An Introduction to the Study of the Maya Hieroglyphs

by Sylvanus Griswold Morley

3. Black numbers, which show the distances between the days designated by (1) and (2).

The number of the day signs in (1), usually 4, 5, or 10, shows the number of parts into which the tonalamatl is divided. Every red number in (2) is used once with every day sign in (1) to designate a day which is reached in counting one of the black numbers in (3) forward from another of the days recorded by (1) and (2). The most important point for the student to grasp in studying the Maya tonalamatl is the fundamental difference between the use of the red numbers and the black numbers. The former are used only as day coefficients, and together with the day signs show the days which begin the divisions and subdivisions of the tonalamatl. The black numbers, on the other hand, are exclusively time counters, which show only the distances between the dates indicated by the day signs and their corresponding coefficients among the red numbers. They show in effect the lengths of the periods and subperiods into which the tonalamatl is divided.

Most of the numbers, that is (2) and (3), in the tonalamatl are presented in a horizontal row across the page or pages[^[241]] of the manuscript, the red alternating with the black. In some instances, however, the numbers appear in a vertical column or pair of columns, though in this case also the same alternation in color is to be observed. More rarely the numbers are scattered over the page indiscriminately, seemingly without fixed order or arrangement.

It will be noticed in each of the tonalamatls given in the following examples that the record is greatly abbreviated or skeletonized. In the first place, we see no month signs, and consequently the days recorded are not shown to have had any fixed positions in the year. Furthermore, since the year positions of the days are not fixed, any day could recur at intervals of every 260 days, or, in other words, any tonalamatl with the divisions peculiar to it could be used in endless repetition throughout time, commencing anew every 260 days, regardless of the positions of these days in succeeding years. Nor is this omission the only abbreviation noticed in the presentation of the tonalamatl. Although every tonalamatl contained 260 days, only the days commencing its divisions and subdivisions appear in the record; and even these are represented in an abbreviated form. For example, instead of repeating the numerical coefficients with each of the day signs in (1), the coefficient was written once above the column of day signs, and in this position was regarded as belonging to each of the different day signs in turn. It follows from this fact that all the main divisions of the tonalamatl begin with days the coefficients of which are the same. Concerning the beginning days of the subdivisions, a still greater abbreviation is to be noted. The day signs are not shown at all, and only their numerical coefficients appear in the record. The economy of space resulting from the above abbreviations in writing the days will appear very clearly in the texts to follow.

In reading tonalamatls the first point to be determined is the name of the day with which the tonalamatl began. This will be found thus:

Rule 1. To find the beginning day of a tonalamatl, prefix the first red number, which will usually be found immediately above the column of the day signs, to the uppermost[^[242]] day sign in the column.

From this day as a starting point, the first black number in the text is to be counted forward; and the coefficient of the day reached will be the second red number in the text. As stated above, the day signs of the beginning days of the subdivisions are always omitted. From the second red number, which, as we have seen, is the

coefficient of the beginning day of the second subdivision of the first division, the second black number is to be counted forward in order to reach the third red number, which is the coefficient of the day beginning the third subdivision of the first division. This operation is continued until the last black number has been counted forward from the red number just preceding it and the last red number has been reached.

This last red number will be found to be the same as the first red number, and the day which the count will have reached will be shown by the first red number (or the last, since the two are identical) used with the second day sign in the column. And this latter day will be the beginning day of the second division of the tonalamatl. From this day the count proceeds as before. The black numbers are added to the red numbers immediately preceding them in each case, until the last red number is reached, which, together with the third day sign in the column, forms the beginning day of the third division of the tonalamatl. After this operation has been repeated until the last red number in the last division of the tonalamatl has been reached—that is, the 260th day—the count will be found to have reentered itself, or in other words, the day reached by counting forward the last black number of the last division will be the same as the beginning day of the tonalamatl.