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How the Aztec calendar works
An Aztec date has the form "2 reed 4 deer".
- The first part, "2 reed" is the name of the year.
- The second part "4 deer" is the name of the day
Three cycles interact to produce the Aztec date.
1. The "day number" cycle counts from 1 to 13 and increments
every day. In our example date "4" is the day number.
2. The "day sign" cycle counts from 1 to 20 and also increments
every day and has names like "deer", "rabbit" and "water".
In our example date "deer" is the "day sign".
So if today were "4 deer", tomorrow would be "5 rabbit".
Similarly if April 1st were "13 deer" then April 2nd would be
"1 rabbit". (see simulation)
3. The "day of the year" cycle counts from 1 to 365 and increments
every day.
So if February 1st were number 365 in the "day of the year"
cycle February 2nd would be number 1 in the "day of the year"
cycle.
The year was named for the "day sign" and "day number"
which happened to appear on the first day of this "day of the year"
cycle (and incidentally was considered new years day)
In our example date "2 reed" is the name of the year and must
have been the name of new years day.
This 365 day period was also divided into 18 months of 20 days a piece
and one month of 5 days.
Taken all together: if February 1st were number 365 in the "day
of the year" cycle and had day name "2 deer" then February
2nd would be number 1 in the "day of the year" cycle would have
day name "3 rabbit". And since this would be the first day of
the "day of the year" cycle, the entire year would be named "3
rabbit" So in this example February 2nd would be "3 rabbit 3
rabbit" (and February 3rd would be "3 rabbit 4 water" etc.)
 
The Sacred Almanac which the priest used for divination was called tonalpohualli ("count of days") and was a 260-day cycle based a combination of numbers 1-13 and the 20 named days.
There are 260 possible parings of name and number, and the Sacred Almanac can be imagined as two intermeshing cog wheels one with 13 teeth (the numbers) the other with 20, representing the days and the day taking its name form the alignment of the two.
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