Ruben Ochoa Count

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Developed by Ruben Ochoa and is based on the Pre-Cuauhtemoc technique of correlating the start of the Mesoamerican solar years to the day following the observable spring equinox on the days cipactli, miquiztli, ozomatli, and cozcacuauhtli. The major premises of the Ochoa Count are: 1. The Mesoamerican calendar counts through the 13 numbers and 20 day signs without stopping throughout the years, 2. 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, 3. Two intercalary adjustments were made to align the calendar with the solar year: a sixth nemontemi day every four years and matching building markers to the location of the sun during the spring equinox. Unlike other counts such as those of Arturo Meza and Alfonso Caso Count, Ochoa utilizes the extant Pre-Cuauhtemoc codices as the basis of his count.

The pre-columbian sources that show the calendar calibration

Click here to view a video lesson on the pre-columbian codices that show the calendar correlation

Starting Days

Codex Borgia

Plate 27 of the Codex Borgia showing the year bearers and their equivalent starting days

Plate 27 of the Codex Borgia portrays Tlaloc within five scenes. On the top left hand corner the year 1-kalli is shown with an accompanying day sign of 1-ozomatli. On the top right hand corner the year 1-tecpatl is shown with an accompanying day sign of 1-miquiztli. On the bottom left hand corner the year 1-tochtli is shown with an accompanying day sign of 1-cozcacuahtli. On the bottom right hand corner, the year 1-acatl is shown with an accompanying day sign of 1-cipactli. The bottom years 1-tochtli and 1-acatl are missing the year bearer sign due to damage to the original codex. [1]

Plate 30 of the Codex Borgia

Plate 30 of the Codex Borgia is identified by Elizabeth Hill Boone as the creation of the 20 day signs which takes place in the mythologies of the Historia de los Mexicanos por sus Pinturas and the Anales de Cuauhtitlan just after the initial creation of the four Tezcatlipocas. Plate 30 shows four Teteo piercing precisely the same four day signs as found in Plate 27 with a bone awl. Whenever a Teotl can be seen using a bone awl, he/she is usually using it to pierce the eyes of newborns to signify birth. Boone suggests the Teteo in this scene are giving birth to these particular days because they represent the 20 days divided up into fours. [2] The problem with this assertion however is that the days represented are the 1st, 6th, 11th, and 16th of the 20-day count which is not an equal quarterly division. The four day signs that the Teteo are giving birth to in Plate 30 are cozcacuauhtli, ozomatli, cipactli, and miquiztli; the same day signs referenced in Plate 27. Their association with birth provides further evidence that these days are intended to coincide with the beginning of the solar year.

Codex Ferjervary-Mayer

Page 1 of the Codex Ferjervary-Mayer showing the year bearers and their equivalent starting days

Page 1 of the Codex Ferjervary-Mayer depicts the four directions along with various teteo, year bearers, and day signs. This page firmly links the starting days with the same year bearers we see in plate 27 of the Codex Borgia. To the east we see the year sign acatl and then cipactli is depicted as the starting day of the year (and each month) while xochitl is depicted as the last day of each month. To the south we see the year sign tochtli and then cozcacuauhtli is depicted as the starting day of the year (and each month) while cuauhtli is depicted as the last day of each month. To the west we see the year sign calli and then ozomahtli is depicted as the starting day of the year (and each month) while itzcuintli is depicted as the last day of each month. To the north we see the year sign tecpatl and then miquiztli is depicted as the starting day of the year (and each month) while coatl is depicted as the last day of each month.

Codex Laud

page 1 of the Codex Laud

Page 1 of the Codex Laud is significant because the four day signs identified as those that start the solar years are grouped together to represent 26 years each for a total of 104 years. This is clearly related to two 52-year cycles however without the associated four year bearers present, we are left with the first day sign of the year for identification. This is clear evidence that the four day signs are in fact the starting days of the solar year.

The Aztec Sun Stone


In the innermost section of the Tonalmachiotl we see the twenty day signs and we can see four year signs corresponding to the four year bearers: calli, tecpatl, acatl, and tochtli. In addition, we can see four larger year signs. The directional location of the year signs correspond precisely to the first page of the Fejervary-Mayer (see above). The year sign in the east (top) is pointing to the day signs cipactli and xochitl. This is telling us that in acatl years, the year begins with the day cipactli. Furthermore, it is telling us that in such years, cipactli will be the first day of each cempoalilhuitl (month) and xochitl will be the last day.

Year signs from various codices, Cycles of Time and Meaning in the Mexican Books of Fate, pg. 219

The year sign in the south (right) is pointing to the day signs cozcacuauhtli and cuauhtli. This is telling us that in tochtli years, the year begins with the day cozcacuauhtli. Furthermore, it is telling us that in such years, cozcacuauhtli will be the first day of each cempoalilhuitl (month) and cuauhtli will be the last day.

The year sign in the west (bottom) is pointing to the day signs ozomahtli and itzcuintli. This is telling us that in calli years, the year begins with the day ozomahtli. Furthermore, it is telling us that in such years, ozomahtli will be the first day of each cempoalilhuitl (month) and itzcuintli will be the last day.

The year sign in the north (left) is pointing to the day signs miquiztli and coatl. This is telling us that in tecpatl years, the year begins with the day miquiztli. Furthermore, it is telling us that in such years, miquiztli will be the first day of each cempoalilhuitl (month) and coatl will be the last day.

Order of the Veintenas

Pre-Cuauhtemoc Sources

first month in the borgia

For many years, scholars believed that there were no Pre-Columbian codices that depicted the months (or Veintenas). This made it difficult to calibrate the Xiuhpohualli since one had to rely on secondary sources to accomplish this task (read more about why this is a recipe for disaster here). In 2015, Susan Milbrath made a compelling argument that pages 33-46 of the Codex Borgia depict months in the Xiuhpohualli (click here to read her full study). Her main source of evidence comes from the similarities in pages between the months depicted in the Primeros Memoriales (a primary source written by Native scribes shortly after the spanish conquest) and this section of the Codex Borgia. If we accept her proposal that these pages depict months, we can use it to calibrate the Xiuhpohualli. At the beginning of the section on page 33, we find that the first month depicted is Tlacaxipehualiztli. If the months are shown in sequential order, we can firmly place Tlacaxipehualiztli as the first month of the Xiuhpohualli.

When compared side by side, it becomes clear that Milbrath was indeed correct and that page 33 of the Codex Borgia does in fact depict the month of Tlacaxipehualiztli. Both scenes contain various people participating in a festival while holding various objects such as pantlis, weapons, and incense bags. There are also priests performing a sacrifice in both scenes. The most important piece of evidence however in the scenes that ties them to the month of Tlacaxipehualiztli is the presence of Xipe Totec because Xipe Totec is the Teteoh that Tlacaxipehualiztli is dedicated to consistently throughout all primary sources. An additional component of the Borgia scene is extremely important for the correlation of the Xiuhpohualli. On the top of Teocalli, there is a priest dressed as Itztli who is observing the sun. Considering the new year begins a day after the spring equinox according to the tonalpohualli correlation and Indigenous people made astronomical structures to mark the equinox all over Mexico, this image firmly places Tlacaxipehualiztli as the first month of the year, one day after the spring equinox.

Post-Cuauhtemoc Sources

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. [3]


We know that 1-Coatl occurred in the year 3-Calli. From our earlier analysis of the Borgia pages, we also know that the year 3-Calli should have began with the day 3-Ozomahtli. If we count backwards from the day 1-Coatl, we find that the day 3-Ozomahtli falls on the Julian date 3/12/1521 which is the day after the spring equinox. Thus we know that the beginning of the year occurred a day after the spring equinox. See the page calendar correlation for the Native-Spanish correlation of the year 1519.

The Tovar Calendar

Although the Spanish cronistas all contradict themselves regarding the first month of the new year Juan de Tovar produced a calendar in his book History of Mexico (published in 1585) which lists Tlacaxipehualiztli as the first month and goes on to say the month correlates to the month of March in the Julian calendar.

The Humboldt Fragment

The Humboldt Fragment depicts tribute sent to Tenochtitlan during four months: Tlacaxipehualiztli, Panquetzaliztli, Ochpaniztli, and Etzalcualiztli. When we count backwards from the day sign 1-Coatl we find that Tlacaxipehualiztli takes place from 3/12/1521 to 3/31/1521, Panquetzaliztli takes place from 11/27/1521 to 12/16/1521, Etzalcualiztli takes place from 5/31/1521 to 6/19/1521, and Ochpaniztli takes place from 9/8/1521 to 9/27/1521. This places Tlacaxipehualiztli during the spring equinox, Panquetzaliztli during the winter equinox, Ochpaniztli during the autumnal equinox, and Etzalcualiztli during the summer solstice. Pages 8-9 depict the death of Cuauhtemoc and then the stoppage of tribute sent to Tenochtitlan. It makes sense that tribute would be due during the equinoxes and solstices because everyone in Mesoamerican tracked the passing of time in the same way and there would be no confusion.

The Florentine Codex

It is stated that "During the feast of Ochpaniztli the cold began. And for one hundred and twenty days - one hundred and twenty suns- this persisted and there was cold. And it ended and disappeared (during the feast) called Tititl." In the ruben ochoa count, Ochpaniztli falls at the beginning of fall and Tititl ends near the end of winter. [4]

Veytia Calendar Wheel No. 4

In the 1700's Mariano Veytia published a series of calendar wheels. His Calendar no. 4 shows Tlacaxipehualiztli as the first month of the solar year.
Veytia Calendar Wheel No. 4

Evidence from the Mayan World

Some Mayan groups call their first month Tacaxepual which some scholars believe is a loan word from the Nahuatl Tlacaxipehualiztli. One account states "The Guatemalans (Mayas) called their first month "Tacaxepual," which according to their understanding means "season of sowing the first milpas." [5]

Counting Without Stopping

Deriving the Starting Day Pattern Mathematically

Ruben Ochoa points out that the year bearer starting days (cipactli, cozcacuauhtli, miquiztli, ozomahtli) discussed above can only be generated by running the 260-day tonalpohualli through 365 solar days without stopping. To view a video that explains how this pattern is derived, click here:

How the calendar correlation naturally unfolds mathematically

Click here to view a video lesson on how starting the day on 1-cipactli naturally generates the pattern that leads to the calendar correlation

Vaticanus A/Codex Rios

Codex Rios Page 34v

While academics agree we count without stopping, Arturo Meza's count is based on the premise that cipactli starts all new years. Page 34v-36r of the Codex Rios shows tables of years 1558 to 1619 along with the Anahuac year bearer. On the right side of the table for each of the years we see a list of nineteen consecutive numbers. The numbers coincide precisely with the starting days of each of the veintenas in Ochoa's count. The nineteeth number corresponds to the nemontemi. [6] The last day of the nemontemi of one year is followed immediately by the following number in the next year. The nemontemi then is treated as the 19th month and does not maintain a separate count.

Starting Days at Sunrise

According to Ruben Ochoa, "all the archaeological evidence supports horizon based astronomy, which by its nature means observation at sunrise, which then supports the idea that the day itself starts at sunrise." Simply put, there is no known mechanism that would allow the ancestors to identify midnight but there are is overwhelming evidence that they utilized many astronomical structures to track sunrise. If they started the day at some other time, we would expect to find a mechanism for how they tracked the passing of hours to then designate that time but that does not exist. In one part of the Florentine Codex, there exists a conversation in which it is claimed that the day started at midnight but the most likely explanation is that this was the result of the scribes no longer using the calendar and therefore they were forced to project Spanish time-keeping practices onto their ancestors [7] As is the case for other components of the calendar, "written sources contradict themselves regarding when the day starts, which is why the focus should always start with pre contact evidence (Ruben Ochoa)."

Diego Duran shared an account in which "at dawn when the sun was rising, the priest again sounded his drum, at the hour when bells ring at daybreak today. With this sound he announced the birth of the day." [8] This supports the archaeological evidence and also reinforces the idea that the Spaniards contradicted themselves every time they wrote about the calendar.

Intercalary Adjustments

Leap Year

We have two surviving dates correlated to the Julian calendar that are crucial in this matter. 8-Ehecatl was recorded as the arrival of the Spaniards and took place on the Julian calendar date November 8,1519. Then we have 1-Coatl which was recorded as the Fall of Tenochtitlan on the Julian calendar date August 13,1521. You can get from 8-Ehecatl to 1-Coatl using the Ochoa count only by adding a sixth nemontemi day to either the acatl or tecpatl year. Mariano Veytia says "most, and those with the best reputation, assert that it (leap year) took place in the year of the fourth character reed, and this is the most regular and in conformity with their system" [9] See the page calendar correlation for a Native-Spanish correlation of the years 1519-1521 with the leap year included.

"As to what he saith, that they lacked the leap year, it is wrong, because in the count which may be called a true calendar they count three hundred and sixth-five days, and once every four years they counted three hundred and sixty-six days with a feast which for this reason they observed every four years." - page 141, florentine book 4

"The five remaining days of the year, ... they named Nemontemi, which meaneth barren days. And they regarded them as unlucky and of evil fortune. There is conjecture that when they pierced the boys' and girls' ears, which was every four years, they set aside six days of Nemontemi, and it is the same as the bissextile which we observe every four years." - page 35, florentine, book 2. This quote provides additional evidence that our leap year occurred during acatl years which coincided with the same year in which the spaniards also had theirs.

On page 6 of the Telleriano Remensis there is a symbol for the Nemontemi leap year. This symbol shows a total of five Nemontemi days inside of a box with the fifth day with a different coloration than the preceding four days. On top of the box is a sixth day with the same coloration as the fifth day. This symbol is intended to show that in leap years, the 365th and 366th days should carry the same name.

The Nemontemi Leap Year Symbol

In his article "The Aztecs Did Not Need a Leap Year, Magnus Pharao Hansen argues that because the Aztecs were anchoring the beginning of their calendar to the day after the spring equinox, there was not a need for a leap year in the first place.

Spring Equinox

The Spanish priest Toribio Motolinia tells us the veintena Tlacaxipeualiztli "took place when the sun stood in the middle of [the Temple of] Huitzilopochtli, which was at the equinox, and because it was a little out of line, [King] Moctezuma wished to pull it down and set it right." [10] Ochoa proposes that buildings like the Templo Mayor were designed to allow one to view the location of the sun during the spring equinox. This viewing of the spring equinox is the secondary intercalary adjustment required to ensure the calendar stays in sync with the solar year. By adding a leap year every four years we actually end up with an extra day every 104 years. This is due to the fact that adding an extra day every four years results in 365.25 days for each of the years in that four year period but the true solar year is 365.24 days. By viewing the spring equinox through the use of a building like the Templo Mayor, the viewer would be able to see that in the 104th year the spring equinox did not appear where it was expected therefore the leap year for that period would not be added to re-calibrate the calendar to the solar year.

the Templo Mayor alignment

In addition to Anthony Aveni, Leonardo Lopez Lujan, a Mexican archaeologist in charge of the Templo Mayor Project since 1991 recently supported the idea that the middle of the Templo Mayor was tied directly to the Spring Equinox based on his own calculations. It should be noted that starting the new year during this time with any other month would throw off the other months including Panquetaliztli and Etzalcualiztli which are also aligned to the Templo Mayor on the respective temples of Huitzilopochtli (red, right) and Tlaloc (blue, left)


  1. Plate 27, Codex Borgia.
  2. Link to Article, 2003 Boone, Elizabeth Hill “The Birth of the Day Count in the Codex Borgia,” in the “Jornadas Académicas en Homenaja a Eduardo Matos Moctezuma,” Instituto Nacional de Antropología e Historia, Mexico, October.
  3. 1997 Vincent H Malstrom. Cycles of the Sun, Mysteries of the moon, pg. 207
  4. Anderson and Dibble. Florentine Codex, Book 7, pg. 19
  5. 2009 Weeks, John M., Prager, Christian, and Sachse, Frauke. Maya Daykeeping : Three Calendars from Highland Guatemala., pg. 20
  6. Rios-Ochoa Alignment, Codex Rios.
  7. 1545 Sahagun, Bernardino de Florentine Codex, Book 6, p.197
  8. 1570 Duran, Diego Book of the Gods and the Rites, p.197
  9. 2000 Veytia, Mariano Ancient America Rediscovered, p.112
  10. 2000 Aveni, Anthony Skywatchers, pgs. 236-238