Two lists that mesh together
The sexagenary cycle is a way of naming time using two lists that run side by side. The first list has ten items, the heavenly stems. The second has twelve, the earthly branches. Each name in the cycle is a pair: one stem and one branch, taken in order. The pairing starts with the first stem and the first branch, then the second of each, and so on. When the stems run out after ten, they start again from the beginning, and the branches continue to their twelfth and then restart.
The stems are traditionally given in Chinese as jia, yi, bing, ding, wu, ji, geng, xin, ren and gui. The branches are zi, chou, yin, mao, chen, si, wu, wei, shen, you, xu and hai. Their meanings in everyday speech were largely lost, and the names are used as labels.
Why sixty
Ten and twelve share a factor of 2, so they do not produce all 120 possible combinations. A stem paired with a branch always has the same parity, meaning that an odd-numbered stem goes with an odd-numbered branch. Counting through, the pair returns to jia-zi after the least common multiple of 10 and 12, which is 60. That is why the cycle has sixty terms, not one hundred and twenty.
A short check using a modern example: 2024 was a jiachen year, because 2024 is 40 years after the jiazi year of 1984, and 40 leaves a remainder of 0 when divided by 10 (back to jia) and 4 when divided by 12 (the fifth branch, chen). Two years later, 2026 is a bingwu year. The next jiazi year after 1984 is 2044.
Older than the year count: naming days
The use of the cycle for counting days is very old. Oracle-bone inscriptions from the late Shang period, which are among the earliest surviving Chinese writing, record dates with these stem and branch pairs. The stems were also used in ritual names, as in the temple names of Shang kings, which is one sign of how deeply they were built into ritual.
The cycle runs without interruption. A day is named jiazi, the next is yichou, and after sixty days the sequence returns to jiazi again. It does not depend on the moon or sun, so it can be combined with any month and year system. Historians use it to check dates, since a source that gives both a date and a day-name can be tested against the cycle.
Counting years in the same way came later. Systematic use for years is generally associated with the Han period and after, though the details of its adoption are less certain than the day count.
The branches and the twelve animals
The twelve branches became linked with a set of twelve animals: rat, ox, tiger, rabbit, dragon, snake, horse, goat, monkey, rooster, dog and pig. The pairing of animals with branches is attested well after the branches themselves and is not part of the original system. Variations in which animal sits in each position exist in neighbouring cultures. A year’s animal is therefore just a way of reading the branch, and the full year name in the cycle contains the stem as well.
The stems and the five phases
The ten stems are commonly grouped in pairs that are associated with the five phases, often rendered as five elements: wood, fire, earth, metal and water. Each phase has two stems, one linked with yin and one with yang. This lets a year be described as, for example, “yang wood dragon” for jiachen. The yin and yang idea is discussed more fully under yin and yang. The five-phase scheme should be set apart from the Western four elements doctrine, since the two are different systems with different members.
What sixty has meant
Because a full cycle is sixty years, a person reaches the year of their birth again at age sixty, the sixtieth anniversary of birth in the traditional count. In Chinese and related cultures this has been marked as a significant birthday, in the way that other cultures mark particular anniversary traditions. The cultural meaning here follows from the arithmetic of the cycle, not from any property attributed to the number.
Sixty is also a convenient number mathematically, being divisible by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30. The Mesopotamian sexagesimal system used sixty as a base for a different reason, and no direct link between the two is established, so they are best treated as independent developments. Within the wider field of Chinese number symbolism, the sexagenary cycle is a counting device and sits apart from the homophone-based luck associated with numbers like eight.
Outside China and beyond the calendar
The system spread to Korea, Japan and Vietnam, which developed their own readings of the stems and branches and their own set of animals. The Japanese eto, for example, uses native Japanese readings alongside the Chinese-derived ones. The cycle is also used outside calendars, in naming events, such as the Chinese-named years of historical episodes, and in some traditional systems of astrology and divination. Those uses are beliefs of the traditions that employ them and are not claims that the cycle reveals anything about people or events.
One more cycle is worth mentioning for contrast. The Aztec 260-day tonalpohualli count also interlocks two lists, one of numbers and one of day signs, but it uses 13 and 20 and produces a cycle of 260 days. The idea of meshing two repeating lists to obtain a long cycle is a general one, which different cultures have used in different ways.