Glyph x of the Supplementary Series of the Maya Inscriptions - Andrews - 2009 - American Anthropologist - Wiley Online Library

7/29/2019 Glyph x of the Supplementary Series of the Maya Inscriptions - Andrews - 2009 - American Anthropologist - Wiley

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G L Y P H X O F T H E S U P PL E M E N T A R Y S ER IE SO F T H E M A YA I N S C R IP T I O N S B y E. WYLLYS ANDREWSN 1916, Sylvanu s G . Morley initiated work o n, Glyph X in his treatiseI on the Supplementary Series appearing in the Holmes AnniversaryVolume. Following his identification of th e glyph a nd its classification a ssuch in a definite place in t he series,2 cam e a hi atu s of sev enteen ye ar s upto th e present time, broken only b y Teeples discovery in 1928 of th ef ac tth a t the re were six forms of this glyp h each of which could app ea r onlywith o ne of tw o consecu tive coefficients of Glyph C.3 His work is summed

up in the following ch ar t (fig. 1) dra w n by M r Lawrence Roys of Moline,Ill. For a reason which will app ear late r, I ha ve given each of these forms th enumber which appears on the chart .As a ch art such as Figure 1 could not possibly present a comprehensiveview of a ll th e form s of Gly ph X, I am giving in Figure 2, several variation sfor each of th e six form s of th e gly ph . It will be noted th a t the distinguish-ing characteristics for Fo rm 1 are very vague. Although the form giventhe number 3 is generally distinguishable by th e tassel to th e left of theglyph, the re is a h ead -va rian t form with the large proboscis-like nose (m-n).

Form 4 s always distinguished by the cross-legs element, although theelement above or below it (0-s) varies considerably. Although Form 5 isgenerally distinguished by a round-nosed face with which th e M ay a scul pto rallowed himself considerable freedom (t-u, x), a serpent va ria nt (v-w) isoften fou nd . Each of the va ria nt s of Glyph X given in Figure 2 was, a s ma ybe assumed, identified as such either by its occurrence with the requiredcoefficients of Glyph C or b y it s correct occurrence with these coefficientsan d its containing one or m ore of th e characteristic eleme nts of the originalform given by R oy s on Figure 1 . Of the seventy tex ts under investigationwhere both Glyphs C an d X are legible, only two cases app ear which do no tagree w i th t he ~or r e l a t i on .~ith th e ad dit iona l material here presented,an d a realization of th e freque ncy of errors in the inscription, these m ay beconsidered mistakes, an d Teeples work accepted a s basically so un d.

1 Sylvanus G. Morley, The Supplementary Seriesof the M aya Inscriptions (Holmes An-2 Ibid. , pp. 374-76.* J o h n E. Teeple, Maya Astronomy (Contributions to American Archaeology, No. 2.4 On Lintel 29 at Yaxchilan, 4X appears with SC, and on Copan, Stela 2 , 3 X appears

niversary Volume, Washington, 1916 , pp. 365-96).

Carnegie Institution ofWashington , 1931, pp. 66 -67).with 1C. 345


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346 AMERICAN ANTHROPOLQGIST [N.s., 36,1934

D b E25201881741579

11

92299124

--

T he first fac t th at one would notice in examining a table of Supp lemen-tary Series arrang ed according to the chronological orde r of their corre-sponding Init ial Series would be th at the v ariation in the forms of Glyph Xan d th e coefficient of Glyph C is one which occurs within ve ry sho rt periodsof time. I n oth er words, th e cycle of changes is a sho rt one. T his m ay be seenby glancing a t Nos. 5 ,6 , and 7 in T able 1.A t 9.14.0.0.0. NO. ), t he numberof the form of Glyph X is equ al to th e coefficient of G ly ph C. A t 9.14.3.0.0.(No. 6), three years later, it is one greater than the coefficient of C, a n dthen a t 9.14.5.0.0. (No. 7), two years later, it is again equal to the coef-ficient of Glyph C. He re we ha ve two ch anges within a period of five yearsor one hotun.

TABLE 1.TABLE OF ALL AVAILABLE DATES BE TWE EN 9.12.5.0.0.N D9.16.5.0.0.WITH UNIFORM C-DATES AND LEGIBLE FORMS OF XC

GroupIVVVVI V

N o. 1 Site I Mon. 1 Date44325

12345678910

54335

1 112

323156

13141516

424256

Piedras NegrasPiedras NegrasCopanCopanUaxactunNaranjoPiedras NegrasQuiriguaCopanYaxchilanPiedras NegrasHolactunYaxchilanPiedras NegrasYaxchilanQuirigua

St. 6St. 4St. JSt. 5St. 1St. 30St. 5St. ESt. DL. inBerlinSt. 10T. ofI.s.L. 6L.St. 1 1St. J

9.12.15.0.0.9.13.10.0.0.9.13.10.0.0.9.13.15.1.0.9.14.0.0.0.9.14.3.0.0.9.14.5.0.0.9.14.13.4.179.15.5.0.0.9.15.6.13.1.9.15.10.0.0.9.15.1 2.6.9.9.15.14.8.149.15.18.3.13.9.16.1 O.O.9.16.5.0.0.

I11 IIIVIIVVI11I11I

As Glyph X occurs no t only near the middle of the Su pp lem en tarySeries, but also is directly dependent upon Glyph C, one is obliged t o ar-rive a t the conclusion t h a t th e former deals ei ther with a lunar phenomenonor a lu na r ceremonial.Second only to the phases of the m oon, in a primitiv'e min d, one wouldexpect to find a n interest in i ts r ising a nd sett ing.


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ANDREWS] T H E M A Y A INS CRIPTIONS 347W ith these three preliminary observations in mind, we m ay e nte r into

the subject a l i t t le more deeply. Tw o obvious lun ar m onth s would be sug-gested to the M aya:

FIG.1.Th e relation of Glyphs C and X.1. T he period from new moon to new moon: 29.53 da ys (which we know2. Th e per iod between a n y two days when the moon would r ise a t ap -was expressed by Glyph C) ;


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348 A M E R I C A N ANTHROPOLOGIST [N.S., 36, 1934

FORM 1

af-0

FORM 3@j

FORM 4

0

FORM 9

b C

f

h

@t U

FORM 6

PFa9

V

h i

m n

r 5

W x

Y z aaFIG. . Forms of Glyph X .


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ANDREWS] T H E M A Iil INS CRIPTIONS 349proximately the same time: 30.5 days (which we believe to be ex-pressed by Glyph X) .T he following equa tion expresses the relationship between the two. A t th een d of exactly five groups of six synodical mo nth s, the m oon would rise a tprecisely the same time on th e same da y of the sam e synodical mon th.M oon rises 48 minutes later each d ay (average) :48x30 (no. of C m on th s in cycle)X 29.530

1440 (no. of min. per day) =29.530.Th erefore t h e following cycle of 885.9 da ys would exist (see fig. 3) .T h e C-cycle would c onsist of five grou ps of six synodical m onth s, andthe X-cycle would consist of four grou ps of six X-m onth s, a nd one groupof five X-months. T h a t is, the X-system would fall exactly one mo nth shorta t the end of this period of time. T his relationship is more clearly a nd ac-curate ly shown by Figure 4 which can be used as a visual confirmation ofany mathematical calculations to follow.T h u s fa r, for the sak e of clar ity, a n explanation of the proposed fun ctionof Glyph X ha s been given purely in te rm s of m odern astronom ical science.Therefore, i t is necessary to realize t h a t the idea would ha ve been expressedin a rather different manner by the Maya, who had no comprehension offractions, an d would therefore have been compelled to express the idea interm s of w hole days. R ath er th an a cycle of th irty m on ths of 29.530 dayseach, the M ay a would hav e conceived of a cycle consisting of sixteen 30-da y mon ths an d fourteen 29-day months. In a similar manner, they wouldSources of forms of Glyph X :

a) Quirigua-StelaJ.b) Naranjo-Stela 29.c) Copan-Stela 3 (nodule).d) Copan-StelaJ.e) Copan-StelaN.f ) Quirigua-StelaD (e).g) Yaxchilan-Stela1.h) Holactun-Temple of Initial Se-i) Piedras Negras-Stela3.j) Ixkun-Stela 2.k) Copan-Stela P .1) Naranjo-Stela 14.m) Quirigua-Stela E (w).

n) Quirigua-StelaI.0 ) Piedras Negras-Stela 1.

ries.

p) Palenque-Templeof the Sun.q) Yaxchilan-Lintel29.r) Copan-Stela7 .s) Yaxchilan-Lintel46.t) Yaxchilan-Altar near Structureu) Chichen Itza-Temple of Initialv) Piedras Negras-Stela 36.w) Naranjo-Stela30.x) Quirigua-Zoomorph P.y) Palenque-Temple of FoliatedCross.z) Copan-Stela M .

aa) Copan-Stela9.

44.Series.


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350 AM E RIC AN ANTHROPOLOGIST [N.S., 36, 1934have conceived of a cycle of twenty-nine months of al ternat ing 30 and 31days' duration, rather than a cycle of twenty-nine months, each of 30.51-

~~ ~

FIG.3. Diagram of cycle between Glyph C and X.days'variation. I n each of the abo ve cases the length of th e cycle will proveto be quite close to th e necessary 885.9 days, although slight inaccuracy isbound to be present.


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A N D B E W S ] T H E M A Y A INSCRIPTIONS 351

X3 1 4 1 5 1 6

By comparison of Figure 1with Figure 3, i t becomes evid ent t h a t i t isinfinitely less confusing to give each form of Glyph X a number ra ther thana name. Figure 3 also de mo nstrates the reason for assigning the num ber 1to the form of X (assigned this number on Figure l ) , .e., because th is formonly corresponds t o coefficientsof both 6 an d 1of G lyph C. Fo r convenience,th e five groups of C-Moons in the C-X cycle have been num bered withRom an numera ls f rom1 oV .Th us a lunar d at e would be written23-IV. C.3,meaning th at 23 days had elapsed since the beginning of the four th moonin Gro up IV.b (See fig. 4 .)

X1 1 ' 2 3 1 4 1 5


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352 AM ERI CAN ANTH ROPOLOGI ST [N.S., 36, 1934recorded on the monuments, and the form of X likewise. In each case, themoon-age date is within two or three days of the value required by theuniform count, and theform o j Glyph X s that which we predict b y the follow -ing mathematical calculations, with the exception of Nos. 2 and 14, wherethere is a variance of three days, a length of time quite within observationalerror, and again in the Calakmul text which we will discuss later.

In the two examples which follow, it should be borne in mind that thestandard Supplementary Series used is that given in No. 7 in Table 1, i.e.,9.14.5.0.0--15D--V.C.4-X4. However it should also be remem-bered t ha t any Supplementary Series in Table 1 may be used equally wellas the standard lunar date. Number 7 has been chosen here as it falls ap-proximately in the middle of the period embraced by the dates in Table 1.N o. 119.15.10.0.0.-9D--? C3-?X.Difference from No. 7 is 1.5.0.0 equals 304 moons, 24 days.Remove largest multiple of 30 (one cycle)-here 300-leaves 4 moons, 24 days.Count forward 4 m., 24 d. (on fig. 4 ) from No. 7 to reach 9-I.C.3.Consult Figure 4, nd the form of X should be 4 .X s Form 4 on inscription. Q. E . D.

N o. 89.14.13.4.7.-7D-?C3-?X.Difference rom No. 7 is 8.4.17. quals 100m., 24 d.Remove the largest multiple of 30, here 90; leaves 10m., 24 d.Count forward on Figure 4 to reach 9.IlI.C.3.Consult Figure 4, and the form of X should be 4.X s Form 4 on inscription. Q. E . D.It must be borne in mind that the function of these calculations is onlyto prove the C . D . E . date uniform and to locate it in a moon group. The

number of days expressed by Glyphs D and E will often vary as much as twoor three days from the amount actually predicted, but the record of theinscription is the one used in the prediction of the form of Glyph X inFigure 4.These two calculations illustrate the method followed in all calculations.In each of the cases in Table 1 the method is the same and the form of Xis predicted correctly with the exception of two 3-day variations noted.Thus, it is evident that in the above sixteen dates, the sum total of all

available inscriptions with a clear, uniform moon-age date, and a legibleGlyph X, our observations are confirmed in every case-amply sufficientevidence to form a clear proof.Before continuing, I should like to bring up a rather interesting inscrip-


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ANDREWS] THE M A Y A I N S C R I P T I O N S 35 3tion th at is not in the above group, as the reading is not a sure one. OnLintel 1 a t E l Cay o, we find the inscription 9.16.0.2.16-3E-lC-2X. Bycalculation, i t ap pears th at the d ate falls in Group 11, and tha t the moon-age reading according to th e uniform requ irements shou ld be 3 an d n ot 23.However if the d ate be read 23 da ys and kep t in th e same group the formof X would be th e correct one, while if the d at e is rea d 3 day s, the w rongform of X would occur. Th is interrelation tend s to throw do ub t on the as-sumpt ion tha t Glyphs D and E were used interchangeably in ce rtain citiesof the Usmacintla valley, although a t the present time one can b u t sur-mise a s to th e rules governing its use a t these sites.One more case comes to our atte ntio n. On Stela 51 a t C alakmul wefind the following in sc ription: 9.14.19.5.0.-14D-4C-X5. B y com-putatio n this would fall into Group IV and the form for X would be wrongbeyond the limit of observational or co m pu tatio na l error-14 days. As thisda te falls in ou r period, only three possibilities occur to us:1. Calakmul did not use the uniform X-system.2. Th is is an actu al mistake in th e inscription.3. Ou r theory is wrong.

The above inscription is the only one from this si te available to the au-tho r which falls within our period a nd ha s a clear moon-age reading thatis uniform, an d it is therefore im possible to decide which of th e two abov eexplanations is the m ost satisfactory .

T his pap er covers all the In itia l Series in th e period between 9.12.5.0.0.an d 9.16.5.0.0. X- da tes falling outside th is period do n ot n ecessarily con-form with ou r observations even when C, D a n d E are uniform. One is thu sled to believe t h a t th e period of X-conform ity is th e above, even as theperiod of C-un iform ity is also from 9.12.2.0.16. to 9.16.5.0.0. O utside thi speriod the X-calculations do not work out by the method here used. Sowhile th e fun ction of Glyph X has been here explained a nd the exact usageof i t during t h e uniform period ha s been established, th ere is still muc h t obe done in th e future. H owever, with the information contained h erein, i twill be possible , in the future to work ou t th e system s used b y the M ay abefore and after the uniform period.

ADDENDAWhile this paper was in press, the following new material has come tothe author s a t t ent ion .Tw o new occu rrences of Glyp h X with a clear Init ial and Supplemen-tary series in the prescribed period, both of which act as excellent checksfor our hypothesis, and conform exactly to the m aterial presented above:


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354 AME RICAN AXTHROPOLOGIST [N.S., 36, 1934No. 17. Pied ras Negras, S tela 3--9.14.0.0.0.-173 (for D)-V.C.3.-X3;No. 18. Yaxchilan, Altar 3-9.16.1.9.3.-173 (for D)--IV.C.S.-XS.T he for m of Glyph X of No. 1 7 a t first appe ars dou btful , bu t upon closerexam ination is surely Fo rm 3. B y position (A8, on left side of monument),it mu st be Glyph X, an d as the coefficient of Gly ph C is 3, i t m ust be eitherForm 3 or Form 4. As i t is clearly no t th e well defined cross-leg Fo rm 4 ,an d bears a gre at resemblance to the face vari an t of Fo rm 3 (see fig. 2, m ),we may acce pt i t as th e lat ter .T he au thor wishes to s ta te th at he now regards the above deciphermentof both the I .S. an d th e Supp l. S. of Stela 1 a t Uaxac tun (No. 5) a s ex -tremely dubious. T hi s would be t he only case on record of Glyphs C an d Xcompressed in to one glyph, a nd furtherm ore he ha s been shown b y DrS. G. Morley th a t the IS. eading has no more th an a n even chance of beingcorrect . This text m ust be regarded as of such a do ubtfu l na ture a s to beof v er y slight va lue as a proof of th is hypo thesis.Also, since this pap er went to press an othe r case has come to t he au-thors atte nt ion where a form of Glyph X occurs with a coefficient of G lyphC th a t does not correspond to th e fund am en tal conformation describedin the first parag raph of this paper a nd i l lustrated on Figure 1. T he inscrip-tion is on Stela 23 a t Naranjo, an d reads as follows:T h e I.S. would place th e S uppl. S. at. 14-II.C.l, and Form 1 of Glyph Xwould be required, as th e inscription is from t he uniform period. N ot onlydo we fail to encounter the required Form 1 , bu t not even the a l t e rna teForm 2. T h e form of X is clearly 5, as is seen in th e d ouble occurrence ofthe round-nosed face with the turban headdress. T his can only be placed inthe sa m e category a s the other two records given in note 4, p. 345, and beregarded as a n error. It is significant in this connection th at a no the r erroroccurs in the sam e text, the Sec. S. terminal da te reading 2 M en 13 Yaxkininste ad of th e correc t 1 M en 13 Yaxkin. T he fact th a t in each of the thre ecases where this fund am ental C-X corresponden ce fails, a different form ofGlyph X is involved confirms the inte rpre tatio n of these as errors. T h ecoe fficient of G lyp h C on this m onument was read by Teeplee as 5 , in whichcase th e form of X would be correct, but a s the monum ent d ate s from themiddle of th e period of u nifo rm ity, and th e unifo rm coefficient of C is 1,the element Teeple regards as an eroded num erical ba r m ay almost surelybe regarded as an eroded ending sign.

9.13.18.4 .18.-15 D-C 1-X5

CHICHENTZA ROJECTCARNEGIENSTITUTIONF WASHINGTONWASHINGTON,. C.Teeple, op. d.,. 52, Table 4, No. 8.

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Glyph x of the Supplementary Series of the Maya Inscriptions - Andrews - 2009 - American Anthropologist - Wiley Online Library