The Mayan calendar system is well known today because of the hysteria aroused by the “predicted” apocalypse on Dec 21, 2012, when the calendar supposedly ended, but actually just began a new cycle. The Mayan calendar uses several cyclic periods of varying lengths. For day-to-day purposes, there are two cycles of interest, the Tzolkin and the Haab, which together form a 52-year cyclic calendar. The Tzolkin has a period of 260 days in which the dates progress through 13 numbers combined with 20 names. At the same time, the Haab calendar runs through 365 days with 18 months, or Uinals of 20 days each, plus a 5 day “epagomenal” period. The same date in both cycles will only repeat after 18,980 days ( 52 x 365 = 73 x 260 ).

To see the workings of the calendar, it is instructive to build a set of interacting wheels bearing the names and numbers of the days and months.

Supplies

6 mm board ( plywood or MDF ) 200 x 600 mm

M4 x 30 mm screws, nuts & washers

Step 1: Construction

Construction begins with cutting a set of gear wheels from the 6 mm board. This can be done either with a laser cutter ( preferred ) or with a scroll saw, or even by hand with a coping saw as an extreme resort. Two 25 mm diameter spacer discs, an extension arm and two ratchet pawls cut from the 6 mm board are also required. The patterns are shown above.

These parts are mounted onto the 200 x 300 mm base board with M4 screws. Rubber bands are used to provide tension for the ratchet pawls. Test the rotation of the gear wheels and smooth off any bumps which may cause jamming.

The graphics for the wheels are shown in the image above, these can be printed onto card stock and preferably laminated, then attached to the gear wheels. Note that the numbered wheels have their sectors centred on the points of the gear teeth, while the wheels with the glyphs have each sector centred on the gaps between the teeth.

Step 2: Using the Calendar

To use the calendar, the wheels must first be adjusted to show the starting date. To do this, you will need to know the Mayan date which corresponds to the modern Gregorian date. Several websites are available for obtaining this information, eg https://maya.nmai.si.edu/calendar/maya-calendar-converter , https://planetcalc.com/547/ etc.

For example if the Mayan date for the starting day was 3 Ik 0 Mac, begin by detaching the 13-day wheel and turn the left-hand Tzolkin wheel to locate the sector for Ik in the position where it contacts the 13-day wheel. The right-hand number wheel is turned to locate the number 0 ( and therefore also the extension arm ) next to the sector for Mac on the Uinal wheel. The 13-day number wheel is then fitted so the wheels are correctly aligned as shown above. Turning the 13-day wheel clockwise will then advance the dates one day at a time.

Note that the 19th Uinal, Wayeb has only 5 days. When the date 4 Wayeb shows, the next day will be 0 Pop, so the right-hand number wheel and Uinal wheel must be realigned to show this date. The positions of the 13-day wheel and the Tzolkin wheel remain unchanged.