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An excerpt from "Tzolkin: Visionary Perspectives and Calendar Studies"
(1992, 1994; pages 23-30).

Introduction to the Mayan Calendar

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And so we begin our journey. There is much to discover and much to learn
about the Sacred Calendar. By the end of this chapter we will have covered
a lot of ground, and I will be sharing some advanced ideas. In an effort
to make this accessible to the beginner, we should try to get a firm
understanding of the basic mechanics of several different cycles and how
they relate. And don't worry, a lot of the basics covered here will be
repeated when necessary throughout this chapter. I'll try to keep this
introduction short and simple. The full meaning of these interlocking
cycles will be explored in later sections.

There are two types of Mayan time keeping:  1)  the Venus Round system,
consisting of the tzolkin, haab and the Venus cycle, and 2) the Long
Count. Let's start where it all begins, with the tzolkin.

Tzolkin, Haab, The Year-Bearers and Venus

The Sacred Calendar, the Earth Calendar, the Sacred Almanac, the Count of
Days, the Tzolkin - all of these terms refer to the 260-day cycle. The
term Sacred Calendar, however, is often used to denote the multiple
interrelated systems, ie., the entire framework of cycles. 260 days is
roughly nine moons.  The cycle consists of 20 day-signs combined with a
number from one to thirteen.  Each day is named by its number and
day-sign, thus giving a total of 260 unique days. The day-signs are
glyphs, and on one level are used in divination. Their meanings cover
important themes in Indian culture and can be loosely translated as
follows:

I.   Alligator	Death	Monkey	Owl
II.	Wind	Deer	Grass	Quake
III.	House	Rabbit	Reed	Knife
IV.	Lizard	Water	Jaguar	Rain
V	Serpent	Dog	Eagle	Flower

These day-signs also have linguistic, astronomical and mythical
references.  The order of the day-signs is universal throughout
Meso-america, and there is evidence that the 260-day Sacred Almanac has
been followed unbroken for some 3000 years; Wind follows Alligator, House
follows Wind, and so on. The 13-day number cycle parallels the sequential
passage of day-signs.  In other words, 1 Wind is followed by 2 House,
followed by 3 Lizard, etc.  In this way, 7 Jaguar (for example) occurs 40
days after 6 Jaguar.  Most likely, the count doesn't "begin" on any
specific day, although the conventional listing begins with Alligator.

The way in which the day-signs have meanings on many different levels of
Mayan culture is characteristic of Sacred Calendar studies.  It would be
difficult, indeed inaccurate, to promote just one origin or use for the
day-signs; the Calendar has what I call "multiple meanings." So why is the
260-day cycle so important? First and foremost, it corresponds to the
9-month gestation period of human beings, which has everything to do with
growth and unfolding. It also corresponds to the interval between Venus
emerging as eveningstar and its emergence as morningstar (about 258 days),
the interval between the planting and harvesting of certain types of corn,
and is related to planetary cycles.  Here we see biological, agricultural
and astronomical references.

The Haab

The 260-day cycle does not directly correspond with any known astronomical
period, yet it serves as a common denominator to synthesize the cycles of
Sun, Mercury, Venus, Moon, Earth and and Mars (as well as the other
planets). In essence, it is the key factor of all the planetary periods.
Strange to think that it corresponds to our own gestation period. The
solar cycle, which is really the 365 days or so that it takes for the
earth to travel around the sun, was conceived as a partner cycle to the
tzolkin. It was called the haab (cycle of rains) and consists of 18 months
of twenty days, with a short month of 5 days at the end.

Haab dates are indicated by a month name and a day-number. (Unlike the
tzolkin dates, the months and numbers of the haab follow like our own
month and days - e.g. 2 Zec in the haab is followed by 3 Zec, 4 Zec, 5 Zec
and so on.) In one sense, these two cycles represent the secular and
sacred interests of the culture. The haab is the obvious yearly cycle,
while the tzolkin structures a hidden dimension, closer to the sacred
spirit realms.  Together, the tzolkin/haab serves as a framework for
predicting eclipses, timing festivals, and for scheduling visits to shrine
sites. The nineteen month-names we will use in this book come from the
Yucatec Maya language:

Kayab	Zec	Sac
Cumhu	Xul	Ceh
Pop	Yaxkin	Mac
Uo	Mol	Kankin
Zip	Chen	Muan
Zotz	Yax	Pax
Vayeb (5 day month)

The Tikal haab began on 0 Pop and numbered months from 0 to 19.  The
Quiche and Ixil haab begins on 1 Kayab and numbered months from 1 to 20.
We will explore this further in the next section of this chapter.

The Year Bearers

This is where it starts getting a little tricky, and we start to see the
mythological uses of the Sacred Calendar.  The quality of a year is
determined by the day-sign which falls on New Years Day - which is the
first day of the haab. This special day is called the year-bearer, or, to
the modern Ixil Maya, the mam.  The 365-day haab is an approximation of
the year.  It is referred to as the vague solar year, or casually, as the
year. Since the twenty day-signs divide into the 365-day haab 18 times
with 5 left over, the year-bearer advances by 5 day-signs every year.  
Furthermore, five goes into 20 four times; thus there are four possible
year-bearers. They correspond to the four directions and (for the Quiche
Maya) the four sacred mountains.  In this way, the Calendar's "windows to
the New Year" are anchored in the directional pillars of the cosmos. The
year-bearer system, then, is the 4-year cycle of senior day-signs which
consecutively fall on New Year's Day. Because the year began on different
days for different Mayan groups, there are 5 possible year-bearer systems,
and they are indicated by Roman numerals in the day-sign chart given
above. In practice, however, only the Type II system seems to still be in
use, among the Mayan groups of Highland Guatemala.

Venus

Venus has a 584-day cycle. In other words, it will rise as morningstar
approximately every 584 days. [no!] This was an important cycle to the
Maya. The astrolo-mythic adventures of Sun and Venus were no doubt tracked
closely by the early Maya, and there is some reason to suspect that the
tzolkin arose, in part, to structure the related cycles of the two
prominent celestial lights (Sun and Venus). This is because the
relationship between the solar and Venus cycles is quite simple: 5 Venus
cycles equals 8 haab. The influence of the third celestial factor, the
Moon, was built into the tzolkin cycle itself.  The cyclic relationship
between Sun and Venus indicates that Venus traces a five-pointed star in
the sky over a period of eight years. And eight is the musical octave, the
number of harmony. More on this later.

Since the twenty day-signs divide into 584 twenty-nine times with 4 left
over, the Venus cycle begins on one of 5 possible day-signs.  As with the
year-bearer system, the Venus day-sign system repeats sequentially, over
and over. The beginning of the Venus cycle is considered to be the day on
which it emerges as morningstar, about 4 days after inferior conjunction
with the sun. The five day-signs which indicate when Venus will emerge as
morningstar serve as a prediction mechanism; the Mayan priest-astronomers
thus tracked, charted and predicted future morningstar appearances.  When
the number-coefficients are considered (which we have ignored for awhile),
the calculations become a bit more complex, and the cycles become larger.

The Calendar Round

The first large cycle we come to is called the Calendar Round. This is
when all the possible combinations of the tzolkin and haab are exhausted
and the same tzolkin day and haab day come together. For example, let's
presume that the year-bearer 1 Wind initiates a New Year. Now, the
year-bearer day-sign alone will return to initiate a New Year in only 4
years time, but when we consider the 13 number-coefficients, then (13 x 4)
= 52 years (or haab)  must pass before 1 Wind returns to initiate the New
Year. This 52-haab cycle is called the Calendar Round. It was widely used
by the Aztecs as well as the Maya, and is still vaguely remembered by the
Ixil Maya of Guatemala. The math of this is as follows:

260 x 73 = 365 x 52 = 18,980 days

This, again, is the shortest time in which the tzolkin and haab can
synchronize. But where does Venus fit into the picture?

The Venus Round

The big cycle of tzolkin, haab and Venus is completed when they
synchronize on the senior emergence day-sign, the Sacred Day of Venus: 1
Ahau. The nature of the tzolkin, haab, and Venus cycles are such that they
all synchronize every 104 haab, which just happens to equal two Calendar
Rounds. The math:

260 x 146 = 365 x 104 = 584 x 65 = 37,960 days

This is an amazing calendrical accomplishment. In addition, the Maya
mythologized this sacred link-up in the Popol Vuh and the Dresden Codex.
The five possible day-signs on which Venus could emerge as morningstar are
recorded in the Dresden Codex as: Flower (Ahau), Lizard, Rabbit, Grass and
Owl. Ahau was the senior day-sign of the five, and 1 Ahau was the Sacred
Day of Venus, representing the big synch of tzolkin, haab and Venus.

Let's take a little side track here - I'll present a puzzle which we will
return to and solve later. Look at the cover of this book. The four
day-signs above the title are of the Type II year-bearer system, the one
allegedly used in the Dresden Codex. They are, from left to right:

Wind, Deer, Grass, and Quake.

The five day-signs at the lower border (one is in the middle of the rising
sun), are the five predictive emergence day-signs from the Dresden Codex:

Lizard, Rabbit, Grass, Owl, and Flower.

Now let's think about this. Obviously, if the three cycles of tzolkin,
haab and Venus are to synchronize, then at least one of the 4 year-bearers
must correspond with at least one of the 5 beginning day-signs of the
Venus cycle. The one that does, which I have placed in the middle of the
rising sun, with Venus rising on the left and the Mars glyph on the right,
is Grass, not Flower! Is our reasoning faulty? What is the truth behind
this? Could it be that Calendar Round and Venus Round observances were not
synchronized? Even though one VR equals exactly 2 CR's, it seems as though
(from evidence in the Dresden Codex) that during the Late Classic Period
the Maya had not yet synchronized Venus emergences with Calendar Round
beginnings.

This imperfect situation, to a people who apparently strived to reveal a
harmony of the heavens, must have been intolerable. As we will see,
perhaps the Venus system in the Dresden Codex was not the most perfect,
and perhaps the Maya continued to perfect the system - during a period of
Mayan history lacking in substantial data.  So the smaller cycles of this
dating system, the tzolkin, haab and Venus cycle, are encapsulated by the
Venus Round, a period of almost 104 years. Here's a brief summary:

Tzolkin: 260 days. 20 day-signs combined with 13 numbers.
Haab: 365 days. 18 months of 20 days each, + a 5-day month.
Venus Cycle: 584 days between each morningstar appearance.
Calendar Round: Synchronization of tzolkin and haab every 52 haab
(18,980 days).
Venus  Round: Equals 2 Calendar Rounds.  Synchronization  of tzolkin,
haab, and the Venus cycle every 104 haab (37,960 days).

The Long Count and the Great Cycle

Another  time-keeping  system was used by the  Maya.  It  is known  as
the Long Count because it deals with larger  cycles  of time. It is
written using dots to indicate placement values  (for example:
8.15.6.0.4).  The  leftward placements  are  of  higher value. The Long
The above date represents the passage of 8 baktuns,  15  katuns, 6 tuns,
zero uinals, and 4 days  since  the zero  date.  The  placement of this
zero date has  been  a  tough question for Mayanists, and we will
discuss this in detail in the next section. The hierarchy of days is as
follows:

LONG COUNT PERIODS	NUMBER OF DAYS
1 day = 1 day	        1
20 days = 1 uinal	20
18 uinal = 1 tun	360
20 tuns = 1 katun	7200
20 katuns = 1 baktun	144,000
13 baktuns = 1 Great Cycle	1,872,000

In this way, 1 Baktun equals 144,000 days, 1 katun equals 7200 days, 1 tun
equals 360 days, and a uinal equals 20 days. Also of importance, in that
it reveals the relationship between humans and the cosmos is the term for
the twenty-day period:  the uinal. The similar term /uinac/ means person!

The 5-decimal Long Count dating system is found on hundreds of
inscriptions from the archeological record. Fortunately, they often occur
alongside tzolkin/haab dates, which has allowed archeologists to correlate
the two systems (they are consistently related). As can be seen, the Long
Count generates a large period of time known as the Great Cycle.

This period of 13 Baktuns is about 5125 years in length, and is due to end
in 2012 A.D.  The end date in 2012 is designated in the Long Count as
13.0.0.0.0 - which means that 13 baktuns, or some 1,872,000 days have
passed since the Great Cycle beginning date. Specifically, the Great Cycle
began on the tzolkin date 4 Ahau, and will also end on 4 Ahau. The Long
Count seems to be the more abstract dating method. Yet, we will see that
the cycles it generates are strangely connected to planetary phenomena and
ultimately to the processes of human unfolding.

The Long Count and tzolkin/haab/Venus system are theoretically unrelated,
yet 37 Venus cycles = 3 katuns. Here are two more connections between the
"long" and the "short" counts: 1) 72 haab = 73 tun; 2) 13 tun = 18
tzolkin. Is this fortuitous, or is there a deeper, hidden pattern at work?
Both the Long Count and tzolkin/haab are used together in many of the
archeological inscriptions throughout Mesoamerica.  With these connection
points, a complex interweaving between the two methods of Mayan
timekeeping could be demonstrated. For now, this will have to serve as a
basic introduction to the mechanics of the tzolkin, haab, Venus,
year-bearer, and Long Count systems.  Grasping all these different systems
and how they relate to each other can initially be confusing. But hang in
there, and if necessary, refer to this section or to the Glossary of Terms
(Appendix I).

The Julian and Gregorian Calendars

I should explain these two calendar systems, as both are used in this
study. The calendar system known as the Julian calendar was established by
Julius Caesar in 46 B.C., which was the year 709 of the Roman Empire. It
made the year-count more accurate by adding an extra day every fourth
year, thus approximating the solar year to 365.25 days. (By comparison,
the Maya had already come up with their year-drift formula which more
accurately calculated the solar year as 365.2422 days.) The extra day was
probably not officially used until 8 A.D., during the reign of Augustus.  
The expansion of the Roman Empire in the subsequent centuries made this
calendar widely recognized.  The system of numbering years by A.D.
designation (/Anno Domini/)  was instituted in 525 A.D. by the Roman abbot
Dionysius Exiguus.

Since the Julian calendar is still slightly inaccurate, a discrepency
built up over the centuries, causing problems in determining the
occurrence of Easter. By the 16th Century, Easter was slipping towards
summer. The problem was resolved by Pope Gregory XIII in 1582. The reform
resynchronized the time-count with respect to the equinoxes by skipping
ten days;  in other words, October 4th of 1582 was followed by October
15th.

However, the sequential cycling of the day-names of the week could not be
broken. This is an interesting fact. Remember, our week days are named
after planet-gods and mythical heros:  Sun, Moon, Thor, Wotan, and Saturn
among others. It suggests a European feeling, similar to the Mayan need to
track an unbroken count of days, that the cycling of day-gods was not to
be fooled with.

The rule for leap year was also changed. In the new Gregorian calendar a
year which is divisible by 4 is a leap-year unless it is divisible by 100
but not by 400. Thus, 1700, 1800, 1900 and 2100 are not leap years.

It took a while for the new calendar to be adopted in all of the European
countries, although Italy, Spain, Portugal and Poland began following it
immediately. Britain and British Colonies didn't follow suit until 1752.
English writers of the time often indicated which system they kept by
noting O.S. (old style) or N.S.  (new style). Russia was the last to
reform;  after the Bolshevik Revolution January 31, 1918 (O.S.) became
February 14, 1919 (N.S.).

Although it may be assumed that dates before 1582 are going to be in the
old Julian calendar, I prefer to clarify the matter by indicating (J) or
(G) whenever necessary.

The Use of Julian Day Numbers

Astronomers have standardized a conventional way of denoting dates, to
simplify long range calculations. By this method days are identified in
reference to an unbroken count begun on January 1st, -4712 (J). The Mayan
zero date of the Great Cycle is therefore referred to by its Julian Day
number, 584283.  This just means that 584283 days have elapsed between
1.1.-4712 (J)  and 8.11.-3113 (G). Another important point is that -4712
is written 4713 B.C.  In other words, astronomers recognize a 0 year for
calculational purposes, whereas historians do not;  there was never a
"zero" year. Therefore, -3113 is the same as 3114 B.C.; a given negative
year number is always one less than its B.C. equivalent.

This should serve as a basic introduction to the Sacred Calendar cycles.
From here, we will delve right into some of the perplexing problems of the
Calendar. I have compromised the accessibility of what follows by gearing
it toward the academic community. In many ways I feel there are some
valuable contributions here.  Yet, in my own thinking, the most valuable
work spills over into the mystical or visionary approach, which will
joyfully receive full expression in Chapter Three. But first, I will be
happy to share the present state of my calendar studies.

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*Arectyng my syght towarde the zodyake,
The sygnes xii for to beholde a farre,
When Mars retrogradant reuersyd his bak,
Lord of the yere in his orbicular,
Put vp his sworde, for he cowde make no warre,
And whan Lucina plenarly did shyne,
Scorpione ascendynge degrees twyse nyne.
*

* - John Skelton - 1495*