16. Cozcaquauhtli. A vulture, signifying old age; associated with Itzpapalotl.

17. Olin. A sign emblematical of movement (used also to signify an earthquake). Variable in fortune, and associated with Nanauatzin.

18. Tecpatl. A stone knife, the emblem of drought and sterility, associated with Tezcatlipoca.

19. Quiauitl. The head of Tlaloc, emblem of rain; an unlucky sign.

20. Xochitl. A flower, implying good craftsmanship; associated with Xochiquetzal.

These signs ran consecutively in the order given above, one being assigned to each day, and the series was repeated ad infinitum. Conjointly with them were repeated the numerals 1 to 13; e.g. 1. cipactli, 2. eecatl, 3. calli, and so on to 13. acatl, which was followed by 1. ocelotl, 2. quauhtli, and so forth. There being no common factor to the numbers 13 and 20, a period of 13 × 20 days, or 260, would elapse before the sign 1. cipactli would recur. This period of 260 days constituted the ritual and divinatory calendar, known as the tonalamatl. The tonalamatl was subdivided in various ways; in some manuscripts each of the twenty thirteen-day periods, or “weeks,” is shown separately, together with the figure of a god who was especially associated with the first day, but whose influence was supposed to extend over the whole “week.” The deities presiding over the successive “weeks” of the tonalamatl are given in one MS. (Vaticanus A) as follows, the date preceding the name of each being that of the first day of each “week.”

There is however some variation in the assignment the week-gods, e.g. Sahagun gives 1. miquiztli to Tezcatlipoca, 1. acatl to Quetzalcoatl, 1. tecpatl to Uitzilopochtli, etc. Within the weeks, many individual days were associated with certain deities, such as 4. olin and 12. itzcuintli with the sun, 5. itzcuintli and 6. quetzpalin with Mictlantecutli, but for a list of these the reader may be referred to Sahagun. Apart from the signs of the days themselves, the presiding deities of the weeks, and the gods of the individual dates, the numerical signs also possessed a lucky or unlucky connotation. Three and four were good numbers, five and six generally bad, seven always good, eight and nine bad, ten, eleven, twelve and thirteen good. Consequently the diviner was obliged to take into account all these possible influences, which in many cases might be contradictory, in considering the fortune attached to a particular day. In some MSS. the tonalamatl is arranged on a different system, viz. in five long horizontal rows of fifty-two days each. Each row, and each vertical column of five days, is provided with a presiding deity or symbol, the influence of which must be assessed. Nor have we yet come to an end of the factors which must be taken into consideration, but before proceeding it will be necessary to explain the solar calendar.

The Mexicans reckoned 365 days to the solar year, which they divided into eighteen months of twenty days each, and a nineteenth period of five days, considered extremely unlucky, at the end of the year. As the days were known by their tonalamatl names, it is obvious that the first 115 days of the year recurred at the end. But it was possible to distinguish between two days of the same name which fell in the same year, owing to the fact that each day was associated with one of a series of nine deities, called “lords of the night,” a series also repeated ad infinitum, save that no “lord” was assigned to any of the five unlucky days at the end of the year, which were called nemontemi or “useless days.” Thus, since the number 260 is not divisible by 9, it was possible to differentiate between two days of the same name falling in one year; and since 9 goes into 360 without remainder, the commencement of the year coincided with the commencement of the series of “lords of the night.” These lords of the night are indicated by the heads or symbols of the following gods: 1. Xiuhtecutli, 2. Itztli, 3. Tonatiuh, 4. Cinteotl, 5. Mictlantecutli, 6. Chalchiuhtlicue, 7. Tlazolteotl, 8. Tepeyollotl and 9. Tlaloc. Nor is this all, a corresponding series of thirteen “lords of day,” which however is not similarly composed in all MSS., accompanied the days (omitting the nemontemi), and the influences of the day- and night-lord assigned to each day respectively constituted two additional features for the consideration of the would-be interpreter of the tonalamatl. It is perhaps hardly necessary to state that the reading of the book of days was in the hands of a professional priesthood and required much study to perform correctly.

Since each “month” consisted of twenty days, and there were twenty day-signs, it is obvious that each month in a given year began with the same sign; but since the last month was followed by the five unlucky days, it follows that each year began with a day-sign five days later than the last. Also since 365 is divisible by 13 with 1 as remainder, it follows equally that each year began with a day-number one in advance of the last. Further, since there were twenty day-signs, and five (the least common multiple of 365 and 20) goes into twenty exactly four times, the year began with one of four signs only. Now the year was always distinguished by the sign of the day on which it began, and it is a peculiar fact that the commencement of the year never coincided with the commencement of the tonalamatl. The four signs which give the names to the years are the signs tecpatl, calli, tochtli and acatl, recurring in that order. Whether the day-number entering into the name of the year was that of the first day, as held by most authorities, or of the first day of the fifth month, as Seler tries to prove, need not be discussed here; the fact remains that the years were named successively, 1. tecpatl, 2. calli, 3. tochtli, and so on, until, after a period of fifty-two years (13 × 4), the same sign occurred again with the same number as the name-date of the year. This period of fifty-two years constituted the shorter cycle of the Mexicans, the longer cycle consisting of twice that number; but before proceeding further it will be necessary to say something about the months (see Appendix II).