The Thirteen Days of Trecena 1

A trecena is a run of thirteen consecutive days, each carrying one of the thirteen numbers in fixed order and each paired with the next day sign in the twenty sign sequence, so Trecena 1 runs from 1 Cipactli through 13 Acatl, the reed, without repeating a day sign and without the numbering restarting until the fourteenth day opens Trecena 2 back at 1.

Twenty such weeks are needed to exhaust all thirteen numbers against all twenty day signs exactly once, the arithmetic behind the tonalpohualli's total length of two hundred and sixty days, thirteen multiplied by twenty. Each of the thirteen numbered days within the trecena carried its own reading, layered under the trecena's overall patron and augury, and the codices assign a patron bird to each of the thirteen numbers themselves, a further register the calendar priests worked alongside the trecena patron and the day sign's own character, per Boone's study of the surviving books of fate. Because a trecena's patron deity governs the whole week rather than one day within it, a client's reading depended on three layered facts at once, the number, the day sign and the trecena, and it is this compounding that gave Mexica diviners their reputation for precision: no two of the 260 days share an identical combination of all three.