The Mexica did not keep one calendar with a sacred portion inside it. They kept two counts, running at once, at different lengths, neither contained in the other. A day was never named by one alone — it was a coordinate in both, fixed the way a point in a weaving is fixed by warp and weft crossing.

The tōnalpōhualli, the 260-day count, is two wheels turning against each other: twenty day signs and the numbers one through thirteen, both advancing a step each day. It opens at 1-Cipactli, then 2-Ehecatl, 3-Calli. At 13-Acatl the numbers restart but the signs keep going, so the next day is 1-Ocelotl. Since 20 and 13 share no factor, every pairing occurs exactly once before the wheels realign — 260 days. This was the count that governed fate: divination, ritual timing, and the character a child was born carrying.

The xiuhpōhualli, the 365-day year, is built differently — eighteen months of twenty days each, the veintenas, plus five days left over at the end. This was the civil and agricultural year, each veintena with its own festival and its own labour. The five leftover days, the nemontemi, belonged to no month and carried no festival. They were considered deeply unlucky, and work stopped where it could. The system built in a structural pause rather than smoothing the year out — the mathematics was allowed to shape lived time directly, including its dead spots.

Where they interlock, a full date reads like 4-Ollin, tenth day of Toxcatl. Because 260 and 365 share a factor of five, that exact combination recurs only every 18,980 days — fifty-two years, or seventy-three complete runs of the sacred count. This is the Calendar Round, the xiuhmolpilli, the binding of the years.

The same arithmetic produces something quieter. Each year takes its name from a day sign, and since 365 leaves a remainder of five when divided by twenty, that sign advances five places annually — meaning only four of the twenty signs can ever name a year: Acatl, Tecpatl, Calli, Tochtli. Meanwhile 365 leaves a remainder of one when divided by thirteen, so the number simply climbs by one. Four signs against thirteen numbers gives fifty-two year names before any repeat. The cycle falls out of the structure twice over, from two directions that never had to agree.

When the round closed, every hearth in the valley was put out. Priests waited on Huixachtlan for the Pleiades to cross the meridian — the sign that time would continue — and drilled new fire, which runners carried outward to relight the temples, then the towns, then each house. Time was not a background condition that simply proceeds here. It was renewed by ritual labour, on a schedule these two counts made visible, and its continuation was understood to be genuinely at risk. The world had ended four times already.

Correlation between these counts and the Gregorian calendar is not settled among scholars; the surviving sources are colonial-era; and different altepetl began the year at different points. The 260-day count and the 52-year round are shared across Maya, Zapotec, Mixtec and other traditions — the Mexica inherited a very old system rather than inventing one.