Twenty Signs Against Thirteen Numbers

The mechanism is a pair of wheels of different sizes turning together. Twenty named day signs run in fixed order, and a number from one to thirteen runs alongside them, both advancing by one each day. Because thirteen and twenty share no factor, a given pairing of number and sign does not return until both cycles have completed a whole number of turns, which takes two hundred and sixty days. Every day in that span carries a unique name, and after it the sequence begins again exactly. That structure has no astronomical anchor and needs none.

The count is not tied to a sunrise, a season or a year, and it has run continuously without intercalation or correction for as long as it can be traced, which is what allows it to be meshed with other counts without ever needing adjustment. Why two hundred and sixty is unsettled and has been argued for over a century. Proposals include the approximate length of human gestation, the interval between the two days each year on which the sun stands directly overhead at certain latitudes in Mesoamerica, the growing season for maize, and the simple product of two numbers that already carried significance. None has become the accepted answer, and the atlas records the question as open rather than choosing among them.