Sexagenary cycle

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Sexegenary cycle

Japanese: 干支 Kan-shi or E-to

From ancient times China had two series of characters used for numbering (not for numbers!). One is the "ten stems" (jik-kan 十干), the other is the "twelve branches" (jûni-shi 十二支). They were combined to make a cycle of 60, the sexegenary cycle. These series spread over east and south-east Asia and were early taken over by the Japanese as part of the Chinese culture[1]. They are still known in Japan, though since the Meiji period (1868-1912) their use has been very limited.

TheTwelve Branches (Jûni-shi 十二支)


The shi characters, translated variously as "branches," "zodiacal characters," "horary characters," etc. are a series of twelve characters used for various "cyclic" purposes. They were used for indicating direction, time, and, together with the kan, for indicating years and days. Often, though, days and years are referred to by the shi element only, without the kan. The shi early on became associated with animals, but the characters for the shi and the animals are completely distinct.


The Twelve Branches 十干
No. Kanji Kun On Time Direction  
1 ne shi 23:00- 1:00 0:00 N (0º) rat
2 ushi chû 1:00- 3:00 2:00 30º ox
3 tora in 3:00-5:00 4:00 60º tiger
4 u 5:00-7:00 6:00 E (90º) hare
5 tatsu shin 7:00-9:00 8:00 120º dragon
6 mi shi 9:00-11:00 10:00 150º snake
7 uma go 11:00-13:00 12:00 S (180º) horse
8 hitusji bi 13:00-15:00 14:00 210º sheep
9 saru shin 15:00-17:00 16:00 240º monkey
10 tori 17:00-19:00 18:00 W (270º) bird
11 inu jutsu 19:00-21:00 20:00 300º dog
12 i kai 21:00-23:00 22:00 330º boar
Kun are Japanese readings, which are normally used. On are Chinese readings.
NE, SE, SW, and NW are 丑寅 (ushi-tora), 辰巳、未申、and 戊亥.

The Ten stems (Jik-kan 十干)


The ten kan characters are the yang (陽) and yin (陰) of the five elements of wood, fire, earth, metal, and water. They were particularly used together with the shi in the sexedecimal cycle. through bo were also sometimes used to designate the night hours from inu to tora. However, now in Japan their use is mainly limited to indicating rankings, as for academic grades, or for distinguishing parties in a contract (such as, " agrees to pay to otsu or an agent that otsu selects..."). In these uses, the Chinese readings are used. The kan are thus not as cyclical as the shi are.


Kan tables

The Ten Stems 十干
No Kanji Kun On  
1 kinoe e. wood
2 kinoto otsu y. wood
3 hinoe hei e. fire
4 hinoto tei y. fire
5 tsuchinoe bo e. earth
6 tsuchinoto ki y. earth
7 kanoe e. metal
8 kanoto shin y. metal
9 mizunoe jin e. water
10 mizunoto ki y. water
Kun is Japanese reading, On is Chinese reading.
e. is “elder brother of”; y. is “younger brother of.”

The sexagesimal (60-character) cycle


When the two cycles are used together, one gets a series of sixty pairs of characters as in the table below. (60 is the least common multiple of 10 and 12.) Note that each shi is used only with either the "elder brother" ("upper") kan or with the "youger brother" ("lower") kan: odd-numbered shi go with odd-number, or upper, kan, and even-numbered shi go with even-numbered, or lower, kan. This means, for example, that a translation of tsuchinoe-tatsu as "Earth-Dragon" instead of "Elder Brother of Earth-Dragon" is unambiguous.

These pairs are normally read using the Japanese readings, as kinoe-ne for 甲子.

From the numbers of a given K(an) and S(hi) the P(osition) in the cycle can be computed as follows: if K>=S: P = (K-S)*5+K; if S>K: P = (12+K-S)*5+K. So kanoto-u (8,4) is the 28th position, and hinoe-tatsu (3,5) is in the 53rd. One can also search in the table below.

The cycle was used to indicate days, and especially year dates. For example, 1504 was a kinoe-ne year. Dating documents by cyclic years was very common, but dating documents by cyclic days was extremely rare in Japan from what I have seen. However, as the cycle repeats every 60 years (or days), the cyclic indication is not enough to determine a date; one has to have some other information. To find the year associated with a kan-shi, use the table below and add or subtract a multiple of sixty as needed, or use the method in the year dates article.

As mentioned above, when used as a date, the Japanese reading is used for the kan-shi. However when a kan-shi is used as part of a proper name, the Chinese reading are used. Thus, the Boshin War (戊辰戦争) took place in 1868, a tsuchinoe-tatsu 戊辰 year, and all high-school baseball players dream of playing in Kôshi-en Stadium (甲子園), which opened the kinoe-ne 甲子 year of 1924. The Chinese readings used in such cases are those given in the tables above, except that 甲子 is sometimes read kasshi as well as kôshi and 乙 can be read as either itsu or otsu, by onbin it- is-, ot- or os-. So we have the 乙丑丸 Itchû-maru, "The Ship 1865".


The 60-Cycle 干支
No. Comb. Kanji Reading Sample Year
1   1,1 甲子 kinoe ne 1504
2   2,2 乙丑 kinoto ushi 1505
3   3,3 丙寅 hinoe tora 1506
4   4,4 丁卯 hinoto u 1507
5   5,5 戊辰 tsuchinoe tatsu 1508
6   6,6 己巳 tsuchinoto mi 1509
7   7,7 庚午 kanoe uma 1510
8   8,8 辛未 kanoto hitusji 1511
9   9,9 壬申 mizunoe saru 1512
10 10,10 癸酉 mizunoto tori 1513
11   1,11 甲戌 kinoe inu 1514
12   2,12 乙亥 kinoto i 1515
13   3,1 丙子 hinoe ne 1516
14   4,2 丁丑 hinoto ushi 1517
15   5,3 戊寅 tsuchinoe tora 1518
16   6,4 己卯 tsuchinoto u 1519
17   7,5 庚辰 kanoe tatsu 1520
18   8,6 辛巳 kanoto mi 1521
19   9,7 壬午 mizunoe uma 1522
20 10,8 癸未 mizunoto hitusji 1523
21   1,9 甲申 kinoe saru 1524
22   2,10 乙酉 kinoto tori 1525
23   3,11 丙戌 hinoe inu 1526
24   4,12 丁亥 hinoto i 1527
25   5,1 戊子 tsuchinoe ne 1528
26   6,2 己丑 tsuchinoto ushi 1529
27   7,3 庚寅 kanoe tora 1530
28   8,4 辛卯 kanoto u 1531
29   9,5 壬辰 mizunoe tatsu 1532
30 10,6 癸巳 mizunoto mi 1533
31   1,7 甲午 kinoe uma 1534
32   2,8 乙未 kinoto hitusji 1535
33   3,9 丙申 hinoe saru 1536
34   4,10 丁酉 hinoto tori 1537
35   5,11 戊戌 tsuchinoe inu 1538
36   6,12 己亥 tsuchinoto i 1539
37   7,1 庚子 kanoe ne 1540
38   8,2 辛丑 kanoto ushi 1541
39   9,3 壬寅 mizunoe tora 1542
40 10,4 癸卯 mizunoto u 1543
41   1,5 甲辰 kinoe tatsu 1544
42   2,6 乙巳 kinoto mi 1545
43   3,7 丙午 hinoe uma 1546
44   4,8 丁未 hinoto hitusji 1547
45   5,9 戊申 tsuchinoe saru 1548
46   6,10 己酉 tsuchinoto tori 1549
47   7,11 庚戌 kanoe inu 1550
48   8,12 辛亥 kanoto i 1551
49   9,1 壬子 mizunoe ne 1552
50 10,2 癸丑 mizunoto ushi 1553
51   1,3 甲寅 kinoe tora 1554
52   2,4 乙卯 kinoto u 1555
53   3,5 丙辰 hinoe tatsu 1556
54   4,6 丁巳 hinoto mi 1557
55   5,7 戊午 tsuchinoe uma 1558
56   6,8 己未 tsuchinoto hitusji 1559
57   7,9 庚申 kanoe saru 1560
58   8,10 辛酉 kanoto tori 1561
59   9,11 壬戌 mizunoe inu 1562
60 10,12 癸亥 mizunoto i 1563


  1. A mirror in Sumida (隅田) Hachiman-gu Shrine in Hashimoto City, Wakayama Prefecture has an inscription that includes the year in cyclic form, 癸未年 (see below). Scholars are mostly divided about whether this refers to 443 A.D. or to 503 A.D., but in any case, one can say that the cycle was used in Japan to indicate years in the fifth century. (Yoshida Yoshirô, The Japanese Calendar, p. 50 (岡田芳朗,日本の暦、木耳社、[Mokujisha],1972).