Plate 25CALENDAR-ROUND DATES ON ALTAR 5, TIKAL
CALENDAR-ROUND DATES ON ALTAR 5, TIKAL
Counting this number forward from4 Ahau 13 Yax, the nearest date to it in the text, the terminal date reached will be found to be6 Ahau 18 Zac, the date which, we have seen, was recorded in A3b B3. It is clear, therefore, that this text records the fact that 3.2.0 has been counted forward from the date4 Ahau 13 Yaxand the date6 Ahau 18 Zachas been reached, but there is nothing given by means of which the position of either of these dates in the Long Count can be determined; consequently either of these dates will be found recurring like any other Calendar-round date, at intervals of every 52 years. In such cases the first assumption to be made is that one of the dates recorded the close of a hotun, or at least of a tun, in Cycle 9 of the Long Count. The reasons for this assumption are quite obvious.
Fig. 83Fig. 83. Calendar-round dates:A, Altar M, Quirigua;B, Altar Z, Copan.
Fig. 83. Calendar-round dates:A, Altar M, Quirigua;B, Altar Z, Copan.
The overwhelming majority of Maya dates fall in Cycle 9, and nearly all inscriptions have at least one date which closed some hotun or tun of that cycle. Referring to Goodman's Tables, in which the tun endings of Cycle 9 are given, the student will find that the date4 Ahau 13 Yaxoccurred as a tun ending in Cycle 9, at 9.15.0.0.04 Ahau 13 Yax, in which position it closed not only a hotun but also a katun. Hence, it is probable, although the fact is not actually recorded, that the Initial-series value of the date4 Ahau 13 Yaxin this text is 9.15.0.0.04 Ahau 13 Yax, and if this is so the Initial-series value of the date6 Ahau 18 Zacwill be:
In the case of this particular text the Initial-series value 9.15.0.0.0 might have been assigned to the date4 Ahau 13 Yaxon the ground that this Initial-series value appears on two other monuments at Quirigua, namely, Stelæ E and F, with this same date.
In figure83,B, is shown a part of the inscription from Altar Z at Copan.[234]In A1 B1 appears a number consisting of 1 kin, 8 uinals, and 1 tun, that is, 1.8.1, and following this in B2-A3 is the date13 Ahau 18 Cumhu, but no record of its position in the Long Count. If13 Ahau 18 Cumhuis the terminal date of the number 1.8.1, the starting point can be calculated by counting this number backward, giving the date12 Cauac 2 Zac. On the other hand, if13 Ahau 18 Cumhuis the starting point, the terminal date reached by counting 1.8.1 forward will be1 Imix 9 Mol. However, since an ending prefix appears just before the date13 Ahau 18 Cumhuin A2 (compare fig.37,a-h), and since another, though it must be admitted a very unusual ending sign, appears just after this date in A3 (compare the prefix of B3 with the prefix of fig.37,o, and the subfix with the subfixes ofl-nandqof the same figure), it seems probable that13 Ahau 18 Cumhuis the terminal date and also a Period-ending date. Referring to Goodman's Tables, it will be found that the only tun in Cycle 9 which ended with the date13 Ahau 18 Cumhuwas 9.17.0.0.013 Ahau 18 Cumhu, which not only ended a hotun but a katun as well.[235]If this is true, the unrecorded starting point12 Cauac 2 Zaccan be shown to have the following Initial-series value:
In each of the above examples, as we have seen, there was a date which ended one of the katuns of Cycle 9, although this fact was not recorded in connection with either. Because of this fact, however, we were able to date both of these monuments with a degree of probability amounting almost to certainty. In some texts the student will find that the dates recorded did not end any katun, hotun, or even tun, in Cycle 9, or in any other cycle, and consequently such dates can not be assigned to their proper positions in the Long Count by the above method.
The inscription from Altar 5 at Tikal figured in plate25is a case in point. This text opens with the date1 Muluc 2 Muanin glyphs 1 and 2 (the first glyph or starting point is indicated by the star).Compare glyph 1 with figure16,m,n, and glyph 2 with figure19,a', b'. In glyphs 8 and 9 appears a Secondary-series number consisting of 18 kins, 11 uinals, and 11 tuns (11.11.18). Reducing this number to units of the first order and counting it forward from the date next preceding it in the text,1 Muluc 2 Muanin glyphs 1 and 2, the terminal date reached will be13 Manik 0 Xul, which the student will find recorded in glyphs 10 and 11. Compare glyph 10 with figure16,j, and glyph 11 with figure19,i, j. The next Secondary-series number appears in glyphs 22 and 23, and consists of 19 kins, 9 uinals, and 8 tuns (8.9.19). Reducing this to units of the first order and counting forward from the date next preceding it in the text,13 Manik 0 Xulin glyphs 10 and 11, the terminal date reached will be11 Cimi 19 Mac, which the student will find recorded in glyphs 24 and 25. Compare glyph 24 with figure16,h, i, and glyph 25 with figure19,w,x. Although no number appears in glyph 26, there follows in glyphs 27 and 28 the date1 Muluc 2 Kankin, which the student will find is just three days later than11 Cimi 19 Mac, that is, one day12 Manik 0 Kankin, two days13 Lamat 1 Kankin, and three days1 Muluc 2 Kankin.
In spite of the fact that all these numbers are counted regularly from the dates next preceding them to reach the dates next following them, there is apparently no glyph in this text which will fix the position of any one of the above dates in the Long Count. Moreover, since none of the day parts show the day signAhau, it is evident that none of these dates can end any uinal, tun, katun, or cycle in the Long Count, hence their positions can not be determined by the method used in fixing the dates in figure83,AandB.
There is, however, another method by means of which Calendar-round dates may sometimes be referred to their proper positions in the Long Count. A monument which shows only Calendar-round dates may be associated with another monument or a building, the dates of which are fixed in the Long Count. In such cases the fixed dates usually will show the positions to which the Calendar-round dates are to be referred.
Taking any one of the dates given on Altar 5 in plate25, as the last,1 Muluc 2 Kankin, for example, the positions at which this date occurred in Cycle 9 may be determined from Goodman's Tables to be as follows:
Next let us ascertain whether or not Altar 5 was associated with any other monument or building at Tikal, the date of which is fixed unmistakably in the Long Count. Says Mr. Teobert Maler, the discoverer of this monument:[236]"A little to the north, fronting the north side of this second temple and very near it, is a masonry quadrangle once, no doubt, containing small chambers and having an entrance to the south. In the middle of this quadrangle stands Stela 16 in all its glory, still unharmed,and in front of it, deeply buried in the earth, we found Circular Altar 5, which was destined to become so widely renowned." It is evident from the foregoing that the altar we are considering here, called by Mr. Maler "Circular Altar 5," was found in connection with another monument at Tikal, namely, Stela 16. But the date on this latter monument has already been deciphered as "6 Ahau 13 Muanending Katun 14" (see pl.21,D; also p.224), and this date, as we have seen, corresponded to the Initial Series 9.14.0.0.06 Ahau 13 Muan.
Our next step is to ascertain whether or not any of the Initial-series values determined above as belonging to the date1 Muluc 2 Kankinon Altar 5 are near the Initial Series 9.14.0.0.06 Ahau 13 Muan, which is the Initial-series date corresponding to the Period-ending date on Stela16. By comparing 9.14.0.0.0 with the Initial-series values of1 Muluc 2 Kankingiven above the student will find that the fifth value, 9.13.19.16.9, corresponds with a date1 Muluc 2 Kankin, which was only 31 days (1 uinal and 11 kins) earlier than 9.14.0.0.06 Ahau 13 Muan. Consequently it may be concluded that 9.13.19.16.9 was the particular day1 Muluc 2 Kankinwhich the ancient scribes had in mind when they engraved this text. From this known Initial-series value the Initial-series values of the other dates on Altar 5 may be obtained by calculation. The texts on Altar 5 and Stela 16 are given below to show their close connection:
Sometimes, however, monuments showing Calendar-round dates standalone, and in such cases it is almost impossible to fix their dates in the Long Count. At Yaxchilan in particular Calendar-round dating seems to have been extensively employed, and for this reason less progress has been made there than elsewhere in deciphering the inscriptions.
Errors in the Originals
Before closing the presentation of the subject of the Maya inscriptions the writer has thought it best to insert a few texts which show actual errors in the originals, mistakes due to the carelessness or oversight of the ancient scribes.
Fig. 84Fig.84. Texts showing actual errors in the originals:A, Lintel, Yaxchilan;B, Altar Q, Copan;C, Stela 23, Naranjo.
Fig.84. Texts showing actual errors in the originals:A, Lintel, Yaxchilan;B, Altar Q, Copan;C, Stela 23, Naranjo.
Errors in the original texts may be divided into two general classes: (1) Those which are revealed by inspection, and (2) those which do not appear until after the indicated calculations have been made and the results fail to agree with the glyphs recorded.
An example of the first class is illustrated in figure84,A. A very cursory inspection of this text—an Initial Series from a lintel at Yaxchilan—will show that the uinal coefficient in C1 represents an impossible condition from the Maya point of view. This glyph as it standsunmistakably records 19 uinals, a number which had no existence in the Maya system of numeration, since 19 uinals are always recorded as 1 tun and 1 uinal.[237]Therefore the coefficient in C1 is incorrect on its face, a fact we have been able to determine before proceeding with the calculation indicated. If not 19, what then was the coefficient the ancient scribe should have engraved in its place? Fortunately the rest of this text is unusually clear, the Initial-series number 9.15.6.?.1 appearing in B1-D1, and the terminal date which it reaches,7 Imix 19 Zip, appearing in C2 D2. Compare C2 with figure16,a, b, and D2 with figure19,d. We know to begin with that the uinal coefficient must be one of the eighteen numerals 0 to 17, inclusive. Trying 0 first, the number will be 9.15.6.0.1, which the student will find leads to the date7 Imix 4 Chen. Our first trial, therefore, has proved unsuccessful, since the date recorded is7 Imix 19 Zip. The day parts agree, but the month parts are not the same. This month part4 Chenis useful, however, for one thing, it shows us how far distant we are from the month part19 Zip, which is recorded. It appears from TableXVthat in counting forward from position4 Chenjust 260 days are required to reach position19 Zip. Consequently, our first trial number 9.15.6.0.1 falls short of the number necessary by just 260 days. But 260 days are equal to 13 uinals; therefore we must increase 9.15.6.0.1 by 13 uinals. This gives us the number 9.15.6.13.1. Reducing this to units of the first order and solving for the terminal date, the date reached will be7 Imix 19 Zip, which agrees with the date recorded, in C2 D2. We may conclude, therefore, that the uinal coefficient in C1 should have been 13, instead of 19 as recorded.
Another error of the same kind—that is, one which may be detected by inspection—is shown in figure84,B. Passing over glyphs 1, 2, and 3, we reach in glyph 4 the date5 Kan 13 Uo. Compare the upper half of 4 with figure16,f, and the lower half with figure19,b, c. The coefficient of the month sign is very clearly 13, which represents an impossible condition when used to indicate the position of a day whose name isKan; for, according to TableVII, the only positions which the dayKancan ever occupy in any division of the year are 2, 7, 12, and 17. Hence, it is evident that we have detected an error in this text before proceeding with the calculations indicated. Let us endeavor to ascertain the coefficient which should have been used with the month sign in glyph 4 instead of the 13 actually recorded. These glyphs present seemingly a regular Secondary Series, the starting point being given in 1 and 2, the number in 3, and the terminal date in 4. Counting this number 3.4 forward from the starting point,6 Ahau 13 Kayab, the terminal date reached will be5 Kan 12 Uo. Comparing this with the terminal date actually recorded, we find that the two agree except for the month coefficient. But since the date recorded represents an impossible condition, as wehave shown, we are justified in assuming that the month coefficient which should have been used in glyph 4 was 12, instead of 13. In other words, the craftsman to whom the sculpturing of this inscription was intrusted engraved here 3 dots instead of 2 dots, and 1 ornamental crescent, which, together with the 2 bars present, would have given the month coefficient determined by calculation, 12. An error of this kind might occur very easily and indeed in many cases may be apparent rather than real, being due to weathering rather than to a mistake in the original text.
Some errors in the inscriptions, however, can not be detected by inspection, and develop only after the calculations indicated have been performed, and the results are found to disagree with the glyphs recorded. Errors of this kind constitute the second class mentioned above. A case in point is the Initial Series on the west side of Stela E at Quirigua, figured in plate24,A. In this text the Initial-series number recorded in A4-A6 is very clearly 9.14.12.4.17, and the terminal date in B6-B8b is equally clearly12 Caban 5 Kayab. Now, if this number 9.14.12.4.17 is reduced to units of the first order and is counted forward from the same starting point as practically all other Initial Series, the terminal date reached will be3 Caban 10 Kayab, not12 Caban 5 Kayab, as recorded. Moreover, if the same number is counted forward from the date4 Ahau 8 Zotz, which may have been another starting point for Initial Series, as we have seen, the terminal date reached will be3 Caban 10 Zip, not12 Caban 5 Kayab, as recorded. The inference is obvious, therefore, that there is some error in this text, since the number recorded can not be made to reach the date recorded. An error of this kind is difficult to detect, because there is no indication in the text as to which glyph is the one at fault. The first assumption the writer makes in such cases is that the date is correct and that the error is in one of the period-glyph coefficients. Referring to Goodman's Table, it will be found that the date12 Caban 5 Kayaboccurred at the following positions in Cycle 9 of the Long Count:
An examination of these values will show that the sixth in the list, 9.14.13.4.17, is very close to the number recorded in our text, 9.14.12.4.17. Indeed, the only difference between the two is that the former has 13 tuns while the latter has only 12. The similarity between these two numbers is otherwise so close and the error in thisevent would be so slight—the record of 2 dots and 1 ornamental crescent instead of 3 dots—that the conclusion is almost inevitable that the error here is in the tun coefficient, 12 having been recorded instead of 13. In this particular case the Secondary Series and the Period-ending date, which follow the Initial-series number 9.14.12.4.17, prove that the above reading of 13 tuns for the 12 actually recorded is the one correction needed to rectify the error in this text.
Another example indicating an error which can not be detected by inspection is shown in figure84,C. In glyphs 1 and 2 appears the date8 Eznab 16 Uo(compare glyph 1 with fig.16,c', and glyph 2 with fig.19,b, c). In glyph 3 follows a number consisting of 17 kins and 4 uinals (4.17). Finally, in glyphs 4 and 5 is recorded the date2 Men 13 Yaxkin(compare glyph 4 with fig.16,y, and glyph 5 with fig.19,k, l). This has every appearance of being a Secondary Series, of which8 Eznab 16 Uois the starting point, 4.17, the number to be counted, and2 Men 13 Yaxkinthe terminal date. Reducing 4.17 to units of the first order and counting it forward from the starting point indicated, the terminal date reached will be1 Men 13 Yaxkin. This differs from the terminal date recorded in glyphs 4 and 5 in having a day coefficient of 1 instead of 2. Since this involves but a very slight change in the original text, we are probably justified in assuming; that the day coefficient in glyph 4 should have been 1 instead of 2 as recorded.
One more example will suffice to show the kind of errors usually encountered in the inscriptions. In plate26is figured the Initial Series from Stela N at Copan. The introducing glyph appears in A1 and is followed by the Initial-series number 9.16.10.0.0 in A2-A6, all the coefficients of which are unusually clear. Reducing this to units of the first order and solving for the terminal date, the date reached will be1 Ahau 3 Zip. This agrees with the terminal date recorded in A7-A15 except for the month coefficient, which is 8 in the text instead of 3, as determined by calculation. Assuming that the date recorded is correct and that the error is in the coefficient of the period glyphs the next step is to find the positions in Cycle 9 at which the date1 Ahau 8 Zip occurred. Referring to Goodman's Tables, these will be found to be:
BUREAU OF AMERICAN ETHNOLOGYBULLETIN 57 PLATE 26
Plate 26INITIAL SERIES ON STELA N, COPAN, SHOWING ERROR IN MONTH COEFFICIENT
INITIAL SERIES ON STELA N, COPAN, SHOWING ERROR IN MONTH COEFFICIENT
The number in the above list coming nearest to the number recorded in this text (9.16.10.0.0) is the next to the last, 9.16.4.17.0. But in order to reach this value of the date1 Ahau 8 Zip(9.16.4.17.0) with the number actually recorded, two considerable changes in it are first necessary, (1) replacing the 10 tuns in A4 by 4 tuns, that is, changing 2 bars to 4 dots, and (2) replacing 0 uinals in A5 by 17 uinals, that is, changing the 0 sign to 3 bars and 2 dots. But these changes involve a very considerable alteration of the original, and it seems highly improbable, therefore, that the date hereintendedwas 9.16.4.17.01 Ahau 8 Zip. Moreover, as any other number in the above list involves at least three changes of the number recorded in order to reach1 Ahau 8 Zip, we are forced to the conclusion that the error must be in the terminal date, not in one of the coefficients of the period glyphs. Let us therefore assume in our next trial that the Initial-series number is correct as it stands, and that the error lies somewhere in the terminal date. But the terminal date reached in counting 9.16.10.0.0 forward in the Long Count will be1 Ahau 3 Zip, as we have seen on the preceding page, and this date differs from the terminal date recorded by 5—1 bar in the month coefficient. It would seem probable, therefore, that the bar to the left of the month sign in A15 should have been omitted, in which case the text would correctly record the date 9.16.10.0.01 Ahau 3 Zip.
The student will note that in all the examples above given the errors have been in the numerical coefficients, and not in the signs to which they are attached; in other words, that although the numerals are sometimes incorrectly recorded, the period, day, and month glyphs never are.
Throughout the inscriptions, the exceptions to this rule are so very rare that the beginner is strongly advised to disregard them altogether, and to assume when he finds an incorrect text that the error is in one of the numerical coefficients. It should be remembered also in this connection that errors in the inscriptions are exceedingly rare, and a glyph must not be condemned as incorrect until every effort has been made to explain it in some other way.
This concludes the presentation of texts from the inscriptions. The student will have noted in the foregoing examples, as was stated in Chapter II, that practically the only advances made looking toward the decipherment of the glyphs have been on the chronological side. It is now generally admitted that the relative ages[238]of most Maya monuments can be determined from the dates recorded upon them, and that the final date in almost every inscription indicates the time at or near which the monument bearing it was erected, or at least formally dedicated. The writer has endeavored to show, moreover,that many, if indeed not most, of the monuments, were "time markers" or "period stones," in every way similar to the "period stones" which the northern Maya are known to[239]have erected at regularly recurring periods. That the period which was used as this chronological unit may have varied in different localities and at different epochs is not at all improbable. The northern Maya at the time of the Spanish Conquest erected a "period stone" every katun, while the evidence presented in the foregoing texts, particularly those from Quirigua and Copan, indicates that the chronological unit in these two cities at least was the hotun, or quarter-katun period. Whatever may have been the chronological unit used, the writer believes that the best explanation for the monuments found so abundantly in the Maya area is that they were "period stones," erected to commemorate or mark the close of successive periods.
That we have succeeded in deciphering, up to the present time, only the calendric parts of the inscriptions, the chronological skeleton of Maya history as it were, stripped of the events which would vitalize it, should not discourage the student nor lead him to minimize the importance of that which is already gained. Thirty years ago the Maya inscriptions were a sealed book, yet to-day we read in the glyphic writing the rise and fall of the several cities in relation to one another, and follow the course of Maya development even though we can not yet fill in the accompanying background. Future researches, we may hope, will reconstruct this background from the undeciphered glyphs, and will reveal the events of Maya history which alone can give the corresponding chronology a human interest.
Chapter VI
THE CODICES
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
Thetonalamatl, 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 usedoncewith 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 exclusivelytime 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; andthe coefficientof the day reached will be the second red number in the text. As stated above, theday signsof the beginning days of the subdivisions are always omitted. From the second red number, which, as we have seen, is thecoefficient of the beginning day of the secondsubdivisionof the first division, thesecond black numberis to be counted forward in order to reach the third red number, which is the coefficient of the day beginning thethird subdivisionof 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 thesecond day signin the column. And this latter day will be the beginning day of thesecond divisionof 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 withthe third day signin the column, forms the beginning day ofthe third divisionof 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 TableIthe black number from the day sign of the beginning day of the preceding division or subdivision, and the day name reached in TableIwill be the day sign desired. If it is at the beginning of one of themain divisionsof the tonalamatl, the day sign reached will be found to be recorded in the column of day signs, but if at the beginning of asubdivisionit 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.
In plate27is 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 designateda, b, andc, abeing applied to the upper part,bto the middle part, andcto 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 page251: (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 figure17will show that the day sign here recorded isIx(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 day1 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 signIx—is to be added to the red number immediately preceding it—in this case1—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 TableIthis same black number, 13, from the preceding day sign, in this caseIx. The day sign reached will beManik. But since this day begins only asubdivisionin this tonalamatl, not one of themain divisions, its day sign will not be recorded, and we have, therefore, the day1 Manik, of which the 1 is expressed by the second red number and the name partManikonly indicated by the calculations.
BUREAU OF AMERICAN ETHNOLOGYBULLETIN 57 PLATE 27