An Introduction to the Study of the Maya Hieroglyphs

Chapter VI: The Codices (1)

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The present chapter will treat of the application of the material presented in Chapters III and IV to texts drawn from the codices, or hieroglyphic manuscripts; and since these deal in great part with the tonalamatl, or sacred year of 260 days, as we have seen (p. 31), this subject will be taken up first.

TEXTS RECORDING TONALAMATLS

The _tonalamatl_, or 260-day period, as represented in the codices is usually divided into five parts of 52 days each, although tonalamatls of four parts, each containing 65 days, and tonalamatls of ten parts, each containing 26 days, are not at all uncommon. These divisions are further subdivided, usually into unequal parts, all the divisions in one tonalamatl, however, having subdivisions of the same length.

So far as its calendric side is concerned,[240] the tonalamatl may be considered as having three essential parts, as follows:

1. A column of day signs.

2. Red numbers, which are the coefficients of the day signs.

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. {252}

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 {253} 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.

It follows from the foregoing that the sum of all the black numbers multiplied by the number of day signs in the column--the number of main divisions in the tonalamatl--will equal exactly 260. If any tonalamatl fails to give 260 as the result of this test, it may be regarded as incorrect or irregular.

The foregoing material may be reduced to the following:

_Rule 2._ To find the coefficients of the beginning days of succeeding divisions and subdivisions of the tonalamatl, add the black numbers to the red numbers immediately preceding them in each case, and, after subtracting all the multiples of 13 possible, the resulting number will be the coefficient of the beginning day desired.

_Rule 3._ To find the day signs of the beginning days of the succeeding divisions and subdivisions of the tonalamatl, count forward in Table I the black number from the day sign of the beginning day of the preceding division or subdivision, and the day name reached in Table I will be the day sign desired. If it is at the beginning of one of the _main divisions_ of the tonalamatl, the day sign reached will be found to be recorded in the column of day signs, but if at the beginning of a _subdivision_ it will be unexpressed.

To these the test rule above given may be added:

_Rule 4._ The sum of all the black numbers multiplied by the number of day signs in the column of day signs will equal exactly 260 if the tonalamatl is perfectly regular and correct. {254}

In plate 27 is figured page 12 of the Dresden Codex. It will be noted that this page is divided into three parts by red division lines; after the general practice these have been designated _a, b_, and _c, a_ being applied to the upper part, _b_ to the middle part, and _c_ to the lower part. Thus "Dresden 12b" designates the middle part of page 12 of the Dresden Codex, and "Dresden 15c" the lower part of page 15 of the same manuscript. Some of the pages of the codices are divided into four parts, or again, into two, and some are not divided at all. The same description applies in all cases, the parts being lettered from top to bottom in the same manner throughout.

The first tonalamatl presented will be that shown in Dresden 12b (see the middle division in pl. 27). The student will readily recognize the three essential parts mentioned on page 251: (1) The column of day signs, (2) the red numbers, and (3) the black numbers. Since there are five day signs in the column at the left of the page, it is evident that this tonalamatl has five main divisions. The first point to establish is the day with which this tonalamatl commenced. According to rule 1 (p. 252) this will be found by prefixing the first red number to the topmost day sign in the column. The first red number in Dresden 12b stands in the regular position (above the column of day signs), and is very clearly 1, that is, one red dot. A comparison of the topmost day sign in this column with the forms of the day signs in figure 17 will show that the day sign here recorded is Ix (see fig. 17, _t_), and the opening day of this tonalamatl will be, therefore, 1 Ix. The next step is to find the beginning days of the succeeding subdivisions of the first main division of the tonalamatl, which, as we have just seen, commenced with the day 1 Ix. According to rule 2 (p. 253), the first black number--in this case 13, just to the right of and slightly below the day sign Ix--is to be added to the red number immediately preceding it--in this case 1--in order to give the coefficient of the day beginning the next subdivision, all 13s possible being first deducted from the resulting number. Furthermore, this coefficient will be the red number next following the black number.

Applying this rule to the present case, we have:

1 (first red number) + 13 (next black number) = 14. Deducting all the 13s possible, we have left 1 (14 - 13) as the coefficient of the day beginning the next subdivision of the tonalamatl. This number 1 will be found as the red number immediately following the first black number, 13. To find the corresponding day sign, we must turn to rule 3 (p. 253) and count forward in Table I this same black number, 13, from the preceding day sign, in this case Ix. The day sign reached will be Manik. But since this day begins only a _subdivision_ in this tonalamatl, not one of the _main divisions_, its day sign will not be recorded, and we have, therefore, the day 1 Manik, of which the 1 is expressed by the second red number and the name part Manik only indicated by the calculations.

{255}

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 {256} 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. {257}

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

---------------------+---------+-----------+---------+---------+---------
|1st |2d |3d |4th |5th
|Division |Division |Division |Division |Division
---------------------+---------+-----------+---------+---------+---------
1st part, 13 days, | | | | |
beginning with day |1 Ix |1 Cimi |1 Eznab |1 Oc |1 Ik
| | | | |
2d part, 26 days, | | | | |
beginning with day |1 Manik |1 Cauac |1 Chuen |1 Akbal |1 Men
| | | | |
3d part, 13 days, | | | | |
beginning with day |1 Ben |1 Chicchan |1 Caban |1 Muluc |1 Imix
| | | | |
Total number of days |52 |52 |52 |52 |52
---------------------+---------+-----------+---------+---------+---------

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 {258} 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: {259}

---------------------+----------+---------+----------+----------
|1st |2d |3d |4th
|Division |Division |Division |Division
---------------------+----------+---------+----------+----------
1st part, 26 days, | | | |
beginning with day |13 Chuen |13 Cib |13 Imix |13 Cimi
| | | |
2d part, 26 days, | | | |
beginning with day |13 Caban |13 Ik |13 Manik |13 Eb
| | | |
3d part, 13 days, | | | |
beginning with day |13 Akbal |13 Lamat |13 Ben |13 Eznab
| | | |
Total number of days |65 |65 |65 |65
---------------------+----------+---------+----------+----------

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. {260} In this manner all of the beginning days could be worked out as below:

---------------------+----------+---------+----------+----------+--------
|1st |2d |3d |4th |5th
|Division |Division |Division |Division |Division
---------------------+----------+---------+----------+----------+--------
1st part, 27 days, | | | | |
beginning with day |8 Ahau |8 Eb |8 Kan |8 Cib |8 Lamat
| | | | |
2d part, 25 days, | | | | |
beginning with day |9 Manik |9 Cauac |9 Chuen |9 Akbal |9 Men
| | | | |
Total number of days |52 |52 |52 |52 |52
---------------------+----------+---------+----------+----------+--------

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:

---------------------+----------+---------+---------+---------+----------
|1st |2d |3d |4th |5th
|Division |Division |Division |Division |Division
---------------------+----------+---------+---------+---------+----------
1st part, 27 days, | | | | |
beginning with day |8 Oc |8 Ik |8 Ix |8 Cimi |8 Eznab
| | | | |
2d part, 25 days, | | | | |
beginning with day |9 Caban |9 Muluc |9 Imix |9 Ben |9 Chicchan
| | | | |
Total number of days |52 |52 |52 |52 |52
---------------------+----------+---------+---------+---------+----------

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.

{261}

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:

---------------------+----------+---------+----------+----------+--------
|1st |2d |3d |4th |5th
|Division |Division |Division |Division |Division
---------------------+----------+---------+----------+----------+--------
1st part, 34 days, | | | | |
beginning with day |5 Ahau |5 Eb |5 Kan |5 Cib |5 Lamat
| | | | |
2d part, 18 days, | | | | |
beginning with day |13 Ix |13 Cimi |13 Eznab |13 Oc |13 Ik
| | | | |
Total number of days |52 |52 |52 |52 |52
---------------------+----------+---------+----------+----------+--------

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:

---------------------+----------+---------+----------+----------+--------
|1st |2d |3d |4th |5th
|Division |Division |Division |Division |Division
---------------------+----------+---------+----------+----------+--------
1st part, 12 days, | | | | |
beginning with day |3 Lamat |3 Ix |3 Ahau |3 Cimi |3 Eb
| | | | |
2d part, 14 days, | | | | |
beginning with day |2 Ahau |2 Cimi |2 Eb |2 Eznab |2 Kan
| | | | |
Total number of days |26 |26 |26 |26 |26
---------------------+----------+---------+----------+----------+--------

{262} (Concluded)

---------------------+----------+---------+----------+----------+--------
|6th |7th |8th |9th |10th
|Division |Division |Division |Division |Division
---------------------+----------+---------+----------+----------+--------
1st part, 12 days, | | | | |
beginning with day |3 Eznab |3 Kan |3 Oc |3 Cib |3 Ik
| | | | |
2d part, 14 days, | | | | |
beginning with day |2 Oc |2 Cib |2 Ik |2 Lamat |2 Ix
| | | | |
Total number of days |26 |26 |26 |26 |26
---------------------+----------+---------+----------+----------+--------

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:

---------------------+----------+---------+----------+----------
|1st |2d |3d |4th
|Division |Division |Division |Division
---------------------+----------+---------+----------+----------
1st part, 13 days, | | | |
beginning with day |1 Ik |1 Manik |1 Eb |1 Caban
| | | |
2d part, 31 days, | | | |
beginning with day |1 Men |1 Ahau |1 Chicchan|1 Oc
| | | |
3d part, 8 days, | | | |
beginning with day |6 Cimi |6 Chuen |6 Cib |6 Imix
| | | |
4th part, 13 days, | | | |
beginning with day |1 Ix |1 Cauac |1 Kan |1 Muluc
| | | |
Total number of days |65 |65 |65 |65
---------------------+----------+---------+----------+----------

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:

{263}

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, {264} 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:

---------------------+----------+---------+---------+---------+--------
|1st |2d |3d |4th |5th
|Division |Division |Division |Division |Division
---------------------+----------+---------+---------+---------+--------
1st part, 17 days, | | | | |
beginning with day |4 Ahau |4 Eb |4 Kan |4 Cib |4 Lamat
| | | | |
2d part, 13 days, | | | | |
beginning with day |8 Caban |8 Muluc |8 Imix |8 Ben |8 Chicchan
| | | | |
3d part, 10 days, | | | | |
beginning with day |8 Oc |8 Ik |8 Ix |8 Cimi |8 Eznab
| | | | |
4th part, 12 days, | | | | |
beginning with day |5 Ahau |5 Eb |5 Kan |5 Cib |5 Lamat
| | | | |
Total number of | | | | |
days |52 |52 |52 |52 |52
---------------------+----------+---------+---------+---------+--------

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: {265}

----------------------+----------+---------+---------+----------+--------
|1st |2d |3d |4th |5th
|Division |Division |Division |Division |Division
----------------------+----------+---------+---------+----------+--------
1st part, 29 days, | | | | |
beginning with day |4 Ahau |4 Eb |4 Kan |4 Cib |4 Lamat
| | | | |
2d part, 23[251] days,| | | | |
beginning with day |7 Muluc |7 Imix |7 Ben |7 Chicchan|7 Caban
| | | | |
Total number of days |52 |52 |52 |52 |52
----------------------+----------+---------+---------+----------+--------

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 {266} 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_.

{267} The student will note the absence of all period glyphs from this Initial Series and will observe that the multiplicands of the cycle, katun, tun, uinal, and kin are fixed by the positions of each of the corresponding multipliers. By referring to Table XIV the values of the several positions in the second method of writing the numbers will be found, and using these with their corresponding coefficients in each case the Initial-series number here recorded may be reduced to units of the 1st order, as follows:

9 × 144,000 = 1,296,000
9 × 7,200 = 64,800
16 × 360 = 5,760
0 × 20 = 0
0 × 1 = 0
----------
1,366,560

Deducting from this number all the Calendar Rounds possible, 72 (see Table XVI), it may be reduced to zero, since 72 Calendar Rounds contain exactly 1,366,560 units of the first order. See the preliminary rule on page 143.

Applying rules 1, 2, and 3 (pp. 139, 140, and 141) to the remainder, that is, 0, the terminal date of the Initial Series will be found to be 4 Ahau 8 Cumhu, exactly the same as the starting point of Maya chronology. This must be true, since counting forward 0 from the date 4 Ahau 8 Cumhu, the date 4 Ahau 8 Cumhu will be reached. Instead of recording this date immediately below the last period of its Initial-series number, that is, the 0 kins, it was written below the number just to the left. The terminal date of the Initial Series we are discussing, therefore, is 4 Ahau 8 Cumhu, and it is recorded just to the left of its usual position in the lower left-hand corner of plate 31. The coefficient of the day sign, 4, is effaced but the remaining parts of the date are perfectly clear. Compare the day sign Ahau with the corresponding form in figure 17, _c', d'_, and the month sign Cumhu with the corresponding form in figure 20, _z-b'_. The Initial Series here recorded is therefore 9.9.16.0.0 4 Ahau 8 Cumhu. Just to the right of this Initial Series is another, the number part of which the student will readily read as follows: 9.9.9.16.0. Treating this in the usual way, it may be reduced thus:

9 × 144,000 = 1,296,000
9 × 7,200 = 64,800
9 × 360 = 3,240
16 × 20 = 320
0 × 1 = 0
----------
1,364,360

Deducting from this number all the Calendar Rounds possible, 71 (see Table XVI), it may be reduced to 16,780. Applying to this number rules 1, 2, and 3 (pp. 139, 140, and 141, respectively), its terminal date will be found to be 1 Ahau 18 Kayab; this date is recorded just to the left below the kin place of the _preceding_ Initial {268} Series. Compare the day sign and month sign of this date with figures 17, _c', d'_, and 20, _x, y_, respectively. This second Initial Series in plate 31 therefore reads 9.9.9.16.0 1 Ahau 18 Kayab. In connection with the first of these two Initial Series, 9.9.16.0.0 4 Ahau 8 Cumhu, there is recorded a Secondary Series. This consists of 6 tuns, 2 uinals, and 0 kins (6.2.0) and is recorded just to the left of the first Initial Series from which it is counted, that is, in the left-hand column.

It was explained on pages 136-137 that the almost universal direction of counting was forward, but that when the count was backward in the codices, this fact was indicated by a special sign or symbol, which gave to the number it modified the significance of "backward" or "minus." This sign is shown in figure 64, and, as explained on page 137, it usually is attached only to the lowest period. Returning once more to our text, in plate 31 we see this "backward" sign--a red circle surmounted by a knot--surrounding the 0 kins of this Secondary-series number 6.2.0, and we are to conclude, therefore, that this number is to be counted backward from some date.

Counting it backward from the date which stands nearest it in our text, 4 Ahau 8 Cumhu, the date reached will be 1 Ahau 18 Kayab. But since the date 4 Ahau 8 Cumhu is stated in the text to have corresponded with the Initial-series value 9.9.16.0.0, by deducting 6.2.0 from this number we may work out the Initial-series value for this date as follows:

9.9.16. 0.0 4 Ahau 8 Cumhu
6. 2.0 Backward
9.9. 9.16.0 1 Ahau 18 Kayab

The accuracy of this last calculation is established by the fact that the Initial-series value 9.9.9.16.0 is recorded as the second Initial Series on the page above described, and corresponds to the date 1 Ahau 18 Kayab as here.

It is difficult to say why the terminal dates of these two Initial Series and this Secondary Series should have been recorded to the _left_ of the numbers leading to them, and not just _below_ the numbers in each case. The only explanation the writer can offer is that the ancient scribe wished to have the starting point of his Secondary-series number, 4 Ahau 8 Cumhu, recorded as near that number as possible, that is, just below it, and consequently the Initial Series leading to this date had to stand to the right. This caused a displacement of the corresponding terminal date of his Secondary Series, 1 Ahau 18 Kayab, which was written under the Initial Series 9.9.16.0.0; and since the Initial-series value of 1 Ahau 18 Kayab also appears to the right of 9.9.16.0.0 as 9.9.9.16.0, this causes a displacement in its terminal date likewise. {269}

Two other Initial Series will suffice to exemplify this kind of count in the codices. In plate 32 is figured page 62 from the Dresden Codex. In the two right-hand columns appear two black numbers. The first of these reads quite clearly 8.16.15.16.1, which the student is perfectly justified in assuming is an Initial-series number consisting of 8 cycles, 16 katuns, 15 tuns, 16 uinals, and 1 kin. Moreover, above the 8 cycles is a glyph which bears considerable resemblance to the Initial-series introducing glyph (see fig. 24, _f_). Note in particular the trinal superfix. At all events, whether it is an Initial Series or not, the first step in deciphering it will be to reduce this number to units of the first order:

8 × 144,000 = 1,152,000
16 × 7,200 = 115,200
15 × 360 = 5,400
16 × 20 = 320
1 × 1 = 1
----------
1,272,921

Deducting from this number all the Calendar Rounds possible, 67 (see Table XVI), it may be reduced to 1,261. Applying rules 1, 2, and 3 (pp. 139, 140, and 141, respectively) to this remainder, the terminal date reached will be 4 Imix 9 Mol. This is not the terminal date recorded, however, nor is it the terminal date standing below the next Initial-series number to the right, 8.16.14.15.4. It would seem then that there must be some mistake or unusual feature about this Initial Series.

Immediately below the date which stands under the Initial-series number we are considering, 8.16.15.16.1, is another number consisting of 1 tun, 4 uinals, and 16 kins (1.4.16). It is not improbable that this is a Secondary-series number connected in some way with our Initial Series. The red circle surmounted by a knot which surrounds the 16 kins of this Secondary-series number (1.4.16) indicates that the whole number is to be counted _backward_ from some date. Ordinarily, the first Secondary Series in a text is to be counted from the terminal date of the Initial Series, which we have found by calculation (if not by record) to be 4 Imix 9 Mol in this case. Assuming that this is the case here, we might count 1.4.16 _backward_ from the date 4 Imix 9 Mol.

Performing all the operations indicated in such cases, the terminal date reached will be found to be 3 Chicchan 18 Zip; this is very close to the date which is actually recorded just above the Secondary-series number and just below the Initial-series number. The date here recorded is 3 Chicchan 13 Zip, and it is not improbable that the {270} ancient scribe intended to write instead 3 Chicchan 18 Zip, the date indicated by the calculations. We probably have here:

8.16.15.16. 1 (4 Imix 9 Mol)
1. 4.16 Backward
8.16.14.11. 5 3 Chicchan 18[252] Zip

In these calculations the terminal date of the Initial Series, 4 Imix 9 Mol, is suppressed, and the only date given is 3 Chicchan 18 Zip, the terminal date of the Secondary Series.

Another Initial Series of this same kind, one in which the terminal date is not recorded, is shown just to the right of the preceding in plate 32. The Initial-series number 8.16.14.15.4 there recorded reduces to units of the first order as follows:

8 × 144,000 = 1,152,000
16 × 7,200 = 115,200
14 × 360 = 5,040
15 × 20 = 300
4 × 1 = 4
----------
1,272,544

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An Introduction to the Study of the Maya HieroglyphsChapter VI: The Codices (1)

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