The Maya Calendar
he Maya employed a complicated set of calendars, most aspects of which go back to earlier Mesoamerican peoples such as the Olmec. But first, a bit about numbers. I'll try to make this as simple as possible.
1. The Vigesimal (Base 20) Notation System
The Maya notation system is simple, elegant, and efficient. It uses three symbols, the dot, the bar, and the shell, which represent units of one, five, and zero respectively. It is a positional system, thanks to the use of the zero, in contrast to simple additive systems such as Roman numerals: numbers are written vertically from bottom to top. Each step in the hierarchy represents a new power of twenty.
To see examples of how the Maya wrote numbers (showing how to interpret the writing), click here.
2. The 260-Count Ceremonial Year (Tzolk'in)
Perhaps the oldest of the Mesoamerican calendars is the so-called tzolk'in (the word is actually of modern origin). Consisting of 260 days, it is rather mysterious in that it bears no obvious relation to celestial phenomenon (most calendars are either solar or lunar). It has been suggested that it may relate to the human gestational period (which is actually 280 days from conception), but as far as I know there is no evidence to confirm this speculation. What is known is that it results from multiplying the number 13 by the number 20. The Maya did not use fractions, and thirteen is the closest whole number of lunations in a solar year, so perhaps this is the root celestial connection. Twenty of course suggests fingers and toes, but there could be other significances as well. Each day in the ceremonial calendar is given a number from one to thirteen and one of twenty names. The progression of names is as follows: Imix, Ik', Ak'bal, K'an, Chik'chan, Kimi, Manik', Lamat, Muluk, Ok, Chuwen, Eb, Ben, Ix, Men, Kib, Kaban, Etz'nab, Kawak, Ahaw. The numbers and the names progress with each passing day, as: 1 Imix, 2 Ik', 3 Ak'bal, 4 K'an, 5 Chik'chan, 6 Kimi, 7 Manik', 8 Lamat, 9 Muluk, 10 Ok, 11 Chuwen, 12 Eb, 13 Ben, 1 Ix, 2 Men, 3 Kib, 4 Kaban, 5 Etz'nab, 6 Kawak, 7 Ahaw, 8 Imix, 9 Ik' ... etc. (The progression of the 13 numbers and 20 names is often portrayed as a pair of interlocked revolving gears of different sizes, but it can be easily understood without that metaphor.) This calendar was used in seasonal activities such as sowing and harvesting, for ceremonial occasions such as enthronement, and for other significant events such as military triumphs; it was also the calendar of fortune telling and divination, and is still used in that way by some Maya today.
3. The "Vague Year" (Haab)
The Maya also required a solar calendar. Although Maya astrologers and historians calculated the solar year very precisely--more precisely than in the Julian calendar--for their workaday solar year, called the haab, they were satisfied with a year of 365 days and did not add leap year corrections to account for the additional quarter day in the solar year (which is why anthropologists call this the "vague year"). The haab consisted of eighteen months of 20 days, followed by a five-day period called the wayeb. (The months are Pop, Wo, Sip, Sotz', Sek, Xul, Yaxk'in, Mol, Ch'en, Yax, Sak, Keh, Mak, K'ank'in, Muwan, Pax, K'ayab, and Kumk'u.) The wayeb was dreaded as un unlucky period.
4. The Calendar Round
Maya dates are most often given both in Tzolk'in and Haab. For example, a certain day may be recorded as 2 Chik'chan 5 Pop, indicating that in the Tzolk'in cycle the 13 numbers have come around to 2 and the 20 names to Chik'chan, while in the concurrent Haab cycle the same day is the 5th day of the month of Pop. It will take 52 Haabs (or 73 Tzolk'ins, that is, 18,980 days--the lowest number divisible by both 260 and 365) before the two cycles will again meet at this same juncture, and another 2 Chik'chan 5 Pop will occurs. This cycle of 52 years is called the calendar round.
5. The Long Count
In order to keep clear all the 2 Chik'chan 5 Pops (for example) of historical time, The Maya used another calendar system called the Long Count. This is a chronological sequence of days dating from the beginning of the present great cycle in August 13, 3114 BCE (a date, called by the Maya 4 Ahaw 8 Kumk'u, whose historical or mythic significance is unknown; a minority view holds that the date was actually August 11). The current great cycle will end (calamitously) on December 23, 2012. Although the Long Count is a cyclical calendar like other Maya calendars, its span is so great--like the Hindu kalpas--that no historical date recurs, so that Long Count dates are absolute and unambiguous. For the Long Count, the Maya used as their basic unit the tun. The tun is a "year" of 360 days--it is the Haab year of 18 20-day months (days are called K'ins, months are called Winals) without the addition of the 5-day wayeb. Applying the vigesimal system to the tun year, the Maya created cycles of enormous length:
Unit Days (K'ins) Approx. Solar Years Tun (20 Winals) 360 0.99 K'atun (20 Tuns) 7200 19.7 Bak'tun (20 K'atuns) 14,000 394 Great Cycle (13 Bak'tuns) 1,872,000 5125
the following units are very seldom used:
Pictun (20 Baktuns) 2,880,000 7885 Calabtun (20 Baktuns) 57,600,000 157,705 Kinchiltun (20 Calabtuns) 1,152,000 3,154,091 Alautun (20 Kinchiltuns) 23,040,000 63,081,809
The Long Count is probably of much more recent origin than the other calendars, but it still predates the real flourishing of the Maya. The earliest Long Count date is 7 December 36 BCE (on Stela 2 at Chiapa de Corzo in central Chiapas). The Long Count calendar may be of Mixe-Zoquean (a non-Maya, possibly Olmec, people now living mainly in western Chiapas) origin.
"Thus a Long Count date conventionally written as 18.104.22.168.11 10 Chuwen 4 Kumk'u would be:
"9 bak'tuns = 1,296,000 days
"10 k'atuns = 72,000 days
"19 tuns = 6,840 days
"5 winals = 100 days
"11 k'ins = 11 days
"or 1,374,951 days since the close of the last Great Cycle, reaching the Calendar Round position 10 Chuwen 4 Kumk'u"
(Michael D. Coe, The Maya (6th ed.), p. 62).