Ruben Ochoa Count
The Ochoa Count is a proposed way of correlating the start of the Mesoamerican solar years to the spring equinox on the days cozcacuauhtli, cipactli, miquiztli, and ozomatli based on the work of Ruben Ochoa. 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.
- 1 Starting Days
- 2 Order of the Veintenas
- 3 Counting Without Stopping
- 4 Intercalary Adjustments
- 5 References
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. 
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.  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.
Aztec Sun Stone
Order of the Veintenas
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.
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.
Counting Without Stopping
Vaticanus A/Codex Rios
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.  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.
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" 
"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 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." 
- Plate 27, Codex Borgia.
- 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.
- Rios-Ochoa Alignment, Codex Rios.
- 2000 Veytia, Mariano Ancient America Rediscovered, p.112
- 2000 Aveni, Anthony Skywatchers, pgs. 236-238