DESIGN OF THE MEXICAN CALENDAR BY TRECENAS
Revised 12 May 2008, added text at end.

    The Mexican calendar designers choose to name twenty ritual days and then count Days in cycles of 13. This can be best demonstrated by making a table of 13 square spaces in each of twenty rows. I will now explain the system by placing day numbers in sequence into the squares, starting with day 1 in row 1 and continuing down the column to row 13. In row 14 the days repeat from 1 and continues counting days as each day number is placed in a new square until the column is filled with day 7 in row 20 then continues to column 2 with day 8, etc,etc. The final row is filled with day 13 and a new table of ritual days can be started in row 1 with day 1. The table of 20 rows and 13 columns has been filled with 260 days. I do not know the prehistoric Mexican reason for this choice of counting days. My guess is that they had a twenty day ceremonial week and decided to extend the calendar by counting ceremonial weeks to correspond to the number of Cosmic Moon Cycles. The result was a 260 day ritual calendar which does not correspond with the agricultural seasons and with more advanced observations of a Cosmic Year Cycle.



There is another viewpoint for the same calendar, organized in columns of 13 sequential number/day names
and rows of 20 trecenas. Each complete row ( a trecena) is then given the name of the first day of this row. The first row is 1 Cipactli, second row 1 Ocelotl, third row 1 Mazatl, etc to the 20th row which is 1 Tochtli. This table contains 260 named days. The name of each day is a combination of the number heading a column and a word from a trecena. This chart can be mounted on wall and  each day can be marked as complete at sunset. At the end of 260 days another identical page can be used starting again with 1 Cipactli. My intuition tells me that some prehistoric timekeepers used exactly this technique for recording days. New pages may be added as long as a sequence of timekeepers keep the record.

This serves me as an example for further examination of calendar construction. There may have been competing timekeepers that used another type of page or even piles of stones, marks on boards, or marked rocks, etc.

I often want to know how the date on my kitchen calendar relates to the sacred calendar. This format of the sacred calendar is useful for observing the relationship because nahuatl day names always have a number followed by a name. I can look down any column headed by the number until finding the name to find the exact location in the 260 day sequence of the sacred calendar. This calendar format is published in my documents at:

http://docs.google.com/Doc?id=d7b4c3p_68f4jp6qz9




Codex Borgia uses another arangement. It shows first four trecenas sequentially from Cipactli, Alligator in lower right of Plate 1 proceeding through four trecenas to Malinalli, grass at the extreme left bottom row on Plaate 8. Proceeding up to next row extreme right to Acatl, to start the next four trecenas which end at extreme left of Plate 8. This sequence of going up one row and filling to the left continues thru the last set of four trecenas from Atl, water to Xocitl, Flower to complete the ritual year of 260 days.

The sequential days were numbered from one to thirteen as the icons were repeated from Cipactli, Alligator to Xochil, Flower and starting again with Cipactli, Alligator. All Icons in a column on a set of two plates would have the same number which can be see n by counting the columns from 1 on the right to 13 on the left of a double age.

Codex Borgia has many other arrangements of the repeating icons which are now the subject of my independent investigation. I will inspect the calendar from views of the Codex Borgia instead of the matrx views presented at the start of this essay.

I will sometimes use the name "quadricena" to refer to a row of four trecenas in a table arranged like the first presentation, Plates 1 thru 8 of the Codex Borgia. This codex preserved a presentation of the ritual calendar as it was used in Mexico before the Spanish conquest. Analysis of the codex in facilitated by adopting a convention of numeration compatible with European mathematics.

I will use spanish numbers uno, dos, tres, quatro, cinco,seis, ocho, nueve, diez, diezyuno, diezydos, diezytres  for  designating columns in this style.
I will use English words to designating the 20 Icons.
I will use arabic numbers in designating the sequential number of a ritual year of 260 days or an extended solar, agricultural, year of 365 days.

Then each qadricena will contain 4x13=52 days, The ritual calendar will contain 5x52=260 days.

Anticipating explanations of Plates in Codex Borgia, some interesting facts will become apparent.two more quadricenas repeating ritual years will be seen to add 2x54=104 days for a total of 364 days in a set of seven quadricenas and one more additional day will make 365 days; one solar year.
I am adopthig