Blinking snake

The 819 Day Count

Constellation band

Introduction


Index
Introduction
Finding the 819-Day Station
Finding the Tzolk’in
Finding the Colors and the Directions
Finding the Haab
Finding the Position in the Calendar Round
Finding the Long Count
References

The 819 day count of the Mayan calendar combines colors, directions and a distance number counting backwards into a cycle that has, as factors, several numbers important to the Maya, the primary ones being 7, 9 and 13 (7 · 9 · 13 = 819).

The 819 day count, or cycle, begins on day -3 of linear time, 1 Kaban 5 Kumk’u. Since 819 is evenly divisible by 13, the trecena day for each 819 day station is a constant and is always one. And since 819 is one less than an even multiple of 20, the veintena decrements by one on each increment of the cycle.

The phrase in the inscriptions, which is sometimes found immediately following the haab month and sometimes between the haab month and the preceding Lunar Supplementary Series, opens with a distance number counting back to a resting place, or station, followed almost always by some form of the T588 verb:

819-day verb 819-day verb 819-day verb 819-day verb 819-day verb 819-day verb 819-day verb 819-day verb

Linda Schele’s reading of this verb is walah, “to place” or “to seat” (Schele and Grube, 1997).

Sometimes, the phrase closes with a “One Rodent-Bone” glyph, or T758/T757:T110:

Hun/one ch’ok/sprout Hun/one ch’ok/sprout Hun/one ch’ok/sprout Hun/one ch’ok/sprout ko ko

This glyph, of course, is one of the alternate forms of Glyph B, and is glossed ch’ok, sprout (ch’o or ch’ok T758 = ch’o, and ko T110 = ko).

The tzolk’in and haab glyphs for the 819 day station come either after the distance number or, as in some examples from Palenque, in the position otherwise occupied by T757/T758. The most complete and complex examples seem to come from Yaxchilan, specifically Lintel 30, E3-F6. Here, in addition to the distance number, T588, the direction, the color and the “Rodent-Bone” glyphs, we have two additional glyphs: the “beetle,” or Glyph Y, and a “Smoking Squirrel” glyph:

Glyph Y Glyph Y Glyph Y Glyph Y   Smoking squirrel Smoking squirrel Smoking squirrel Smoking squirrel

Number Meaning
3 Prime
4 4 World Directions/Colors
7 7 Gods of the Earth
7 Classical Planets
7 Day Glyph Z Cycle
9 9 Lords of the Night
9 Day Glyph G Cycle
13 13 Lords (or Birds?) of the Day
Trecena
63 7 · 9 (Seven of Nine ;-))
91 1/4th of the Computing Year, 364
13 · 7
117 13 · 9
Rain God Cycle
Mercury Synodic Period
273 1 Tzolk’in + 1 Trecena
21 · 13
3 · 7 · 13

Finally, in at least three examples, all from Yaxchilan, there is an additional glyph that follows the Calendar Round date for the 819 station, which has a numerical coefficient of 6; since G6 is the Lord of the Night for all 819 stations, Thompson (1943, 1971) speculates that this might be a form of the G6 glyph, which would be fortunate, as we have only one other verifiable example in the corpus:

Proposed G6 Proposed G6 Proposed G6 Proposed G6 Proposed G6 Proposed G6 Proposed G6 Proposed G6 Proposed G6 Proposed G6

The distance numbers for the 819 day cycle are almost always of the compressed variety, i.e., either a tun or a uinal glyph with two numerical coefficients expressed to the left and on the top. Sometimes there is a third coefficient, which is positioned to the top right of the upper number.

Further, since each 819 day “station” is referenced to (or under the control of) a different direction/color, the full cycle is actually 3276 days, adding the ritually important number 4.

Number Meaning
364 The Computing Year
4 · 91
3276 4 World Directions · 819 Ritual Cycle
4 · 819
9 · 364
12 · 273
28 · 117
36 · 91
4 · 7 · 9 · 13

Mathematics

Finding the 819-Day Station

819 day calculations are not complicated, once you have the “Maya Day” (m), i.e., the Julian Period Day (JPDAY) minus the “Correlation Constant” (CC). See the Mayan Correlation Constant page for further information. If your preferred CC is 584285 and your JPDAY is, for example, 2450765, then the m would be 1866480. Once you have m, simply add 3 to it (1866483) and modulo it by 819 to obtain m8:

8st = (m + 3) % 819

gives, for our example:

8st = (1866480 + 3) % 819

8st = 801

meaning that it is 801 days past the last 819 day station. Or, using the “Distance Number” (DN) format, 2 Tuns, 4 Uinals, 1 Kin (2.4.1). The actual day of an 819 day station, then, would be marked as “0 Tuns, 0 Uinals, 0 Kin,” or “0.0.0,” and the largest DN you could possibly see would be 818, or “2.4.18.”

To find the day of the 819 day station, subtract the 819 day position (801 in our example above) from the current m:

m8 = JPDAY - 8st
m8 = 1866480 - 801
m8 = 1865679

The trecena for 819 day stations is always one, since 819 is evenly divisible by 13, and since the base day for the count is set at three days before “zero” (4 Ahaw 8 Kumk’u), and 4 - 3 is 1.

The veintena can be found directly, by taking the 819 day station (m8) modulo 20:

veintena = m8 % 20
veintena = 1865679 % 20
veintena = 19
veintena = Kawak

Note that the veintena day decrements by one at each successive station: this is because 819 is one less than a multiple of 20 (820).

Thus, for the base date of “three days before zero,” we can determine the trecena, veintena and haab with little difficulty:

4 Ahaw (day 0) 8 Kumk’u
- 3 is

1 Kaban (day 17) 5 Kumk’u

Determing the Lord of the Night for the base date is equally simple; for m 0, the Lord of the Night is G9, and three days before that would necessarily be G6. Thus, all 819 day stations are under the influence (protection?) of G6 (819 is evenly divisible by 9, of course). Refer to The G and F Glyphs of the Lunar Supplementary Series for a more detailed discussion of the mathematics of the Glyph G sequence. The next station, at m 816, would be:

1 Kib (day 16) 9 Sots (Zotz) G6

Finding the Tzolk’in

Once the m of the 819 day station (m8) is known, then we can find the tzolk’in position using this formula:

ptzolkin = (m8 + 159) % TZOLKIN

We add 159 because the tzolk’in does not start on day 0 (4 Ahaw 8 Kumk’u) of the Long Count, but on 1 Imix, and 4 Ahaw is day 159. So, for our example,

ptzolkin = (1865679 + 159) % 260
ptzolkin = 1865838 % 260
ptzolkin = 78

And then, with the tzolk’in position, we can easily find both the trecena and veintena:

trecena = (ptzolkin + 1) % 13

(We add 1 because day 0 in the tzolk’in is 1 Imix; our modulo function in this case will never return 0, but for other positions in the tzolk’in, a return value of 0 should be replaced with 13.)

trecena = (78 + 1) % 13
trecena = 1

And 1 is exactly what we expect and require.

veintena = (ptzolkin + 1) % 20

veintena = (78 + 1) % 20
veintena = 19
veintena = Kawak

(We add 1 here also, because Imix is day 1 and Ahaw is day 0.)

Finding the Colors and the Directions

Once we know the position in the tzolk’in, we can derive the color and direction very easily:

color = ptzolkin % 4
color = 78 % 4
color = 2
color = Black

direction = ptzolkin % 4
direction = 78 % 4
direction = 2
direction = Chikin (West)



Index Color Direction Veintena Days
0 Chak (Red) Chak, red Chak, red Likin (East) East, Likin ’Imix
Imix
1
Chik’chan
Chikchan
5
Muluk
Muluk
9
Ben
Ben
13
Kaban
Kaban
17
1 Sak (White) Sak, white Sak, white Xaman (North) Xaman, North Ik
Ik
2
Kimi
Kimi
6
Ok
Ok
10
’Ix
Ix
14
’Etz’nab
Etznab
18
2 Ek (Black) Ek, black Ek, black Chikin (West) West, Chikin Ak’bal
Akbal
3
Manik’
Manik
7
Chuwen
Chuwen
11
Men
Men
15
Kawak
Kawak
19
3 Kan (Yellow) Kan, yellow Kan, yellow Nohol (South) South, Nohol K’an
Kan
4
Lamat
Lamat
8
’Eb
Eb
12
K’ib
Kib
16
’Ahaw
Ahaw
0

Finding the Haab

Again, once we know the m of the 819 day station, we can figure out the haab position using:

phaab = (m8 + 348 ) % HAAB

We add 348 to the m because the haab does not start on day 0 (4 Ahaw 8 Kumk’u) of the Long Count, but at 0 Pohp; 8 Kumk’u is day 348. For our example, the position in the haab would be:

phaab = (m8 + 348) % 365
phaab = 1866027 % 365
phaab = 147

Once this position in the haab is known, it’s almost trivial to find the haab month and day:

hmonth = (int) phaab / 20
hmonth = 147 / 20
hmonth = 7
hmonth = Mol (Pop is month 0)

hday = phaab % 20
hday = 147 % 20
hday = 7

So our haab is 7 Mol, giving a complete Calendar Round date of 1 Kawak 7 Mol.

Finding the Position in the Calendar Round

The Calendar Round (CR) does start on day 0 (4 Ahaw 8 Kumk’u) of the Long Count. The last day of a CR is, then, always 3 Kawak 7 Kumk’u, for a total of 18,980 days. Lounsbury (n.d.) gives several formulae for determining the CR position, but the most direct way to calculate it is by taking the m of the 819 day cycle modulo CALROUND:

pCR = m8 % CALROUND
pCR = 1865679 % 18980
pCR = 5639

For a fuller explanation of why this works, and to see Lounsbury’s more detailed formulae, refer to the Calendar Round Page.

Once you have found the position in the Calendar Round, you can easily find the tzolk’in and haab positions:

ptzolkin = (pCR + 159) % TZOLKIN
ptzolkin = (5639 + 159) % 260
ptzolkin = 5798 % 260
ptzolkin = 78

phaab = (pCR + 348) % HAAB
phaab = (5639 + 348) % 365
phaab = 5987 % 365
phaab = 147

These positions can, of course, be used above for finding the haab day and month, and for finding the trecena and veintena.

Finding the Long Count

Using the m8 found above, simply apply the standard techniques explained on the Long Count Page.

To find previous and next 819-day stations from any given Long Count dates, click here 819-day verb.

References

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