The Maya Calendar


The Maya calendar in its final form probably dates from about the 1st century B.C. Although highly complex, it was
the most accurate known to humans until the introduction of the Gregorian calendar.The basic structure of the Maya calendar is common to all calendars of Meso-America (i.e., the civilized part of ancient Middle America).
It consists of two types of calendar systems : a ritual cycle of 260 named days and a vague year cycle of 365 days. Since the least common multiple of 260 and 365 is 18 980, these cycles run concurrently after 18 980 days, or 52 years of 365 days, called a "calendar Round", at the end of which a designated day recurs in the same position in the year.

The native Maya name for the 260-day cycle is unknown.Some authorities call it the Tzolkin(Count of Days); others refer to it as the Divinatory Calendar, the Ritual Calendar, or simply the day cycle. It is formed by the combination of numerals 1 through 13, meshing day by day with an ordered series of 20 Maya day names.


The days were believed to have a fateful character, and the Tzolkin was used principally in divination. Certain passages in the Mayan manuscripts Dresden Codex, one of the three that survived the conquest, show various Tzolkins.

The vague year or Haab of 365 days, similar to our modern calendar, consists of 18 named months of 20 days each, with an additional five days of evil omen, named Uayeb.


Thus, the Maya new year starts with 1 Pop followed by 2 Pop until 19 Pop followed by 0 Uo, 1 Uo etc. The Maya solar year is thought to have begun when the sun crossed the zenith on July 16. To indicate the date they denoted the sacred form followed by the vague notation, f.e. : 13 ahau 18 cumhu.

The 52-year cycle was not good enough to link events over longer periods of time. Mayan interest in history, genealogy, and astrology required accurate records of events far in the past. To connect dates to one another, the Maya expressed distances between them by a count of days and their multiples. They used the so called Long Count what was essentially a vigesimal place-value system of numeration, which is one based on a count of 20, but modified it by substituting 18 for 20 as the multiplier of units of the second order, so that each unit in the third place had the value of 360 days instead of 400. In monumental inscriptions, the digits are usually accompanied by the names of their periods their units represent, although in the manuscripts the period names are omitted and placement alone indicates the value of the units. The period names in ascending order are: kin (1 day); uinal (20 days); tun (18 uinals or 360 days); katun (20 tuns or 7 200 days); baktun (20 katuns or 144 000 days); pictun (20 baktuns or 2 880 000 days) and so on up to higher periods as calabatun, kinchiltun and alautun.

The following example could be written as or as :

By introducing an odd multiplier to form the tun, the Maya multiplication and division turned out to be rather difficult and therefore we find in the Dresden Codex long tables of multiples of numbers that could be more simply manupulated by addition and subtraction.

To correlate all historical records and to anchor dates firmly in time, the Maya started the Long Count on their zero date, about 3 114 B.C., which completed a round of 13 baktuns far in the past. There were several ways in which one could indicate the position of a Calendar Round dated in the Long Count. The most direct and unambiguous was to use an Initial-Series (IS) notation. The series begins with an outsized composition of signs called the Initial-Series introducing glyphs, which is followed by a count of periods written in descending order. On the earliest known monument, Stela 29 from Tikal in Guatemala, the Initial Series gives : 8 baktuns, 12
, 14 tuns, 8 uinals, 15 kins, which is written: It shows that the Calendar Round date of this Stela falls 1 243 615 days (just under 3 405 years) after the zero date of the Long Count.

The basic elements of the Mayan calendar had little to do with astronomy. A lunar count was, however, included in a Supplimentary Series appended to Initial-Series dates(see picture on the left : on the east side of Stela E in Quirigua is carved : 9 baktuns, 17 katuns, 0 tuns, o uinals, 0 kins and 13 ahau). After the Long Count, the series is composed of hieroglyphs labelled Glyphs G, F, E or D, C, B, and A, and a varying number of others. Glyph G changes its form daily, making a round of nine days, possibly corresponding to the nine gods of the lower world. Glyph F is closely associated with Glyph G and does not vary. Starting the Supplementary Series, glyphs E and D have numerical coefficients that give the age of the current Moon within an error of two or three days; Glyph C places it in a lunar half year; and Glyph A shows whether it is made up of 29 or 30 days. The meaning of Glyph B is unknown. The third count in the Maya inscriptions is the Secondary Series which seems to have been a calendar-correction formula, somewhat like our leap-year correction. With these second series the Maya priests took care of the discrepancy between the calendar year and the true solar year.

The correction formula worked out at Copan in the 7th century was even slightly more accurate than our Gregorian leap-year correction introduced in 1582.

Length of the year according to modern astronomy : 365,2422 days
Length of our present, corrected Gregorian year : 365,2425 days
Length of the year according to the Maya astronomy : 365,2420 days

The identification of certain architectural assemblages as observatories of solstices and equinoxes is rather difficult to substantiate. So far, it has not been demonstrated how the Maya reckoned the seasons of their agricultural cycle or whether they observed the tropical or the sidereal year.

In colonial times, the star group known as the Pleiades was used to mark divisions of the night, and the constellation Gemini was also observed. A computation table in the Dresden Codex records intervals of possible eclipses of the Sun and Moon. Another correlates five revolutions of the planet Venus around the Sun with eight 365-day years and projects the count for 104 years, when it returns to the beginning Tzolkin date. Three sets of month positions associated with the cycle suggest its periodical correction. Other computations have not been adequately explained, among them some very long numbers that transcend the Long Count. Such numbers appear also on monuments and indicate a grandiose conception of the complexity and the almost infinite extent of time.

We have to admit that, even with all our present sophisticated technology, many ghyphs are still undeciphered, but without use of any modern instrument the ancient Maya achieved a very high degree of astronomical accuracy.


The Ancient Maya (G.Morley) Stanford University Press
De grootste mysteries aller tijden, Reader's Digest

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