Glass. 
 Book. 
 
 F\A5S 
 
 ^\A*.>-A>V.w''»-Ar'»^-v-<u,*;!^ 
 
MAYAN NOMENCLATURE 
 
 BY «««_. 
 
 CHARLES P. BOWDITCH 
 
 Privately Printed 
 
 CAMBRIDGE 
 
 THE UNIVERSITY PRESS 
 
 1906 
 
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 In 
 
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MAYAN NOMENCLATURE 
 
 By CHARLES P. BOWDITCH 
 
 It has long been well known that the Mexican numeration is 
 vigesimal, and, as far as I know, there is no proof that it was ever 
 used in the calculation of long reaches of time. The Cakchiquel 
 numeration is also vigesimal, and Brinton states (Maya Chronicles, 
 p. 44) that the Maya numeration is also vigesimal, giving 
 
 20 units = one kal =20 
 
 20 kal = one bak = 400 
 
 20 bak = one pic = 8000 
 
 20 pic = one calab = 160000, etc. 
 
 But this Maya system is never used in connection with days. 
 Wherever a long number of days is referred to, we find invariably 
 the following system in use : 
 
 20 units = one of the second term 
 
 18 of the second term = one of the third term 
 20 of the third term = one of the fourth term 
 20 of^the fourth term = one of the fifth term. 
 
 And this system is, as far as we know, used for nothing else but 
 for reckoning days. The only difference between the first system 
 and the second is that in the first system twenty of the second 
 term equal one of the third, while in the second system eighteen 
 of the second equal one of the third. This difference is, of course, 
 essential, and it seems most probable that the change was intro- 
 duced in order to bring the third term as near the length of the 
 year as possible, and to conform the day numeration to the num- 
 ber of days and months in the year. 
 
 Professor 'Cyrus Thomas is unwilling to see in this anything 
 more than the counters by which to count the days, and denies to 
 it the name of a calendar; but as the system of day numeration is 
 
2 MAYAN NOMENCLATURE 
 
 different from the usual system, and is used only for counting days, 
 and as this system counts forward in almost every case in the in- 
 scriptions, and in a majority of cases in the Dresden Codex, from a 
 fixed date, 4 Ahau 8 Cumhu, it seems impossible to see any differ- 
 ence between it and a calendar system. 
 
 It was certainly to be hoped that the designations which Dr. 
 Seler gave to these Maya periods of time in his " Die Monumente 
 von Copan, etc.," ^ would have been accepted by Americanists, 
 especially since very good reasons were given by Seler for their 
 adoption. But this view does not meet the approval of Dr. Forste- 
 mann or Dr. Thomas. The latter in his " Maya Calendar, Part II.," 
 published in the " Report of the Bureau of American Ethnology," 
 still calls the period of 20 days a chuen and that of 360 days an 
 ahau, while the former in his article on " Die Lage der Ahaus bei 
 den Mayas," published in Part I. of the 1904 issue of the " Zeit- 
 schrift fur Ethnologic," makes the following statement : " The 
 katun has also been supposed to be 24 X 365 = 8760 days long 
 (and I held this view for a long time), indeed the long period of 
 52 X 365 = 18,980 days is also occasionally designated with the 
 word, while the sixth multiple of this member or 113,800 is called 
 an ahaukatun." He uses the terms " day," " uinal," and " ahau " 
 for the periods of i, 20, and 7200 days respectively. 
 
 Such statements from such learned scholars must attract atten- 
 tion, especially as it is not the first time that they have made 
 similar statements. If they give a correct statement of facts, it 
 shows that the system of the Maya numeration or calendar was in 
 a woful condition, as far as its nomenclature was concerned. It 
 will be well, therefore, to take up this question of nomenclature 
 anew. In all matters of this kind it is wise, while giving due value 
 to the views of later writers, to place the most dependence for the 
 solution of such questions upon contemporary or nearly con- 
 temporary evidence. 
 
 1 See Seler, " Gesammelte Abhandlungen zur Amerikanischen Sprach- und 
 Alterthumskunde," Vol. I. p. 722. 
 
MA VAN NOMENCLA TURE 3 
 
 And where is such evidence to be found ? Though there are 
 several Spanish writers who hved in the sixteenth century who 
 have written on the Nahuas, Bishop Landa is the earliest Spanish 
 authority who has dealt with Maya customs and history. And the 
 only Maya authorities of an early date that the student has access 
 to are the papers contained in Brinton's Maya Chronicles, the 
 principal of which are the Books of Chilan Balam, which Dr. 
 Brinton declares " to constitute about all that remains to us . . . 
 of the ancient history of the peninsula " as far as he knows. Yet, 
 in making objection to certain views of Dr. Seler, Dr. Forstemann 
 says, " It is based on certain statements in the Books of Chilan 
 Balam, a very dubious source according to Seler's own assertion." 
 I am at a loss to know why such sweeping condemnation should 
 be made of these books, for though the copies from which Dr. 
 Brinton quotes may not be very old, these copies hand down to us 
 records which must be of very great age. Dr. Forstemann him- 
 self quotes from them with approval, and it is certain that whatever 
 may be their historical value, the evidence which they give inci- 
 dentally cannot fail to be of great value. This evidence will, I 
 think, prove — 
 
 First, that the period of 20 times 360 days was called a katun 
 and not an ahau. 
 
 Second, that each of the constituent parts of a katun was called 
 a tun. 
 
 Third, that no such period of time as an ahaukatun is men- 
 tioned in the Books of Chilan Balam. 
 
 The first assertion may seem difficult to prove when in far the 
 larger number of cases where a separate katun is mentioned in the 
 Books of Chilan Balam the word " ahau " seems to be substituted 
 for " katun." This is true in all five of the Books of Chilan Balam 
 published by Brinton. But the reason of this is very evident, for 
 it will be seen by a careful perusal that the word " ahaus " is never 
 used when katuns in general are spoken of, and that whenever the 
 word " ahau " is apparently given as a synonym of " katun," it is 
 
4 MAYAN NOMENCLATURE 
 
 merely the name of a particular katun and it always has a number 
 attached to it and this number is the number of the day ahau with 
 which a given katun ended. Further, this number is never an 
 ordinal number, as translated by Brinton, but a cardinal number. 
 Therefore i, 2, 3, 4, 5, 6, etc. should be substituted in Brinton's 
 translation for ist, 2d, 3d, 4th, 5th, 6th, etc., and in the quotations 
 from Brinton this substitution is made. 
 
 It may be here stated that the inscriptions all show that where 
 an even uinal is given (and therefore where an even tun, katun, or 
 cycle is given) the day is Ahau. If then it was desirable to dis- 
 tinguish the katuns from each other, two methods could be used : 
 either count them numerically, i, 2, 3, 4, etc., or name them from 
 the day Ahau with which the preceding katun had ended. The 
 former method is found in the inscriptions and the Dresden Codex, 
 the latter in the Books of Chilan Balam. The second method 
 would not be possible if each katun ended with the same numbered 
 ahau. But 7200 is not divisible by 13, .without a remainder, but 
 equals 13 X 553 + ii. If then a particular katun ended with 13 
 Ahau, the next would end with Ahau, but the number attached to 
 Ahau would be 13 + 11, or, deducting thirteens, 11. The next 
 katun would end with 9, the next with 7, and so on. The katuns 
 then would be known as katuns, 13 Ahau, 11 Ahau, 9 Ahau, 
 7 Ahau, 5 Ahau, 3 Ahau, i Ahau, 12 Ahau, 10 Ahau, 8 Ahau, 
 6 Ahau, 4 Ahau, 2 Ahau, 13 Ahau, etc. 
 
 Taking up, therefore, No. I. of the Books of Chilan Balam, pub- 
 lished by Brinton — that of Mani — we find in the paragraph num- 
 bered I by Brinton " This is the arrangement of the katuns " not 
 " of the ahaus," and in paragraph numbered 2 " Four katuns had 
 passed, etc." not " four ahaus." This is followed by the statement 
 " When they set out for this country, it was Ahau 8," not " the 8th 
 Ahau." And then follows " 6 Ahau, 4 Ahau, 2 Ahau, fourscore 
 years and one year, for it was Tun i, 13 Ahaii when, etc." That 
 6 Ahau, 4 Ahau, 2 Ahau refer to the katuns is very clear, and that 
 4 katuns with the names 8 Ahau, 6 Ahau, 4 Ahau, and 2 Ahau are 
 
MAYAN NOMENCLATURE 
 
 5 
 
 called fourscore years is equally clear. In paragraph 4 we have 
 "4 Ahau, 2 Ahau, 13 Ahau — threescore years they ruled Ziyan 
 caan, etc." Here three katuns are called threescore years. 
 
 This would seem to show that the katuns called 4 Ahau, 2 
 Ahau, 13 Ahau, were each equal to a score of years of 365 days 
 each. When, however, we try to account for the numbering of the 
 katuns on this basis, we find that the numbers of the ahaus ending 
 each katun would come in the following order: 11 . 5 . 12 . 6 . 13 . 
 7. I. 8. 2. 9. 3. 10. 4. II, etc., while the real order is given in the 
 books as II .9.7. 5 .3 . I . 12. 10.8.6.4.2. 13 , etc. If the word 
 "haab" or the Spanish "anos,"^ which occurs in paragraph 3, is 
 taken literally, there would seem to be no explanation of this 
 difficulty ; but if we consider that these books used these words as 
 we often use them now as meaning approximately "years," and if 
 we substitute the third term of the numeral series as found in the 
 codices for the word " years " — in other words, if we substitute 360 
 for 365 — we find then that the katuns or scores of 360 days will 
 end with a day Ahau with the numbers 11. 9. 7. 5. 3.1. 12. 10, 
 etc., as has been said and as given in the Books of Chilan Balam. 
 This has been shown by Seler, Goodman, and others. 
 
 It will then be a good working theory that the score of 360 
 days is called a katun, and that each katun is distinguished by the 
 name of an ahau with its proper number, with which a katun 
 ended. That the ahau and its number are merely the name of the 
 katun and not the katun itself is shown in No. 5 of Brinton's Books 
 of Chilan Balam, — the Book of Chumayel. Here in paragraph i 
 we have " 4 Ahau was the name of the katun," in paragraph 3 " 4 
 Ahau was the name of the katun," and in paragraph 7 " 1 1 Ahau 
 was the name of the katun." To say that " ahau " was a synonym 
 for " katun " would be as foolish as to say of a family containing 
 John Smith, Mary Smith, and James Smith, that John and Mary 
 and James were all synonyms of Smith, when they were merely 
 names to distinguish one Smith from another. 
 
 1 It is very probable that " anos " is merely a gloss — and an erroneous one 
 at that. 
 
6 MAYAN NOMENCLATURE 
 
 This is also shown in the Book of Mani (pp. 96 et seq. of 
 Brinton's " Maya Chronicles "}, where 
 
 Par, 8 says " Lai u katunil cabil ahau," " In the katun 2 Ahau." 
 " 9 says " Lai u katunil buluc ahau," " In the katun 11 Ahau." 
 " 10 says " Laili u katunil uaxac ahau," " In the katun 8 Ahau." 
 " 12 says "lay u katunil uac ahau," " In the katun 6 Ahau." 
 " 15 says " u katunil ho ahau," " In the katun 5 Ahau." 
 Also in the Book of Tizimin (pp. 139 et seq. of Brinton) : 
 Par. 6, " Uaxac ahau — lay u katunil," " 8 Ahau — in this katun." 
 " 14, " Bolon ahau — lai — u katunil," " 9 Ahau — in this 
 
 katun." 
 " 15, "Vuc ahau — u katunil," " 7 Ahau — in this katun." 
 Also in the first Book of Chumayel (pp. 154 et seq. of 
 Brinton) : 
 
 Par. 2, " Uaxac ahau — layli u katunil," " 8 Ahau — in this katun." 
 " 8, "Bolon ahau — u katunil," "9 Ahau — in this katun." 
 Also in the second Book of Chumayel (pp. 166 et seq. of 
 Brinton) : 
 
 Par. 3, " Uaxac ahau u katunil," " 8 Ahau in this katun." 
 " laix u katunil," " in this katun." 
 " 5, " Hun ahau — lay u katunil," " i Ahau — in this katun." 
 " 8, " Buluc ahau — laix u katunil," " 1 1 Ahau — in this katun." 
 " Buluc ahau. Laix u katunil," "11 Ahau in this katun." 
 " 9, " Bolon ahau — lay katun," " 9 Ahau — in this katun." 
 " Uac Ahau — lay u katunil," " 6 Ahau — in this katun." 
 
 I can find no excuse for considering " ahau " as a synonym for 
 " katun " in these Books of Chilan Balam. And a priori it is diffi- 
 cult to conceive of a numeral system being made up by a nation 
 as cultivated as the Mayas, by which the name of a day should be 
 taken to mean a period of time, with all the chances of error which 
 might arise from such use. Moreover, if this were the case, it 
 would be natural to suppose that in the inscriptions and codices 
 the day sign ahau might be found meaning 7200 days, and yet I am 
 
MAYAN NOMENCLATURE 
 
 7 
 
 unaware that a single instance of this exists on the monuments or 
 in the codices. There are one or two cases in the inscriptions 
 where this has been suggested as being possible, but it is very far 
 from being proved or from even having strong evidence in favor 
 of such an explanation. 
 
 Dr. Forstemann says that at times the name " katun " was given 
 to the period of 18,980 days; but the only authority for this use is, 
 as far as I know, Pio Perez, who says that some applied the name 
 to a "lustre of 4 years," while others thought that " 13 years com- 
 pleted the katun." ^ Again Pio Perez speaks of " the cycle of 52 
 years called by the Indians katun." In none of these cases is any 
 authority given for this use.^ 
 
 It is probably safe to say that any use of the word " ahau " as 
 meaning a katun, or any use of the word " katun " as meaning any- 
 thing but 20 times 360 days, or any use of the day symbol ahau as 
 meaning a period of time, does not occur in any evidence which 
 could be called contemporary or even approximately so. Don Pio 
 Perez is, I fear, the only author who can be cited for the other side, 
 and his opinion, though worthy of being listened to, is not to be 
 relied upon without the support of, or against the evidence of, early 
 authorities. 
 
 The second question as to the name to be given to the period 
 of 360 days must be decided by the same authority. 
 
 We have found that a katun is probably a score of periods of 
 360 days each, and it would be natural to suppose that the con- 
 stituent parts of the katun, as mentioned in the Books of Chilan 
 Balam, would be these periods of 360 days, but of this there is 
 no absolute proof in the Books of Chilan Balam. The proof of 
 this, however, is so strong in the Dresden Codex, where the series 
 runs, 20 of the first order equals i of the second order, 18 of the 
 second order equals i of the third order, and 20 of the third order 
 equals i of the fourth, that no time need be wasted upon this part 
 
 1 Stephens, " Travels in Yucatan," Appendix, p. 439. 
 
 2 Ibid., p. 440. 
 
8 MAYAN NOMENCLATURE 
 
 of the question. We do know, however, that each of these con- 
 stituent parts is called a tun and that they are numbered as high 
 as 13. 
 
 The following list gives, I think, all the cases where the word 
 " tun " is used in the Books of Chilan Balam : 
 
 Book of Mani, paragraph 2, " Hun piztun oxlahun ahau," which 
 Brinton translates " the first year of the thirteenth ahau." I think 
 the proper translation to be "Tun i of Ahau 13," meaning that 
 I tun had passed of Katun 13 Ahau. 
 
 Paragraph 9, " tu lahun tun uaxac ahau " is translated by 
 Brinton, " and it was the tenth year of the eighth ahau," while it 
 should be " in Tun 10 of Katun 8 Ahau." 
 
 In the Book of Tizimin we find that in 
 
 Paragraph i, " tu humpiztun ahoxlahunahau " is translated " to 
 the first year of the thirteenth ahau," while it should be " to 
 (or in) Tun i of Katun 13 Ahau." 
 
 Paragraph ii, "Cabil ahau; oxlahun tun" is translated "The 
 second ahau ; on the thirteenth, etc." It should be " on Katun 2 
 Ahau Tun 13, etc." 
 
 Also in the second Book of Chumayel, we find in 
 
 Paragraph 2, " tu yoxpiztun ychil hun ahau," which is trans- 
 lated " on the third year in the first ahau," when it should be " in 
 Tun 3 of Katun i Ahau." 
 
 Paragraph 3, " Tu uucpiztun uaxac ahau u katunil " is trans- 
 lated " in the seventh year of the eight Ahau katun," when it 
 should be " in Tun 7 of Katun 8 Ahau." 
 
 Paragraph 8, " tu hunpiztun Buluc ahau. Laix u katunil" is 
 translated " in the first year of the eleventh ahau, it was also in 
 this katun," when it should be " on Tun i of Katun 1 1 Ahau. In 
 this Katun, etc." Also " tu uucpiztun Buluc ahau u katunil " is 
 translated " in the seventh year of the eleventh ahau katun," when 
 it should be " in Tun 7 of Katun 1 1 Ahau." 
 
 These two katuns are evidently the same — one date being in 
 Tun I and the other in Tun 7 of the same katun — and yet Brinton 
 
MAYAN NOMENCLATURE g 
 
 translated the first as being in the nth katun and the other as be- 
 ing in the nth ahau katun. 
 
 Paragraph 9, " tu uacpiztun ychil ahBolon ahau katun lae." is 
 translated " in the sixth year of the ninth ahau katun." It should 
 be " in Tun 6 of Katun 9 Ahau." 
 
 Although Brinton has almost always translated " tun " by 
 "year," it is very evident from the above that the Mayas called 
 the native division of the katun " tun." 
 
 It may further be noted that the word " kin " is used for day in 
 the way of numeration in the Book of Mani, paragraph 13, "9 
 Imix was the day on which Ahpula died " and in paragraph 13 of 
 the Book of Tizimin and paragraph 7 of the first Book of Chuma- 
 yel, the same statement is made. 
 
 May it not then be fairly assumed that the Mayas called the 
 day or the unit of their calendrical numeration " kin," their 360- 
 day period " tun," and the period of 20 tuns " katun," as Dr. Seler 
 has suggested? 
 
 The third question is as to the so-called period of " ahau 
 katun." I give below all the cases in which Brinton has used the 
 word, and in all but one of them the Maya has " ahau u katunil" ; 
 and in one case Brinton has translated a sentence as " it was the 
 eleventh ahau katun," while exactly similar phrases (with the ex- 
 ception of the number) have been translated by him as "4 Ahau 
 was the name of the katun." In the phrase in paragraph 9 of the 
 second Book of Chumayel, where " ah Bolon ahau katun " appears, 
 the whole context makes it evident that a katun and not an ahau 
 katun, if there was such a period, is meant. The paragraph says 
 " 9 Ahau ; no stone was taken at this time ; in this katun came 
 the Bishop Brother Francisco Toral ; he arrived in Tun 6 of Katun 
 9 Ahau " ; and yet Brinton makes it read in the first clause that 
 while Bishop Toral came in a katun called 9 Ahau, he " arrived 
 in Tun 6 " of the " ninth Ahau katun." 
 
 Dr. Tozzer, whose knowledge of the Maya languages, gained 
 in long residence among the Maya Indians of Yucatan and Chiapas, 
 
lO MAYAN NOMENCLATURE 
 
 enables him to speak with authority, writes me as follows : " The 
 form u katunil of ahau ukatunil, for example," in paragraph 3 of 
 the second Book of Chumayel, p. 167, " is probably possessive, and 
 it would then be literally ' the Ahau 8, its Katun ' (the Ahau's 
 Katun) which might strengthen the point against joining the two 
 together as Ahaukatun." 
 
 In the second Book of Chumayel, p. 167, paragraph 3, "uuc- 
 piztun uaxac ahau u katunil; laix u katunil, etc." Brinton trans- 
 lates " in the 7th year of the 8th Ahau katun, in this katun, etc." 
 There is no authority for translating ahau u katunil " ahau katun." 
 It should be " In Tun 7 of Katun 8 Ahau, in this katun, etc.," or, 
 as suggested by Dr. Tozzer, " In Tun 7 of Ahau eight's Katun." 
 
 Again, in paragraph 5, the translation of" Hun ahau — tu hun- 
 piztun ychil hun ahau u katunile " is given, " The first ahau — in 
 the first year of the first ahau katun." It should be " i Ahau — 
 in Tun i of the Katun i Ahau, &c." 
 
 Again, in paragraph 8 " tu uucpiztun Buluc Ahau u katunil " is 
 translated " in the seventh year of the eleventh ahau katun," 
 when it should be " in Tun 7 of Katun 1 1 Ahau." Just above 
 " Tun I of 1 1 Ahau " is given and followed by " in this katun." 
 
 Again in paragraph 9 we read " Bolon Ahau — lay katun yax 
 ulci obispo Fray Fran'co to Ral huli tu uacpiztun ychil ahBolon 
 ahau katun lae," which Brinton translates " The ninth ahau — in 
 this katun first came the bishop Brother Francisco Toral; he 
 arrived in the sixth year of the ninth ahau katun." It should be 
 "9 Ahau — in this katun — in Tun 6 of Katun 9 Ahau." This is 
 the only place in the Maya where the words " ahau katun " appear 
 together. But the context makes it clear that " ahau katun " is not 
 a period of time. The paragraph begins with "9 Ahau," and 
 speaks of it as a katun during which Bishop Toral arrived, and 
 then proceeds to say that he arrived in Tun 6 of this " ahBolon 
 ahau katun," which can mean nothing else than the " Katun 9 
 Ahau." 
 
 In the third Book of Chumayel, paragraphs 5 and 6, Brinton 
 
MAYAN NOMENCLATURE 1 1 
 
 translates " Can ahau u katunil " as " The fourth ahau katun " in- 
 stead of " Katun 4 Ahau." 
 
 In paragraph 7 " Uaxac ahau u katunil " is translated " The 
 eighth ahau katun " instead of " Katun 8 Ahau " (note here that 
 this is the same ** 8 Ahau," when Chichen Itza was deserted for 
 Champoton). 
 
 Also " Oxlahun ahau u katunil" is translated " In the thirteenth 
 ahau katun " instead of" Katun 13 Ahau." 
 
 Also " Buluc ahau u kaba u katunil " is here translated " it was 
 the eleventh ahau katun," while in paragraph 3 a similar sentence 
 is translated " 4 Ahau was the name of the katun," 
 
 Thus an ahau katun is not mentioned in the Books of Chilan 
 Balam in spite of Brinton's translation, and neither is it mentioned 
 by Landa, in spite of Brasseur de Bourbourg's insertions. In fact 
 the only evidence of it is the assertion of Don Pio Perez. I do not 
 mean to say that the period of 6 X 52 years = 312 years may not 
 have had a name, nor that " ahau katun " may not be the name of 
 some period, but so far we have no trustworthy contemporary 
 evidence of either of these statements. 
 
q 
 

 MAYAN NOMENCLATURE 
 
 BY 
 
 CHARLES P. BOWDITCH 
 
 Privately Printed 
 
 CAMBRIDGE 
 
 THE UNIVERSITY PRESS 
 
 1906 
 
:y-tr'^-> 
 
 With the Compliments of the Author