**
TIWANAKU CALENDAR
the calendar of Tiwanaku and of the Muisca, the lost calendar of the Andes
**

by Jim Allen

author

Atlantis: the Andes Solution

The Atlantis Trail

Atlantis: Lost Kingdom of the Andes

Atlantis and the Persian Empire

Tiwanaku: a City Lost in Time

**
Background**
**
In the year 2,000, I found myself in Tiwanaku with the
Discovery Channel filming for “Atlantis in the Andes” and in the company of Oscar
Corvison, a Bolivian Archeoastronomer who was keen to explain his
interpretation of the vigesimal (base 20) system of the Tiwanaku calendar.
**

Oscar explained that it was not the Sun Gate which was the Tiwanaku calendar, but a wall which today is to one side of the Sun Gate, inside a courtyard called the “Kalasasaya”. He was particularly upset because he said, in the reconstruction of the western wall of the Kalasaya, one of the large stones which had originally been part of the calendar had not been restored, but left laying in a field a couple of hundred metres to the west of the wall.

**
Above, left, The Gate of the Sun with the calendar wall behind. The position of the missing pillar
is arrowed. Above, right, Oscar Corvison shows us the missing pillar in the field behind.
**

**Oscar
gave me a self-produced booklet which explained how the wall functioned, and it
seemed simple enough to understand that the year had been divided into 20 parts
as he claimed, so I thought no more of it until the end of December 2008, when
it became necessary to give some book references to my editor who was going
over the draft of my
“Atlantis: Lost Kingdom of the Andes” for publishing on 21
May 2009 by Floris Boooks.**

**Since my own fascination is for ancient measurements rather
than calendars, I began to study Posnansky's measurement of the wall, and
discovered the wall was not simply a solar calendar as had been previously
thought, but incorporated a sophisticated calendar based on sidereal lunar
months.
**

**
The rest of this essay and the discovery of
the sidereal lunar calendar follows on from Oscar Corvison's
pioneering discovery of the base 20 system in the Tiwanaku calendar.
**

**
above, the Gate of the Sun, early engraving by George Squier
**

**
The Kalasasaya in 1851 with the Sun Gate
**

**
The Kalasasaya in ancient times before restoration.
**

**
The calendar wall as it appeared in 1873. We can see one pillar fallen on the ground,
besides, another pillar is missing.
**

**
The wall as it appeared in 1884. We can see one pillar fallen on th eground
and the Sun Gate broken and half buried.
**

**
The Kalasasaya at the time of the French Mission of 1903. View from the Akapana pyramid.
We can see 9 pillars of the calendar wall.
**

**
Pillar "J" was restored to its original location by the French Mission of 1903.
**

**
The Kalasasaya at the time Posnansky was writing. The wall which
exists today was built in the 1960's and the standing stones incorporated into it.
**

**
The calendar wall with the new stones inserted in between the original pillars.
**

**
Detail of the calendar wall showing the new stones between the original pillars.
**

**
We can see the space where the missing pillar has never been restored to the wall.
**

**
The missing pillar was originally discovered by Posnansky in the field behind the calendar wall.
**

**
View from the field behind the reconstructed calendar wall, we can see the position of the missing pillar just behind
the person running and marked by the arrow
**

**
The stone gateway which is today in the Kalasasaya is baptised
‘the Gate of the Sun’ and ‘Kalasasaya’ according to Arthur Posnansky who spent a lifetime studying the site,
simply means
‘standing stones’.
When he investigated Tiwanaku the stone pillars had more of
the appearance of a 'Stonehenge', there was no wall there as there is today,
(most of the wall was assumed to have been carried off so in the 1960’s as part
of a reconstruction project the spaces between the pillars were filled in to form a
wall. The Gate of the Sun was moved to its present position
inside the Kalasasaya and next to the calendar wall at some unknown time and restored in its present form in 1903.
At Posnansky's time, only 10 of
the giant pillars remained. The 11th missing pillar may be
found laying face down in a field some 229 metres to the west. According to
Oscar Corvison, a Bolivian archeo-astronomer who studied the site, the eleven
pillars represented the division of the year into periods of 20 (Corvison
1996). This seems more logical, since if you count from the central pillar
(representing the equinox) out to the end pillar on the right (representing the
north solstice), then back past the centre to the far left pillar
(representing the south solstice), then back to the centre again, you arrive at
a division of 20.**

**
Plan view of the pillars. The sun follows the numbering shown from 1 to 20.
**

**
This satellite image shows the Kalasasaya courtyard with
the calendar wall to the west and the observation stone marked the viewing position.
**

**
The Sun Gate and to the left, the calendar wall.
**

**
The icons and the frieze on the Gate of the Sun are the keys as to how to operate the calendar.
**

**
the frieze.
**

The frieze which appears in the lower part of the Sun Gate shows how to follow

the oribit of the sun around the pillars counting in twenties. i.e. 10 from one solstice to the other solstice plus 10 for the return journey.

Each icon represents one of the pillars on the calendar wall which is the actual calendar
at the side of the Gate of the Sun.

**
This is how it works. In the
centre of the Kalasasaya courtyard there is a large block of stone which is said to represent the original
observation point. From here the sun could be watched setting on the horizon
over the pillars each night. When the sun set over the central pillar, the day
would be the 22nd September and Spring would begin. When the sun set over the
next pillar to the left, one twentieth of a year would have passed and so on
until reaching the pillar at the far left a quarter of a year later on the 21st
December marking the Summer Solstice. (Seasons reversed in southern
hemisphere).**

**
From this "viewing stone", observations could be made of the sun setting over the pillars of the calendar wall each evening.
According to Posnansky, the block of stone which is now split in two, was originally at ground level and intended as a base upon which the Gate of the Sun would be constructed.
**

**
From a position in the centre of the Kalasasaya, one could observe the setting of the sun each evening.
On the 20th of march, the sun would set over the central pillar marking the autumn equinox.
**

**
When the sun reached the first pillar to the right, 18 days or a 1/20th part of a year would have passed,
then the sun continued with the sunset each night over the wall and each 18 days arriving above a pillar to the right
marking a 1/20th part of the year.
**

**
The sun reached the pillar at the extreme right on the 21st of June, marking the winter solstice
and the Aymara New Year when they held the great festival of Inti Raimi, the sun appears to stand still.
**

**
The sun moves to the left and 5 pillars or three months later arrives at the central pillar,
marking the equinox of 22nd September. Each pillar on the wall corresponds to one of the icons on the Gate of the Sun.
**

**
Half a year later, the sun sets over the pillar on the extreme left of the wall,
marking the summer solstice and the pillars have divided the half-year into 10 divisions of 18 days.
**

**
Another three months later the sunset is once again over the central pillar, marking the equinox of 20th March.
**

**
Another three months later the sunset is once more over the pillar on the extreme right,
the year has been divided into 20 divisions of 18 days by the pillars, another year has ended and another year begins
according to the Aymara calendar. (Explanation thanks to Oscar Corvison).
**

**
Calendar animation
**

**
The animation shows how the sun would set progressively over the various pillars, counting in twenties
and following the route shown on the frieze.
**

**Each evening one could observe the sunset over the calendar wall, if we begin for example on the
20th March marking the Autumn equinox, then continuing to the right, reaching the end pillar on the 21st June marking the
winter solstice and the beginning of
the Aymara New Year (the great festival of Inti Raimi when the sun appears to "stand still").
From there one could follow the progress of the sun the whole year, progressing to the opposite end pillar and returning at the end of another Aymara year.
(Explanation thanks to Oscar Corvison).**

**
Posnansky seems to have
considered the row of pillars as representing a calendar based upon a month of 30 days - probably
because 30 small figures called Chasquis appear on the Gate of the Sun -
and
states that the solar year of twelve months was used with the sun showing
through the gap between the pillars each month. But there’s a flaw with that.
With eleven pillars, there are only 10 gaps or spaces, not 12 …
**

**
In order for this type of calendar to count twelve months, it would
have been necessary to construct thirteen pillars, not eleven
and a row of thirteen towers
has recently been found in Peru, which according to the system above
would
represent the division of the year into 24 and correspond to 12 solar
months,
suggesting the ancient calendar was later reformed into 12 months of 30
days which
may have misled some scholars in their attempts to understand the
original
Andean calendar.
(click for report)**

**
Above, in Chankioo Peru, there still exists a row of 13 towers
- these divide the year into 24 parts seen when the sun arrives above the towers making divisions of half-months
and every two towers marks a month of 30 days in a year of 12 months.
**

**
Posnansky would
have done better to pay attention to one of his own quotes, in section E, note
78 of his own book "Tihuanacu, the Cradle of American Man" where he quotes a sixteenth century Peruvian
historian as saying ‘They
divided the year into twelve months by the moons. Already each moon or month
had its marker or pillar around Cuzco, where the sun arrived that month.’
(Ondegarda 1571)**

**
The calendar wall (left) and the Sun Gate which holds the key to understanding the calendar. It is not the
Sun Gate which is the calendar, but the row of pillars built into the wall seen on the left of the photo.
At some time the Sun Gate was moved from the position where it was found to its present position next to the Calendar wall
in the Kalasasaya. Posnansky thought that the original position was in the Kalasasaya itself, more or less in the centre and
providing an entrance from the "sanctissimum" to the western section where observations could be made of the calendar wall.
Posnsnaky - "The observation stone of the third period of the priests and astronomers of Tihuanacu. It is located in the
highest part of the Sun Temple and was planned as a base or foundation for a lower structure which in turn was to support
above as a central block of the Sun Temple the famous door, today called the Sun Door of Tihuanacu. This block, which is
in the highest part of the temple, forms the crowning part of the external west wall of the "sanctissimum" and as such was
supposed to serve, in our opinion, as the base for the Sun Door; that is to say, when the base and the Sun Door were completely
finished."
Others today think because of the style it was originally part of the Puma Punka complex. However, it is clear that whoever
originally moved it to its present position in the corner next to the calendar wall, must have understood its significence as a
key to the calendar.
**

**
Posnansky's interpretation of the Sun Gate calendar is wrongly based upon an assumption that
the year was divided into 12 months of thirty days (based upon the Inca calendar). He has counted the central icon twice and arranged
the months so that in some instances they pass from pillar to pillar and in other instances they leapfrog over the pillars
in order to make it fit his interpretation. It is purely a diagram and not something that works in practice.
**

**
There are 11 chasqui icons which represent the 11 pillars of the wall,
counting the progress of the sun from one end pillar to the opposite end
and back again divides the year into 20 divisions, not 12.
**

**
By the time of the Inca empire, a calendar of 12 months of 30 days had been introduced, not to be
confused with the original calendar of Tiwanaku and the Sun Gate. The Inca calendar
is reported by Acosta and also Guaman Poma to have begun with the festival of Ccapac Raime in December, whereas the Aymara calendar is today still celebrated in Tiwanaku
at the beginning of the Aymara New Year on 21st June.
**

**
Above, describing the Inca calendar in "Peruvian Antiquities", (1858),the writer tells us
sometimes the year was calculated from the summer solstice in June other times from the December solstice... But in Peru,
the June solstice is the winter solstice as seasons are reversed compared to northern hemisphere.
**

**
Confusion in the interpretation of the Inca calendar may also occur when comparing it
to European calendars, Acosta for example writes that "the first month was called Rayme and answereth to our
month of December," but that could also mean that it was comparable to the Spanish December on account of the seasons being reversed in the southern hemisphere.
**

**
Above, Acosta describes 12 solar towers.
**

**
Acosta writing in the year 1600, tells us that 12 towers were set
up which divided the year by the sunrise and sunset into 12 months. But Acosta was not familiar
with how the system worked, and thinking in European terms, assumed because Europeans used a calendar of
12 months, then each of the towers represented a month on a calendar of 12 months. But that's not how it works.
The towers are used to track the position of the sun either rising or setting along the horizon throughout the year.
So if there were 12 towers in a line, the sun rising or setting upon each tower would divide the year into
22 divisions or "months" - not consistent with any known measurement system of the years. There again, if we viewed the sun in the space in between the towers, that
would mean 11 spaces which would divide the year into 20 divisions or "months".
But the sun cannot both rise and set upon the same pillar, it rises in the east and sets in the west.
So if the 12 pillars were arranged
6 to the east, and 6 to the west of Cuzco, that would mean the year was divided decimally into 10 months.
**

The Inca Empire which spanned the length of the Andes was effectively brought to an end by the capture of their leader, Atahualpa by the Spanish conquistador, Francisco Pizarro at Cajamarca in 1532. The first conquistador to visit the site of Tiwanaku and write an account was Pedro Cieza de Leon who describes it in his "Chronica del Peru" of 1549.

**Cieza de Leon records that the city was already long abandoned in the time of the first Inca, it had not been built by
the Incas and the locals had no idea who had built it. He also recorded that the people of that region, that is to say,
the Aymara, used a year of 10 months.
**

**
The first recorded description of the Collao (region around Lake Titcaca)
by Cieza de Leon in 1549 describes a year of "10 months to 10 months".
This is consistent with the Tiwanaku calendar counting 10 months from one solstice and 10 months to the other solstice.
**

**
Above, Acosta tells us the Inca calendar was reformed by Pachacutec....
Perhaps it was at this time the Inca calendar was changed from the ancient 10 or 20 month division to the 12 month division which
is more commonly spoken of.
And thus, the original ancient calendar of Tiwanaku and the Aymaras became forgotten.**

**
They say that the Incas were People of the Sun, whilst the Aymara were People of the Moon; so I asked myself whether in effect,
the pillars could have also represented a soli-lunar calendar which we call "Saros Cycle", with lunar eclipses which repeat themselves
every 20 "Inca" years and every 20 "Inca" years of 12 months of 27.32 days is very close to the 18 solar years of 365.24 days
(Allen 1998 and Aveni 1990). The people who constructed Tiwanaku were before the Incas and possibly even pefore the Aymaras. On the other hand
if only used for agricultural purposes, it could simply have been marking the winter and summer solstices with correspondng pillars
or spaces between the pillars marking the return of the sun indicating the time for sowing. Posnansky thought this was the purpose of the calendar in the first instance.
**

**
Although Corvison was correct in identifying the use of the calendar based in divisions of 20
(and this should not be a surprise considering the Aztecs and Maya also counted in 20's, he does not seem to
have considered the possibility that the calendar was also a lunar calendar.
**

**
When the sun reaches the first pillar, 1/20th of the year will have passed with a month of 18 days counting
a year of 360 days. The
5¼ extra days are "lost" when the sun stands still at each end of the calendar wall.
**

**
When the sun reaches 1½ pillars, one sidereal lunar month will have passed.
**

**On the above basis, when the sun
reached the first pillar it would have travelled a 1/20th of a solar year which is
18.26 days. By the time it reached midway to the next pillar, it would have
travelled half as much again, which when added to the first figure means 27.39
days would haved passed — virtually a sidereal lunar month —
every one and a half pillars would
add another sidereal month and continuing the process would take us back to the
central pillar after 13 and a third such sidereal lunar months (or divisions)
had passed, completing a solar year and making it a dual purpose, soli-lunar
calendar.**

*
Above, the frieze on the Gte of the Sun represents eleven pillars on the calendar wall. Each pillar marks the position of the setting
sun on a 1/20th of the Earth's orbit, and a sidereal lunar month corresponds to the distance between one and a half pillars
representing 3/40th's of the orbit. Drawing by J.M. Allen after Oscar Corvison's interpretation of the
vigesimal calendar system with additional lunar interpretation by J.M. Allen.
*

**
Now I wondered if this in some way tied in with
the Saros cycle and since it takes thirteen and a third sidereal lunar months to circle round the calendar stones
in order to complete one 'lap' and come back to a full year, how many ‘laps’ would it take to fulfil the Saros
cycle?**

**
Well, three ‘laps’ round the pillars would make
the sun once more over the central pillar and represent 40 sidereal lunar
months and since each lap around the pillars is a solar year, a total of 18
‘laps’ round the pillars would complete the Saros cycle, the sun would be back
again over the central pillar and the cycle would all begin all over again!
**

**
Maybe that’s why the Amautas
(mathematicians) of the Aymara thought they had discovered the most perfect
calendar in the world. Could this be the calendar of Atlantis? Some people
thought so (Corvison 1996), but they failed to realise the Altiplano was
Atlantis.**

**
In addition to counting
the Inca lunar year of 12 sidereal lunar months (328 days) the calendar also represents a year of 360 days
as well as a
year of 365.24 days. How it could do that may be something like this. From the
centre to the centre of the end pillars is taken as 360 days (counting from one
end to the other end then back again) then the distance from the outside to the
outside of the opposite pillar (and back again) would represent 365.24 days. In
this way, the calendar could mesh the Solar calendar with the Lunar calendar,
the extra five and a quarter days being ‘lost’ (to view) when the sun reaches
the end pillars and appears to stand still before returning in the opposite direction.
Each division from pillar to pillar would be 18 days, which could be arranged in groups of
2 x 9 days. **

**
It seems that in the Andes, a work
period of six weeks of nine days was used, which would therefore
correspond to three divisions of the pillar calendar and be two sidereal lunar
months. **

**
The key to the calendar was said to be built
into the Gate of the Sun, today found near the Kalasasaya pillar wall and put
there when the Kalasasaya was restored. It consists of a giant block of stone
with a gate cut into its lower half and an elaborate decoration on the upper
part. In the centre of the decoration there is a representation of the
‘weeping’ god — presumably Viracocha and in his hands he carries two
staffs, which look like measuring or mathematical staffs since although the
rest of the monument is symmetrical, the staffs are different, the one in his
right hand has two sets of three circles and the one in his left hand has two
vertical lines over three circles. But who can read the monument today?
**

**
The upper part of the Gate of the Sun shows the key to using the calendar.
**

**
On the upper level, on
each side there are three rows of iconic figures called ‘chasquis’ — messengers
of the gods, each row has eight chasquis, but it is thought that the outer three were meant to be a continuation
on the walls each side of the gate which today are missing. They are arranged so that each side of the central figure
there are two blocks each of three rows of five chasquis. It can also
be noted that two rows of two x five of the chasquis making twenty chasquis have faces looking forwards
and one row of two x five chasquis making ten chasquis has condor heads looking upwards.
**

**
The frieze with eleven icons represents the calendar wall with eleven pillars.
**

**
Beneath these chasquis
there is a continuous row of smaller icons arranged so that eleven of them
stand apart from the rest. We can assume that these eleven represent the
pillars of the calendar. Now it has usually been wrongly assumed that because
the upper chasquis in horizontal rows total fifteen on each side (not counting
the outer ones) that the total of thirty chasquis represent a month of 30 days since a
solar year of 360 days divided by 12 months would give a 30 day month. But as explained
above, the actual calendar is divided by 20, which would make solar divisions of 18 days.
And work periods of 18 days were used in the Andes.**

**
The reason why people can’t
see the correct number of chasquis on the lower freize of the Sun Gate is
because the eleven chasquis in a row represent a circular or elliptical orbit,
so the two end chasquis represent the solstices when the sun reaches the ends
of the orbit, but the remaining nine chasquis conceal another chasqui behind
them so to speak (if viewing the orbit in plan view) so the total is two end
chasquis plus eighteen ‘double’ chasquis making 20 all told.**

**
Apart from the end chasquis, each chasqui conceals
a twin behind it representing the same position on the other side of
the orbit
**

**
This is clearly shown on the frieze
itself where there is like a route marked round the chasquis telling you to go
round the calendar in an orbit, then there are 20 condor head symbols in pairs
on the upper part of the freize, and 20 condor head symbols on the lower part
of the frieze in pairs, telling you to count in twenties and forties.
**

**
The frieze shows forty condor heads in two rows of twenty also indicating that the calendar is based
upon divisions of twenty.
**

**Many people have
mistakenly thought that the Gate of the Sun was the calendar, but it isn’t. The
pillar stones built into the west wall are the calendar and it could be
instead, that the chasquis are telling you how to operate the calendar.
**

**Instead of reading horizontally,
if we read vertically, they seem to be saying, ‘count in blocks of
three.’ But blocks of three what? When we studied the operation of the stones
on the wall, we found that every one and a half pillars represented one
sidereal lunar month. Therefore every half division between the pillars
represented one fortieth of the year or a third of a sidereal lunar month, the
month itself being the prime unit. Now on the Gate of the Sun there are a total
of 48 Chasqui icons which could therefore represent 48 sidereal lunar months.
Tahuantinsuyo, the empire of the Incas was ‘the land of the four quarters, or
four divisions’ so dividing the 48 Chasquis by 4 results in 12 Chasquis —
meaning 12 sidereal lunar months —
which was the Inca lunar year of 328 days. In turn 328 days
divided by 4 gave the 82 day (three month) period at the end of which the moon would be
visible against the same group of stars etc and that I believe, is the message
of the Chasquis — how to operate the calendar.
**

**
The Muisca
were a pre-Columbian people who lived in the territory now known as Columbia in South America.
**

**
In
1795, Dr Jose Domingo Duquesne, a priest of the church of Gachancipa in
Columbia published a paper detailing the Muisca calendar, which
information he claimed to have received from the Indians themselves.
His paper was later ridiculed as being nothing but an invention of his.
**

**
Yet
the figures given by Duquesne do in fact relate to a lunar calendar
although Duquesne himself may not have fully understood the workings of
it since it seems possible that the calendar was more sophisticated
than might appear at first glance, and two types of lunar month may
have been used, the Sidereal Lunar Month when the moon returns to the
same position relative to the stars (27.32 days) and the Synodic Month
which is the period between full moon and full moon (29.53 days).
**

**
Background
At Tiwanaku we found how the solar year
was divided into 20 months of 18 days and also interlocked with the Inca calendar of 12 sidereal
lunar months of 27.32 days (making 328 days) so that 3 x solar
years also equalled 40 sidereal lunar months and the two calendars
came together every 18 solar years which equalled 20 Inca years when
the cycle started all over again (also known as the Saros Cycle).
**

**
Duquesne
At first difficult to read and understand,
Duquesne's paper
begins with a background about the Americas and the Egyptians and how the Muiscas counted
by their fingers with names for each number up to ten, and then on to twenty.
**

**
He then relates their calendar to harvesting and sowing and begins:
El año constaba de veinte lunas, y el siglo de veinte años
**

(the year consisted of twenty moons, and the century of twenty years) then goes on to relate this to lunar phases and harvests.

**
The first thought on reading this, was that as at Tiwanku, they might have divided the Solar Year
into twenty for their months, but the text implies that 20 lunar months made the year and it also
implies that Synodic or phase months were intended. This year of twenty months he tells us was called
a "Zocam"
year.
Now a period of 20 x 20 months which Duquesne mentions might seem worthy of fitting into an Aztec or
Mayan calendar since 20 x 20 gives 400, but further down the text, if we read closely, Duquesne says that
**

*
"Twenty moons, then, made the year. When these were finished, they counted another twenty,
and thus succesively, continuing in a continuous circle until concluding twenty times twenty.
The inclusion of one moon, which it is necessary to make after the thirty-sixth, so that the
lunar year corresponded to the solar year, and thus they conserved the regularity of the seasons,
which they did with consumate ease."*

**
Now, here is a question, not of translation, but of meaning. Because a little further along, Duquesne explains
how the year of 37 months was a period of 36 months plus a "deaf" month so that the year adjusts to the solar year.
This year of 37 months is called an "Acrotom"
year. He also tells us that 20 x 37 of these
months corresponds to 60 of our years, divided into four parts so that each part was ten Muisca years which equalled
fifteen of ours.
**

**
From this we can easily work out that 60 of our solar years divided by 20 x 37 gives a month of 29.61 days
suggesting that here, the synodic or phase month from full moon to full moon was intended since the synodic
month has an average of 29.53 days.
**

**
Above, the Synodic month is based upon the time taken from full moon to full moon.
**

**But returning to the earlier statement
**

**
"Twenty moons, then, made the year. When these were finished, they counted another twenty, and thus succesively,
continuing in a continuous circle until concluding twenty times twenty. The inclusion of one moon, which it is
necessary to make after the thirty-sixth, so that the lunar year corresponded to the solar year, and thus they
conserved the regularity of the seasons, which they did with consumate ease".
**

**
What I think is meant here, is that they counted in twenty times twenty then added an extra month
in the same manner as they added an extra month to 36 months to make 37, so the real figure here is not
20 x 20 = 400 but 20 x 20 + 1 = 401.
**

**
There is also another difference. I think they were running two calendars in parallel with each other,
so the 37 month calendar was in Synodic Months of 29.53 days while the 20 month and 401 month
calendar was in Sideral Lunar Months of 27.32 days, although at the same time Duquesne counts the 37 month
year as being 20 months + 17 months (because the counting system was based on twenties) making 37 months
when the solar and lunar calender synchronised, in this instance these 20 would be synodic months the same
as the 17 months and he also explains this another way, as the extra month being inserted at the end of
every three lunar years so they counted two x lunar years of 12 months then one of 13 months, the thirteenth
month being the "sordo" (deaf) or extra month. So after 1 x Muisca year of 37 synodic months (3 solar years),
sowing would begin again on the same day in January, while the intervening two years had a system of counting
the months on the fingers as Duquesne puts it...
**

**
But
returning to the calendar of 20 months running continuously as 20 x 20
months with an extra month inserted to give 401 months, we can check
the figure of 401 Sidereal Lunar Months to see if it relates to a solar
year and 401 x 27.32 days comes to a great period of 30 Solar Years,
which in turn equals 10 Muisca Acrotom years of 37 x synodic months of
29.53 days....
**

**
Every three solar years equals the Muisca "Acrotom" year of 37 Synodic Months of 29.53 days
and at the same time corresponds to 40 Sidereal Lunar Months of 27.32 days, and every one and a half
solar years corresponds to a "sidereal lunar year" of 20 Sidereal Lunar Months which is the true "Zocam" year of the Muiscas.
**

**So to sum up so far,
1 x Tiwankau Solar year = 20 "months" of 18 days (using a rounded-off 360 day year divided by 20).
1 x Tiwanaku Lunar year = 12 sidereal lunar months of 27.32 days (328 days) - also used by Incas.
1 x Muisca Zocam year = 20 sidereal lunar months of 27.32 days = 1½ solar years
2 x Muisca Zocam years of 20 sidereal months of 27.32 days = 1 Muisca Acrotom year of 37 synodic months
1 x Muisca Acrotom year = 37 x synodic months of 29.53 days
1 x Muisca Acrotom year = 3 x solar years = 40 x sidereal lunar months of 27.32 days = 2 x Muisca Zocam years
½ Muisca Acrotom year = 1½ solar years = 20 x sidereal lunar months of 27.32 days = 1 x Muisca Zocam year
18 solar years = 20 Inca years = 6 x Muisca years of 37 x 29.61 days = the Saros Cycle
10 Muisca Acrotom years = 30 solar years = 401 sidereal lunar months of 27.32 days = 20 Zocam years.
20 Muisca Acrotom years = 60 solar years = 2 x 401 sidereal lunar months of 27.32 days = 40 Zocam years.
**

30 solar years = 400 sidereal lunar months when 1 extra month has to be added to the calendar

30 solar years = 370 synodic lunar months when 1 extra month has to be added to the calendar.

360 solar years = 20 Saros cycles of 20 Inca years of 12 sidereal lunar months.
>/font>

**
It might appear that Duquesne made an error when stating that "the 'century' of the Muiscas consisted of
20 intercalcated years of 37 months each, which corresponded to 60 of our years, which comprised four
revolutions counted in fives, each one of which equalled ten Muisca years, and fifteen of ours until
completing the twenty...."
**

**
Since 1 x Muisca year of 37 months equals 3 solar years, then 10 x Muisca years should be 30 solar years
as per the table above, and since Duquesne was talking about how they counted up to twenty in periods
of fives which corresponded to five fingers, what he should have said here was that each of the
five was five Muisca years of 37 months equalling fifteeen of ours. But in fact he is correct except
it is 10 x Sidereal lunar month years of 20 x 27.32 days which equal the fifteen solar years.....
**

** 5 Muisca Acrotom years of 37 synodic months of 29.53 days would be 15 solar years
10 Muisca Zocam years of 20 sidereal months of 27.32 days would be 15 solar years
**

**
I suspect therefore, and it is fairly clear, that the 20 month year which Duquesne called the "Zocam" year
was actually the sidereal year of 20 sidereal months but the name may have mis-understood by Duquesne as a
period of 20
synodic months if Duquesne were unaware of a different type of lunar month in use, otherwise there would
have been little point in having years of 20 synodic months running continuously when they were actually
grouped in 37 month years and by contrast 2 x 20 sidereal months mesh both with the Acrotom year and solar
year at 3 year intervals and over longer periods.
**

**To see how they compare at three year intervals,
37 synodic months of 29.53 days would be 1092.61 days
40 sidereal months of 27.32 days would be 1092.8 days
3 solar years of 365.2524 days would be 1095.72 days
**

**
Because of the small discrepency, over long periods of time some adjustments would probably be necessary such as
the extra month inserted after 400 sidereal months on the Zocam calendar making
401 sidereal months of 27.32 days = 10955.32 days
10 Muisca Acrotom years = 370 synodic months of 29.53 days = 10926 days
but if they added another month that would bring them to 10955.5 days and back into line with the Zocam sidereal
lunar calendar and closer to the
30 solar years of 365.24 days = 10957.26 days
**

**
The Muisca "Acrotom" 37 month synodic month calendar with the phases of the moon was probably a more
"user friendly" calendar for the
man in the field, whereas the "Zocam" 20 month sidereal lunar calendar was probably of more interest to the
time keeping priesthood and for bringing the other calendar into alignment periodically.
**

**
Duquesne also tell us that the Muisca "week" was a period of three days, and at face value, this would appear
to have no relationship to the Muisca calendar whether using sidereal or synodic months, but then the calendar
itself, in spite of Duquesne's explanation as a usage for agriculture does not seem really practical for agriculture
or at least not as practical as the Tiwanaku one but perhaps having the advantage that no construction of pillars
or standing stones was required.
**

**The calendar which is practical for agriculture is the one found at Tiwanaku where the solar year is divided
by twenty and determined by the setting of the sun over a pillar, so it would be fairly easy to note the same
pillar where the sun would return to each year, and this is the calendar which is easily divided into periods
of three days, and period of nine days were also known to have been worked in that region.
**

**So perhaps the Muisca also ran a solar calendar, undiscovered but in the same style as Tiwanaku, or perhaps their
customs were left over from some forgotten era, based on the same mathematicas as Tiwanaku with it's interlocking
sidereal lunar calendar and counting in twenties.
**

**
Return to Tiwanaku**

The Muisca calendar then, is another important piece in the jigsaw of the lost knowledge of the Andes.

**
If the origins of the Muisca calendar were to be found at Tiwanaku, then perhaps they were also built
into the Gate of the Sun which gives the clues to the workings of the Tiwanaku calendar.
**

**
Many people have studied the icons on the Gate of the Sun at Tiwanaku and tried to relate them to a calendar.
The icons are called "chasquis" or Messengers of the Gods and because there are fifteen of them on each side, some
people have thought that they represented a thirty day month in a solar year of twelve months. But as explained
earlier, this calendar at Tiwanku is not based upon a divison of the solar year into twelve, but into twenty,
and this is represented by the eleven smaller icons forming the freize at the bottom which represents the eleven
pillars on the west side of the Kalasasayo which is the actual calendar. So if you count from the central icon or
pillar out to the right hand end, then back past the central icon to the left hand end, then back to the centre,
you will have effectively counted in twenty divisons and followed the path of the sun over a year.
**

**
So if the chasquis do not relate to the days in whichever number of days we choose for the months of the year,
could it be that the chasquis represent the years themselves?
**

**
Above, detail of the "Gate of the Sun" at Tiwanaku, Bolivia showing the principal grouping
of thirty "chasqui" figures with beneath them the freize showing eleven icons and forty condors heads
arranged in two rows of twenty heads.
**

**
If each chasqui were to represent a solar year, then each column of three chasquis would represent
three revolutions of the sun around the eleven pillar calendar wall and three solar years are equivalent
to 1 x Muisca Acrotom year of 37 synodic months of 29.53 days and also equivalent to 2 x Muisca Zocam
years of 20 sidereal months of 27.32 days.
**

**
Above, each Chasqui represents a Solar Year and counting in threes, then three Chasquis
or years make 1 x Acrotom year of 37 synodic lunar months or 2 x Zocam years of 20 x sidereal lunar months.
**

**
The freize beneath the Chasquis shows forty condor heads in two rows of twenty representing
two x zocam years of 20 sidereal months
and also indicating that the calendar is based upon divisions of twenty.
**

*
"Twenty moons then made the year. When these had passed, they counted another twenty, and thus succesively, going round
in a continuous circle until they concluded twenty times tweny. The intercalculation of a month, which is necessary to
come to thirty six in such a manner that the lunar year corresponds to the solar year, and thus they maintained the regularity of the seasons,
which they did with consumate ease." Duquesne ...
*

**
There are fifteen chasquis on each side of the central figure and each block of 15 chasquis would represent
fifteen solar years which would be
**

5 Muisca Acrotom years of 37 synodic months of 29.53 days or

10 Muisca Zocam years of 20 sidereal months of 27.32 days

**
Above, the 15 Chasquis represent 15 solar years, equal to one quarter of the Muisca "Great Century"
and respectively 5 x Zocam years or 10 x Acrotom years.
**

**The total number of chasquis is thirty chasquis representing thirty solar years which would be
10 Muisca Acrotom years of 37 synodic months of 29.53 days or
20 Muisca Zocam years of 20 sidereal months of 27.32 days
**

**The choice of thirty chasquis as thirty solar years is no random figure, because after thirty solar
years have gone by, it becomes necessary to add one sidereal lunar month to the Muisca Zocam calendar
making it 20 x 20 + 1 = 401 sidereal lunar months to bring it back into line with the solar year.
**

**At the same time of adding one sidereal month to the Zocam sidereal calendar, it also becomes necessary
to add one synodic lunar month to the Muisca Acrotom calendar making it 10 x 37 + 1 synodic lunar months
to also bring it into line with both the sidereal lunar calendar and the actual solar year.
**

**
Each of the sections with fifteen chasquis corresponds to the period of fifteen solar years which
Duquesne tells us was one quarter of the great "century" of the Muiscas so to sum up, each block
of fifteen chasquis represents fifteen solar years which is 10 Muisca Zocam years or 5 Muisca
Acrotom years, the two blocks together make 30 chasquis representing 30 solar years which is
20 Muisca Zocam years or 10 Muisca Acrotom years and 2 x the 30 chasquis gives 60 chasquis
representing 60 solar years completing the great "century" of the Muiscas which was therefore,
40 Muisca Zocam years or 20 Muisca Acrotom years.
**

**
Above, detail of the "Gate of the Sun" at Tiwanaku, Bolivia, the 30 Chasquis represent
30 Solar years,
equal to 20 Zocam years of 20 sidereal lunar months or 10 Acrotom years of 37 synodic lunar months.
At the end of this period, 1 x lunar month had to be added to the lunar calendars to bring them
back into phase with the solar year..**

**
**

**
Above, the "Gate of the Sun" at Tiwanaku, Bolivia, the 30 Chasquis represent
30 Solar years,
equal to 20 Zocam years of 20 sidereal lunar months or 10 Acrotom years of 37 synodic lunar months.
At the end of this period, 1 x lunar month had to be added to the lunar calendars to bring them
back into phase with the solar year.. Beneath the chasquis can be seen the freize with 11 smaller
chasqui heads representing the 11 pillars on the calendar wall which in turn divide the solar year into
20 months of
18 days, and the 40 condor heads represent the
40 sidereal months which mesh with the solar calendar every three years.
**

**
Above, when the sun reached the end of the pillars,it appeared to "stand still" before beginning
its journey back in the opposite direction.
**

**
Above, Each chasqui
represents 1 solar year
and every
3 years was equal to 40 sidereal lunar months represented by 40 condors heads.
At the end of thirty years, an extra lunar month was added to the calendar
to synchronise the two calendars
(making 401 sidereal lunar months)
**

**Animation of 1 year of the calendar, counting 40 weeks of 9 days, 20 half-months of 18 days,
10 months of 36 days: sidereal lunar months, zocam years of 20 sidereal months, acrotom years of 40 sidereal months or 3 solar years,
the Saros cycles of 18 solar years = 20 Inca years of 12 sidereal months.
click here for 3 years animation
**

**
The chasquis on the calendar count 30 solar years when an extra month
has to be added to the lunar calendars.
**

**
Above, the chasqui icons are arranged vertically in threes -
every three solar years was equal to 40 sidereal lunar months, marked by the 40 condor's heads
on the freize,
there are 30 chasquis because
every thirty years an extra sidereal lunar month was added to synchronise the solar and lunar calendar.
**

**the calendar counts:30 solar years of 10 months solar
20 zocam years of 20 months lunar
10 acrotom years of 40 months lunar
**

**
Above, left, winter solstice ceremony, 21 June 2010 at Tiwanaku.
above right, summer solstice ceremony 21 June 2010 at Stonehenge.
**

**
and now, the Calendar wall
**

**
visit www.atlantisbolivia.org bookstore for printed editions of Tiwanaku Calendar and other books.
**

**
webpage compiled 11 December 2009, updated 11 June 2019.
Jim Allen
webatlantis@hotmail.com
**