Sylvanus Griswold Morley

“ 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 ”

“ Every one of the Serpent numbers has six terms, and they represent by far the highest numbers to be found in the codices. The black number in the first, or left-hand serpent in plate 32, reads as follows: 4.6.7.12.4.10, which, reduced to units of the first order, reads:
The next question which arises is, What is the starting point from which this number is counted? Just below it the student will note the date 3 Ix 7 Tzec, which from its position would seem almost surely to be either the starting point or the terminal date, more probably the latter. ”

“ Omitting this row, however, the remaining numbers, those which are multiples of 2,920, admit of an easy explanation.
In the first place, the opening term 2,920, which serves as the unit of increase for the entire series up to and including the 13th term, is the so-called Venus-Solar period, containing 8 Solar years of 365 days each and 5 Venus years of 584 days each. This important period is the subject of extended treatment elsewhere in the Dresden Codex (pp. 46-50) , in which it is repeated 39 times in all, divided into three equal divisions of 13 periods each. ”

“ The 13th term of our series 37,960 is, as we have seen, 13 × 2,920, the exact number of days treated of in the upper divisions of pages 46-50 of the Dresden Codex. The 14th term (75,920) is the exact number of days treated of in the first two divisions, and finally, the 15th, or next to the last term (113,880) , is the exact number of days treated of in all three divisions of these pages.
This 13th term (37,960) is the first in which the tonalamatl of 260 days comes into harmony with the Venus and Solar years, and as such must have been of very great importance to the Maya. ”

“ The student will note in the middle division of plate 27 that the pictures are so arranged that one picture stands under the first subdivisions of all the divisions, the second picture under the second subdivisions, and the third under the third subdivisions. It has been conjectured that these pictures represent the gods who were the patrons or guardians of the subdivisions of the tonalamatls, under which each appears. In the present case the first god pictured is the Death Deity, God A (see fig. 3) . ”

“ Aside from these points the Initial Series from the two sources differ but little. All proceed from identically the same starting point, the date 4 Ahau 8 Cumhu, and all have their terminal dates or related Secondary-series dates recorded immediately after them.
The first example of an Initial Series from the codices will be found in plate 31 (Dresden 24) , in the lower left-hand corner, in the second column to the right. The Initial-series number here recorded is 9.9.16.0.0, of which the zero in the 2d place (uinals) and the zero in the 1st place (kins) are expressed by red numbers. ”

“ These commence at the bottom of the page and increase toward the top, every other number in the series being a multiple of the first, or beginning number. One example of this class will suffice to illustrate all the others.
In the lower right-hand corner of plate 31 a series of this kind commences with the day 9 Ahau. [25] Of this series the number 8.2.0 just above the 9 Ahau is the first term, and the day 9 Ahau the first terminal date. As usual in Maya texts, the starting point is not expressed; by calculation, however, it can be shown to be 1 Ahau [26] in this particular case. ”

“ As explained on page 92, however, numeration by position—that is, columns of units—was impossible in the tonalamatls, in which many of the numbers appear in a horizontal row, consequently some character had to be devised which by itself would stand for the number 20. ”