Mesoamerican Long Count calendar

Detail showing three columns of glyphs from 2nd century AD La Mojarra Stela 1. The left column gives a Long Count date of 8.5.16.9.9, or 156 AD. The two right columns are glyphs from the Epi-Olmec script.

The Mesoamerican Long Count calendar is a non-repeating, vigesimal (base-20) calendar used by several Mesoamerican cultures, most notably the Maya. For this reason, it is sometimes known as the Maya (or Mayan) Long Count calendar. Using a modified vigesimal tally, the Long Count calendar identifies a day by counting the number of days passed since August 11, 3114 BC (Gregorian). Because the Long Count calendar is non-repeating, it was widely used on monuments.

Background

Among other calendars devised in pre-Hispanic Mesoamerica, two of the most widely used were the 365-day solar calendar (Haab' in Mayan) and the 260-day ceremonial calendar, which had 20 periods of 13 days. This 260-day calendar was known as the Tzolk'in to the Maya and tonalpohualli to the Aztecs.

The Haab' and the Tzolk'in calendars identified and named the days, but not the years. The combination of a Haab' date and a Tzolk'in date was enough to identify a specific date to most people's satisfaction, as such a combination did not occur again for another 52 years, above general life expectancy.

Because the two calendars were based on 365 days and 260 days respectively, the whole cycle would repeat itself every 52 Haab' years exactly. This period was known as a Calendar Round.

To measure dates over periods longer than 52 years, the Mesoamericans devised the Long Count calendar.

Long Count periods

The Long Count calendar identifies a date by counting the number of days from August 11, 3114 BC. Rather than using a base-10 scheme, like Western numbering, the Long Count days were tallied in a base-20 scheme. Thus 0.0.0.1.5 is equal to 25, and 0.0.0.2.0 is equal to 40.

The Long Count is not consistently base-20, however, since the second digit (from the right) only counts to 18 before resetting to zero. Thus 0.0.1.0.0 does not represent 400 days, but rather only 360 days.

The following table shows the period equivalents as well as Mayan names for these periods.

Table of Long Count units

Days	Long Count period	Long Count period	Approx solar years
1		= 1 K'in
20	= 20 K'in	= 1 Winal	1/18th
360	= 18 Winal	= 1 Tun	1
7,200	= 20 Tun	= 1 K'atun	20
144,000	= 20 K'atun	= 1 B'ak'tun	395

The Mayan name for a day was k'in. Twenty of these k'ins are known as a winal (or uinal). Eighteen winals or 360 k'in make one tun. Twenty tuns are known as a k'atun. Twenty k'atuns make a b'ak'tun. There are also four rarely-used higher-order periods: piktun, kalabtun, k'inchiltun, and alautun.

Calculating Long Count dates

File:Maya.svg

Mayan numerals

Mesoamerican numerals

Long Count dates are written with Mesoamerican numerals, as shown on this table. A dot represents one 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.

See also History of zero

File:Tres Zapotes Stela.C.back.Pt1.jpg

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 BC (Gregorian). The glyphs surrounding the date are what is thought to be one of the few surviving examples of Epi-Olmec script.

Syntax

The Long Count dates are written vertically, with the higher periods (i.e. b'ak'tun) on the top and then the number of each successively smaller order periods until the number of days (k'in) are listed. As can be seen at left, the Long Count date shown on Stela C at Tres Zapotes is 7.16.6.16.18.

7	× 144000	= 1,008,000 days (k'in
16	× 7200	= 115,200 days (k'in)
6	× 360	= 2,160 days (k'in)
16	× 20	= 320 days (k'in)
18	× 1	= 18 days (k'in)
	Total days	= 1,125,698 days (k'in)

The date on Stela C, then, is 1,125,698 days from August 11, 3114 BC, or September 1, 32 BC.

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) hab’ [patron of Haab' month] ("revered was the year-count with the patron [of the month]"). Next come the 5 digits of the Long Count, followed by the tzolk'in date written as single gylph, and then by supplementary information. Most of this supplementary series is optional and has been shown to be related to lunar data, for example, the age of the moon on the day and the calculated length of current lunation. The date is concluded by a glyph stating the day and month of the Haab year. The text then continues with whatever activity occurred on that date.

A drawing of a full Maya Long Count inscription is shown below (click here).

Origin of the Long Count calendar

The earliest Long Count inscription yet discovered is on Stela 2 at Chiapa de Corzo, Chiapas, Mexico, showing a date of 36 BC. This table lists the 6 artifacts with the 8 oldest Long Count dates.

Archaeological site	Name	Gregorian Date (based on Aug 11)	Long Count digits	Location
Chiapa de Corzo	Stela 2	December 10, 36 BC	7.16.3.2.13	Chiapas, Mexico
Tres Zapotes	Stela C	September 3, 32 BC	7.16.6.16.18	Veracruz, Mexico
El Baúl	Stela 1	March 6, 37 AD	7.19.15.7.12	Guatemala
Abaj Takalik	Stela 5	May 20, 103 AD	8.3.2.10.15	Guatemala
' '	' '	June 6, 126 AD	8.4.5.17.11	' '
La Mojarra	Stela 1	July 14, 156 AD	8.5.16.9.7	Veracruz, Mexico
' '	' '	May 22, 143 AD	8.5.3.3.5	' '
Near La Mojarra	Tuxtla Statuette	March 15, 162 AD	8.6.2.4.17	Veracruz, Mexico

Of the 6 sites, three are on the western edge of the Maya homeland and three are several hundred kilometers further west, leading most researchers to believe that the Long Count calendar predates the Maya. La Mojarra Stela 1, the Tuxtla Statuette, Tres Zapotes Stela C, and Chiapa Stela 2 are all inscribed in an Epi-Olmec, not Maya, style. El Baúl Stela 2, on the other hand, was created in the Izapan style. The first unequivocally Maya artifact is Stela 29 from Tikal, with the Long Count date of 292 AD (8.12.14.8.15), more than 300 years after Stela 2 from Chiapa de Corzo.

Correlations between Western calendars and the Long Count calendar

JDN correlations
to the Maya creation date
(after Thompson 1971, et al.)

Name	Correlation
Willson	438,906
Smiley	482,699
Makemson	489,138
Spinden	489,384
Teeple	492,662
Dinsmoor	497,879
-4CR	508,363
-2CR	546,323
Stock	556,408
Goodman	584,280
Martinez-Hernandez	584,281
GMT	584,283
Lounsbury	584,285
Pogo	588,626
+2CR	622,243
Kreichgauer	626,927
+4CR	660,203
Hochleitner	674,265
Schultz	677,723
Ramos	679,108
Valliant	679,183
Weitzel	774,078

There have been various methods proposed to allow us to convert from a Long Count date to a Western calendar date. These methods, or correlations, are generally based on dates from the Spanish conquest, where both Long Count and Western dates are known with some accuracy.

The commonly-established way of expressing the correlation between the Maya calendar and the Gregorian or Julian calendars is to provide number of days from the start of the Julian Period (Monday, January 1, 4713 BC) to the start of creation on 0.0.0.0.0 (4 Ajaw, 8 Kumk'u).

The most commonly accepted correlation is the "Goodman, Martinez, Thompson" correlation (GMT correlation). The GMT correlation establishes that the 0.0.0.0.0 creation date occurred on 3114 BC September 6 (Julian) or 3114 BC August 11 (Gregorian), Julian day number (JDN) 584283, the number of days since the start of the Julian Period. This correlation fits the astronomical, ethnographic, carbon dating, and historical sources. However, there have been other correlations that have been proposed at various times, most of which are merely of historical interest, except that by Floyd Lounsbury, two days after the GMT correlation, which is in use by some Maya scholars.

Today, 04:14, Friday April 19, 2024 (UTC), in the Long Count is Template:Maya date.

The use of software that is based on the proleptic Gregorian calendar can be problematic for:

1. Historical research. For example the G.M.T. correlation is based dates in both calendars in the Chronicle of Oxcutzcab, Bishop Diego de Landa's Relación de las Cosas de Yucatán, and the Chilam Balam. If one were to try to correctly derive the G.M.T. correlation by using these dates in a program that used the proleptic Gregorian calendar it would fail because the Gregorian calendar was not in use at that time.
2. Astronomical research. For example, to study ancient observations on stelae or in the codices, one may convert a Long Count to days, months, and years. This date would then be entered into an astronomy program. The astronomy program will use the standard Julian/Gregorian calendar so this will cause a major error.

A list of the start dates for 13 Baktuns

Long Count	Proleptic Gregorian Calendar Date
0.0.0.0.0	August 11, 3114 BC
1.0.0.0.0	November 13, 2720 BC
2.0.0.0.0	February 16, 2325 BC
3.0.0.0.0	May 21, 1931 BC
4.0.0.0.0	August 23, 1537 BC
5.0.0.0.0	November 26, 1143 BC
6.0.0.0.0	February 28, 748 BC
7.0.0.0.0	June 3, 354 BC
8.0.0.0.0	September 5, 41 AD
9.0.0.0.0	December 9, 435 AD
10.0.0.0.0	March 13, 830 AD
11.0.0.0.0	June 15, 1224 AD
12.0.0.0.0	September 18, 1618 AD
13.0.0.0.0	December 21, 2012 AD

2012 and the Long Count

According to the Popol Vuh, a book compiling details of creation accounts known to the K'iche' Maya of the Colonial-era highlands, we are living in the fifth world. The Popol Vuh describes the first four creations that the gods failed in making and the creation of the successful fifth world where men were placed. In the Maya Long Count, the previous creation ended at the start of a 13th b'ak'tun.

The previous creation ended on a long count of 12.19.19.17.19. Another 12.19.19.17.19 will occur on December 20 2012, followed by the start of the thirteenth b'ak'tun, 13.0.0.0.0, on December 21, 2012. It has been suggested in many New Age articles and books that this will be the end of this creation, the next pole shift or something else entirely. In this age we are approaching the same count again, only there is a common misconception of the Maya's practice of abbreviating their dates to five decimal places. On monuments where the full date is shown, the end of creation is said to be October 21, 4772 AD. According to the Maya there will be a baktun ending in 2012, a significant event being the end of the 13th 400 year period, but not the end of the world.

Inscriptions beyond 2012

Maya stela occasionally show dates beyond 2012. Most of these are in the form of "distance dates", where a Long Count date is given with a distance date to be added. For example, on Tikal Stela 10 we find the following Long Count date: 9.8.9.13.0 8 Ahau 13 Pop (24th March 603 AD Gregorian) with a distance date of 10.11.10.5.8. The resulting date is given as 1.0.0.0.0.8 5 Lamat 1 Mol, or 21st October 4772 AD – almost 3,000 years into the future.

Summary

Despite the publicity generated by the 2012 date, "we have no record or knowledge that [the Maya] would think the world would come to an end" in 2012.

"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, Fla. To render Dec. 21, 2012, as a doomsday or moment of cosmic shifting, she says, is "a complete fabrication and a chance for a lot of people to cash in."

Calculating a full Long Count date

As stated, a full Long Count date not only includes the 5 digits of the Long Count, but the 2-character Tzolk'in and the 2-character Haab' dates as well. The 5 digit Long Count can therefore be confirmed with the other 4 characters (the "calendar round date").

Taking as an example a Calendar Round date of 9.12.2.0.16 (Long Count) 5 Kib' (Tzolk'in) 14 Yaxk'in (Haab'). 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 Kumk'u, and show how the date 5 Kib' 14 Yaxk'in is derived.

9	× 144000	= 1296000
12	× 7200	= 86400
2	× 360	= 720
0	× 20	= 0
16	× 1	= 16
	Total days	= 1383136 k'in

Calculating the Tzolk'in date portion

The Tzolk'in date is counted forward from 4 Ajaw. To calculate the numerical portion of the Tzolk'in date, we must add 4 to the total number of days given by the date, and then divide total number of days by 13.

(4 + 1383136) / 13 = 106395 and 5/13

This means that 106395 whole 13 day cycles have been completed, and the numerical portion of the Tzolk'in date is 5.

To calculate the day, we divide the total number of days in the long count by 20 since there are twenty day names.

1383136 / 20 = 69156 and (16/20)

This means 16 day names must be counted from Ajaw. This gives Kib'. Therefore, the Tzolk'in date is 5 Kib'.

Calculating the Haab' date portion

The Haab' date 8 Kumk'u is the ninth day of the eighteenth month. Since there are twenty days per month, there are eleven days remaining in Kumk'u. The nineteenth and last month of the Haab' year contains only five days, thus, there are sixteen days until the end of the Haab' year.

If we subtract 16 days from the total, we can then find how many complete Haab' years are contained.

1383136 - 16 = 1383120

Dividing by 365, we have

1383120 / 365 = 3789 and (135/365)

Therefore, 3789 complete Haab' have passed, with 135 days into the new Haab'.

We then find which month the day is in. Dividing the remainder 135 days by 20, we have six complete months, plus 15 remainder days. So, the date in the Haab' lies in the seventh month, which is Yaxk'in. The fifteenth day of Yaxk'in is 14, thus the Haab' date is 14 Yaxk'in.

So the date of the long count date 9.12.2.0.16 5 Kib' 14 Yaxk'in is confirmed.

Piktuns and higher orders

As mentioned in the Syntax section, there are also four rarely-used higher-order periods above the b'ak'tun: piktun, kalabtun, k'inchiltun, and alautun.

It is a matter of dispute whether the first piktun occurs after 13 or after 20 b'ak'tun. Most Mayanists think that in the majority of inscriptions, where only the last five Long Count positions are used, the count recycles at 13 b'ak'tuns, whereas, if longer cycles are used, the count continues to the end of the 20th b'ak'tun (b'ak'tun 19) before a pictun is registered. In the same way, the fact that a 13-katun cycle was used, didn't negate the fact that there are 20 katuns in a b'ak'tun.

The inscription on Quirigua stela F, or 6, shows a Long Count date of 9.16.10.0.0 1 Ahau 3 Zip (15th March 761 AD Gregorian). The huge distance date of 1.8.13.0.9.16.10.0.0 is subtracted and the resulting date is given as (18.)13.0.0.0.0.0.0.0 1 Ahau 13 Yaxkin, which is equivalent to a day over 90 million years in the past. However, there is another distance date on Quirigua Stela D or 4, that gives a date of 9.16.15.0.0 7 Ahau 18 Pop (17th February 766 AD Gregorian), to which is added 6.8.13.0.9.16.15.0.0, to give a date of (13.)13.0.0.0.0.0.0.0. This is over 400 million years after the date the stela was erected! It was by calculating a number of these distance dates that Eric Thompson was able to determine that the date of creation in 3114 BC – 13.0.0.0.0 was actually 0.1.13.0.0.0.0.0.0 in the extended version.

At Yaxchilan, on a temple stairway, there is an inscription that includes four levels above the alautuns. The inscription reads: 13.13.13.13.13.13.13.13.9.15.13.6.9 _3 Muluc 17 Mac. This is equivalent to 19th October 744 AD, but the higher cycles do not conform to Thompson’s calculation. The same applies to 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 b'ak'tun.

File:Morley 1915 ISglyphs.jpg

A drawing by Sylvanus Morley showing the Maya hieroglyphic inscription on a lintel in Chichen Itza, the only inscription in the site known to show a Long Count date. The date shown here (starting row 2, ending at A5) is 10.2.9.1.9, 9 Muluk, 7 Sak, equivalent to July 30, 878 CE.

See also

• Aztec calendar
• Maya calendar
• Mayan codices
• Mesoamerican calendars

References

• Template:Aut (2002). "The Dos Pilas-Tikal Wars from the Perspective of Dos Pilas Hieroglyphic Stairway 4" (PDF). Mesoweb Articles. Mesoweb. http://www.mesoweb.com/features/boot/DPLHS4.pdf. Retrieved 2007-03-15. 

• [[wikipedia:Michael D. Coe |Template:Aut]] (1994a). Breaking the Maya Code. London: Penguin Books. 

• [[wikipedia:Michael D. Coe |Template:Aut]] (1994b). Mexico: from the Olmecs to the Aztecs (4th edition ed.). New York: Thames & Hudson. Template:Hide in printTemplate:Only in print. 

• [[wikipedia:Richard Diehl |Template:Aut]] (2004). The Olmecs: America's First Civilization. Ancient Peoples and Places. New York: Thames & Hudson. Template:Hide in printTemplate:Only in print. 

• Template:Aut (2006). "Glyphs G and F: Identified as Aspects of the Maize God" (PDF). Wayeb Notes 22: pp.1—23. Template:Hide in printTemplate:Only in print. http://www.wayeb.org/notes/wayeb_notes0022.pdf. Retrieved 2007-04-04. 

• Template:Aut (28 March 2007). "Does Maya calendar predict apocalypse very soon?". USA Today: 11D. 

• Template:Aut; and Template:Aut (2005). "Photographic Documentation of Monuments with Epi-Olmec Script/Imagery". The Foundation Granting Department: Reports Submitted to FAMSI. Foundation for the Advancement of Mesoamerican Studies, Inc. (FAMSI). http://www.famsi.org/reports/05084/index.html. Retrieved 2007-04-04. 

• [[wikipedia:Linda Schele |Template:Aut]]; and Template:Aut (1992). A Forest of Kings: The Untold Story of the Ancient Maya (Reprint edition ed.). New York: Harper Perennial. Template:Hide in printTemplate:Only in print. 

• [[wikipedia:J. Eric S. Thompson |Template:Aut]] (1929). "Maya Chronology: Glyph G of the Lunar Series". American Anthropologist, New Series 31 (2): pp.223—231. Template:Hide in printTemplate:Only in print. Template:Hide in printTemplate:Only in print. 

• [[wikipedia:J. Eric S. Thompson |Template:Aut]] (1971). Maya Hieroglyphic Writing, an Introduction. 3rd edition. Norman. 

• Template:Cite conference

• Template:Aut (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 Press. pp. pp.280–293. Template:Hide in printTemplate:Only in print. Template:Hide in printTemplate:Only in print. 

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
• Maya Calendar notes by M. Finlay, Maya Astronomy (Uses the proleptic Gregorian calendar.)
• The Maya Calendar by the Maya World Studies Center in Yucatan Mexico
• Maya calendar on michielb.nl, with conversion applet from Gregorian calendar to Maya date (Uses the proleptic Gregorian calendar.)
• Convert date from Maya long count to Gregorian calendar (Uses the proleptic Gregorian calendar and converts to/from long count only.)
• UT Mesoamerica Center Discussion Board. (David Stuart's translation of Monument 6 at Tortuguero.)
• Maya Calendar and Links on diagnosis2012.co.uk (The calculator uses the proleptic Gregorian calendar. The site has a huge number of links to Maya calendar sites.)
• "The How and Why of the Mayan End Date in 2012 A.D." by John Major Jenkins.
• Culture and History of the Ancient and Modern Maya Includes pdf files of "Popol Vuh: The Book of the Counsil" and "Chilam Balam of Chumayel" (The page about the calendar uses the "astronomical" (Lounsbury) correlation.)
• Template:Gutenberg 1897 text by Cyrus Thomas.

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