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Vladimir Ladma

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Correlation of Mayan and Julian calendar

Long count

Mayan syntax of dates makes possible to observe accuracy of conjunctions of Earth (E) with Mars (R) and lunar line of nodes (Ln). These conjunctions E-Ln-R frame certain raster with period 12 tzolkin, i.e. 3120 days (8.542 years).

In the following schema the rows step with period of conjunctions Earth-Mars. Period 13 tun (18 tzolkin) is highlighted (bold).

Beginning of long count:
 -------------------------
 0. 0. 0. 0. 0 (      0) 
 0. 0. 2. 3. 0 (    780)
 0. 0. 4. 6. 0 (   1560)
 0. 0. 6. 9. 0 (   2340)
--------------------------
 0. 0. 8.12. 0 (   3120)
 0. 0.10.15. 0 (   3900)
 0. 0.13. 0. 0 (   4680) 
 0. 0.15. 3. 0 (   5460)
--------------------------
 0. 0.17. 6. 0 (   6240)
 0. 0.19. 9. 0 (   7020)
 0. 1. 1.12. 0 (   7800)
 0. 1. 3.15. 0 (   8580)
--------------------------
 0. 1. 6. 0. 0 (   9360) 
.....

End of long count:
-----------------------
12.19. 2.12. 0 (1865760)
12.19. 4.15. 0 (1866540)
12.19. 7. 0. 0 (1867320) 
12.19. 9. 3. 0 (1868100)
-----------------------
12.19.11. 6. 0 (1868880)
12.19.13. 9. 0 (1869660)
12.19.15.12. 0 (1870440)
12.19.17.15. 0 (1871220)
-----------------------
13. 0. 0. 0. 0 (1872000)

Congruences

We test connections of Mayan dates with help of congruences (remainder classes).
E.g. the following dates are congruent according to module 260 days (tzolkin):

 Mayan date          D [days]      D/260   [D mod 260]
 -----------------------------------------------------
 9.16. 0.13.17       1411477      5428.7577   197
 9.16. 4. 6.17       1412777      5433.7577   197
 9.16.12. 5.17       1415637      5444.7577   197
 9.17.19.13.16       1425516      5482.7538   196

Serpent numbers

Group of 10 (2*4+2) numbers in Dresden codex.

 Mayan date          D [days]      D/3120  [D mod 3120]
 -----------------------------------------------------
 1/ 9.17.8. 8.5        1421445      455.5913  [1845]
 2/ 10.11.5.14.5       1521285      487.5913  [1845]
 3/ 10. 7.4. 3.5       1491905      478.1746  [ 545]
 4/ 9.18.5.16.4        1427724      457.6038  [1884]
 ------------------
 5/ 10. 8.5. 0.6       1499406      480.5788  [1806]
 6/ 10. 4.6.15.4(14)   1471264(74)  471.5590  [1744(54)]
 7/ 9.18.4. 8.4        1427204      457.4372  [1364]
 8/ 10. 6.10.6.3       1486923      476.5779  [1803]
 -----------------------------------------------------
 9/ 9.16. 8.5.12       1414192      453.2667  [ 832]
10/ 9.17.15.6.14       1423934      456.3891  [1214]

Rates to period Y = 3120 days (12 tzolkin) are on right.
Dates 1,2,(4) and 5,(6),8 seems to be congruent according to 3120 days.

Difference of date 1 and 2 is 99840 days (273.3 years).
After this period lunar line of nodes points not only to Mars, but also to Venus. It concerns exact interval of conjunctions V-E-R (V-E-Ln-R) or (rather) straight line alignment of E-V-R (E-Ln-V-R).
99840 = 9 *19 *583.85965 days = 2^7 *3 tzolkin = 2^5 *Y

Symmetric configurations and period tzolkin

Some synodic and resonant periods of outer planets are nearly exact multiples of period tzolkin (z).
E.g.

See Symetric configurations.

From ([J,U],[S,N]) = 50z and ([J,S],[U,N]) = 28z it follows: (J,N) = 700z/39 and (S,U) = 700z/11 (but 13 tun= 18z = 702z/39). If 3*J = 50z then N = 13*(J,N) = 700z/3.
Period 700z = 700*260 days = 182000 days = 498.29 years is one of periods of multiple conjunctions.

Let (J,S/3,-U,-N/3)= P/25 (9*z), ([J,S],[U,N])/2= P/16 (14z) and ([J,U],[S,N])/2 = P/9 (25*z). Period P is common multiple of mentioned periods and is equal to 224 (14*16) or 225 (9*25) tzolkin, c. 160 years.
See Stable resonance J-S-U.

Test of correlations

Each correlation is a result of a set of conditions. To determine right correlation it is necessary to establish right set of conditions.

Let us have e.g. the following conditions: 

8.16.14.15.4 (1272544) 	conjunction J-S   (|Lj-Ls|<90°)
9.15.9.15.10 (1407550) 	conjunction V-E   (|Lv-Le|<10°)
9.15.9.15.14 (1407554) 	conjunction M-E   (|Lm-Le|<10°)
9.15.9.15.14 (1407554) 	conjunction M-E   (|Lm-Le|<10°)
9.16.4.11.18 (1412878)  Moon at node      (|Ln-L |<10°)
9.17.8.8.5   (1421445)  E-V-R in line     (|Li-Lj|<10°)

On interval (-4000,-2000) for begining of long count we get these correlations:
322720, 325047, 336748, 517737, 622258 , 650301 , 757150, 887387, 889714, 982534.

Number 622258 coresponds to correlation Bohm&Bohm (622261).
Below we will follow correlation 650301-650302.

Correlation 650302

In view of Thompson correlation (584283):

In view of correlation Bohm&Bohm (622261):

Symmetry of planets at the beginnings of particular baktuns
([A,B][C,D] denote, that axis A-B align with axis C-D).

 baktun  configuration deviation
 --------------------------------------
  13.    [J,S][U,N]     1°
   1.    [J,N][S,U]    15°
   2.    [J,S][U,N]    10°
   3.    [J,N][S,U]    11°
   4.    [J,S][U,N]    26°
   5.    [J,N][S,U]    19°
   6.    [J,S][U,N]    31°
   7.    [S,N][J,U]    13°
   8.    [S,N][J,U]    26°
   9.    [J,S][U,N]    36°
  10.    [J,N][S,U]    23°
  11.    [J,S][U,N]    30°
  12.    [J,N][S,U]     1°
  13.    [J,S][U,N]     5°

Origin of baktuns:

-----------------------------------------------------------
                                             13.  6.6.
   1.   6.9.     2.   6.12.     3.   8.3.     4.  7.6.
   5.   7.9.     6.   7.12.     7.   8.3.     8.  8.6.
   9.   7.9.    10.   8.12.    11.   9.3.    12. 20.6
-----------------------------------------------------------
  13.  22.9.

Examples of correlations

Mayan cycles