Eighteen Months of Twenty, and Five Days Over

The arithmetic is deliberate rather than awkward. Eighteen periods of twenty days give three hundred and sixty, a figure that fits the vigesimal counting used throughout Mesoamerican mathematics, and the remaining five days are appended as a separate short period at the end. Those five stand outside the regular structure and were treated as a dangerous interval, a time for restraint rather than for undertaking anything. The way dates are written inside a month is worth noting because it surprises modern readers.

Positions are counted from a seating of the month, so the first day of a period is its seating and the numbering of ordinary days runs from there to nineteen before the next seating arrives. A date therefore states that so many days of a named period have elapsed, rather than naming the day directly. The same eighteen and five arrangement appears across Mesoamerica with different month names, including in the Aztec year count, which indicates a shared inheritance rather than parallel invention. What differs between systems is where the year begins and how the five day period is treated, and those differences are among the sharpest markers of which tradition a given inscription or document belongs to.