Maya Long Count Calendar:

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 BCE (Gregorian).^[1] 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 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 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:

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.

Syntax

The Long Count dates are written with the higher periods (i.e. 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.

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]").^[2] 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.^[3] 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.

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.^[4] This table lists the 6 artifacts with the 8 oldest Long Count dates.

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.^[5] 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.^[6] 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.^[7]

Correlations between Western calendars and the Long Count calendar

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, 12:09, Wednesday June 11, 2008 (UTC), in the Long Count is 12.19.15.7.6 (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.

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.

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.

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.

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.

Distance Numbers

Long Count inscriptions are frequently followed by a description of the event that occurred on that date. The inscription frequently separates events with what modern scholars 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 it will be displayed with 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 is 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.^[8]

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 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.^[9]

Maya Long Count Calendar

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