LOST CALENDAR OF THE ANDES
the calendar of Tiwanaku and of the Muisca

by Jim Allen
author
Atlantis: the Andes Solution
The Atlantis Trail
Atlantis: Lost Kingdom of the Andes (Floris Books, 2009)

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.

Tiwanaku soli lunar calendar    Tiwanaku soli lunar calendar
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.

Kalasasaya outside wall
View from the field showing the reconstructed wall, the position of the missing pillar can be easily seen, just behind where the person appears to be running.

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.

gate of sun
above, the Gate of the Sun, early engraving

kalasasaya stones     perron
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 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.

gate of sun freize
The pillars seen in plan view. The sun follows the numbering as shown from 1 to 20.

gate of sun freize orbit
The freize on the lower part of the Gate of the Sun tells you to follow the orbit of the sun around the pillars,
counting like this, in twenties

Tiwanaku calendar wall reconstruction
Above, reconstruction showing the missing pillar restored.

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

tiwanaku calendar viewing stone
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.

tiwanaku calendar equinox
Above, artist's impression of the equinox sun setting over the calendar wall.

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).

tiwanaku calendar animation
The animation shows how the sun would set progressively over the various pillars, counting in twenties

The sun would now begin to move back towards the centre, reaching here another quarter of a year later on March 22, marking the Autumn equinox, then it would continue to the right, reaching the end pillar on June 21st 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") and returning back over the centre pillar one year later on the following 22nd September to mark the beginning of another Spring. (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 …

chankillo towers 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)

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.


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...


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, the writer from Peruvian Antiquities appears to make the same mistake since he says the year began with the festival of Inti Raimi at the winter solstice, but the winter solstice in Peru is in June, not December.

gate of sun
Above, Acosta describes 12 solar towers.

calendar 12 towers
Above, viewing the sunrise through 12 pillars would divide the year into 20, not 12.

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.

calendar 12 towers
Above, with 6 pillars, the year would be divided into 10 with the sun rising or setting on the top of each pillar as it progresses throughout the year along the horizon from solstice to solstice and back again. It is not the number of pillars which represents the number of months, but the number of time intervals as the sun moves either from pillar to pillar, or from space to space between the pillars

calendar 12 towers
Above, when the sun reaches the end pillars at the solstices, it appears to stand still.

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. This is consistent with an early Inca calendar of 10 months using 6 towers to the east and 6 towers to the west of Cuzco.

It is also the same as the Tiwanaku calendar since a year of 10 months of 36 days is also
20 "half months" of 18 days or
40 "weeks" of 9 days.

gate of sun
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, although at the same time the Inca also used a lunar calendar of 12 sidereal months.....

gate of sun
Above, Garcilaso tells us that at Cuzco, eight towers were set up to the east and eight towers to the west of the city, to calculate the year which was divided into 12 months.

gate of sun
With eight towers, the sun is observed through the spaces between the towers
resulting in a division of 12 months.

gate of sun
Above, at Chankillo in Peru, there still exists a row of thirteen solar towers - these would divide the year into 24 parts viewed when the sun set or rose over the towers, making each division a half-month and every two towers a month of 30 days in a 12 month year.

gate of sun
Above, in Tiwanaku, the 11 pillars divided the year into 20 "half-months" of 18 days
or 10 "months" of 36 days.

tiwanaku calendar 1 year animation
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

tiwanaku calendar 30 year 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.
winter in the southern hemisphere is summer in the northern hemisphere.


Above, satellite photo with superimposed sight lines showing the positions for calculating the rising sun solstice sight lines described by Posnansky.

kalasasaya sight lines
Above, to the west (sunset) the inner blue triangle dotted line shows sight lines based upon drawing to the left, the solid blue line shows sight line to present western wall "of the third period" based on observation block in centre of Kalasasaya. The yellow lines show sight lines to the original corner stones which Posnansky calls "of the second period". To the east, (sunrise) the yellow sight line is to the original solstice pillars of the compound. The viewing positions are marked by large stone blocks which were recovered on site. The viewing stone shown here (dotted line) is approximately 42.65 metres from the centre pillar of the wall, (measured in Google Earth) while the central viewing stone is 56.93 metres from the central pillar, measured in Google Earth. According to Posnansky, the large stone block now split in two and used as the observation stone was originally positioned in a wall on the western side of the inner "sanctissimum" and intended to support the Gate of the Sun. Oscar Corvison gives a viewing distance of 53.112 metres from the central pillar for the viewing stone (which he calls 30 "lokas" but is more likely 100 cubits), so it is not clear without actual confirmation by observation on site which was the actual position used for viewing the western calendar wall. The angle of view according to Corvison is 49.04º.

The Inca were sometimes said to be people of the sun, whereas the Aymara were sometimes said to be people of the moon, so I wondered whether in fact the pillars may also have been a soli-lunar calendar since what is called the ‘Saros’ cycle of lunar eclipses repeats itself every 20 ‘Inca’ years and 20 ‘Inca years’ of 12 months of 27.32 days is very close to 18 solar years of 365.24 days (Allen 1998 and Aveni 1990) and the people who built Tiwanaku were a race long before the Inca and possibly even before the Aymara. On the other hand, if used for agricultural purposes, it may simply have marked the winter and summer solstices with the appropriate pillar or space between the pillars marking the return of the sun to a suitable time for plantings crops, which is what Posnansky thought the purpose of the calendar was in the first place.

Although Corvison was correct in identifying the use of a solar calendar based on divisions of 20, (and this should not be a surprise since both the Aztec and Maya civilisations used a base 20 calendar) he does not seem to have considered the possibility it could also have been a lunar calendar.

Tiwanaku solar lunar calendar
When the sun crosses from the centre to the first pillar, 1/20th of the solar year has passed giving a month of 18 days counting the year as 360 days. The remaining 5¼ days are "lost" when the sun stands still at each end of the calendar.

Tiwanaku lunar calendar
When the sun has crossed 1½ pillars, one sidereal lunar month will have gone by.

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.

Tiwanaku Calendar

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?

gate of sun icons
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.

gate of sun freize
The freize with eleven icons represents the eleven pillars of the wall.

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.

Tiwanaku orbit
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 freize 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 freize in pairs, telling you to count in twenties and forties.

gate of sun freize
The freize 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.

Cracking the Muisca 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.
360 solar years =

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?

Tiwanaku gate of sun icons
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.

Tiwanaku gate of sun icons
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.

gate of sun freize
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.

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

Tiwanaku gate of sun icons
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.

gate of sun reconstruction
Above, reconstruction from Edmund Kiss (1937) of how the Gate of the Sun may have been incorporated into a wall and was part of an entrance within the Kalasasaya compound.

gate of sun reconstruction by Edmund Kiss
Above, reconstruction from Edmund Kiss (1937) of how the Gate of the Sun may have been incorporated into a wall and was part of an entrance within the Kalasasaya compound. Note the number of chasquis with 20 in each horizontal row (ten per side) and a total of 60 chasquis - so if each chasqui represents one year, the total number of sixty chasquis represents the "Great Century" of the Muisca calendar, and an extra lunar month was added to the calendar at the end of each 30 year period.

gate of sun reconstruction
Above, in the preceeding reconstruction by Edmund Kiss (1937) the upper rows of chasquis did not balance with the 11 chasqui heads on the lower freize since there was a portion of the lower freize left over at each end, however we can extend them in Paintshop so that now there are 30 chasquis in each horizontal row, each row on the upper portion representing a period of 30 years after which an extra sidereal month had to be added to balance the calendar giving 401 sidereal months as equal to 30 solar years.. On the lower freize, there are now 3 x complete sections of 11 chasqui heads, each section representing one year and each three year period being equal to 40 sidereal lunar months represented by 40 condor heads on the freize.
The width of the carved panels now occupies a space of 300" or 10 great cubits of 30" or 12 sacred cubits of 25" or 15 x cubits of 20" (25 English feet).

It is thought that the calendar freize may have extended right around the wall of the temple. If that were so, then from the space available we can calculate what the length of the wall might have been and the symbolic total of chasquis and years represented might have been.

Posnansky states that the width of the terrace upon which the Gate of the Sun was probably located, had a "width of 63.60 meters." In feet and inches, that would be 208ft 7.92ins or 2503.9 inches, which if we divide by the original width of a panel section which was 100 inches, suggests that a terrace side might have included 25 of these sections in total with 750 chasquis representing 750 years and being 100 x sacred cubits wide.

gate of sun location reconstruction
Above, reconstruction of 25 sculptured panels set into west wall of inner compound, based upon a modified drawing of Edmund Kiss (1937) and using width of terrace measurement recorded by Posnansky. The position of a viewing stone for observing the setting sun over the calendar wall is also marked.

Tiwanaku gate of sun icons
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..

Tiwanaku gate of sun icons

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.

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

Tiwanaku gate of sun calendar
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)

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webpage compiled 11 December 2009, updated 16 January 2012 with new animation
J.M. Allen
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"Atlantis: Lost Kingdom of the Andes"