Monday, April 02, 2018

Azteca/Mexica Calendar Correlations: the Good, the Bad, and the Completely Useless

Amazing blog. This article that compares the pre-Colombian to the Gregorian calendar is fascinating. I hadn't quite thought about calendars in a good while.  And there is a lot here to ponder. It makes one realize in a fresh way how humans are social animals and meaning-makers that make use of symbolic systems of knowledge in order to create beauty, order, and make life more predictable and manageable.

-Angela Valenzuela

Azteca/Mexica Calendar Correlations: the Good, the Bad, and the Completely Useless

There are many Aztec/Mexica calendar correlations out there and it can be very intimidating to try to figure out which correlation is the most accurate.  This entry will help sort out the different calendar correlations in a simplified way.  Please note that this is by no means an exhaustive list of all of the calendar correlations available but rather the most widely used by scholars and cultural practitioners.  Hopefully, by understanding how the Azteca/Mexica calendar works and correlates to Earth’s position around the sun, you will be able to critique other calendar correlations that you come upon.
Only recently has there been a good calendar correlation that actually aligns to the calendar that was maintained in Tenochtitlan at the time of the arrival of the Spaniards.  The fact that it has taken so long for us to have an accurate calendar correlation available to us is interesting considering that we have a wide range of primary sources that reference the calendar.  The problem we have when it comes to primary sources is the Spanish and Native chroniclers who wrote about the calendar pretty much all disagreed with each other.  This point illustrates how bad the problem is: in 1967, Alfonso Caso undertook the most exhaustive study on the Nahua calendar surveying 42 sources ranging from the 16th to the 20th century. Caso documented the starting months of the year in these sources and according to his analysis, 14 cited Tlacaxipehualiztli, 14 cited Atlcahualo, 7 cited Izcalli, 3 cited Tititl, 2 cited Atemoztli, 1 cited Panquetzalli, and 1 cited Toxcatl.  It doesn’t end there and it is a similar situation when one wants to find out about the first day of the year and intercalary corrections.  At one point in the Florentine Codex, two Spanish chroniclers actually have a heated argument about whether or not the Native Mexican calendars incorporated a leap year.  The situation can be explained with this quote from Zelia Nuttal:
Therefore, the reason for their disagreements is probably related to the fact that the Native and Spanish chroniclers who were documenting the calendar were working years after the Spanish conquest, long after the calendar fell into disrepair as the tonalpoque were no longer making the necessary corrections.   Fortunately for us however, there are 13 surviving Pre-Cuauhtemoc books, many of which contain valuable information regarding the calendar.  In addition, our ancestors were expert astronomers and much of their work is still available to us in the form of ceremonial buildings and inscriptions.  As you can imagine, the most reliable calendar correlations are those that align to these valuable pre-cuauhtemoc sources.  The primary sources dealing with the calendar are not completely useless though because when we compare the pre-cuauhtemoc sources to the works of the Spanish and Native chroniclers it is clear that the following historians had a good understanding of the workings of the calendar: Mariano Veytia, Juan Tovar, Diego Duran, Toribio Motolinia, and Ixtlilxochitl.
Solar Calendars 101
To understand the Azteca/Mexica calendar, it is important that you first understand how solar calendars work.  Put simply, solar calendars use dates to indicate the position of Earth on its revolution around the sun.  Solar calendars can be useful for helping people understand when the optimal time to plant their crops is or when the seasons change for example.  The problem that all solar calendars face is the Earth takes 365.24255 days to orbit the sun which can’t be expressed with whole numbers.  Solar calendars get around this problem by adding an extra day to their calendars every four years (a leap year).  What the leap year does is adds .25 days to the solar calendar each year which makes each year 365.25 days long to better approximate the actual solar year of 365.24255.   The leap year does not address the problem fully however because it actually adds .01 extra days every year.  This results in an extra day added to the calendar about every 100 years which throws the calendar off because it results in the days taking place 1 day later than they are supposed to.  The Gregorian calendar is the calendar used in most places of the world and it has a correction for that error built in so that the extra day is not added every 100 years (previously, the Julian calendar was used which incorporated a leap year but no secondary correction).  You can read more about that correction elsewhere but for our purposes, that explanation is sufficient.  
Native Mexican calendars
Native Mexicans utilized a solar calendar, called the xiuhpohualli in combination with a ceremonial calendar, called the tonalpohualli.  The xiuhpohualli functions in the same way that our own (gregorian) calendar works.  To compare, our calendar contains 12 months with either 28, 29, 30, 31 days which add up to 365 days while the xiuhpohualli contains 18 months with 20 days each and a 19th month with 5 days which add up to 365 days as well.  To specify a day in the gregorian calendar, we say the first day of January.  To specify a day in the xiuhpohualli calendar, we say the first day of Tlacaxipehualiztli.  Because they are both solar calendars, they are used to designate a particular time of the year that is recurrent.  We know for example that December will always be cold because it falls in winter.  We can say the same for the month of Panquetzaliztli in the Xiuhpohualli because it also occurs during winter every year.
Click here to learn more about the months of the Xiuhpohualli and here to learn more about how the years are named.
The tonalpohualli on the other hand is a ceremonial calendar which runs along side the xiuhpohualli.  It only has 260 days so it can’t be used as a solar calendar and is therefore useless for telling us what time of year it is when used alone.  We can’t for instance say that the day 12-Xochitl will always fall during winter because it will take place during a different part of the xiuhpohualli every year.  One year it might fall on 13-Tlacaxipehualiztli whereas the following year it might fall on 13-Panquetzaliztli.  In fact, in some cases, 12-Xochitl appears twice in the same year.  In Pre-Cuauhtemoc society however, the tonalpohualli was very important because this is how people got their calendar names.  It was also used to determine how strong or weak the tonalli of the person was which was then used to determine fate.  A person born on the day 13-Ozomahtli for example was said to be highly respected because he was compassionate, and was a great speaker whereas a person born on the day 6-Cuetzpallin would have a life full of misery because he was very hot-tempered and he talked too much.  Although the tonalpohualli contains only 260 days, when it is combined with the xiuhpohualli, the tonalpohualli count falls into a recurring and predictable pattern which led Native people and also modern day researchers to treat it as another set of solar count days.  In pre-cuauhtemoc times, people would have grown accustomed to having cipactli days start each month for the first 18 months and having xochitl ending them in acatl years for example.  In addition, in calli years, ozomahtli falls on the first day of each month while itzquintli  falls on the last day of each month.  Tonalpohualli days are also grouped into 20 13-day periods called trecenas which further assisted people in understanding where the tonalpohualli count was in relation to the solar calendar.  In fact, when we reconstruct the original calendar correlation we find that Native and Spanish chroniclers were much more accurate with their documentation of the tonalpohualli days compared to their documentation of the days of the months.
Click here to learn about the days of the Tonalpohualli and here to learn more about how the trecenas are used to organize the Tonalpohualli.
The Calendar Correlations
Zelia Nuttal (September 6, 1857 – April 12, 1933) - Although her work has been largely ignored, Zelia Nuttal made some major discoveries which have contributed to our understanding of the Azteca/Mexica calendar.
- She was the first to identify the pattern of four starting days that match up with the year bearer:  tochtli years always start on cozcacuauhtli days, Acatl years always start on cipactli days, Tecpatl years always start on miquiztli days, Kalli years always start on ozomatli days
- She discovered that the first day of the year was linked to the spring equinox
- She was the first to realize the connection between the Native Mexican practice of tracking the sun and the calendar (this seems odd considering the entire purpose of a solar calendar is to track the position of the Earth in relation to the sun)
- She was the first to correlate the start of the new year to the first day of Tlacaxipehualiztli
With the above discoveries, it should have been the end of the discussion however, for reasons unknown, she did not take the next step and apply the necessary intercalary corrections (such as the leap year) to create a functional calendar.
To read more about Nuttal’s calendar correlation, click here: Note_on_the_Ancient_Mexican_Calendar_Sys
After Zelia Nuttal, the next researcher to contribute to the calendar correlation was Alfonso Caso (February 1, 1896 in Mexico City – November 30, 1970 in Mexico City) which is the calendar correlation that can be found at  The Caso count is also the one used by U.S. scholars specializing in Mesoamerican history.  For reasons unknown, Caso seemed to have started from scratch and did not consult Zelia Nuttal’s work. His major contribution was the discovery of three correlation dates that match up when we count backward from 1-coatl.  1-Coatl corresponds to 8-13-1521, the Fall of Tenochtitlan and it is the one date that is consistently documented by many different people, both Native and Spanish, which greatly increases it’s validity.  It’s important to note that without dates that anchor the Native calendar to a specific time of year, we would not be able to reconstruct the calendar at all because there would be no starting point in which to reconstruct the calendar.  Here are his three correlation dates:
08/11/1519 2- Quecholli (Xiuhpohualli) 8-Ehecatl (Tonalpohualli) Arrival of Spaniards to Tenochtitlan 
30/06/1520 11-Tecuilhuitontli (Xiuhpohualli), 8-Cozcacuauhtli (Tonalpohualli) Noche Triste 
01/07/1520 12-Tecuilhuitontli (Xiuhpoalli), 9-Ollin (Tonalpohualli) Noche Triste
13/08/1521 15-Miccailhuitontli (Xiuhpohualli) 1-Coatl (Tonalpohualli) Fall of Tenochtitlan 
For reasons unknown, Caso did not incorporate a leap year which has resulted in his calendar moving forward 120 days.  Days in Caso’s count for example that fall in spring should actually be taking place in winter.
To read more about Alfonso Caso’s calendar correlation, click here: CasoLosCalendariosPrehispanicos
Click here to see the tonalpohualli and xiuhpohualli dates from 1519-1521 (remember that Caso did not use leap years but a leap year has been applied in the acatl year to show the successful correlation between the three Caso dates):
Rafael Tena’s calendar correlation builds on the work of Alfonso Caso with the addition of a leap year although he also appears to have ignored the work of Zelia Nuttal.  Tena’s calendar correlation is the one that is widely used by Mexican scholars specializing in Mesoamerican history.  Because he ignores Nuttal’s work, Tena relies on Spanish chroniclers to determine the starting point of his calendar which as we discussed above is a big mistake.  Tena starts his years on February 26th on the day 1 Atlcahualo which leaves him way off the mark of the  correct correlation.  Because he began counting from 1-Coatl and incorporated leap years however, his tonalpohualli count is only off by 7 days.    His tonalpohualli count is off because although he incorporated a leap year, he failed to incorporate a secondary correction for the extra day that accumulates.
Arturo Meza – the Arturo Meza calendar correlation  is widely used by danzantes and other cultural practitioners in Mexico and the U.S.  This calendar correlation is also utilized by many Mexicayotl teachers including Mazatzin Aztekayolokalli, and Ocelocoatl.  Arturo Meza’s calendar correlation is almost entirely based on Spanish sources so it has the same problems as the Rafael Tena calendar: incorrect starting day and incorrect month order.  Additionally, Meza does not run the tonalpohualli count through a full 365 days; he runs the tonalpohualli through 360 days, stops, interjects a separate nemontemi count, and then starts the new year again on the same day every year: Cipactli.  Curiously, Meza incorporates a leap year by adding 1/4 a day every year by starting the day of each consecutive year at different times: midnight, sunrise, noon, and sunset.  These practices are not supported by any primary source document.  He also incorporates a secondary intercalary correction that he says derives from oral history.  This calendar correlation  is unsupported by any pre-cuauhtemoc or Native Mexican astronomical sources and it does not build on the work of any of the above researchers.  As a result of the aforementioned errors, Meza’s correlation is by far the most inaccurate available.
Ruben Ochoa – In contrast to Tena and Caso, Ruben Ochoa’s calendar correlation utilizes Zelia Nuttal’s discoveries and incorporates appropriate intercalary corrections to ensure the days remain anchored to Earth’s position to the sun without accumulated error.  In addition to a leap year, his correlation also utilizes ancient Mexican astronomical markers to prevent the accumulation of an extra day every 100 years.  Ruben Ochoa’s calendar correlation is also the only one that relies almost entirely on Pre-Cuauhtemoc sources and Native Mexican astronomy which avoids any reliance on Spanish primary sources which we have demonstrated are all contradictory.
Here are the major discoveries that Ruben Ochoa made which have contributed to our understanding of the Azteca/Mexica calendar.
- He confirmed the validity of the three Caso dates (see above) by adding a leap year to the year 1-Acatl (1519)
- He was the first to confirm Nuttal’s pattern of four starting days that match up with the year bearer ( tochtli years always start on cozcacuauhtli days, Acatl years always start on cipactli days, Tecpatl years always start on miquiztli days, Kalli years always start on ozomatli days) through the correlation of Pre-Cuauhtemoc books including the codex borgia, laud, and Ferjervary-Mayer.
- He confirmed that the first day of the year is linked to the spring equinox by correlating Native astronomical markers to the calendar.
If you are interested in learning more about the sources used to support the Ruben Ochoa calendar correlation, please visit:
To see the Ruben Ochoa calendar count which eventually will contain dates going back to 1519, please visit: 
Here’s a description of how the calendar dates from the website above are organized:
As you can see, the Ruben Ochoa calendar correlation is the only one available that incorporates all of the components required of a solar calendar to guarantee it remains accurate.  His correlation successfully builds off of the work of his predecessors to generate both an accurate xiuhpohualli count and an accurate tonalpohualli.
The Secondary Correction (read if you want to know more about how the astronomical markers work as the secondary correction for the Xiuhpohualli)
In addition to over-reliance on contradictory primary sources, many people in the past have tried to correlate the Azteca/Mexica calendar with the Gregorian calendar. The problem with this approach is that it makes us dependent on the Gregorian calendar and it throws off the Azteca/Mexica calendar. This is because the Gregorian calendar does not utilize astronomical observations such as equinoxes and solstices to anchor itself to the correct position of the sun. It utilizes the leap year and a mathematical secondary correction that are independent of any astronomical event.  Tena’s correlation for example starts on February 26th and Meza’s correlation starts on March 11th but those two dates do not correlate to any observable astronomical phenomena which forces the use of the Gregorian calendar as a reference point because it is not possible to know it is the first day of the new year without first knowing the Gregorian date.  The Azteca/Mexica calendar on the other hand utilizes both the astronomical observations of the spring equinox and winter solstice as anchor points guaranteeing that the calendar never strays from the correct position of the sun.

Here in this graphic from the Codex Borgia, we can see clearly the two spring equinox and winter solstice anchor points. We can also see that each graphic contains correlation days for the year 1-Acatl. The day 1-Cipactli corresponds to exactly one day after the observable spring equinox in Mexico. The day 4-Ollin corresponds to exactly one day after the observable winter solstice in Mexico. Astronomical markers all across Mexico track the spring equinox and winter solstice and were used to keep the calendar aligned with the sun. Anthony Aveni has identified at least two sighting devices from the Bodley and Selden that the ancients used to make these precise observations. None of the most widely used calendar correlations (Arturo Meza, Alfonso Caso, and Rafael Tena) align with these two crucial correlation pages. The Ruben Ochoa calendar correlation is the only one that aligns with these crucial correlation pages and is also the only one that utilizes the same astronomical practices as the Azteca/Mexica to keep the calendar aligned with the path of the sun without relying on the Gregorian calendar at all.
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*Post script*
After I published this article, somebody argued that all of the above calendar correlations can be correct and there is not only one that is correct.  I thought it was important to point out this article is referring to the calendar that was used in Mexico-Tenochtitlan at the time of the conquest.  Arguing that there are many correct calendar correlations in this context is equivalent to me saying today is January 19th and somebody else saying today is June 19th and us both being correct.  Of course this is ridiculous.  If we both claim to be using the Gregorian calendar, only one of us can be correct.  This is the same situation that we find ourselves in with all of the different correlations that are available to us.  Here is an image I made that illustrates the accuracy of each calendar correlation mentioned in this article:

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