Plate 9GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF BAR AND DOT NUMERALS AND HEAD-VARIANT PERIOD GLYPHS
GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF BAR AND DOT NUMERALS AND HEAD-VARIANT PERIOD GLYPHS
In plate9,B, is figured the Initial Series on an altar in front of Structure 44 at Yaxchilan.[146]The introducing glyph appears in A1 B1 and is followed by the number in A2-A4. The period glyphs are all expressed as head variants and the coefficients as bar and dot numerals. Excepting the kin coefficient in A4, the number is quite easily read as 9.12.8.14.? An inspection of our text shows that the coefficient must be 0, 1, 2, or 3. Let us work out the terminal dates for all four of these values, commencing with 0, and then see which of the resulting terminal days is the one actually recorded in A4. Reducing the number 9.12.8.14.0 to units of the first order by means of TableXIII, we have:
Deducting from this number all the Calendar Rounds possible, 73 (see TableXVI), and applying rules 1, 2, and 3 (pp.139,140, and141, respectively), to the remainder, the terminal day reached will be11 Ahau 3 Pop. Therefore the Initial-series numbers 9.12.8.14.1, 9.12.8.14.2, and 9.12.8.14.3 will lead to the three days immediately following 9.12.8.14.011 Ahau 3 Pop. Therefore our four possible terminal dates will be:
Now let us look for one of these four terminal dates in the text. The day reached by an Initial Series is almost invariably recorded immediately after the last period glyph; therefore, if this inscription is regular, the day glyph should be B4. This glyph probably has the coefficient 12 (2 bars and 2 numerical dots), the oblong element between probably being ornamental only. This number must be either 11 or 12, since if it were 13 the 3 dots would all be of the same size, which is not the case. An inspection of the coefficient in B4 eliminates from consideration, therefore, the last two of the above four possible terminal dates, and reduces the possible values for the kin coefficient in A4 to 0 or 1. Comparing the glyph in B4 with the day signs in figure16, the form here recorded will be found to be identical with the sign forImixin figure16,a. This eliminates the first terminal date above and leaves the second, the day part of whichwe have just seen appears in B4. This further proves that the kin coefficient in A4 is 1. The final confirmation of this identification will come from the month glyph, which must be4 Popif we have correctly identified the day as12 Imix. If, on the other hand, the day were11 Ahau, the month glyph would be3 Pop. Passing over A5 B5, A6 B6, C1 D1, and C2, we, reach in D2a the closing glyph of the Supplementary Series, here showing the coefficient 9. Compare this form with figure65. The month glyph, therefore, should appear in D2b. The coefficient of this glyph is very clearly 4, thus confirming our identification of B4 as12 Imix. (See TableVII.) And finally, the month glyph itself isPop. Compare D2b with figure19,a. The whole Initial Series in plate9,B, therefore reads 9.12.8.14.112 Imix 4 Pop.
In plate10, is figured the Initial Series from Stela 3 at Tikal.[147]The introducing glyph, though somewhat effaced, may still be recognized in A1. The Initial-series number follows in B1-B3. The head-variant period glyphs are too badly weathered to show the determining characteristic in each case, except the uinal head in A3, the mouth curl of which appears clearly, and their identification rests on their relative positions with reference to the introducing glyph. The reliability of this basis of identification for the period glyphs of Initial Series has been thoroughly tested in the texts already presented and is further confirmed in this very inscription by the uinal head. Even if the large mouth curl of the head in A3 had not proved that the uinal was recorded here, we should have assumed this to be the case because this glyph, A3, is the fourth from the introducing glyph. The presence of the mouth curl therefore confirms the identification based on position. The student will have no difficulty in reading the number recorded in B1-B3 as 9.2.13.0.0.
Reducing this number by means of TableXIIIto units of the first order, we obtain:
Deducting all the Calendar Rounds possible from this number, 69 (see TableXVI), and applying rules 1, 2, and 3 (pp.139,140, and141, respectively) to the remainder, the terminal date reached will be4 Ahau 13 Kayab. It remains to find this date in the text. The glyph in A4, the proper position for the day glyph, is somewhat effaced, though the profile of the human head may yet be traced, thus enabling us to identify this form as the day signAhau. Compare figure16,h', i'. The coefficient of A4 is very clearly 4 dots, that is, 4, and consequently this glyph agrees with the day as determined by calculation,4 Ahau. Passing over B4, A5, B5, and A6, we reach in B6 the closing glyph of the Supplementary Series, here recorded with a coefficient of 9. Compare B6 with figure65. The month glyph follows in A7 with the coefficient 13. Comparing this latter glyph with the month signs in figure19, it is evident that the monthKayab(fig.19,d'-f') is recorded in A7, which reads, therefore,13 Kayab. Hence the whole text records the Initial Series 9.2.13.0.04 Ahau 13 Kayab.
BUREAU OF AMERICAN ETHNOLOGYBULLETIN 57 PLATE 10
Plate 10GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF BAR AND DOT NUMERALS AND HEAD-VARIANT PERIOD GLYPHS—STELA 3, TIKAL
GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF BAR AND DOT NUMERALS AND HEAD-VARIANT PERIOD GLYPHS—STELA 3, TIKAL
BUREAU OF AMERICAN ETHNOLOGYBULLETIN 57 PLATE 11
Plate 11GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF BAR AND DOT NUMERALS AND HEAD-VARIANT PERIOD GLYPHS—STELA A (EAST SIDE), QUIRIGUA
GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF BAR AND DOT NUMERALS AND HEAD-VARIANT PERIOD GLYPHS—STELA A (EAST SIDE), QUIRIGUA
This Initial Series is extremely important, because it records the earliest contemporaneous[148]date yet found on a monument[149]in the Maya territory.
In plate11is figured the Initial Series from the east side of Stela A at Quirigua.[150]The introducing glyph appears in A1-B2 and the Initial-series number in A3-A5. The student will have little difficulty in picking out the clasped hand in A3, the oval in the top of the head in B3, the fleshless lower jaw in A4, the mouth curl in B4, as the essential characteristic of the cycle, katun, tun, and uinal heads, respectively. The kin head in A5 is the banded-headdress variant (compare fig.34,i, j), and this completes the number, which is 9.17.5.0.0. Reducing this by means of TableXIIIto units of the first order, we have:
Deducting from this number all the Calendar Rounds possible, 73 (see TableXVI), and applying rules 1, 2, and 3 (pp.139,140, and141,respectively) to the remainder, the terminal day reached will be found to be6 Ahau 13 Kayab.
In B5 the profile variant of the day sign,Ahau, is clearly recorded (fig.16,h', i'), and to it is attached a head-variant numeral. Comparing this with the head-variant numerals in figures51-53, the student will have little difficulty in identifying it as the head for 6 (see fig.51,t-v). Note the so-called "hatchet eye" in A5, which is the determining characteristic of the head for 6 (see p.99). Passing over A6 B6, A7 B7, A8 B8, we reach in A9 the closing glyph of the Supplementary Series, here showing the head-variant coefficient 10 (see fig.52,m-r). In B9, the next glyph, is recorded the month13 Kayab(see fig.19,d'-f'). The whole Initial Series therefore reads 9.17.5.0.06 Ahau 13 Kayab.
All the Initial Series heretofore presented have had normal-form numerals with the exception of an incidental head-variant number here and there. By this time the student should have become thoroughly familiar with the use of bar and dot numerals in the inscriptions and should be ready for the presentation of texts showing head-variant numerals, a more difficult group of glyphs to identify.
In plate12,A, is figured the Initial Series on the tablet from the Temple of the Foliated Cross at Palenque.[151]The introducing glyph appears in A1 B2, and is followed by the Initial-series number in A3-B7. The student will have little difficulty in identifying the heads in B3, B4, B5, B6, and B7 as the head variants for the cycle, katun, tun, uinal, and kin, respectively. The head in A3 prefixed to the cycle glyph in B3 has for its determining characteristic the forehead ornament composed ofmore than one part(here, of two parts). As explained on page97, this is the essential element of the head for 1. Compare A3 with figure51,a-e, and the two glyphs will be found to be identical. We may conclude, therefore, that in place of the usual 9 cycles heretofore encountered in Initial Series, we have recorded in A3-B3 1 cycle.[152]The katun coefficient in A4 resembles closely the cycle coefficient except that its forehead ornament is composed of but a single part, a large curl. As explained on page97, the heads for 1 and 8 are very similar, and are to be distinguished from each other only by their forehead ornaments, the former having a forehead ornament composed of more than one part, as in A3, and the latter a forehead ornament composed of but one part, as here in A4. This head, moreover, is very similar to the head for 8 in figure52,a-f; indeed, the only difference is that the former has a fleshless lower jaw. This is the essential element of the head for 10 (see p.100); when applied to the head for any other numeral it increases the value of the resulting head by 10. Therefore we have recorded in A4 B4, 18 (8 + 10) katuns. The tun coefficient in A5 has for its determining characteristic the tun headdress, which, as explained on page99, is the essential element of the head for 5 (see fig.51,n-s). Therefore A5 represents 5, and A5 B5, 5 tuns. The uinal coefficient in A6 has for its essential elements the large bulging eye, square irid, and snaglike front tooth. As stated on page98, these characterize the head for 4, examples of which are given in figure51,j-m. Consequently, A6 B6 records 4 uinals. The kin coefficient in A7 is quite clearly 0. The student will readily recognize the clasped hand, which is the determining characteristic of the 0 head (see p.101and fig.53,s-w). The number recorded in A3-B7 is, therefore, 1.18.5.4.0. Reducing this number to units of the 1st order by means of TableXIII, we obtain:
BUREAU OF AMERICAN ETHNOLOGYBULLETIN 57 PLATE 12
Plate 12GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF HEAD-VARIANT NUMERALS AND PERIOD GLYPHS
GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF HEAD-VARIANT NUMERALS AND PERIOD GLYPHS
Deducting from this number all the Calendar Rounds possible, 14 (see TableXVI), and applying rules 1, 2, and 3 (pp.139,140, and141, respectively), the terminal date reached will be1 Ahau 13 Mac. Of this date, the day part,1 Ahau, is recorded very clearly in A8 B8. Compare the head in A8 with the head in A3, which, we have seen, stood for 1 and also with figure51,a-e, and the head in B8 with figure16,h', i', the profile head for the day signAhau. This text is irregular in that the month glyph follows immediately the day glyph, i.e., in A9. The glyph in A9 has a coefficient 13, which agrees with the month coefficient determined by calculation, and a comparison of B9 with the forms for the months in figure19shows that the monthMac(fig.19,w, x) is here recorded. The whole Initial Series therefore reads 1.18.5.4.01 Ahau 13 Mac.
In plate12,B, is figured the Initial Series on the tablet from the Temple of the Sun at Palenque.[153]The introducing glyph appears in A1-B2 and is followed by the Initial-series number in A3-B7. The student will have no difficulty in identifying the period glyphs in B3, B4, B5, B6, and B7; and the cycle, katun, and tun coefficients in A3, A4, and A5, respectively, will be found to be exactly like the corresponding coefficients in the preceding Initial Series (pl.12,A, A3, A4, A5), which, as we have seen, record the numbers 1, 18, and 5, respectively. The uinal coefficient in A6, however, presents a new form. Here the determining characteristic is the banded headdress, or fillet, which distinguishes the head for 3, as explained on page98(see fig.51h, i). We have then in A6 B6 record of 3uinals. The kin coefficient in A7 is very clearly 6. Note the "hatchet eye," which, as explained on page99, is the essential element of this head numeral, and also compare it with figure51,t-v. The number recorded in A3-B7 therefore is 1.18.5.3.6. Reducing this to units of the first order by means of TableXIII, we obtain:
Deducting from this number all the Calendar Rounds possible, 14 (see TableXVI), and applying rules 1, 2, and 3 (pp.139,140, and141), respectively, to the remainder, the terminal date reached will be13 Cimi 19 Ceh. If this inscription is regular, the day part of the above date should follow in A8 B8, the former expressing the coefficient and the latter the day sign. Comparing A8 with the head numerals in figures51-53, it will be found to be like the second variant for 13 in figure52,x-b', the essential element of which seems to be the pendulous nose surmounted by a curl, the protruding mouth fang, and the large bulging eye. Comparing the glyph in B8 with the day signs in figure16, it will be seen that the form here recorded is the day signCimi(fig.16,h, i). Therefore A8 B8 expresses the day13 Cimi. The month glyph is recorded very irregularly in this text, since it occurs neither immediately after the Supplementary Series or the day sign, but the second glyph after the day sign, in B9. A comparison of this form with figure19,u-v, shows that the monthCehis recorded here. The coefficient is 19. Why the glyph in A9 should stand between the day and its month glyph is unknown; this case constitutes one of the many unsolved problems in the study of the Maya glyphs. This whole Initial Series reads 1.18.5.3.613 Cimi 19 Ceh.
The student will note that this Initial Series records a date 14 days earlier than the preceding Initial Series (pl.12,A). That two dates should be recorded which were within 14 days of each other, and yet were more than 3,000 years earlier than practically all other Maya dates, is a puzzling problem. These two Initial Series from the Temple of the Sun and that of the Foliated Cross at Palenque, together with a Secondary-series date from the Temple of the Cross in the same city, have been thoroughly reviewed by Mr. Bowditch (1906). The conclusions he reaches and the explanation he offers to account for the occurrence of three dates so remote as these are very reasonable, and, the writer believes, will be generally accepted by Maya students.
Fig. 69Fig.69. Initial Series showing head-variant numerals and period glyphs:A, House C of the Palace Group at Palenque;B, Stela P at Copan.
Fig.69. Initial Series showing head-variant numerals and period glyphs:A, House C of the Palace Group at Palenque;B, Stela P at Copan.
In figure69,A, is shown the Initial Series inscribed on the rises and treads of the stairway leading to House C in the Palace at Palenque.[154]The introducing glyph is recorded in A1, and the Initial-series number follows in B1-B3. The student will readily recognize the period glyphs in B1b, A2b, B2b, A3b, and B3b. The head expressing the cycle coefficient in B1a has for its essential element the dots centering around the corner of the mouth. As explained on page100, this characterizes the head for 9 (see fig.52,g-l, where variants for the 9 head are figured). In B1, therefore, we have recorded 9 cycles, the number almost always found in Initial Series as the cycle coefficient. The essential element of the katun coefficient in A2a is the forehead ornament composed of a single part. This denotes the head for 8 (see p.100, and fig.52,a-f; also compare A2a with the heads denoting 18 in the two preceding examples, pl.12,A, A4, and pl.12,B, A4, each of which shows the same forehead ornament). The tun coefficient in B2a is exactly like the cycle coefficient just above it in B1a; that is, 9, having the same dotting of the face near the corner of the mouth. The uinal coefficient in A3a is 13. Compare this head numeral with A8, plate12,B, which also denotes 13, and also with figure52,x-b'. The essential elements (see p.101)are the large pendulous nose surmounted by a curl, the bulging eye, and the mouth fang, the last mentioned not appearing in this case. Since the kin coefficient in B3a is somewhat effaced, let us call it 0 for the present[155]and proceed to reduce our number 9.8.9.13.0 to units of the first order by means of TableXIII:
Deducting from this number all the Calendar Rounds possible, 71 (see TableXVI), and applying rules 1, 2, and 3 (pp.139,140, and141, respectively) to the remainder, we reach as the terminal date8 Ahau 13 Pop. Now let us examine the text and see what is the terminal date actually recorded. In A4b the student will have little difficulty in recognizing the profile variant of the day signAhau(see fig.16,h', i'). This at once gives us the missing value for the kin coefficient in B3, for the dayAhaucan never be reached in an Initial Series if the kin coefficient is other than 0. Similarly, the dayImixcan never be reached in Initial Series if the kin coefficient is other than 1, etc. Every one of the 20 possible kin coefficients, 0 to 19, has a corresponding day to which it will always lead, that is,AhautoCauac, respectively (see TableI). Thus, if the kin coefficient in an Initial-series number were 5, for example, the day sign of the resulting terminal date must beChicchan, sinceChicchanis the fifth name afterAhauin TableI. Thus the day sign in Initial-series terminal dates may be determined by inspection of the kin coefficient as well as by rule 2 (p.140), though, as the student will see, both are applications of the same principle, that is, deducting all of the 20s possible and counting forward only the remainder. Returning to our text, we can now say without hesitation that our number is 9.8.9.13.0 and that the day sign in A4b isAhau. The day coefficient in A4a is just like the katun coefficient in A2a, having the same determining characteristic, namely, the forehead ornament composed of one part. A comparison of this ornament with the ornament on the head for 8 in A2a will show that the two forms are identical. The bifurcate ornament surmounting the head in A4a is a part of the headdress, and as such should not be confused with the forehead ornament. The failure to recognize this point might cause the student to identifyA4a as the head for 1, that is, having a forehead ornament composed of more than one part, instead of the head for 8. The month glyph, which follows in B4b, is unfortunately effaced, though its coefficient in B4a is clearly the head for 13. Compare B4a with the uinal coefficient in A3a and with the heads for 13 in figure52,x-b'. As recorded, therefore, the terminal date reads8 Ahau 13?, thus agreeing in every particular so far as it goes with the terminal date reached by calculation,8 Ahau 13 Pop. In all probability the effaced sign in B4b originally was the monthPop. The whole Initial Series therefore reads 9.8.9.13.08 Ahau 13 Pop.
In figure69,B, is shown the Initial Series from Stela P at Copan.[156]The introducing glyph appears in A1-B2 and is followed by the Initial-series number in A3-B4. The student will readily identify A3, B3, and A4 as 9 cycles, 9 katuns, and 10 tuns, respectively. Note the beard on the head representing the number 9 in both A3a and B3a. As explained on page100, this characteristic of the head for 9 is not always present (see fig.52,g-i). The uinal and kin glyphs have been crowded together into one glyph-block, B4, the uinal appearing in B4a and the kin in B4b. Both their coefficients are 0, which is expressed in each case by the form shown in figure47. The whole number recorded is 9.9.10.0.0; reducing this to units of the first order by means of TableXIII, we obtain:
Deducting from this number all of the Calendar Rounds possible, 71 (see TableXVI), and applying rules 1, 2, and 3 (pp.139,140, and141, respectively) to the remainder, the terminal date reached will be2 Ahau 13 Pop. In A5a the day2 Ahauis very clearly recorded, the day sign being expressed by the profile variant and the 2 by two dots (incorrectly shown as one dot in the accompanying drawing).[157]Passing over A5b, B5, and A6 we reach in B6a the closing glyph of the Supplementary Series, and in the following glyph, B6b, the month part of this terminal date. The coefficient is 13, and comparing the sign itself with the month signs in figure19, it will be seen that the form ina(Pop) is the month recorded here. The whole Initial Series therefore reads 9.9.10.0.02 Ahau 13 Pop.
Fig. 70Fig.70. Initial Series, showing head-variant numerals and period glyphs, from Zoömorph G at Quirigua.
Fig.70. Initial Series, showing head-variant numerals and period glyphs, from Zoömorph G at Quirigua.
In figure70is illustrated the Initial Series from Zoömorph G at Quirigua.[158]The introducing glyph appears in A1-B2 and is followed in C1-H1 by the Initial-series number. Glyphs C1 D1 record 9 cycles. The dots on the head for 9 in C1 are partially effaced. In C2 is the katun coefficient and in D2 the katun sign. The determining characteristic of the head for 7 appears in C2, namely, the scroll passing under the eye and projecting upward and in front of the forehead. See page100and figure51,w. It would seem, then, at first sight that 7 katuns were recorded in C2 D2. That this was not the case, however, a closer examination of C2 will show. Although the lower part of this glyph is somewhat weathered, enough still remains to show that this head originally had a fleshless lower jaw, a character increasing its value by 10. Consequently, instead of having 7 katuns in C2 D2 we have 17 (7 + 10) katuns. Compare C2 with figure53,j-m. In E1 F1, 15 tuns are recorded. The tun headdress in E1 gives the value 5 to the head there depicted (see fig.51,n-s) and the fleshless lower jaw adds 10, making the value of E1 15. Compare figure53,b-e, where examples of the head for 15 are given. Glyphs E2 and F2 represent 0 uinals and G1 H1 0 kins; note the clasped hand in E2 and G1, which denotes the 0 in each case. This whole number therefore reads 9.17.15.0.0. Reducing this to units of the first order by means of TableXIII, we have:
Deducting from this number all the Calendar Rounds possible, 75 (see TableXVI), and applying rules 1, 2, and 3 (pp.139,140, and141, respectively), to the remainder, the terminal day reached will be5 Ahau 3 Muan. The day is recorded in G2 H2. The day sign in H2 is quite clearly the grotesque head variant forAhauin figure16,j'-k'. The presence of the tun headdress in G2 indicates that the coefficient here recorded must have been either 5 or 15, depending on whether or not the lower part of the head originally had a fleshless lower jaw or not. In this particular case there is no room for doubt, since the numeral in G2 is a day coefficient, and day coefficients as stated in Chapter III, can never rise above 13. Consequently the number 15 can not be recorded in G2, and this form must stand for the number 5.
BUREAU OF AMERICAN ETHNOLOGYBULLETIN 57 PLATE 13