Qadar

“ The proper combination of these two, the tonalamatl, or "round of days," and the haab, or year of uinals, and the xma kaba kin, formed the Calendar Round, to which the tonalamatl contributed the names of the days and the haab the positions of these days in the divisions of the year. The Calendar Round was the most important period in Maya chronology, and a comprehension of its nature and of the principles which governed its composition is therefore absolutely essential to the understanding of the Maya system of counting time. ”

“ This method of describing a date may be called "dating by period endings." It was far less accurate than Initial-series or Secondary-series dating, since a date described as occurring at the end of a certain katun could recur after an interval of about 18,000 years in round numbers, as against 374,400 years in the other 2 methods. For all practical purposes, however, 18,000 years was as accurate as 374,400 years, since it far exceeds the range of time covered by the written records of mankind the world over. ”

“ The next or the 11 Ahau would commence in the year 10 Cauac, which combination in its rotation would happen after a lapse of twenty-four years. The third or 9 Ahau would begin in 8 Cauac twenty-four years later, in illustration of which we follow out the rotation of the four names of the years, Kan, Muluc, Ix and Cauac, through the indictions of thirteen years each, until we have noted the numerals accompanying them during twenty-four years. Our starting point will be the commencement of the second Ahau Katun on the second day of 10 Cauac. ”

“ The Calendar Round, as we have seen, determined the position of a given day within a period of only 52 years. Consequently, in order to prevent confusion of days of the same name in successive Calendar Rounds or, in other words, to secure absolute accuracy in dating events, it was necessary to use additional data in the description of any date.
In nearly all systems of chronology that presume to deal with really long periods the reckoning of years proceeds from fixed starting points. ”

“ Hence to reduce a date according to this era to our own reckoning, it is necessary, for common years, to add 283 years and 240 days; but if the date belongs to the first three months of the year following the intercalation, or, which is the same thing, if in the third year of the Julian cycle it falls between the 30th of August and the end of the year, we must add 283 years and 241 days. The Ethiopians do not reckon the years from the beginning of the era in a consecutive series, but employ a period of 532 years, after the expiration of which they again begin with 1. ”

“ INTRODUCTION. The ancient civilised peoples appear in history with a fully-developed system of time-reckoning—the Egyptians with the shifting year of 365 days, which comes as nearly as possible to the actual length of the year, counting only whole days and neglecting the additional fraction; the Babylonians and the Greeks with the lunisolar, varying between twelve and thirteen months and arranged by the Greeks from the earliest known period of history in the cycle of the Oktaeteris. ”

“ No one could have forgotten the number of the current cycle.
When we come to the next lower period, however, the katun, we find a different state of affairs. The numbers belonging to this period were changing every 20 (exactly, 19.71 +) years; that is, three or four times in the lifetime of many individuals; hence, there was plenty of opportunity for confusion about the number of the katun in which a particular event occurred. Consequently, in order to insure accuracy the katun is almost always the unit used in Period-ending dating. ”

“ All periods less than the day, as hours, minutes, and seconds, are referred to in terms of past time; and (2) the day and all greater periods are referred to in terms of current time.
The Maya seem to have used only the former of these two methods in counting time; that is, all the different periods recorded in the codices and the inscriptions seemingly refer to elapsed time rather than to current time, to a day passed, rather than to a day present. ”

“ In reckoning years from any fixed epoch in constant succession, the number denoting the years is necessarily always on the increase. But rude nations and illiterate people seldom attach any definite idea to large numbers. Hence it has been a practice, very extensively followed, to employ cycles or periods, consisting of a moderate number of years, and to distinguish and reckon the years by their number in the cycle. The Chinese and other nations of Asia reckon, not only the years, but also the months and days, by cycles of sixty. ”

“ It is possible that the days of one group indicate the year intended; that is, whether it is a Cauac, Kan, Muluc, or Ix year.
For example, column No. 4 (Table IV) , or some other, one of the four, may relate to Kan years; No. 1 to Muluc years; No. 2 to Ix years, and No. 3 to Cauac years. Assuming this to be correct, then the example heretofore given, where the days named are 1 Cib, 1 Ahau, 1 Kan, 1 Lamat, and 1 Eb, and the month the first (Pop) , would indicate only the years 7 Muluc, 3 Muluc, 12 Muluc, 8 Muluc, and 11 Muluc. These would all come in Ahau No. ”

“ The Kalends were invariably the first day of the month, and were so denominated because it had been an ancient custom of the pontiffs to call the people together on that day, to apprise them of the festivals, or days that were to be kept sacred during the month. The Ides (from an obsolete verb iduare, to divide) were at the middle of the month, either the 13th or the 15th day; and the Nones were the ninth day before the Ides, counting inclusively. ”

“ If the numbers hitherto examined refer to a time not very far from the present, we now come to numbers which lie in so remote a future that they can hardly suggest anything else than the destruction of the world or a sort of twilight of the gods. Nevertheless the starting-point of the whole, the series, which is built up with the number 91, i.e., the Bacab period or the quarter of a ritual year, continually comes to view. ”

“ A little careful study of this subject will suffice to convince any one at all acquainted with this calendar that by simply knowing the number and name of the last intercalated day of any year will be sufficient to enable him to determine what year of the cycle it is If he forgets the key he can easily find it by the continued subtraction of 4, commencing with 1 3, adding 1 3 when the number to be subtracted from is 4 or less than 4. The only thing necessary to be remembered is that the years Cauac, Kan, Muluc, Ix terminate, respectively, with the days Akbal, Lamat, Ben, and Ezanab. ”

“ Here there is one dot too many, which we may attribute to a mistake of the original artist. Assuming XII to be correct, 8 more bring us to 7 Chuen; 8 more to 2 Cauac; 8 more to 10 Manik; 8 more to 5 Men; 8 more to 13 Akbal, and to the end of our table; thus, if we include the first seventeen days, completing the series of thirteen months or 260 days.
These illustrations will probably satisfy any one that the black numerals in these lines denote the intervals between the days indicated by the symbols and that the series so far examined are to be read from left to right. ”

“ Although the month did not always commence with the same day, the order of the days as here given, to wit, Kan, Chicchan, Cimi, Manik, Lamat, Muluc, Oc, Chuen, Eb, Ben, Ix, Men, Cib, Caban, Ezanab, Cauac, Ahau, Ymix, Ik, Akbal, was always preserved. For example, if the month began with Muluc, the second day would be Oc, the third Chuen, and so on to Akbal; then followed Kan, just as we would name seven days commencing, say, with Wednesday, then Thursday, Friday, Saturday, Sunday, Monday, &c. ”

“ Dividing the given number by 20, we have: 9,663 ÷ 20 = 4833⁄20. Counting the numerator of the fractional part of this quotient, 3, backward from the day sign of the starting point, Imix, in Table I, we reach Eznab as the day sign of the terminal date (Ahau, Cauac, Eznab) ; consequently the day reached in the count will be 12 Eznab. Dividing the given number by 365, we have 9,663 ÷ 365 = 26173⁄365. Counting backward the numerator of the fractional part of this quotient, 173, from the year position of the starting point, 4 Uayeb, the year position of the terminal date will be found to be 11 Yax. ”

“ These groups, each consisting of twenty years, not only fall within the lines marking the Katunes, but come in regular succession, leaving four uncounted yeai's between each two periods—two belonging to one and two to that which follows. In other words, while the Katun or Ahau as a whole, according to the theory upon which I am now proceeding, always commenced with a Cauac year, the twenty "counted years" in the present example begin with a Muluc year. But, as appears from what has already been shown, this is not always true in regard to these periods, yet it is generally the case. ”

“ The mitzvah is for each individual to count for himself. One should count standing, and recite a blessing first. The days and weeks are counted. How? On the first day one says: "Today it is one day (in the Omer) ," until seven days are reached; then he says: "Today it is seven days that are one week (in the Omer) ." On the eighth day one says: "Today it is eight days that are one week and one day (in the Omer) ," and so on till fourteen days are reached. [Then] one says: "Today it is fourteen days that are two weeks (in the Omer) ." In this manner one goes on counting, up to forty-nine days. ”

“ Such confusion indeed is only to be expected from a system of counting time and recording events which was so loose as to permit the occurrence of the same date twice, or even thrice, within the span of a single life; and when a system so inexact was used to regulate the lapse of any considerable number of years, the possibilities for error and misunderstanding are infinite. ”

“ The beginning day in each case is the day Kan, which thereby indicates its position as the first.
2. The last three starting-points are the same; the first three end dates, at least, are the same in the Tonalamatl, though not in the year.
3. The two numbers 2b and 4b are exactly the same.
4. The first three numbers are each divisible without a remainder by 17, the interval from XIII Akbal to IV Ahau, which was true also of the 1,268,540 in the second column on page 63, although only this last number has anything to do with these important days, of which the other three numbers are independent. ”

“ As there are four different series of years in the Maya calendar, the Cauac years, Kan years, Muluc years, and Ix years, it is necessary that we have four different tables, similar to that given for the Cauac years, to represent them, or to combine all in one table. ”

“ Hence the expression “from Kaf to Kaf,” signifying from one extremity of the earth to the opposite. The mountain Kaf was further supposed to be the abode of spirits, fairies, and giants.
The Arabian lexicographers describe this mountain as being formed of emerald. In the Borhani-Kati, a valuable Persian Dictionary, we have the following description of it: “Kaf, the name of a famous mountain which surrounds the four quarters of the earth. They say that its altitude is five hundred farasangs (nearly two thousand English miles!) and for the most part the sea washes the base of it,” &c. ”

“ The former began at the autumnal equinox, the season at which they imagined the world was created; while the latter, by Divine appointment, commenced about six months earlier, the period when their fathers were delivered from the thraldom of Egypt. Their months always began with the new moon; and before the captivity they were merely named according to their order, the first, second, third, and so on down to the twelfth. ”

“ These documents are all dated in such and such a month of such and such a year of some king’s reign; the months are the same (at first under their earlier Accadian names [3] ) as those we [5] find in the almanacs translated by Epping and Strassmaier, and we meet in them, and in other historical inscriptions, with the intercalary months, the second Elul, and the second Adar. It would seem, then, that it was the same calendar, worked in the same way, that held its place through these two thousand years. ”

“ From 1,352,400 to 1,364,360 is 11,960 days, which period we have already found once on this page by computation. 11,960, however, is equal to 104 × 115 and 46 × 260, i.e., the Mercury revolution and the Tonalamatl combined. 11,960 is again equal to 32 × 365 + 280, and from the year 10 Kan to 3 Kan it is actually 32 years, and from the date 18 Zip to 18 Kayab it is, in fact, 280 days. The day I Ahau must be common to both dates. ”

“ For which reason the Greeks and the Jews insert three intercalary months every eight years. For 8 times 111⁄4 days make 3 months. The 475 years, therefore, contain 59 periods of 8 years and three months over: thus, the three intercalary months for every 8 years being added, we get 15 years, and these together with the 475 years make 70 weeks. Let no one now think us unskilled in the calculations of astronomy, when we fix without further ado the number of days at 3651⁄4. ”

“ The interval between 5 Kan and 7 Ahau is 11 months, 16 days, which, added to the preceding, gives 2 years, 5 months, 0 day, agreeing with the figures under 7 Ahau, if the symbol represented by 0 signifies nought. That this rule holds good throughout the entire series, by making one correction, is shown by the following additions:
The proof of the correctness of the theory advanced may, therefore, be considered conclusive, as it amounts, in fact, to a mathematical demonstration. ”