MAYAN NOMENCLATURE


  BY
  CHARLES P. BOWDITCH


  _Privately Printed_


  CAMBRIDGE
  THE UNIVERSITY PRESS
  1906


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 introduced in order to bring
the third term as near the length of the year as possible, and to
conform the day numeration to the number 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 different from
the usual system, and is used only for counting days, and as this
system counts forward in almost every case in the inscriptions, and in
a majority of cases in the Dresden Codex, from a fixed date, 4 Ahau
8 Cumhu, it seems impossible to see any difference 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.,”[1] 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. Förstemann 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 “Zeitschrift für Ethnologie,” makes the following
statement: “The katun has also been supposed to be 24 × 365 = 8760 days
long (and I held this view for a long time), indeed the long period
of 52 × 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 1, 20, and 7200 days respectively.

[1] See Seler, “Gesammelte Abhandlungen zur Amerikanischen Sprach- und
Alterthumskunde,” Vol. I. p. 722.

Such statements from such learned scholars must attract attention,
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 contemporary evidence.

And where is such evidence to be found? Though there are several
Spanish writers who lived 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. Förstemann 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. Förstemann himself quotes
from them with approval, and it is certain that whatever may be their
historical value, the evidence which they give incidentally 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 mentioned 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 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 1, 2, 3, 4, 5, 6, etc. should be substituted
in Brinton’s translation for 1st, 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 distinguish the
katuns from each other, two methods could be used: either count them
numerically, 1, 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 × 553 + 11. 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, 1
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, published by
Brinton--that of Mani--we find in the paragraph numbered 1 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 1, 13 Ahau 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 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. 1. 8. 2. 9. 3. 10. 4. 11, etc.,
while the real order is given in the books as 11. 9. 7. 5. 3. 1. 12.
10. 8. 6. 4. 2. 13, etc. If the word “haab” or the Spanish “años,”[2]
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.

[2] It is very probable that “años” is merely a gloss--and an erroneous
one at that.

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 1 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 “11 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.

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,” “1 Ahau--in this katun.”
   ”   8, “Buluc ahau--laix u katunil,” “11 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 difficult 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 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. Förstemann 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 completed the
katun.”[3] 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.[4]

[3] Stephens, “Travels in Yucatan,” Appendix, p. 439.

[4] Ibid., p. 440.

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 anything 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 constituent 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 1 of
the second order, 18 of the second order equals 1 of the third order,
and 20 of the third order equals 1 of the fourth, that no time need be
wasted upon this part of the question. We do know, however, that each
of these constituent 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 1 of Ahau 13,” meaning that 1 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 1, “tu humpiztun ahoxlahunahau” is translated “to the first
year of the thirteenth ahau,” while it should be “to (or in) Tun 1 of
Katun 13 Ahau.”

Paragraph 11, “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 translated “on the
third year in the first ahau,” when it should be “in Tun 3 of Katun 1
Ahau.”

Paragraph 3, “Tu uucpiztun uaxac ahau u katunil” is translated “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 1 of Katun 11 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 11
Ahau.”

These two katuns are evidently the same--one date being in Tun 1 and
the other in Tun 7 of the same katun--and yet Brinton translated the
first as being in the 11th katun and the other as being in the 11th
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 Chumayel, 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 exception 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, 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, “uucpiztun uaxac
ahau u katunil; laix u katunil, etc.” Brinton translates “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 hunpiztun ychil
hun ahau u katunile” is given, “The first ahau--in the first year of
the first ahau katun.” It should be “1 Ahau--in Tun 1 of the Katun 1
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 11 Ahau.” Just above “Tun 1 of 11 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 translates
“Can ahau u katunil” as “The fourth ahau katun” instead 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 × 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.