The beginning day of the next subdivision of the tonalamatl may now be calculated from the day 1 Manik by means of rules 2 and 3 (p. 253). Before proceeding with the calculation incident to this step it will be necessary first to examine the next black number in our tonalamatl. This will be found to be composed of this sign (*) to which 6 (1 bar and 1 dot) has been affixed. It was explained on page 92 that in representing tonalamatls the Maya had to have a sign which by itself would signify the number 20, since numeration by position was impossible. This special character for the number 20 was given in figure 45, and a comparison of it with the sign here under discussion will show that the two are identical. But in the present example the number 6 is attached to this sign thus: (**), and the whole number is to be read 20 + 6 = 26. This number, as we have seen in Chapter IV, would ordinarily have been written thus (†): 1 unit of the second order (20 units of the first order) + 6 units of the first order = 26. 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.

Returning to our text, we find that the "next black number" is 26 (20 + 6), and this is to be added to the red number 1 next preceding it, which, as we have seen, is an abbreviation for the day 1 Manik (see rule 2, p. 253). Adding 26 to 1 gives 27, and deducting all the 13s possible, namely, two, we have left 1 (27 - 26); this number 1, which is the coefficient of the beginning day of the next subdivision, will be found recorded just to the right of the black 26.

The day sign corresponding to this coefficient 1 will be found by counting forward 26 in Table I from the day name Manik. This will give the day name Ben, and 1 Ben will be, therefore, the beginning day of the next subdivision (the third subdivision of the first main division).

The next black number in our text is 13, and proceeding as before, this is to be added to the red number next preceding it, 1, the abbreviation for 1 Ben. Adding 13 to 1 we have 14, and deducting all the 23s possible, we obtain 1 again (14 - 13), which is recorded just to the right of the black 13 (rule 2, p. 253).^[243] Counting forward 13 in Table I from the day name Ben, the day name reached will be Cimi, and the day 1 Cimi will be the beginning day of the next part of the tonalamatl. But since 13 is the last black number, we should have reached in 1 Cimi the beginning day of the second main division of the tonalamatl (see p. 253), and this is found to be the case, since the day sign Cimi is the second in the column of day signs to the left. Compare this form with figure 17, i, j. The day recorded is therefore 1 Cimi.

The first division of the tonalamatl under discussion is subdivided, therefore, into three parts, the first part commencing with the day 1 Ix, containing 13 days; the second commencing with the day 1 Manik, containing 26 days; and the third commencing with the day 1 Ben, containing 13 days.

The second division of the tonalamatl commences with the day 1 Cimi, as we have seen above, and adding to this the first black number, 13, as before, according to rules 2 and 3 (p. 253), the beginning day of the next subdivision will be found to be 1 Cauac. Of this, however, only the 1 is declared (see to the right of the black 13). Adding the next black number, 26, to this day, according to the above rules the beginning day of the next subdivision will be found to be 1 Chicchan. Of this, however, the 1 again is the only part declared. Adding the next and last black number, 13, to this day, 1 Chicchan, according to the rules just mentioned the beginning day of the next, or third, main division will be found to be 1 Eznab. Compare the third day sign in the column of day signs with the form for Eznab in figure 17, z, a'. The second division of this tonalamatl contains, therefore, three parts: The first, commencing with the day 1 Cimi, containing 13 days; the second, commencing with the day 1 Cauac, containing 26 days; and the third, commencing with the day 1 Chicchan, containing 13 days.

Similarly the third division, commencing with the day 1 Eznab, could be shown to have three parts, of 13, 26, and 13 days each, commencing with the day 1 Eznab, 1 Chuen, and 1 Caban, respectively. It could be shown, also, that the fourth division commenced with the day 1 Oc (compare the fourth sign in the column of day signs with figure 17, o), and, further, that it had three subdivisions containing 13, 26, and 13 days each, commencing with the days 1 Oc, 1 Akbal, and 1 Muluc, respectively. Finally, the fifth and last division of the tonalamatl will commence with the day 1 Ik. Compare the last day sign in the column of day signs with figure 17, c, d; and its three subdivisions of 13, 26, and 13 days each with the days 1 Ik, 1 Men, and 1 Imix, respectively. The student will note also that when the last black number, 13, has been added to the beginning day of the last subdivision of the last division, the day reached will be 1 Ix, the day with which the tonalamatl commenced. This period is continuous, therefore, reentering itself immediately on its conclusion and commencing anew.

There follows below an outline^[244] of this particular tonalamatl:

Next tonalamatl: 1st Division, 1st part, 13 days, beginning with the day 1 Ix, etc.

We may now apply rule 4 (p. 253) as a test to this tonalamatl. Multiplying the sum of all the black numbers, 13 + 26 + 13 = 52, by the number of day signs in the column of day signs, 5, we obtain 260 (52 × 5), which proves that this tonalamatl is regular and correct.

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). Note the fleshless lower jaw, the truncated nose, and the vertebræ. The second deity is unknown, but the third is again the Death God, having the same characteristics as the god in the first picture. The cloak worn by this deity in the third picture shows the crossbones, which would seem to have been an emblem of death among the Maya as among us. The glyphs above these pictures probably explain the nature of the periods to which they refer, or perhaps the ceremonies peculiar or appropriate to them. In many cases the name glyphs of the deities who appear below them are given; for example, in the present text, the second and sixth glyphs in the upper row^[245] record in each case the fact that the Death God is figured below.

The glyphs above the pictures offer one of the most promising problems in the Maya field. It seems probable, as just explained, that the four or six glyphs which stand above each of the pictures in a tonalamatl tell the meaning of the picture to which they are appended, and any advances made, looking toward their deciphering, will lead to far-reaching results in the meaning of the nonnumerical and noncalendric signs. In part at least they show the name glyphs of the gods above which they occur, and it seems not unlikely that the remaining glyphs may refer to the actions of the deities who are portrayed; that is, to the ceremonies in which they are engaged. More extended researches along this line, however, must be made before this question can be answered.

The next tonalamatl to be examined is that shown in the lower division of plate 27, Dresden 12c. At first sight this would appear to be another tonalamatl of five divisions, like the preceding one, but a closer examination reveals the fact that the last day sign in the column of day signs is like the first, and that consequently there are only four different signs denoting four divisions. The last, or fifth sign, like the last red number to which it corresponds, merely indicates that after the 260th day the tonalamatl reenters itself and commences anew.

Prefixing the first red number, 13, to the first day sign, Chuen (see fig. 17, p, q), according to rule 1 (p. 252), the beginning day of the tonalamatl will be found to be 13 Chuen. Adding to this the first black number, 26, according to rules 2 and 3 (p. 253), the beginning day of the next subdivision will be found to be 13 Caban. Since this day begins only a subdivision of the tonalamatl, however, its name part Caban is omitted, and merely the coefficient 13 recorded. Commencing with the day 13 Caban and adding to it the next black number in the text, again 26, according to rules 2 and 3 (p. 253), the beginning day of the next subdivision will be found to be 13 Akbal, represented by its coefficient 13 only. Adding the last black number in the text, 13, to 13 Akbal, according to the rules just mentioned, the beginning day of the next part of the tonalamatl will be found to be 13 Cib. And since the black 13 which gave this new day is the last black number in the text, the new day 13 Cib will be the beginning day of the next or second division of the tonalamatl, and it will be recorded as the second sign in the column of day signs. Compare the second day sign in the column of day signs with figure 17, v, w.

Following the above rules, the student will have no difficulty in working out the beginning days of the remaining divisions and subdivisions of this tonalamatl. These are given below, though the student is urged to work them out independently, using the following outline simply as a check on his work. Adding the last black number, 13, to the beginning day of the last subdivision of the last division, 13 Eznab, will bring the count back to the day 13 Chuen with which the tonalamatl began:

Next tonalamatl: 1st division, 1st part, 26 days, beginning with the day 13 Chuen, etc.

Applying the test rule to this tonalamatl (see rule 4, p. 253), we have: 26 + 26 + 13 = 65, the sum of the black numbers, and 4 the number of the day signs in the column of day signs,^[246] 65 × 4 = 260, the exact number of days in a tonalamatl.

The next tonalamatl (see the upper part of pl. 27, that is, Dresden 12a) occupies only the latter two-thirds of the upper division, the black 12 and red 11 being the last black and red numbers, respectively, of another tonalamatl.

The presence of 10 day signs arranged in two parallel columns of five each would seem at first to indicate that this is a tonalamatl of 10 divisions, but it develops from the calculations that instead there are recorded here two tonalamatls of five divisions each, the first column of day signs designating one tonalamatl and the second another quite distinct therefrom.

The first red numeral is somewhat effaced, indeed all the red has disappeared and only the black outline of the glyph remains. Its position, however, above the column of day signs, seems to indicate its color and use, and we are reasonably safe in stating that the first of the two tonalamatls here recorded began with the day 8 Ahau. Adding to this the first black number, 27, the beginning day of the next subdivision will be found to be 9 Manik, neither the coefficient nor day sign of which appears in the text. Assuming that the calculation is correct, however, and adding the next black number, 25 (also out of place), to this day, 9 Manik, the beginning day of the next part will be 8 Eb. But since 25 is the last black number, 8 Eb will be the beginning day of the next main division and should appear as the second sign in the first column of day signs. Comparison of this form with figure 17, r, will show that Eb is recorded in this place. In this manner all of the beginning days could be worked out as below:

The application of rule 4 (p. 253) to this tonalamatl gives: 5 × 52 = 260, the exact number of days in a tonalamatl. As previously explained, the second column of day signs belongs to another tonalamatl, which, however, utilized the same red 8 as the first and the same black 27 and 25 as the first. The outline of this tonalamatl, which began with the day 8 Oc, follows:

The application of rule 4 (p. 253) to this tonalamatl gives: 5 × 52 = 260, the exact number of days in a tonalamatl. It is interesting to note that the above tonalamatl, beginning with the day 8 Oc, commenced just 130 days later than the first tonalamatl, which began with the day 8 Ahau. In other words, the first of the two tonalamatls in Dresden 12a was just half completed when the second one commenced, and the second half of the first tonalamatl began with the same day as the first half of the second tonalamatl, and vice versa.

The tonalamatl in plate 28, upper division, is from Dresden 15a, and is interesting because it illustrates how certain missing parts may be filled in. The first red number is missing and we can only say that this tonalamatl began with some day Ahau. However, adding the first black number, 34, to this day ? Ahau, the day reached will be 13 Ix, of which only 13 is recorded. Since 13 Ix was reached by counting 34 forward from the day with which the count must have started, by counting back 34 from 13 Ix the starting point will be found to be 5 Ahau, and we may supply a red bar above the column of the day signs. Adding the next black number, 18, to this day 13 Ix, the beginning day of the next division will be found to be 5 Eb, which appears as the second day sign in the column of day signs.

The last red number is 5, thus establishing as correct our restoration of a red 5 above the column of day signs. From here this tonalamatl presents no unusual features and it may be worked as follows:

Applying rule 4 (p. 253), we have: 5 × 52 = 260, the exact number of days in a tonalamatl. The next tonalamatl (see lower part of pl. 28, that is, Dresden 15c) has 10 day signs arranged in two parallel columns of 5 each. This, at its face value, would seem to be divided into 10 divisions, and the calculations confirm the results of the preliminary inspection.

The tonalamatl opens with the day 3 Lamat. Adding to this the first black number, 12, the day reached will be 2 Ahau, of which only the 2 is recorded here. Adding to 2 Ahau the next black number, 14, the day reached will be 3 Ix. And since 14 is the last black number, this new day will be the beginning of the next division in the tonalamatl and will appear as the upper day sign in the second column.^[247] Commencing with 3 Ix and adding to it the first black number 12, the day reached will be 2 Cimi, and adding to this the next black number, 14, the day reached will be 3 Ahau, which appears as the second glyph in the first column. This same operation if carried throughout will give the following outline of this tonalamatl:

Applying rule 4 (p. 253) to this tonalamatl, we have: 10 × 26 = 260, the exact number of days in a tonalamatl.

The tonalamatl which appears in the middle part on plate 28—that is, Dresden 15b—extends over on page 16b, where there is a black 13 and a red 1. The student will have little difficulty in reaching the result which follows: The last day sign is the same as the first, and consequently this tonalamatl is divided into four, instead of five, divisions:

Applying rule 4 (p. 253) to this tonalamatl, we have: 4 × 65 = 260, the exact number of days in a tonalamatl. The tonalamatls heretofore presented have all been taken from the Dresden Codex. The following examples, however, have been selected from tonalamatls in the Codex Tro-Cortesianus. The student will note that the workmanship in the latter manuscript is far inferior to that in the Dresden Codex. This is particularly true with respect to the execution of the glyphs.

The first tonalamatl figured from the Codex Tro-Cortesianus (see pl. 29) extends across the middle part of two pages (Tro-Cor. 10b, 11b). The four day signs at the left indicate that it is divided into four divisions, of which the first begins with the day 13 Ik.^[248] Adding to this the first black number 9, the day 9 Chuen is reached, and proceeding in this manner the tonalamatl may be outlined as follows:

Applying rule 4 (p. 253) to this tonalamatl, we have: 4 × 65 = 260, the exact number of days in a tonalamatl.

Another set of interesting tonalamatls is figured in plate 30, Tro-Cor., 102.^[250] The first one on this page appears in the second division, 102b, and is divided into five parts, as the column of five day signs shows. The order of reading is from left to right in the pair of number columns, as will appear in the following outline of this tonalamatl:

Applying rule 4 (p. 253) to this tonalamatl, we have: 5 × 52 = 260, the exact number of days in a tonalamatl. The next tonalamatl on this page (see third division in pl. 29, that is, Tro-Cor., 102c) is interesting chiefly because of the fact that the pictures which went with the third and fourth parts of the five divisions are omitted for want of space. The outline of this tonalamatl follows:

Applying rule 4 (p. 253) to this tonalamatl, we have: 5 × 52 = 260, the exact number of days in a tonalamatl. The last tonalamatl in plate 29, Tro-Cor., 102d, commences with the same day, 4 Ahau, as the preceding tonalamatl and, like it, has five divisions, each of which begins with the same day as the corresponding division in the tonalamatl just given, 4 Ahau, 4 Eb, 4 Kan, 4 Cib, and 4 Lamat. Tro-Cor. 102d differs from Tro-Cor. 102c in the number and length of the parts into which its divisions are divided.

Adding the first black number, 29, to the beginning day, 4 Ahau, the day reached will be 7 Muluc, of which only the 7 appears in the text. Adding to this the next black number, 24, the day reached will be 5 Ben. An examination of the text shows, however, that the day actually recorded is 4 Eb, the last red number with the second day sign. This latter day is just the day before 5 Ben, and since the sum of the black numbers in this case does not equal any factor of 260 (29 + 24 = 53), and since changing the last black number from 24 to 23 would make the sum of the black numbers equal to a factor of 260 (29 + 23 = 52), and would bring the count to 4 Eb, the day actually recorded, we are justified in assuming that there is an error in our original text, and that 23 should have been written here instead of 24. The outline of this tonalamatl, corrected as suggested, follows:

Applying rule 4 (p. 253) to this tonalamatl, we have: 52 × 5 = 260, the exact number of days in a tonalamatl.

The foregoing tonalamatls have been taken from the pages of the Dresden Codex or those of the Codex Tro-Cortesiano. Unfortunately, in the Codex Peresianus no complete tonalamatls remain, though one or two fragmentary ones have been noted.

No matter how they are divided or with what days they begin, all tonalamatls seem to be composed of the same essentials:

1. The calendric parts, made up, as we have seen on page 251, of (a) the column of day signs; (b) the red numbers; (c) the black numbers.

2. The pictures of anthropomorphic figures and animals engaged in a variety of pursuits, and

3. The groups of four or six glyphs above each of the pictures.

The relation of these parts to the tonalamatl as a whole is practically determined. The first is the calendric background, the chronological framework, as it were, of the period. The second and third parts amplify this and give the special meaning and significance to the subdivisions. The pictures represent in all probability the deities who presided over the several subdivisions of the tonalamatls in which they appear, and the glyphs above them probably set forth their names, as well as the ceremonies connected with, or the prognostications for, the corresponding periods.

It will be seen, therefore, that in its larger sense the meaning of the tonalamatl is no longer a sealed book, and while there remains a vast amount of detail yet to be worked out the foundation has been laid upon which future investigators may build with confidence.

In closing this discussion of the tonalamatl it may not be out of place to mention here those whose names stand as pioneers in this particular field of glyphic research. To the investigations of Prof. Ernst Förstemann we owe the elucidation of the calendric part of the tonalamatl, and to Dr. Paul Schellhas the identification of the gods and their corresponding name glyphs in parts (2) and (3), above. As pointed out at the beginning of this chapter, the most promising line of research in the codices is the groups of glyphs above the pictures, and from their decipherment will probably come the determination of the meaning of this interesting and unusual period.

Texts Recording Initial Series

Initial Series in the codices are unusual and indeed have been found, up to the present time, in only one of the three known Maya manuscripts, namely, the Dresden Codex. As represented in this manuscript, they differ considerably from the Initial Series heretofore described, all of which have been drawn from the inscriptions. This difference, however, is confined to unessentials, and the system of counting and measuring time in the Initial Series from the inscriptions is identical with that in the Initial Series from the codices.

The most conspicuous difference between the two is that in the codices the Initial Series are expressed by the second method, given on page 129, that is, numeration by position, while in the inscriptions, as we have seen, the period glyphs are used, that is, the first method, on page 105. Although this causes the two kinds of texts to appear very dissimilar, the difference is only superficial.

Another difference the student will note is the absence from the codices of the so-called Initial-series "introducing glyph." In a few cases there seems to be a sign occupying the position of the introducing glyph, but its identification as the Initial-series "introducing glyph" is by no means sure, and, moreover, as stated above, it does not occur in all cases in which there are Initial Series.

Another difference is the entire absence from the codices of Supplementary Series; this count seems to be confined exclusively to the monuments. 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. This use of red numbers in the last two places is due to the fact that the zero sign in the codices is always red.