__
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 Tz**olkin**(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 8.11.0.14.0 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*
katuns*, 14

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.

**Sources**

http://www.criscenzo.com/jaguar/calendr.html

http://www.magnet.ch/serendipity/hermetic/cal_stud/maya/chap1.htm

http://personal.msy.bellsouth.net/msy/b/m/bmartin3/

http://www.halfmoon.org

The Ancient
Maya (G.Morley) Stanford University Press

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