in Codex Borhonicus, pp. 21-22

George Kubler
An Aztec Calendar
of 20,176 Non-Repeating Years
in Codex Borhonicus, pp. 21-22
A partir de
1 8 8 0 se han h e c h o n u m e r o s o s e s f u e r z o s in-
f r u c t u o s o s p o r explicar la relación de una aparente rueda calendárica marcada p o r 5 2 días p o r t a d o r e s del a ñ o en secuencia
regular, c o n una secuencia enigmática de l o s nueve S e ñ o r e s de
la N o c h e . La c o n e x i ó n pretendida p o r el escriba p r e c o l o m b i n o ,
sin e m b a r g o , era simple. Se e x p l i c a p e r f e c t a m e n t e al c o m p r o bar q u e la intrincada secuencia de l o s nueve S e ñ o r e s de la
Noche
se c o n v i e r t e en una serie repetida de 2 0 . 1 7 6
vagos
a ñ o s solares de 3 6 5 días, l u e g o de c o m p l e t a r d o s e x p a n s i o n e s
p e r i ó d i c a s de la aparente rueda calendárica. Estas e x p a n s i o n e s
c o n s t a n de ( 7 x 5 2 ) + 1 = 3 6 5 , y ( 8 x 5 2 ) + 1 = 4 1 7 , c o m o se
muestra en el c u a d r o 4 . T o d a s las c o n d i c i o n e s de la c o m p u t a c i ó n calendárica m e s o a m e r i c a n a son satisfechas c o n la s o l u c i ó n
d e presumir una sola c o n t i n u i d a d ( c o m p r o b a d a en 1 9 2 9 p o r
J . E . S . T h o m p s o n para la serie m a y a de l o s nueve Señores de la
N o c h e ) . La s o l u c i ó n p r o p u e s t a a q u í para estas d o s páginas del
C ó d i c e B o r b ó n i c o , ni origina p r o b l e m a s i n t r í n s e c o s a la rueda
calendárica ampliada c o n e c t a d a c o n l o s nueve Señores de la
N o c h e , ni es refutada p o r ninguna otra f u e n t e primaria c o n o cida.
Codex Borbonicus is a screenfolded or pleated manuscript painted
on panels o f ficus-hark paper (each 28 X 28 cm). It is named after its
present location in the library o f the Palais Bourbon, which houses the
Chamber o f Deputies in Paris. The aftermath o f the Napoleonic wars in
123
Spain probably brought the manuscript from the Escorial to France before 1826. Being o f pre-Conquest style f o r the most part, it refers entirely
to calendrical and ritual matters in the Mexican (or A z t e c ) tradition, as
o f about A . D . 1500.
The left scene o n p. 21 shows the invention o f the calendar b y an aged
mythological couple, O x o m o c o (left) and Cipactonal (right). The right
scene on p. 22 portrays t w o major deities Quetzalcóatl (left) and Tezcalipoca (right) w h o appear as "regents" o f divisons o f the 52-part calendar.
The glosses in Spanish refer to the " m o n t h s " ( " m e s e s " ) and to birthdeities ("dioses de las parteras"), but they betray no awareness o f the
larger calendrical meaning o f the t w o pages.
These pages o c c u p y the center o f the manuscript. Before it came other
pages, each showing one o f twenty " w e e k s " o f thirteen days in the 2 6 0 day ritual calendar. After the center are pages showing the rituals o f the
nineteen " m o n t h s " o f the 365-day year. Pages 2 1 — 2 2 therefore literally
bind together the ritual calendar o f 2 6 0 days and the vague solar-year
calendar o f 365 days, in the 52-year cycle o f 18,980 days.
Inconsistent theories about the pre-Columbian A z t e c calendar have
long been based on pp. 21 - 22 o f Codex Borbonicus. In 1899, J. T. E.
Hamy interpreted the joining o f nine Night-Lord names with f i f t y - t w o
year-bearer day signs as a " d o u b l e table, calculated for future use, to find
instantly in the tonalamatl (ritual calendar o f 2 6 0 days) the first day o f
any solar year o f 365 days" (Codex Borbonicus 1899: 14 f.; author's
translation).' Hamy also assumed without p r o o f that such Night Lord cum
year-bearer days were spaced 105 days apart, and that they complemented
one another functionally, without interruption or cessation. Actually
Hamy was right only in assuming the unbroken, perpetual continuity o f
the Night-Lord cycle, but he was wrong in thinking that the year-bearer
days were spaced 105 days apart. Table 1 shows that the 105-day interval
in a sequence o f 365-day years will produce a repeating sequence coinciding only with three Night Lords (4, 1, 7, ...) instead o f the non-repeating sequence geared with all nine, shown in C o d e x Borbonicus, as diagrammed in Table 2.
C. P. Bowditch, on the other hand, correctly noted in 1900^ that the
Night Lords were "repeated with irregular intervals ... regulated b y the
number o f Tonalamatls ( o f 260 days) ending in each solar year. Apparently, therefore, the Tonalamatls succeeded each other, continuously
lapping over f r o m one year to the other, while the Lords o f the Night
1
O n l y D. R o b e r t s o n ( 1 9 5 9 : 9 0 ) has suggested that it is o f early c o l o n i a l date, b e t w e e n 1 5 2 2 and 1 5 4 0 . Caso ( 1 9 6 7 : 1 0 5 ) believed it t o b e p r i o r t o the Spanish
Conquest.
2
B o w d i t c h ( 1 9 0 0 : 1 5 2 ) , p r e c e d e d b y Paso y T r o n c o s o ( 1 8 9 8 : 9 4 ) .
124
accompanied the Tonalamatls." Bowditch then wrongly supposed that the
Night Lords "lost one o f their number with the ending o f each Tonalamatl."
Recent variations o f Bowditch's view appear in studies b y C. Lizardi
Ramos ( 1 9 5 3 : 101), L. Satterthwaite ( 1 9 4 7 : 14), K. A. N o w o t n y ( 1 9 6 1 :
2 4 1 ) , and A. Caso ( 1 9 6 7 : 128). These scholars all believe that the Night
Lords were a discontinuous count, either b y dropping o n e every 365 days,
or by having every 260th day be accompanied b y t w o Night Lords as
shown for example in the Aubin Tonalamatl (Seler 1 9 0 0 / 0 1 : 20). By
these modern assumptions the presence o f t w o Night Lords o n 13 xochitl
was read as marking a " c a r r y o v e r " to the first day o f the next 2 6 0 - d a y
cycle (Fig.). Only one 260-day period is presented. The next o n e would
have begun again with 1 cipactli accompanied b y Night Lord 1 (Xiuhtecutli).
UNBROKEN G E A R I N G OF THE NIGHT LORDS WITH THE D A Y COUNT
In view o f the proofs by J. E. S. T h o m p s o n ( 1 9 2 9 ) that the Maya
Night Lord count was continuously geared to other cycles,^ it is reasonable to make the same assumption f o r the Night-Lord cycle o n the Mexican plateau in the Aztec period o f C o d e x Borbonicus. The results are
plausible, and they satisfy the mind better than Bowditch's unsupported
hypothesis o f uncounted Night Lords, or Hamy's 105-day intervals,
regularly repeating as 4 , \ ,1, ...ad infinitum.
The usually accepted numerical coefficients and generic meanings
that have been supplied in recent literature f o r the Night Lords are as
follows (Caso 1967: 116 f.):
1.
2.
3.
4.
5.
6.
7.
8.
9.
Xiuhtecutli (fire)
Itztli ( o b s i d i a n )
Piltzintecutli ( n o b l e s )
Cinteotl ( m a i z e )
Mictiantecutli ( d e a t h )
Chalchiutlicue ( w a t e r )
Tlazolteotl (love)
TepeyoUotl (earth)
T l a l o c (rain)
On pp. 21 — 22 o f C o d e x Borbonicus, the fifty-two year-bearer day
signs, beginning with 1 tochtli and continuing in sequence through 13
calli, are accompanied b y the Night Lords in a seemingly irregular order
3
N o d e i t y n a m e s are k n o w n f o r the f o r m s o f G l y p h G .
125
by numerical coefficient as shown on Table 2, where the order o f reading
begins at the lower left-hand comer o f p. 21, continuing counterclockwise around the oblong, and passing to the lower left-hand corner o f
p. 22, again reading counterclockwise. This sequence reveals a peculiar
shift o f Night Lord coefficient from year bearer to year bearer. Instead o f
advancing regularly by five place (1, 6, 2, 7, 3, 8, 4, 9, 5, 1, ...), as it
would if year bearers were separated by intervals o f 365 days, the shift is
alternately by intervals o f seven and six places, and also by paired intervals
o f six. These shifts were required, as shown by C. P. Bowditch (1900:
153) and O. Apenes (1953: 102) by the occurrences o f two or three
distinct 260-day counts within the 365-day year (Table 3). Thus in a year
2 tecpatl, the first 260-day count must end on a day 13 xochitl and the
second must begin the following day on 1 cipactli. But the next year, or
3 calli, contains three counts of 260 days. The first ends on 13 xochitl
at day 9 7 ; the second begins on 1 cipactli on day 9 8 ; and the third begins
on day 358.
THE INVIOLABLE ENNEAD OF THE NIGHT LORDS
The traditional solution since F. del Paso y Troncoso's (1898: 77 —
96), and including its adaptation by A. Caso (1967: 120 f.) has been,
as mentioned earlier, to interpret too literally the doubled Night Lord
attached to the terminal day, only when the count does not exceed
260 days (see also Lizardi Ramos 1969). In the Aubin (Seler 1900/01),
Bologna (1898), and Telleriano Codices (1899), the last day (260), which
is always 13 xochitl, has as companion both Night Lords 8 and 9 (Fig.).
Paso y Troncoso, who quotes A. Chavero (1901: 7), assumed without
explanation that this doubling o f the Night Lords every 260th day removed the insoluble irregularity in Codex Borbonicus.
Thus the hope of all modern commentators has been to reduce the
cycle on Borbonicus 2 1 - 2 2 to a short repeating cycle o f only fiftytwo years, by wrongly cancelling the one-to-one correspondence between
each o f the nine Night Lords and each day position without exception
in the eternal sequence o f 260-day counts.
Yet there is better reason to accept the scribes' intention in all cases
as being to indicate only that the 261st day would not break or interrupt the inviolable ennead of the Night Lords.
We already know that the 260-day count in these pages is uninterrupted and unbroken. If we now assume that the nine Night Lord sequence
is likewise uninterrupted and continuous, as in the Maya count, then
126
these apparently irregular intervals will eventually appear as a series repeating ad infinitum.
THE LONG PERPETUAL C A L E N D A R SOLUTION
The difference between the long perpetual calendar proposed here and
other solutions is that this one expands the f i f t y - t w o year-bearer day
signs f r o m the canonical number as 4 X 13 X 3 6 5 , or fifty-two vague solar
years, totalling 18,980 days, to the number o f 388 X 52, or 2 0 , 1 7 6 years,
or 7 , 3 6 4 , 2 4 0 days. This is the smallest number after which the given
series o f the Night Lords are stated in Borbonicus (and only there) will
repeat forever their seemingly irregular sequence.
Aevum is a scholastic term o f the thirteenth century f o r such a duration, having a beginning but no end. It seems appropriately used, for a
perpetual calendar o f which both we and the Aztecs have occupied only
the initial aeon, as one o f an infinite number in th& aevum.
MAYA AND AZTEC CALENDARS
The resemblance o f this long perpetual calendar to that o f the Maya
Initial Series day count, as geared to the nine forms o f the Maya Glyph G
(see T h o m p s o n 1929), is more structural than functional. The function
differs in central Mexico. The Maya day count o f the classic period ( A . D .
3 0 0 - 9 0 0 ) was calculated by periods o f 3 6 0 days (the tun). But the
peoples o f central Mexico preferred to count b y years o f 365 days. These
were designated by e p o n y m o u s day names occurring only o n the 360th
day o f each vague solar year, before the ill-omened five final days (or
nemontemi).
Table 4 places the fifty-two year-bearer days in a row across the top.
The numbered 52-year cycles called calendar Rounds that are required
to fit the Night Lords to the year-bearer days appear in the column at the
extreme left, 388 in number. In calendar Round 1, which is 52 X 365
or 18,980 days, the year-bearer days are always 365 days apart, and
the year-bearer day itself always occupies the 360th day in each year,
as shown in Table 1.
If the f i f t y - t w o year-bearer days (across the t o p o f Table 4 ) correspond
in Borbonicus 2 1 - 2 2 to years in sequence, then the accompanying
Night Lords must repeat their sequence after every nine positions: 5 , 1 , 6 ,
2, 7, 3, 8, 4, 9, ... as shown in the first eight calendar R o u n d s on Table 5.
Only the expansion o f the calendar Rounds b y multiples o f 7 and 8, or
127
(7 X 52) + 1 = 365 and (8 X 52) + 1 = 417 can bring the Night Lords
into conjunction with year-bearer days, as indicated on the rest o f
Table 4. The diagonal marks the only way the Borbonicus sequence can
occur. Here only the stated conjunctions are shown at the required
intervals o f 7 and 8 calendar Rounds (shown at left), in a series that
repeats itself only after 388 X 52 or 20,176 years, thereafter cycling
through ever-identical concatenations of fifty-two year-bearer days with
nine Night Lords.
The year-bearer days across the top were but four in number, corresponding to days 3, 8, 13 and 18 in a day list o f twenty names permutating with 365 positions in the solar calendar. The four year-days also
filled cycling positions in the ritual calendar o f twenty weeks o f thirteen
numbered day names. These seem to be their position on pp. 21 - 22
o f Codex Borbonicus, but there they are not in ordinal sequence as we
learn from the seriation of the nine Night Lords. Instead, they can be
spaced only by intervals o f either 365 years (7 X 52) + 1, or 417 years
(8 X 52) + 1. These intervals approximate seven and eight cycles o f fiftytwo years each, as laid out at the left on Table 4.
THE SCRIBE'S INTENTION
The question now arises, as to how the scribe meant us to understand
the chronological position in eternity o f his calendar as given in Codex
Borbonicus. If he meant to record the first use o f the calendar by its
inventors, who are portrayed as the old couple o f deities on p. 21, we
may begin by supposing that the stated aeon o f 20,176 years had reached
13 calU in the recent past at A . D . 1505. This would place the "invention"
in 18,671 B.C.
But it would be more "historical" to suppose for the invention a date
like the Maya zero (or beginning) date for the day count late in the fourth
millenium B.C. In this case, the year A . D . 1505 would correspond to
about 4500 elapsed years since the invention o f the calendar. This assumption places the completion of the first age (or quarter-aeon) o f 5044
years in the future during the twenty-first century after Christ, and the
fulfillment o f the full aeon 17,000 years in the future.
Historically speaking, we may suppose that A . D . 1505 was the date
when the Night-Lord count was adapted to the 365-day year. This was
done in order to achieve a perpetual calendar that would indefinitely
repeat the same intervals as on pp. 21 — 22 o f Codex Borbonicus. In this
case we might consider 1 tochth ( A . D . 1506) as the starting date o f a new
age, and as an anniversary o f the original invention.
128
In addition, these two pages may record an effort in Aztec historiography to devise (ca. A . D . 1500) an adequate manner o f recording and
remembering events in extended time. If so, the Mexicans seem to have
reverted with improvements to the interlocicing cycles o f classic Maya
Initial Series records. The new system, however, could not revise the
clumsy baktun o f 4 0 0 Maya years o f 3 6 0 days without adopting the Maya
periodic structure. Yet it does introduce periods o f 365 and 417 years,
which are labelled unequivocally as in the Maya Initial Series inscriptions,
by the nine Night Lords in immutable and perpetual sequence with the
year-bearer days through 388 calendar Rounds.
AZTEC COSMOGONIC THEORY
The long periods suggested b y this arithmetic (Table 4 ) may relate to
the sixteenth-century history o f the universe outhned in "Historia de los
Mexicanos por sus pinturas" ( 1 8 9 1 : 2 2 8 ) . T h e r e , f r o m Creation to the
Spanish Conquest, 3,145 years are given as elapsed. O x o m o c o and Cipactonal invented the calendar 6 0 0 years after Creation. Then, for the periods
o f 676 years each (13 X 52 = (6 + 7) X 52), Quetzalcoatl and Tezcatlipoca, as well as Tlaloc and Chalchiutlicue, functioned for 2 7 0 4 years as suns.
This text lends support to an interpretation o f C o d e x Borbonicus, as
presenting a perpetual calendar that was still approaching only the end o f
the first age o f 5,044 years. This was but the first quarter o f an aeon
recorded by the meshing o f the nine Night Lords with the fifty-two
year-bearer days, in a cycle repeating itself indefinitely after the first
2 0 , 1 7 6 years.
Figure: A f t e r Seler ( 1 9 0 0 / 0 1 : pi. 2 0 ) . In these c o l o n i a l
versions, where o n l y o n e " m o d e l " 2 6 0 - d a y c o u n t appears
with N i g h t - L o r d c o m p a n i o n s , the last d a y , w h i c h is always
13 X ó c h i t l , will usually be a c c o m p a n i e d b y the eighth
and ninth Night L o r d s . Most m o d e r n scholars believe that
this " d o u b l i n g " o f Night L o r d s o n the 2 6 0 t h day c o u l d
resolve the difficulties presented b y B o r b o n i c u s 21 — 2 2 ,
but the " d o u b l i n g " o c c u r s o n l y where a single and initial
m o d e l is set f o r t h , in c o l o n i a l and m o d e r n writings, as
the paradigm f o r all successive ones.
4
This text is dated n o t later than 1533 -
1 5 3 4 ( G a r c i a Icazbalceta 1 9 4 7 , II: 1 3 8 ) .
129
REFERENCES
A p e n e s , Ola
1953
" L a s páginas 21 y 2 2 del C ó d i c e B o r b ó n i c o . " In Yan,
México.
2: 102 -
104,
B o w d i t c h , Charles P.
1900
" T h e L o r d s o f the Night and the T o n a l a m a t l o f the C o d e x B o r b o n i -
cus." In American
2: 146 -
Anthropologist,
154, New Y o r k .
Caso, A l f o n s o
1967
Los calendarios
prehispánicos.
México.
Chavero, A l f r e d o
1901
Calendario
o rueda del año de los antiguos indios.
appeared as an appendix to vol. 1 o f his Pinturas
México (originally
jeroglificas
of the
same date).
Codex Borbonicus
1899
Codex Borbonicus.
Manuscrit
mexicain
de la Bibliotheque
du Palais
Ed. b y J. T. E. H a m y . Paris.
Bourbon.
C o d e x Cospi
1898
Descripción del Códice Cospiano. Manuscrito
guos ñauas que se conserva en ta Biblioteca
pictórico de los antide la Universidad de
Facs., e d . b y F. del Paso y T r o n c o s o . R o m a .
Bolonia.
C o d e x Telleriano-Remensis
1899
Codex
Telleriano-Remensis.
Ch. M. Le
Mansucrit
mexicain
du
Cabinet
de
E d . b y J. T. E. H a m y . Paris.
Tellier.
García Icazbalceta, J o a q u í n
1947
Don Fray Juan de Zumárraga,
primer obispo y arzobispo
de
México.
4 vols., M é x i c o .
Historia de l o s M e x i c a n o s
1891
"Historia
de l o s M e x i c a n o s p o r sus p i n t u r a s . " In J o a q u í n
Icazbalceta (ed.): Nueva colección
de México, 3: 228 - 263. México.
de documentos
para la
García
historia
Lizardi R a m o s , César
1953
" L o a s a c o m p a ñ a d o s del X i u h m o l p i l l i en el C ó d i c e B o r b ó n i c o . " In
Yan, 2 : 9 5 - 1 0 1 , M é x i c o .
1969
"Los
calendarios prehispánicos
Cultura Náhuatl,
N o w o t n y , Karl A .
1061
130
Tlacuilolli.
de A l f o n s o C a s o . " In Estudios
8 : 3 1 3 - 3 6 9 , México.
Berlin.
de
Paso y T r o n c o s o , F r a n c i s c o del
1898
Descripción, historia y exposición del códice pictórico de los antiguos nahuas que se conserva en la Biblioteca de la Cámara de Diputados de París (antiguo Palais Bourbon). Firenze.
Robertson, Donald
1959
Mexican Manuscript Painting of the Early Colonial
Metropolitan
Schools.
New Haven (Yale Historical
History of Art, 12).
Period.
The
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Satterthwaite Jr., L i n t o n
1947
Concepts
and Structures
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Calendrical
Arithmetics.
Phila-
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Seler, Eduard
1900 - 1901
The Tonalamatl
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T h o m p s o n , J o h n Eric S.
1929
"Maya Chronology:
Anthropologist,
Berlin and London.
G l y p h G o f the Lunar Series." In
American
31.2: 223 - 231, New York.
131
EXPLANATIONS ON THE FOLLOWING TABLES
T a b l e 1: T w o successive 3 6 5 - d a y years are each divided b y eighteen c o l u m n s o f
t w e n t y - d a y m o n t h s plus a nineteenth m o n t h o f five days. T h e far left c o l u m n gives
the t w e n t y - d a y names, w h i c h c o n t i n u e in nineteen a d j o i n i n g c o l u m n s as n u m b e r e d
p o s i t i o n s in repeating c o u n t s o f t w e n t y w e e k s o f thirteen d a y s each.
A c c o m p a n y i n g these day p o s i t i o n s w i t h o u t break is a n o t h e r c y c l e o f nine Night
Lords. Each r o u n d o f nine is marked o n the table by b o l d n u m b e r s , t o signify that the
ninth Night L o r d , T l a l o c , is the c o m p a n i o n here.
T h e 3 6 0 t h day give the year its d a y - n a m e bearer, o f w h i c h the s e q u e n c e o f c o m p a n i o n s f o l l o w s the order given in Table. 4 .
A l s o marked are the 1 0 5 - d a y intervals, as p r o p o s e d in 1 8 9 9 b y H a m y , that can
o c c u r o n l y with Night L o r d s 4 , 1, and 7 in a repeating series. T h e Night L o r d s are
entered o n the table diagonally b e l o w the day n u m b e r s o f the year bearers as assumed
b y H a m y . He s u p p o s e d w i t h o u t p r o o f that the 1 0 5 - d a y p e r i o d s were separated b y
intervals o f 2 6 0 days.
T a b l e 2 : Pages 21 — 2 2 o f Borbonicus
s h o w the f i f t y - t w o year-bearer day names with
the nine Night L o r d c y c l e , beginning at the l o w e r left c o r n e r and m o v i n g c o u n t e r c l o c k w i s e in eight frames o f seven and six. Each page displays t w e n t y - s i x day n a m e s ,
and b o t h pages taken t o g e t h e r enumerate f i f t y - t w o d a y - n a m e and N i g h t - L o r d p o s i tions. These were n o t meant b y the scribe t o be read as a single c y c l e o f f i f t y - t w o
years, but as p o s i t i o n s spaced at intervals o f 3 6 5 and 4 1 7 years, as s h o w n in T a b l e 4 ,
during a p e r i o d o f 20,1 76 years, after w h i c h the c y c l e will repeat perpetually.
T a b l e 3 : T w o 3 6 5 - d a y years are diagrammed in s e q u e n c e . In 2 tecpatl o n l y t w o
c o u n t s o f 2 6 0 d a y s appear, dividing the year in t w o parts ( 2 0 2 + 1 6 3 ) . In 3 calli,
three c o u n t s are present, dividing the year in three parts ( 9 7 + 2 6 0 + 8 ) . Each 2 6 0 day c o u n t ends o n 13 x o c h i t l , and its successor is always 1 cipactli. In years like 2 t e c patl with t w o c o u n t s , these days appear o n l y o n c e ; in years hke 3 calli with three
c o u n t s t h e y appear t w i c e .
T a b l e 4 : T h e f i f t y - t w o year-bearer day names appear across the t o p as Usted in the
C o d e x . T h e e x t r e m e left c o l u m n enumerates the " C a l e n d a r R o u n d s " , o f c y c l e s o f
f i f t y - t w o years e a c h , since the m y t h o l o g i c a l i n v e n t i o n o f the calendar. T h e first
eight Calendar R o u n d c o r r e s p o n d e n c e s are given in f u l l ; thereafter o n l y the c o r r e s p o n d e n c e s in the C o d e x are tabled. T h e first eight Calendar R o u n d s state the n u m b e r o f
the Night L o r d a c c o m p a n y i n g each year-bearer day n a m e , in a repeating series o f nine
p o s i t i o n s as 5 - 1 - 6 - 2 — 7 - 3 — 8 - 4 — 9 , each separated b y five places in a
c y c l e o f nine. T h e r e a f t e r the c o n j u n c t i o n s o f Night L o r d s with year-bearer days
appear as in the C o d e x , appearing at intervals o f ( 7 x 5 2 ) + 1 = 3 6 5 years, and ( 8 x 5 2 )
+ 1 = 4 1 7 years. N o n e will recur until 3 8 8 x 5 2 , o r 2 0 , 1 7 6 years have elapsed.
132
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a
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2 4 9 5 1 62 7 3 8 4 9 5 1 6 27 3 8 4 9 5 1 6 27 3 8 4 9 5 1 6 2 7 3 8 4 9 5 1 6
3 3 8 4 9 5 1 6 2 7 3 8 4 9 5 1 6 2 7 3 8 4 9 5 1 6 2 7 3 8 4 9 5 1 6 2 7 3 8 4 9 5
4 2 7 3 8 4 9 5 1 6 2 7 3 8 4 9 5 1 6 2 7 3 8 4 9 5 1 6 2 7 3 8 4 9 5 1 6 2 7 3 8 4
5 1 6 2 7 3 8 4 9 5 1 6 2 7 3 8 4 9 5 1 6 2 7 3 8 4 9 5 1 6 2 7 3 8 4 9 5 1 6 2 7 3
6 9 5 1 62 7 3 84 9 5 1 6 2 7 3 8 4 9 5 1 6t 7 3 8 4 9 5 1 62 7 3 84 9 5 1 6 2
7 8 4 9 5 1 6 2 7 3 8 4 9 5 1 6 2 7 3 8 4 9 5 1 6 2 7 3 8 4 9 5 1 6 2 7 3 8 4 9 5 1
8 7 3 8 4 9 5 1 6 2 7 3 8 4 9 5 1 6 2 7 3 8 4 9 5 1 6 2 7 3 8 4 9 5 1 6 2 7 3 8 4 9
16
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2 7 3 84
1 6 2 7 3
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84 9 5 1 6 2 7 3 84
7 3 8 4 9 5 1 6 2 7 3
6 2 7 3 8 4 9 5 1 6 2
5 1 6 2 7 3 8 4 9 5 1
7
31
4
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259
1
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282
8
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6
297
3
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1
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320
327
335
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342
350
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358
9
365
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373
4
380
2
388
7
6
7
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6
26
Table 4 :
Year-bearers and Night L o r d s o f Borbonicus
3 8 8 c y c l e s o f 5 2 years, o r 2 0 , 1 7 6 years.
136
7
S
6
26
21-22,
showing occurrence
during