General Aztecs Maya Tocuaro Kids Contact 4 Jun 2020/9 Wind
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Graphic representation of how the Tzolk’in and Haab Calendar cycles intermeshed to create the 52-year Calendar Round cycle

How do the solar and lunar calendars combine?

Grasping how the ancient Mesoamerican calendars work(ed) is anything but child’s play. Here we attempt to show, as simply and clearly as we can, how the two main calendars - solar and lunar - combined. This applies to both the Aztecs/Mexica and the Maya. The graphic we use here as an example is Maya, but the principle (and the maths involved) is identical. The Maya 365-day solar calendar is the Haab’, the Aztec equivalent is the Xiuhpohualli. The Maya 260-day lunar calendar is the Tzolk’in, the Aztec equivalent is the Tonalpohualli (Written by Ian Mursell/Mexicolore).

Pic 1: 260-day ritual calendar in the Maya Codex Madrid (L); graphic based on the Aztec Sunstone (R)
Pic 1: 260-day ritual calendar in the Maya Codex Madrid (L); graphic based on the Aztec Sunstone (R) (Click on image to enlarge)

The basics are:-
• In both calendars, for Aztecs and Maya, there were/are 20 days in a ‘month’
• In the solar (sun), agricultural or civic/festival calendar, there were 18 cycles of these ‘months’, followed by a mini-month of 5 ‘useless’/unlucky days = 365 days in total
• In the lunar (moon) or ritual/sacred calendar, there were 13 cycles of these ‘months’ = 260 days in total
• Each of the 20 days had a name
• Scholars argue about how Mesoamericans allowed for the equivalent of our ‘leap’ years
• In the lunar calendar, each day was a combination of one of the 20 day names or signs and a number, from 1 to 13. The next day could be read by moving forward a number and a day sign in the cycle.

Pic 2: Illustration of how the tzolk’in and haab’ calendars combined
Pic 2: Illustration of how the tzolk’in and haab’ calendars combined (Click on image to enlarge)

We’ve taken, by way of illustration, the graphic titled ‘Diagram showing the enmeshing of the 365-day calendar (B) with the 260-day sacred year (A)’, from the classic work The Ancient Maya by Sylvanus G. Morley (p. 270) and added one or two notes of our own, in colour (pic 2). He represents the two calendars graphically as two cogwheels, the smaller on the left (A) having 260 cogs, each named for one of the 260 days of the Tzolk’in, and the larger wheel (B) having 365 cogs, ‘each intercog space being named for one of the 365 positions of the Haab or calendar year.’
It’s important to imagine revolving both wheels at the same time, A to the right (clockwise) and B to the left, anti-clockwise. As it stands, the date shown is ‘2 Ik’ in the Tzolk’in (A) and ‘0 Pop’ in the Haab’. The aim is ‘to find out how many revolutions each wheel will have to make before the cog named “2 Ik” on Wheel A will return to the intercog-space named “0 Pop” on Wheel B.’

Pic 3: Tzolk’in and Haab’ calendars, annotated to show the sequence in each
Pic 3: Tzolk’in and Haab’ calendars, annotated to show the sequence in each (Click on image to enlarge)

The arbitrary date depicted here, then, is ‘2 Ik 0 Pop’. Tomorrow’s date will be: ‘3 Akbal 1 Pop’: the Tzolk’in moves forward a number and a day sign, the Haab’ moves forward a number within the same month. Here we need to draw attention to a key distinction between the numbering system in the calendars between Maya and Aztecs.
For the MAYA, in the Haab’ the numbers go from 0 to 19 (= 20)
For the AZTECS, in the equivalent Xiuhpohualli the numbers go from 1 to 20 (= 20)
In BOTH, the numbers in the ritual, sacred calendar go from 1 to 13.
You will very likely be confused by the sequence shown in the Haab’. Morley chose to show the last day in the last regular month, called Cumhu - ie ‘19 Cumhu’ - followed by the 5 specially unlucky days, called Uayeb (sometimes spelt Wayeb), followed by the first five days in the first month of the year, called Pop.

Pic 4: The date 4 Ajaw 3 Kank’in (for Dec. 21, 2012) - graphic showing combination of Tzolk’in and Haab’ dates
Pic 4: The date 4 Ajaw 3 Kank’in (for Dec. 21, 2012) - graphic showing combination of Tzolk’in and Haab’ dates (Click on image to enlarge)

In the visually more pleasing graphic (main picture, top, and pic 4) the combined date shown is ‘4 Ajaw 3 Kank’in’ (for Dec. 21, 2012). Notice (big wheel on the right) that the Kank’in month doesn’t change - the numbers just chug through the month (from 0-19).
Only 52 of the 260 differently named Tzolk’in days could ever occupy first/start position in the Haab’ (this is because only four of the 20 day signs were special enough to serve also as ‘year-bearer’ signs; 4 x 13 numbers = 52).
Returning to the question posed above (when the same date will appear again in both calendar cycles), the solution lies in finding the lowest common multiple of 260 and 365 (13 x 4 x 5 x 73), leading to the figure 18,980 days - a length of time known as the ‘calendar round’.
In other words, in pictures 2 and 3, Wheel A will make 73 complete revolutions, while Wheel B will make 52 complete revolutions, before the cog ‘2 Ik’ of Wheel A returns to the intercog space ‘0 Pop’ of Wheel B.

Pic 5: For the Aztecs 52 years was a ‘bundle of years’
Pic 5: For the Aztecs 52 years was a ‘bundle of years’ (Click on image to enlarge)

Simply put, every 52 of our calendar years, the two main Mesoamerican calendars matched or coincided (pic 5). This period of time - notionally something similar in value to our ‘century’ - was central to all calculations of time in that part of the world. The Mexica gave it a special term in Nahuatl: xiuhmolpilli, a ‘bundle’ of years, and every 52 years, to celebrate - after five days of excruciating anxiety - the rise of the Sun at the start of a new xiuhmolpilli, a massive ceremony took place, commonly known as the New Fire Ceremony. It was a time of fundamental renewal, a nationwide celebration of the fact that, as Morley put it, ‘The gods had given mankind another 52-year lease of life.’

Quotes from:-
The Ancient Maya by Sylvanus G. Morley, Stanford University Press, California, 1947.

Picture sources:-
• Main pic & pic 4: Illustration courtesy and © Paul Johnson / Crab Nebula image - NASA, ESA
• Pic 1 (L): image downloaded from http://www.latinamericanstudies.org/madrid-codex.htm; (R) original line drawing by and thanks to Tomás Filsinger; colour graphic overlay by Phillip Mursell
• Pix 2 & 3: Original line drawing scanned from Morley (see above)
• Pic 5: Illustration by Phillip Mursell/Mexicolore.

This article was uploaded to the Mexicolore website on May 23rd 2020

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