entry date for the eclipse table of the [[Dresden Codex]].{{cite web |url=http://www.biblioteces.net/ciencia/dresden/dresdencodex03.htm |title=The Dresden Codex eclipse table |first=Michael John |last=Finley |access-date=1 January 2018}}{{efn|According to ThompsonThompson, J. Eric S. (1950). Maya Hieroglyphic Writing, an Introduction. p. 236 "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 ..."}} Using the third method, the Palenque system,Aveni 2001 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."Sighting the Crescent Moon", ''Sky & Telescope'', July 1994, 14"In Quest of the Youngest Moon", ''Sky & Telescope'', December 1996, 104–105"Young Moons and the Islamic Calendar", ''Sky & Telescope'', December 1996, 106"Seeking Thin Crescent Moons", ''Sky & Telescope'', February 2004, 102–106"Young-Moon Hunting in 2005", ''Sky and Telescope'', February 2005, 75–76{{cite web |title=What's the Thinnest Crescent Moon You Can See? |date=13 December 2017 |publisher=Sky and Telescope |url=http://www.skyandtelescope.com/astronomy-news/observing-news/thinnest-crescent-moon/}} 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 {{nowrap|October 10, 755}} and a new Moon when the lunar phase day was 1.7 at 6 pm on {{nowrap|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 [[Nicolaus Copernicus|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.{{cite book |title=The Mayan and Other Ancient Calendars |author=Stray, G. |date=2007 |publisher=Walker |isbn=978-0-8027-1634-7 |url=https://books.google.com/books?id=GdlzA3yUlTUC&pg=PA40 |page=40}} 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{{cite book | first=Andreas | last=Fuls | year=2007 | title=Ancient Mesoamerica | chapter=18 | pages=273–282 | publisher=Cambridge University Press}} 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 node|ascending]] or [[Ascending node|descending]] node and an [[eclipse]] is likely to occur. Dates converted using the GMT correlation agree closely with the Dresden Codex eclipse tables.Bricker and Bricker pp. 249–366 The [[Dresden Codex]] contains a [[Venus]] table which records the [[heliacal rising]]s of Venus. Using the GMT correlation these agree closely with modern astronomical calculations.Bricker and Bricker pp. 163–248 '''Archaeological''': Various items that can be associated with specific Long Count dates have been [[Isotope dating|isotope dated]]. In 1959 the [[University of Pennsylvania]] [[carbon dating|carbon dated]] samples from ten wood lintels from [[Tikal]].{{Cite journal |author=Ralph, Elizabeth K. |year=1965 |title=Review of radiocarbon dates from Tikal and the Maya calendar correlation problem |journal=American Antiquity |volume=30 |issue=4 |pages=421–427 |jstor=277941 |doi=10.2307/277941|s2cid=163676704 }} These were carved with a date equivalent to 741 AD, using the GMT correlation. The average [[carbon dating|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.{{cite journal |last1=Kennett |first1=Douglas J. |last2=Hajdas |first2=Irka |last3=Culleton |first3=Brendan J. |last4=Belmecheri |first4=Soumaya |last5=Martin |first5=Simon |last6=Neff |first6=Hector |last7=Awe |first7=Jaime |last8=Graham |first8=Heather V. |last9=Freeman |first9=Katherine H. |last10=Newsom |first10=Lee |last11=Lentz |first11=David L. |last12=Anselmetti |first12=Flavio S. |last13=Robinson |first13=Mark|last14=Marwan |first14=Norbert |last15=Southon |first15=John |last16=Hodell |first16=David A. |last17=Haug |first17=Gerald H. |display-authors=6 |title=Correlating the ancient Maya and modern European calendars with high-precision AMS 14C dating |date=11 April 2013 |journal=Scientific Reports |volume=3 |article-number=1597 |doi=10.1038/srep01597 |doi-access=free|bibcode=2013NatSR...3.1597K |pmid=23579869 |pmc=3623374}} In 2012, using modern AMS radiocarbon dating, a single beam from Tikal was dated, also strongly supporting the GMT.{{cite journal | last1=Kennett | first1=Douglas J. | last2=Hajdas | first2=Irka | last3=Culleton | first3=Brendan J. | last4=Belmecheri | first4=Soumaya | last5=Martin | first5=Simon | last6=Neff | first6=Hector | last7=Awe | first7=Jaime | last8=Graham | first8=Heather V. | last9=Freeman | first9=Katherine H. | last10=Newsom | first10=Lee | last11=Lentz | first11=David L. | last12=Anselmetti | first12=Flavio S. | last13=Robinson | first13=Mark | last14=Marwan | first14=Norbert | last15=Southon | first15=John | last16=Hodell | first16=David A. | last17=Haug | first17=Gerald H. | title=Correlating the Ancient Maya and Modern European Calendars with High-Precision AMS 14C Dating | journal=Scientific Reports | date=2013 | volume=3 | article-number=1597 | doi=10.1038/srep01597 | doi-access=free| pmid=23579869 | pmc=3623374 | bibcode=2013NatSR...3.1597K | url=https://www.nature.com/articles/srep01597.pdf }} 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: [[Floyd Lounsbury|Lounsbury]],A Derivation of the Maya-to-Julian Calendar Correlation From the Dresden Codex Venus Chronology, in ''The Sky In Mayan Literature'' (1992) Fuls, ''et al.'',{{cite web |url=http://www.archaeoastronomie.de/mayaeng/corrtabl.htm |title=The Correlation Question |first=Andreas |last=Fuls |website=archaeoastronomie.de |access-date=2015-09-06}} Böhm and Böhm{{cite web |url=http://www.hermetic.ch/cal_stud/maya/boehm/korelaceangl.doc |title=Mayan Dating |author1=Vladimir Böhm |author2=Bohumil Böhm |website=hermetic.ch |access-date=2015-09-06}}{{cite web |url=http://www.volny.cz/paib/ |title=Mayan dating, Mayan astronomy, Correlation MD/JD |website=volny.cz |access-date=2015-09-06}} and Stock. Today, {{Date}} ([[UTC]]), in the Long Count is {{Maya date}} (using GMT correlation). {| class="wikitable" align=left style="margin-left: 1.5em" |+'''[[Julian day number|JDN correlations]]
to the Maya creation date'''
(after Thompson 1971, et al. and Aveni 1980) !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 (Lounsbury)||584,285 |- |Pogo||588,626 |- |+2CR||622,243 |- |Böhm & Böhm||622,261 |- |Kreichgauer||626,927 |- |+4CR||660,203 |- |Fuls, ''et al.''||660,208 |- |Hochleitner||674,265 |- |Schultz||677,723 |- |Escalona–Ramos||679,108 |- |Vaillant||679,183 |- |Weitzel||774,078 |} {{Clear right}} {| class="wikitable" align=right style="margin-right: 1.5em" ! Long Count ! [[Proleptic Gregorian calendar|(proleptic before 1582) Gregorian date]]
GMT (584,283) correlation ! [[Julian day]]
number |- | align="center"| 0.0.0.0.0
(13.0.0.0.0) || align="center"|Mon, Aug 11, 3114 BCE || align="right"|584,283  |- | align="center"| 1.0.0.0.0 || align="center"|Thu, Nov 13, 2720 BCE || align="right"|728,283  |- | align="center"| 2.0.0.0.0 || align="center"|Sun, Feb 16, 2325 BCE || align="right"|872,283  |- | align="center"| 3.0.0.0.0 || align="center"|Wed, May 21, 1931 BCE || align="right"|1,016,283  |- | align="center"| 4.0.0.0.0 || align="center"|Sat, Aug 23, 1537 BCE || align="right"|1,160,283  |- | align="center"| 5.0.0.0.0 || align="center"|Tue, Nov 26, 1143 BCE || align="right"|1,304,283  |- | align="center"| 6.0.0.0.0 || align="center"|Fri, Feb 28, 748 BCE || align="right"|1,448,283  |- | align="center"| 7.0.0.0.0 || align="center"|Mon, Jun 3, 354 BCE || align="right"|1,592,283  |- | align="center"| 8.0.0.0.0 || align="center"|Thu, Sep 5, 41 CE || align="right"|1,736,283  |- | align="center"| 9.0.0.0.0 || align="center"|Sun, Dec 9, 435 || align="right"|1,880,283  |- | align="center"| 10.0.0.0.0 || align="center"|Wed, Mar 13, 830 || align="right"|2,024,283  |- | align="center"| 11.0.0.0.0 || align="center"|Sat, Jun 15, 1224 || align="right"|2,168,283  |- | align="center"| 12.0.0.0.0 || align="center"|Tue, Sep 18, 1618 || align="right"|2,312,283  |- | align="center"| 13.0.0.0.0 || align="center"|Fri, Dec 21, 2012 || align="right"|2,456,283  |- | align="center"| 14.0.0.0.0 || align="center"|Mon, Mar 26, 2407 || align="right"|2,600,283  |- | align="center"| 15.0.0.0.0 || align="center"|Thu, Jun 28, 2801 || align="right"|2,744,283  |- | align="center"| 16.0.0.0.0 || align="center"|Sun, Oct 1, 3195 || align="right"|2,888,283  |- | align="center"| 17.0.0.0.0 || align="center"|Wed, Jan 3, 3590 || align="right"|3,032,283  |- | align="center"| 18.0.0.0.0 || align="center"|Sat, Apr 7, 3984 || align="right"|3,176,283  |- | align="center"| 19.0.0.0.0 || align="center"|Tue, Jul 11, 4378 || align="right"|3,320,283  |- | align="center"|1.0.0.0.0.0 || align="center"|Fri, Oct 13, 4772 || align="right"|3,464,283  |} {{clear}} ==2012 and the Long Count== {{main|2012 phenomenon}} According to the ''[[Popol Vuh]]'', a book compiling details of [[Mesoamerican creation accounts|creation accounts]] known to the [[Kʼicheʼ people|Kʼicheʼ Maya]] of the Colonial-era highlands, humankind lives in the fourth world.Schele & Freidel (1990), pp. 429–30 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.{{efn|Various sources place this on other dates, notably on December 23.Schele and Friedel (1992).}} There are only two references to the current creation's 13th bʼakʼtun in the fragmentary Mayan corpus: [[Tortuguero (Maya site)|Tortuguero]] Monument 6, part of a ruler's inscription and the recently discovered La Corona Hieroglyphic Stairway 2, Block V.{{cite web |url=http://decipherment.wordpress.com/2012/06/30/notes-on-a-new-text-from-la-corona/ |title=Notes on a New Text from La Corona |series=Maya Decipherment |website=decipherment.wordpress.com |date=30 June 2012 |access-date=2015-09-06}} 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 13th ''bʼakʼtun'' 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 80th Calendar 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 5 Lamat 1 Mol, at Long Count 9.9.2.4.8 equivalent to 27 July 615 CE in the [[proleptic Gregorian calendar]]).Gregorian, using GMT correlation JDN=584283. It does this by commencing with Pakal's birthdate 9.8.9.13.0   8 Ajaw 13 Pop (24 March {{nowrap|603 CE Gregorian}}) and adding to it the Distance Number 10.11.10.5.8.Schele (1992, pp. 93–95) This calculation arrives at the 80th Calendar Round since his accession, a day that also has a CR date of {{nowrap|5 Lamat 1 Mol}}, but which lies over 4,000 years in the future from Pakal's time—the day 21 October in the year 4772. The inscription notes{{Citation needed|date=December 2010}} 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''—13 October 4772—were to be written out in Long Count notation, it could be represented as 1.0.0.0.0.0. The 80th CR anniversary date, eight days later, would be 1.0.0.0.0.8   5 Lamat 1 Mol.Schele & Freidel (1990, p. 430 ''n.''39) 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.{{cite news | title=Does Maya calendar predict 2012 apocalypse? | work=USA Today | first=G. Jeffrey | last=MacDonald | publisher=[[Gannett Company]] | url=http://usatoday30.usatoday.com/tech/science/2007-03-27-maya-2012_n.htm | date=March 27, 2007 }} ''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.{{'"}} "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."{{cite news |url=http://tulane.edu/news/newwave/062508_maya.cfm |title=The sky is not falling |work=New Wave |publisher=[[Tulane University]] |date=June 25, 2008 |first=Ryan |last=Rivet |url-status=dead |archive-url=https://web.archive.org/web/20110418060227/http://tulane.edu/news/newwave/062508_maya.cfm |archive-date=April 18, 2011 }} ==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 calendar|Julian]] and [[Gregorian calendar|Gregorian]] calendars when calculating a Western calendar date from a Long Count date.{{efn|In 46 BC Julius Caesar adopted the convention of having three years of twelve months of approximately 30 days each to make a year of 365 days and a leap year of 366 days. This made the length of the civil year 365.25 days, close to the length of the solar year of 365.2422 days. This is the [[Julian calendar]]. By 1582 there was an appreciable discrepancy between the [[winter solstice]] and [[Christmas]] and the [[Equinox|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 46 BC are calculated as [[Proleptic Julian calendar|proleptic Julian dates]]. There is no year zero in historical dating. In historical dating the year 1 BCE is followed by the year 1 CE For example, the year −3113 (astronomical dating) is the same as 3114 BCE (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 October 1582. 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]].}} 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 [[Proleptic Julian calendar|Julian]] astronomical). {| class="wikitable" style="margin:1em auto;" |- align=right | 9 ||× 144,000||= 1,296,000 |- align=right | 10 ||× 7,200 ||= 72,000 |- align=right | 11 ||× 360 ||= 3,960 |- align=right | 17 ||× 20 ||= 340 |- align=right | 0 ||× 1 ||= 0 |- | ||Total days||= 1,372,300 |} Then add the GMT correlation to the total number of days. : 1,372,300 + 584,283 = 1,956,583 This number is a '''[[Julian day]]'''. To convert a [[Julian day]] to a [[Proleptic Gregorian calendar]] date:{{cite web |url=http://www.wayeb.org/download/resources/wh2014english.pdf |title=Introduction to Maya Hieroglyphs |last1=Kettunen |first1=Harri |last2=Helmke |first2=Christophe |date=2014 |website=Wayeb |publisher=Comenius University |place=Bratislava |department=The Slovak Archaeological and Historical Institute}} 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 600 CE. {| class="wikitable" |- ! 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 365 days (vague year). : 16,377 / 365 = 44.86849 The remainder is 44.86849 years, which is 44 years and 317 days. The full year date is 644 CE. Now calculate the month and day number, taking into account leap days over the 44 years. 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 644 CE. 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 644 CE, which is November 3. To summarize: the Long Count date 9.10.11.17.0 corresponds to November 3, 644 CE, in the [[Proleptic Gregorian calendar]]. To convert a [[Julian day]] to a Julian/Gregorian astronomical date ([[Proleptic Julian calendar]] before 46 BCE): Use an astronomical algorithm such as the Method of [[Jean Meeus|Meeus]]{{cite book |first=Jean |last=Meeus |orig-year=1991 |year=2009 |title=Astronomical Algorithms |edition=Second |publisher=Willman-Bell |isbn=978-0-943396-61-3 |chapter=Chapter 7: Julian Day |page=63 |quote=with corrections as of 10 August 2009}} to convert the [[Julian day]] to a Julian/Gregorian date with astronomical dating of negative years:{{efn|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 year numbering|Astronomical dating]] has a year 0. In historical dating the year 1 BCE is followed by the year 1 CE. Astronomical years before 0 are written with a negative sign. For example, the year 3114 BCE is the year −3113 astronomical.}} In this example: '''input:''' Julian day ''J'' ''J'' = ''J'' + 0.5 ''// 1,956,583.5'' ''Z'' = integer part of ''J'' ''// 1,956,583'' ''F'' = fraction part of ''J'' ''// 0.5'' '''if''' ''Z'' < 2,299,161 '''then''' ''// Julian?'' ''A'' = ''Z'' '''else''' ''alpha'' = floor((''Z'' - 1,867,216.25) / 36,524.25) ''// 15'' ''A'' = ''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) = -2'' '''end if''' ''B'' = ''A'' + 1524 ''// 1,958,107'' ''C'' = floor((''B'' - 122.1) / 365.25) ''// 5,360'' ''D'' = floor(365.25 × ''C'') ''// 1,957,740'' ''E'' = floor((''B'' - ''D'') / 30.6001) ''// 11'' ''day'' = ''B'' - ''D'' - floor(30.6001 × ''E'') + ''F'' ''// 31.5'' '''if''' ''E'' < 14 '''then''' ''month'' = ''E'' - 1 ''// 10'' '''else''' ''month'' = ''E'' - 13 '''end if''' '''if''' ''month'' > 2 '''then''' ''year'' = ''C'' - 4716 ''// 644'' '''else''' ''year'' = ''C'' - 4715 '''end if''' '''return''' (''year'', ''month'', ''day'') In this example the [[Julian calendar|Julian]] date is noon October 31, 644. The Method of [[Jean Meeus|Meeus]] is not valid for negative year numbers (astronomical), so another method such as the method of Peter Baum{{cite web |title=Date conversion method |first=Peter |last=Baum |url=http://mysite.verizon.net/aesir_research/date/date0.htm |url-status=dead |archive-url=https://web.archive.org/web/20140910060704/http://mysite.verizon.net/aesir_research/date/date0.htm |archive-date=2014-09-10}} should be used. ===Calculating a full Long Count date=== [[File:Morley 1915 ISglyphs.svg|thumb|right|160px|[[Chichen Itza]] Initial Series inscription. This date (glyphs A2, B2, ..., A5) is 10.2.9.1.9   9 Muluk 7 Sak, equivalent to July 28, 878 (GMT Gregorian).]] {{More citations needed section|date=August 2020}} A full Long Count date not only includes the five digits of the Long Count, but the 2 character 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) 5 Kibʼ (Tzolkʼin) 14 Yaxkʼin (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 4 Ajaw 8 Kumkʼu and show how the date 5 Kibʼ 14 Yaxkʼin is derived. {| class="wikitable" style="margin:1em auto;" |- align=right | 9 ||× 144000||= 1296000 |- align=right | 12 ||× 7200 ||= 86400 |- align=right | 2 ||× 360 ||= 720 |- align=right | 0 ||× 20 ||= 0 |- align=right | 16 ||× 1 ||= 16 |- | ||Total days||= 1383136 |} ===Calculating the Tzolkʼin date portion=== The Tzolkʼin date is counted forward from 4 Ajaw. 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 13 day 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 16 day names must be counted from Ajaw. This gives Kibʼ. Therefore, the Tzolkʼin date is 5 Kibʼ. ===Calculating the Haabʼ date portion=== The Haabʼ date 8 Kumkʼu is the ninth day of the eighteenth month. There are 17 days to the start of the next year. Subtract 17 days from the total, to find how many complete Haabʼ years are contained. :1,383,136 − 17 = 1,383,119 Divide by 365: :1,383,119 / 365 = 3,789 and (134/365) Therefore, 3,789 complete Haabʼ have passed and the remainder 134 is the 135th day 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 15th day. 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 14 Yaxkʼin. So the date of the long count date 9.12.2.0.16   5 Kibʼ 14 Yaxkʼin 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.{{harvnb|Thompson|1960|pp=314, 316, 148–49}} 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."{{cite book|last=Grofe|first=Michael John|year=2007|title=The Serpent Series: Precession in the Maya Dresden Codex|page=55|quote=On occasion, the Maya also recorded intervals of time even greater than 13 Bʼakʼtuns, such as one Piktun, composed of 20 Bʼakʼtuns. This is relevant to the current discussion concerning the Serpent Series.}}{{efn|"... 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 1 Piktun, the next unit above the Bakʼtun, in 4772 CE.}}{{cite web |url=https://www.penn.museum/sites/expedition/time-kingship-and-the-maya-universe-maya-calendars/ |author=Martin|title=Time, Kingship, and the Maya Universe |website=penn.museum}} Many inscriptions give the date of the current creation as a large number of 13s preceding 13.0.0.0.0   4 Ahau 8 Kumkʼu. For example, a Late Classic monument from [[Coba]], Stela 1. 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.''Fig. 444'' in {{harvnb|Wagner|2006|p=283}}{{harvnb|Schele|Freidel|1992|p=430}}{{cite book|first1=D.|last1=Freidel|first2=L.|last2=Schele|first3=J.|last3=Parker|title=Maya Cosmos: Three Thousand Years On The Shaman's Path|year=1993|volume=62, Fig. 2:1}}{{cite web |url=http://research.famsi.org/schele_list.php?_allSearch=Coba&hold_search=&tab=schele&title=Schele+Drawing+Collection&x=34&y=12|title=Schele Drawing Collection|website=research.famsi.org|access-date=2015-09-06}} Some authors think that the 13s were symbolic of a completion and did not represent an actual number.{{cite web |url=http://www.traditionalhighcultures.org/20_or_13_Baktuns_in_Pictun.pdf |first=Lloyd B. |last=Anderson |year=2008 |title=20 or 13 Baktuns in a Pictun? |website=traditionalhighcultures.org |access-date=2015-09-06 |url-status=dead |archive-url=https://web.archive.org/web/20150514043431/http://www.traditionalhighcultures.org/20_or_13_Baktuns_in_Pictun.pdf |archive-date=2015-05-14}} 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) Palenque Temple of the Cross, tablet, Schele (1987 p.)
12.19.13.4.0   8 Ajaw 18 Tzek in the prior era
6.14.0 Distance number linking to the "era date"
13.0.0.0.0   4 Ajaw 8 Kumkʼu Palenque Temple XIX, South Panel G2-H6 Stuart (2005 pp. 60, 77)
12.10.1.13.2   9 Ikʼ 5 Mol   (seating of GI in the prior era)
2.8.3.8.0
1.18.5.3.2   9 Ikʼ 15 Keh   (rebirth of GI, this date also in Temple of the Cross) The tablet of the inscriptions contains this inscription:
9.8.9.13.0   8 Ajaw 13 Pop
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. [[Ernst Förstemann|Förstemann]]{{cite book|author=Förstemann, Ernst|title=Commentary on the Maya Manuscript in the Royal Public Library of Dresden|publisher=Peabody Museum of American Archaeology and Archaeology and Ethnography, Harvard University|volume=IV. No. 2|pages=222–264}} identified these, but Wilson (1924){{rp|pages=24–25}} later clarified the way in which they operate. Ring Numbers are intervals of days between the Era Base date 4 Ajaw 8 Kumkʼu 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 [[J. Eric S. Thompson|Thompson]]{{harvnb|Thompson|1972|pp=20–21}} 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.{{cite book|author=Grofe, Michael John|year=2007|title=The Serpent Series: Precession in the Maya Dresden Codex|page=55}} Ring number     (12) 12.12.17.3.1   13 Imix 9 Wo (7.2.14.19 before (13) 13.0.0.0.0)
distance number (0) 10.13.13.3.2
Long Count              10.6.10.6.3   13 Akʼbal 1 Kankʼin 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 [[J. Eric S. Thompson|Thompson]]{{harvnb|Thompson|1972|pp=20–22}} contains a table of typical long reckonings after Satterwaite.{{cite web|url=http://www.traditionalhighcultures.org/Distances_across_Era_Date.pdf|title=Distances across Era Date|website=traditionalhighcultures.org|last=Thompson|first=J. Eric S.|author-link=J. Eric S. Thompson|access-date=2013-01-13|url-status=dead|archive-url=https://web.archive.org/web/20091117031111/http://www.traditionalhighcultures.org/Distances_across_Era_Date.pdf|archive-date=2009-11-17}} table from Thompson 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).{{cite journal|last=Beyer|first=Hermann|year=1933|title=Emendations of the 'Serpent Numbers' of the Dresden Maya Codex|journal=Anthropos (St. Gabriel Mödling bei Wien)|volume=28|pages=1–7}}{{cite book|year=1943|title=The Long Count Position of the Serpent Number Dates|publisher=Proc. 27th Int. Cong. Of Amer., Mexico, 1939|location=Mexico|volume=I|pages=401–05}}{{cite book|author=Grofe, Michael John|year=2007|title=The Serpent Series: Precession in the Maya Dresden Codex|page=63}} ==See also== * [[Aztec calendar]] * [[Maya astronomy]] * [[Maya calendar]] * [[Maya codices]] * [[Mesoamerican calendars]] ==Notes== {{notelist|1}} ==References== {{reflist}} ==Bibliography== {{refbegin|indent=yes}} * {{cite web |last=Boot |first=Eric |date=2002 |title=The Dos Pilas-Tikal Wars from the Perspective of Dos Pilas Hieroglyphic Stairway 4 |url=http://www.mesoweb.com/features/boot/DPLHS4.pdf |series=Articles |website=Mesoweb |access-date=2007-03-15}} * {{cite book |last1=Bricker |first1=Harvey M. |last2=Bricker |first2=Victoria R. |year=2011 |title=Astronomy in the Maya Codices |location=Philadelphia |publisher=American Philosophical Society |isbn=978-0-87169-265-8 }} * {{cite book |author=Coe, Michael D. |author-link=Michael D. 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Juergen |date=2000 |title=Kʼakʼ-u-pakal, Hun-pik-tokʼ and the Kokom: The Political Organisation of Chichen Itza |book-title=3rd European Maya Conference (1998) | url= http://ecoyuc.com.mx/articles.php?task=detail&aid=1 |format=[[PDF]] | access-date = 2005-10-26}} * {{cite book |last=Wagner | first = Elizabeth |date=2006 |chapter=Maya Creation Myths and Cosmology |pages=280–293 |editor=Nikolai Grube |others=Eva Eggebrecht and Matthias Seidel (assistant eds.) |title=Maya: Divine Kings of the Rain Forest |location=Cologne |publisher=Könemann |isbn=3-8331-1957-8 |oclc=71165439}} {{refend}} ==External links== *[https://phys.org/news/2026-06-oldest-maya-calendar-date-reveal.html Oldest Maya Long Count calendar date may reveal how royalty turned time into power - Phys.org - Paul Arnold - June 9, 2026] *[https://onlinelibrary.wiley.com/doi/pdf/10.1111/1467-968X.12320 Sandoval, Rich A. "The Ancient Maya Script of Hand Forms Embedded in Figural Art: A Decipherment of Numerals Signed by the Rulers of Altar Q 1." Transactions of the Philological Society 2025] * [http://research.famsi.org/schele_selects.php?image_number=490 Coba Stela 1 (Schele #4087)], partial illustration from the Linda Schele Drawings Collection of the monument from Coba with an expanded Long Count date * [http://www.michielb.nl/maya/calendar.html Maya calendar on michielb.nl, with conversion applet from Gregorian calendar to Maya date] (Uses the proleptic Gregorian calendar.) * [http://jqjacobs.net/archaeology/maya_astronomy.html The Dresden Codex Lunar Series and Sidereal Astronomy] * {{gutenberg|no=18973|name=Day Symbols of the Maya Year}} 1897 text by Cyrus Thomas. {{Calendars}} {{Authority control}} {{DEFAULTSORT:Mesoamerican Long Count Calendar}} [[Category:Mesoamerican calendars|Long Count]] [[Category:Maya Classic Period]] [[Category:Specific calendars]] [[Category:Chronology]] [[Category:Obsolete calendars]] [[Category:2012 phenomenon]] [[it:Calendario maya#Il Lungo computo]]