Mesoamerican Long Count calendar Totally Explained

Everything about The Mesoamerican Long Count Calendar totally explained

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's 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 BCE (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 didn't 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 is generally known as the 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 BCE in the proleptic Gregorian calendar or September 6 (Julian). 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 isn't 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 doesn't represent 400 days, but rather only 360 days.
The following table shows the period equivalents as well as Mayan names for these periods:

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

Calculating Long Count dates

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. ť See also History of zero

Syntax

The Long Count dates are written with the higher periods (for example b'ak'tun) at the beginning 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 BCE, or September 1, 32 BCE.
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’ [patronof Haab' month] ("revered was the year-count with the patron [ofthe month]"). Next come the 5 digits of the Long Count, followed by the tzolk'in date written as single glyph, 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 relating a contemporary event is on Stela 2 at Chiapa de Corzo, Chiapas, Mexico, showing a date of 36 BCE. This table lists the 6 artifacts with the 8 oldest Long Count dates.

Archaeological site	Name	Gregorian Date(based on August 11)	Long Count digits	Location
Chiapa de Corzo	Stela 2	December 10, 36 BCE	7.16.3.2.13	Chiapas, Mexico
Tres Zapotes	Stela C	September 3, 32 BCE	7.16.6.16.18	Veracruz, Mexico
El Baúl	Stela 1	March 6, 37 CE	7.19.15.7.12	Guatemala
Abaj Takalik	Stela 5	May 20, 103 CE	8.3.2.10.15	Guatemala
' '	' '	June 6, 126 CE	8.4.5.17.11	' '
La Mojarra	Stela 1	July 14, 156 CE	8.5.16.9.7	Veracruz, Mexico
' '	' '	May 22, 143 CE	8.5.3.3.5	' '
Near La Mojarra	Tuxtla Statuette	March 15, 162 CE	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 CE (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, Makemson 1946, 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	626,928
+4CR	660,203
Hochleitner	674,265
Schultz	677,723
Ramos	679,108
Valliant	679,183
Dittrich	698164
Weitzel	774,078

A list of the start dates for 13 Baktuns>

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

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, as well as aligning astronomic events that appear in the Maya inscriptions with modern calculations of when those event occurred.
   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 BCE in the Julian calendar) 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 BCE September 6 (Julian) or 3114 BCE August 11 (Gregorian), Julian day number (JDN) 584283. 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, such as Linda Schele.
   Today,, in the Long Count is (GMT correlation).

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. ť (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. ť 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. ť 1383136 - 16 = 1383120

Dividing by 365, we have ť 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've 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.

Distance Numbers

Long Count inscriptions are frequently followed by a description of the event that occurred on that date. Then the inscription will give what is called a Distance Number. A Distance Number is distinguished from a Long Count by having the glyph for the smallest unit, usually the k'in, appear first and as many other digits as necessary to show the time span. A particular glyph indicates whether this Distance Number should be added or subtracted from the Long Count that preceded it. The date arrived at is most often shown with just a Calendar Round date, but sometimes another Long Count.

Piktuns and higher orders

As mentioned in the Syntax section, there are also a number of rarely-used higher-order periods above the b'ak'tun named by modern scholars, the piktun, kalabtun, k'inchiltun, and alautun.
   The inscription on Quirigua stela F, or 6, shows a Long Count date of 9.16.10.0.0 1 Ahau 3 Zip (15 March 761 Gregorian). The huge Distance Number of 1.8.13.0.9.16.10.0.0 is subtracted and the resulting date is a date 1 Ahau 13 Yaxk'in over 90 million years in the past. However, there's another date on Quirigua Stela D or 4, that gives a date of 9.16.15.0.0 7 Ahau 18 Pop (17 February 766 Gregorian), to which is subtracted the Distance Number of 6.8.13.0.9.16.15.0.0. This is over 400 million years before the date the stela was erected!
   At Yaxchilan, on a temple stairway, there's 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 19 October 744The same applies to a Late Classic monument from Coba, Stela 1 where 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.

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