Maya Time Keeping

Basic Concepts

• Maya time relied on the counting of completed days.
• They used a number system based on the vigesimal (base 20) system of counting.
• There are two types of glyph;
• those that are found on concertina like books known currently as codices (plural of codex) and
• those on carved or moulded stelae and architecture.
• Time zero begins on a date known as 4 Ahau 8 Cumhu

Time Periods

The basic unit of counting Maya time was the day, known as 'Kin'. They build up successively larger periods in accordance to the vigesimal system of counting as follows:
```
1 day   =  1 Kin

20 days  = 20 Kin        = 1 Uinal

360  "    = 18 Uinal      = 1 Tun         =         1 year  approximately

7 200  "    = 20 Tun        = 1 Katun       =        20 years       "

144 000  "    = 20 Katun      = 1 Bactun      =       395   "         "

2 880 000  "    = 20 Bactun     = 1 Pictun,     =     7 885   "         "

57 600 000  "    = 20 Pictun     = 1 Kinchiltun  =   157 703   "         "

115 200 000  "    = 20 Kinchiltun = 1 Alautun     = 3 154 069   "         "

```

But, they rarely used Pictun, Kinchiltun and Alautun depictions. Their usual calculations mostly concerned terms up to Baktun, since 8000 years would be a significantly broad enough time to consider.

Mayan Numerals

Glyph TypeCodex TypeNumeral
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
0

(Codex glyph only)
0

Mayan numerals come in several forms. In the codices, they are usually written in columns, with the Kin value lowermost and successively greater time periods above. The relative positions of these are sufficient to show the time recorded. These numerals are black if they are positive in value, whilst red, if they must be the number need to subtract from the black numerical value of time in days.

For glyphic representation on monuments and stelae, they are carved in the vertical form. However, there are also head variants which represent numerals. These are sadly lacking in some of the sequence, so they have not been included here. Only the zero half-flower is shown.

Maya Day Names

There are 20 day names in the Maya week. In order of their appearance, they are :

Codex GlyphNameMeaning
ImixWater, Wine, Sea Dragon
IkAir, Life
AkbalNight
KanCorn
ChicchanSerpent
CimiDeath
ManikDeer, grasp
LamatRabbit
MulucRain
OcDog
ChuenMonkey
EbBroom
BenReed
IxTiger, Magician
MenBird, Eagle, Wise One
CibOwl, Vulture
CabanForce, Earth
EznabFlint Knife
CauacStorm, Tun
AhauLord

Maya Month Names

There are 19 month names, the first 18 have a time length of 20 days, whilst the last, Uayeb, has only 5 days. In order of appearance, as follows:

Stelae GlyphsNameMeaning
PopMat
UoFrog
ZipStag
ZotzBat
TzecSkull
XulTermination
YaxkinRed
MolTo Gather
ChenA Well
YaxGreen
SacWhite
CehA Forest
MacA Cover
KankinYellow, Skeleton, Ribs
MuanFalcon, An Owl
PaxA Drum
KayabTurtle
CumhuDark
UayebA Ghost
[# I'd like to thank Michael Pereira for providing me with a list of translations for the monthnames.]

The Haab

This a 365 day period composed of the nineteen 'months' named above. The dates were numbered 0 through to 19 with the month name attached after it.
```
0 Pop      1 st day of the Haab

1 Pop      2 nd  "  "   "    "

2 Pop      3 rd  "  "   "    "

3 Pop      4 th  "  "   "    "

4 Pop      5 "   "  "   "    "

5 Pop      6 "   "  "   "    "

6 Pop      7 "   "  "   "    "

7 Pop      8 "   "  "   "    "

8 Pop      9 "   "  "   "    "

9 Pop     10 "   "  "   "    "

10 Pop     11 "   "  "   "    "

11 Pop     12 "   "  "   "    "

12 Pop     13 "   "  "   "    "

13 Pop     14 "   "  "   "    "

14 Pop     15 "   "  "   "    "

15 Pop     16 "   "  "   "    "

16 Pop     17 "   "  "   "    "

17 Pop     18 "   "  "   "    "

18 Pop     19 "   "  "   "    "

19 Pop     20 "   "  "   "    "

0 Uo      21 st  "  "   "    "

1 Uo      22 nd  "  "   "    "

2 Uo      23 rd  "  "   "    "

3 Uo      24 th  "  "   "    "

.

.

18 Cumhu  359 "   "  "   "    "

19 Cumhu  360 "   "  "   "    "

0 Uayeb  361 st  "  "   "    "

1 Uayeb  362 nd  "  "   "    "

2 Uayeb  363 rd  "  "   "    "

3 Uayeb  364 th  "  "   "    "

4 Uayeb  365 "   "  "   "    "

```

The Tzolkin or Tonalamatl

This is a 260 day period relying on two factors. The repeated count 1 to 13 inclusive, and the cyclic use of the 20 day names made up the 260 day period. The count starts at 1 Imix, then proceed to increase the number and advance the day name after it. So, it would go

```
1 Imix        1 st day of the Tzolkin

2 Ik          2 nd  "   "   "    "

3 Akbal       3 rd  "   "   "    "

4 Kan         4 th  "   "   "    "

5 Chicchan    5  "  "   "   "    "

6 Cimi        6  "  "   "   "    "

7 Manik       7  "  "   "   "    "

8 Lamat       8  "  "   "   "    "

9 Muluc       9  "  "   "   "    "

10 Oc         10  "  "   "   "    "

11 Chuen      11  "  "   "   "    "

12 Eb         12  "  "   "   "    "

13 Ben        13  "  "   "   "    "

1 Ix         14  "  "   "   "    "

2 Men        15  "  "   "   "    "

3 Cib        16  "  "   "   "    "

4 Caban      17  "  "   "   "    "

5 Eznab      18  "  "   "   "    "

6 Cauac      19  "  "   "   "    "

7 Ahau       20  "  "   "   "    "

8 Imix       21 st  "   "   "    "

9 Ik         22 nd  "   "   "    "

10 Akbal      23 rd  "   "   "    "

11 Kan        24 th  "   "   "    "

12 Chicchan   25  "  "   "   "    "

13 Cimi       26  "  "   "   "    "

1 Manik      27  "  "   "   "    "

2 Lamat      28  "  "   "   "    "

3 Muluc      29  "  "   "   "    "

4 Oc         30  "  "   "   "    "

5 Chuen      31 st  "   "   "    "

6 Eb         32 nd  "   "   "    "

7 Ben ...    33 rd  "   "   "    "

.

.

7 Imix      241 st  "   "   "    "

8 Ik        242 nd  "   "   "    "

9 Akbal     243 rd  "   "   "    "

10 Kan       244 th  "   "   "    "

11 Chicchan  245  "  "   "   "    "

12 Cimi      246  "  "   "   "    "

13 Manik     247  "  "   "   "    "

1 Lamat     248  "  "   "   "    "

2 Muluc     249  "  "   "   "    "

3 Oc        250  "  "   "   "    "

4 Chuen     251 st  "   "   "    "

5 Eb        252 nd  "   "   "    "

6 Ben       253 rd  "   "   "    "

7 Ix        254 th  "   "   "    "

8 Men       255  "  "   "   "    "

9 Cib       256  "  "   "   "    "

10 Caban     257  "  "   "   "    "

11 Eznab     258  "  "   "   "    "

12 Cauac     259  "  "   "   "    "

13 Ahau      260  "  "   "   "    "

```

These are the twenty daynames of the Maya 'week'. The term week is applied loosely, and corresponds to the same idea as Monday, Tuesday.....Sunday does in the Western Calendar. Like the Western Calendar, the 20 daynames are cyclic, that is, they repeat again and again each in sequence. Their names are, Imix, Ik, Akbal, Kan, Chicchan, Cimi, Manik, Lamat, Muluc, Oc, Chuen, Eb, Ben, Ix, Men, Cib, Caban, Etznab, Cauac, Ahau. These are but stylised glyphs taken from codex representations. There are a whole separate grouping of glyphs which are found only in stone and stucco stelae.

Calendrical symbols

See above section on Time Periods also.
GlyphName
Kin
Uinal
Tun
Katun
Bactun
Pictun
Kinchiltun
Alautun

These calendrical symbols are based in part to the Mayan vegesimal system of counting. The basic unit of astronomic calculations is the day, or Kin. 20 Kin = 1 Uinal. Next, a break from the vegesimal system occurs, with 18 Uinal = 360 Kin = 1 Tun. 20 Tun = 1 Katun, 20 Katun = 1 Bactun, 20 Bactun = 1 Pictun, 20 Pictun = 1 Kinchiltun, 20 Kinchiltun = 1 Alautun. These are stelae and stucco glyphs from various buildings.

But, they rarely used Pictun, Kinchiltun and Alautun depictions. Their usual calculations mostly concerned terms up to Baktun, since 8000 years would be a significantly broad enough time to consider.

The Calendar Round

The Calendar Round was a name which applied to a length of time corresponding to 18980 days. This is achieved by using both the Tzolkin and Haab in concert. Within this period, there are exactly 73 Tzolkin, and 52 Haab. This means that a Calendar Round date must have components of both these systems. The zero date 4 Ahau 8 Cumhu from which the Maya referenced all calculations is typical of this representation.

We can demonstrate this by the following, the start and end of a Calendar Round.

```
=============================  ====================    ===================   ==========

Day of the Tzolkin          Day of the Haab       Calendar Round Date   Day Number

=============================  ====================    ===================   ==========

Day    1 of the   1st Tzolkin; Day   1 of  1st Haab =  1 IMIX      0 POP   = DAY     1

Day    2 of the   1st Tzolkin; Day   2 of  1st Haab =  2 IK        1 POP   = DAY     2

Day    3 of the   1st Tzolkin; Day   3 of  1st Haab =  3 AKBAL     2 POP   = DAY     3

Day    4 of the   1st Tzolkin; Day   4 of  1st Haab =  4 KAN       3 POP   = DAY     4

Day    5 of the   1st Tzolkin; Day   5 of  1st Haab =  5 CHICCHAN  4 POP   = DAY     5

Day    6 of the   1st Tzolkin; Day   6 of  1st Haab =  6 CIMI      5 POP   = DAY     6

Day    7 of the   1st Tzolkin; Day   7 of  1st Haab =  7 MANIK     6 POP   = DAY     7

Day    8 of the   1st Tzolkin; Day   8 of  1st Haab =  8 LAMAT     7 POP   = DAY     8

Day    9 of the   1st Tzolkin; Day   9 of  1st Haab =  9 MULUC     8 POP   = DAY     9

Day   10 of the   1st Tzolkin; Day  10 of  1st Haab = 10 OC        9 POP   = DAY    10

Day   11 of the   1st Tzolkin; Day  11 of  1st Haab = 11 CHUEN    10 POP   = DAY    11

Day   12 of the   1st Tzolkin; Day  12 of  1st Haab = 12 EB       11 POP   = DAY    12

Day   13 of the   1st Tzolkin; Day  13 of  1st Haab = 13 BEN      12 POP   = DAY    13

Day   14 of the   1st Tzolkin; Day  14 of  1st Haab =  1 IX       13 POP   = DAY    14

Day   15 of the   1st Tzolkin; Day  15 of  1st Haab =  2 MEN      14 POP   = DAY    15

Day   16 of the   1st Tzolkin; Day  16 of  1st Haab =  3 CIB      15 POP   = DAY    16

Day   17 of the   1st Tzolkin; Day  17 of  1st Haab =  4 CABAN    16 POP   = DAY    17

Day   18 of the   1st Tzolkin; Day  18 of  1st Haab =  5 EZNAB    17 POP   = DAY    18

Day   19 of the   1st Tzolkin; Day  19 of  1st Haab =  6 CAUAC    18 POP   = DAY    19

Day   20 of the   1st Tzolkin; Day  20 of  1st Haab =  7 AHAU     19 POP   = DAY    20

Day   21 of the   1st Tzolkin; Day  21 of  1st Haab =  8 IMIX      0 UO    = DAY    21

Day   22 of the   1st Tzolkin; Day  22 of  1st Haab =  9 IK        1 UO    = DAY    22

Day   23 of the   1st Tzolkin; Day  23 of  1st Haab = 10 AKBAL     2 UO    = DAY    23

Day   24 of the   1st Tzolkin; Day  24 of  1st Haab = 11 KAN       3 UO    = DAY    24

Day   25 of the   1st Tzolkin; Day  25 of  1st Haab = 12 CHICCHAN  4 UO    = DAY    25

. .

Day  253 of the  73rd Tzolkin; Day 358 of  52nd Haab =  6 CIB     16 CUMHU = DAY 18973

Day  254 of the  73rd Tzolkin; Day 359 of  52nd Haab =  7 CIB     17 CUMHU = DAY 18974

Day  255 of the  73rd Tzolkin; Day 360 of  52nd Haab =  8 CIB     18 CUMHU = DAY 18975

Day  256 of the  73rd Tzolkin; Day 361 of  52nd Haab =  9 CIB     19 CUMHU = DAY 18976

Day  257 of the  73rd Tzolkin; Day 362 of  52nd Haab = 10 CABAN    1 UAYEB = DAY 18977

Day  258 of the  73rd Tzolkin; Day 363 of  52nd Haab = 11 EZNAB    2 UAYEB = DAY 18978

Day  259 of the  73rd Tzolkin; Day 364 of  52nd Haab = 12 CAUAC    3 UAYEB = DAY 18979

Day  260 of the  73rd Tzolkin; Day 365 of  52nd Haab = 13 AHAU     4 UAYEB = DAY 18980

=============================  ====================    ===================   ==========

Day of the Tzolkin          Day of the Haab       Calendar Round Date   Day Number

=============================  ====================    ===================   ==========

This gives 18980 unique Calendar Round dates.

```

Calendar Round Calculations

To calculate a date, one must find out how may days have elapsed since the zero date 4 Ahau 8 Cumhu. The numerals can be represented in arabic numerals in the following way:

9.15.2.6.4

The right most numeral represents the Kin value. Here we have 4 Kin. Next to the left, is the number of Uinals in this date, 6 and so on. The following gives the calculation of the total number of days in arabic numerals of the vigesimal Mayan date 9.15.2.6.4 :

```
1 day   x  4 Kin        =          4

20 days  x  6 Uinal      =        120

360  "    x  2 Tun        =        720

7 200  "    x 15 Katun      =     108000

144 000  "    x  9 Bactun     =   11664000

======================================================

Total number of days is   11772844 days

```
• Calculation of the Tzolkin part of the Calendar Round date:

The total number of days 11772844 must first be divided by 13, and find the remainder.
11772844 divided by 13 is 905603 with a remainder of 5.
Next, the total number of days 11772844 must first be divided by 20, and find the remainder.
11772844 divided by 20 is 588642 with a remainder of 4.

The use of the remainders will give us the necesary information on how to advance the Tzolkin part of the zero date 4 Ahau, to the sample date 9.15.2.6.4.

Add the first remainder, 5, to 4 (of 4 Ahau). This gives 9. If the result is greater than 13, then all multiples of 13 must be taken to give a remainder. Since our result is 9, we proceed to the next part.

This involves advancing daynames forward from Ahau by the number of days given by the second remainder, 4. This would lead us to Kan.

So the Tzolkin part of the date is 9 Kan.

• Calculation of the Haab part of the Calendar Round date. The total number of days 11772844 must be divided by 365. The remainder is the number of days that must be advanced from the zero date 4 Ahau 8 Cumhu, in the 8 Cumhu part of the Calendar Round Date.

11772844 divided by 365 is 32254 with a remainder of 134.

Hence 134 days must be advanced from the Haab date 8 Cumhu.

Since Cumhu is the 18th month, 8 Cumhu is the ninth day. Since there are 20 days in this month, there are 11 remaining plus the five of the Uayeb month. This makes 16 days. Subtracting 16 from 134 leaves 118 days. This has 5 completed months of 20 days, and 18 days into the sixth month. The Haab date is therefore 17 Xul.

• 9.15.2.6.4 9 Kan 17 Xul is the Calendar Round Date. Though the representation is slighlty wrong with the mixing of stelae and codex glyphs, the following gives an idea of how a double column stela's appearance. The glyphs are read A to G in our example.

A

B

C

D

E

F

G
Typical Codex
column
representation
of
9.15.2.6.4

The Tzolkin and Haab dates and the numeral values of the time periods can be used to check if the the calculations are correct.