THE TONALAMATL AND THE SOLAR CALENDAR
It will be asked: “In what manner did the soothsayers reconcile the days of the tonalamatl with those of the calendar?” By what method did they find such and such a day in the tonalamatl in the tonalpohualli, or solar calendar? How was the one adjusted to the other? In order to reply clearly to this question, it will first be necessary to describe briefly the nature of the Mexican solar calendar or time-count proper. The Mexican solar year consisted of 365 days, divided into 18 periods of 20 days each, called cempohualli, or “months,” and one period of 5 days, known as nemontemi, or “useless” or “unlucky” days.
The Cempohualli.—The names of the 18 cempohualli, or “months,” were[8]:
| Month | Seasonal Character | Presiding God |
| Atlacahualco | Ceasing of rain | Tlaloquê |
| Tlacaxipeuliztli | Seed time | Xipe |
| Tozoztontli | Rain desired | Tlaloquê |
| Ueitozoztli | Worship of new maize | Chicomecoatl |
| Toxcatl | Commencement of rainy season | Uitzilopochtli and Tezcatlipocâ |
| Etzalqualiztli | Rain desired | Tlaloc |
| Tecuilhuitontli | Rain desired | Uixtociuatl |
| Ueitecuilhuitl | Adoration of the ripening maize | Xilonen |
| Tlaxochimaco | First-flowering | Uitzilopochtli |
| Xocohuetzi | Heat for ripening | Xiuhtecutli |
| Ochpaniztli | Refreshment of the Earth-mother | Tlazolteotl |
| Teotleco | Return of the gods from rest | Tezcatlipocâ |
| Tepeilhuitl | Rain | Tlaloc |
| Quecholli | Rain | Mixcoatl |
| Panquetzaliztli | Winter solstice | Uitzilopochtli |
| Atemoztli | Rain | Tlaloquê |
| Tititl | The season of sereness | Ilamatecutli |
| Izcalli | Toasting of the corn supply | Xiuhtecutli |
Eight out of eighteen of these festivals are thus connected with the appeal for rain, or the celebration of its appearance. The remainder celebrate the growth of the maize in its various stages, rejoice at the appearance of these blossoms which were [[368]]so dear to the Mexican heart, are held in honour of the Earth-mother, or mark the solstices.
To the combination of the tonalamatl and the solar calendar the tonalamatl contributed the names of the days, and the solar calendar the divisions of the year in which the days found positions. The tonalamatl and the solar year thus went side by side, each recommencing whenever it reached its own limits. The days in the solar year were known by the names of the days in the tonalamatl which were affixed to them. Thus it is plain that 105 of the 260 tonalamatl day-names had to be repeated in the solar year of 365 days.
NAMES OF THE YEARS
The year was known by the tonalamatl sign of the day with which it began. As there were 20 day-signs, and 5, the least common multiple of 365 and 20, goes into 20 exactly 4 times, the year could begin with one of the four signs only. These were Acatl, Tecpatl, Calli, Tochtli.
Each month of a given year began with the same tonalamatl day-sign. The 20 day-signs always occupied the same position in all the months of a given year, as there were 20 days in a Mexican month. But since the last month was followed by the 5 nemontemi, or “unlucky” days, it follows that each year began with a day-sign five days later than the last. Also, since 365, the number of days in a year, is divisible by 13 with 1 as remainder, it follows that each year began with a day-number one in advance of the last.
The commencement of the year coincided with the commencement of the tonalamatl once in four years.