The Mayan Calendar

The Mayans, the culture of which had its classical period from 300 until around 800 CE, developed two calendars used simultaneously. There was a religious calendar, called Tzolkin, with a "year" of 260 days. The civil calendar, named Haab, had a solar year of 365 days. There were no leap years. The "years" of the Haab weren't counted as weren't those of the Tzolkin. Unfortunately, many artifacts of the Mayan culture have been destroyed by Spanish conquerers and Catholic missionaries by burning Mayan codices systematically, especially under the rule of bishop Diego de Landa (r. 1558 to 1579).

A cycle of 260 days was used by different peoples besides the Mayans - Zapotecs, Olmecs, Aztecs, and Toltecs - in around 500 BCE already. The Long Count was developed probably by the Olmecs in the first century BCE.

Tzolkin

This religious calendar was based on two cycles with lengths of 20 and 13 days respectively. The days of the 20 day cycle had a fixed sequence and were given names, as the following table shows.

	No.	Name
	1	Imix
	2	Ik
	3	Akbal
	4	Kan
	5	Chicchan
	6	Cimi
	7	Manik
	8	Lamat
	9	Muluc
	10	Oc
	11	Chuen
	12	Eb
	13	Ben
	14	Ix
	15	Men
	16	Cib
	17	Caban
	18	Eznab
	19	Cauac
	20	Ahau

Within the 13 day cycle, the days were numbered from 1 to 13. A day was designated by its number within the 13 day cycle followed by the name the day bore within the 20 day cycle. The lowest common multiple of 13 and 20 is 260, which is the length of a Tzolkin "year". With the system described, any of these 260 days had a unique designation. Interestingly, both cycles were increased every day, which made day 1 Imix be followed by day 2 Ik. The day after 13 Ben was 1 Ix. The designations of the first 25 days of a Tzolkin "year" are shown in the table below.

	No.	Name
	1	Imix
	2	Ik
	3	Akbal
	4	Kan
	5	Chicchan
	6	Cimi
	7	Manik
	8	Lamat
	9	Muluc
	10	Oc
	11	Chuen
	12	Eb
	13	Ben
	1	Ix
	2	Men
	3	Cib
	4	Caban
	5	Eznab
	6	Cauac
	7	Ahau
	8	Imix
	9	Ik
	10	Akbal
	11	Kan
	12	Chicchan

Haab

The civil year of the Haab calendar had a length of 365 days, divided into 18 months(1) of 20 days each. The 18th month was followed by five additional days, called Uayeb, which were considered to be an unlucky period. For the names and sequence of the "months" see the following table.

	No.	Name
	1	Pop
	2	Uo
	3	Zip
	4	Zotz
	5	Tzec
	6	Xul
	7	Yaxkin
	8	Mol
	9	Chen
	10	Yax
	11	Zac
	12	Ceh
	13	Mac
	14	Kankin
	15	Muan
	16	Pax
	17	Kayab
	18	Cumku
	19	Uayeb

Amazingly, the days within the months were numbered from 0 to 19 (instead of 1 to 20). At the same time, when Europeans did their calculations with abacuses and wrote them down with Roman numbers, Mayan scientists were about to discover the digit zero. A Haab date consisted of the number of the day within the current month and the name of that month, e. g. 7 Kankin described the eighth (!) day of the month Kankin.

To write down a date completely, Mayans gave the Tzolkin date as well as the Haab date of a day, which made every day within 52 Haab years have a unique designation(2).

Long Count

As the years weren't counted, Mayans used a third calendar for chronological purposes. This system, similar to the Julian day number, gives evidence of how far Mayan culture and science had developed.

The basic unit of this so called Long Count was the day, called Kin. 20 Kin constituted a "month" named Uinal. A "year" (Tun) consisted of 18 Uinal with a total length of 360 days. There were another six time units the lengths and names of which can be seen in the table:-

		days	Haab	trop. years
unit		length measured in ...
Kin		1
Uinal	= 20 Kin	20
Tun	= 18 Uinal	360	1
Katun	= 20 Tun	7200	20	19,7
Baktun	= 20 Katun	144000	400	394,3
Pictun	= 20 Baktun	2880000	8000	7885,2
Calabtun	= 20 Pictun	57600000	160000	157704
Kinchiltun	= 20 Calabtun	1152000000	3200000	3154072
Alautun	= 20 Kinchiltun	23040000000	64000000	63081431

Days were counted beginning from a certain event, and written using the units mentioned. Thus a date could have been 7 Baktun 17 Katun 18 Tun 13 Uinal 1 Kin, shortly written as 7.17.18.13.1. The beginning of the counting is widely believed to be 6 September 3114 BCE, but there are different dates, too.

1
Although the length of these months had nothing to do with the lunar months or their approximations in other calendars the term "month" is used here.

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2
The lowest common multiple of the cycle lengths (365 days and 260 days) is 18980 days, or 52 Haab years, or 73 Tzolkin years.

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