6. The Chinese Calendar
The Chinese calendar is a lunisolar calendar based on calculations of the positions of the Sun and Moon. Months of 29 or 30 days begin on days of astronomical New Moons, with an intercalary month being added every two or three years. Since the calendar is based on the true positions of the Sun and Moon, the accuracy of the calendar depends on the accuracy of the astronomical theories and calculations.
Although the Gregorian calendar is used in the Peoples' Republic of China for administrative purposes, the traditional Chinese calendar is used for setting traditional festivals and for timing agricultural activities in the countryside. The Chinese calendar is also used by Chinese communities around the world.
| Celestial Stems | Earthly Branches |
| 1. jia | 1. zi (rat) |
| 2. yi | 2. chou (ox) |
| 3. bing | 3. yin (tiger) |
| 4. ding | 4. mao (hare) |
| 5. wu | 5. chen (dragon) |
| 6. ji | 6. si (snake) |
| 7. geng | 7. wu (horse) |
| 8. xin | 8. wei (sheep) |
| 9. ren | 9. shen (monkey) |
| 10. gui | 10. you (fowl) |
| 11. xu (dog) | |
| 12. hai (pig) |
| 1. jia-zi | 16. ji-mao | 31. jia-wu | 46. ji-you |
| 2. yi-chou | 17. geng-chen | 32. yi-wei | 47. geng-xu |
| 3. bing-yin | 18. xin-si | 33. bing-shen | 48. xin-hai |
| 4. ding-mao | 19. ren-wu | 34. ding-you | 49. ren-zi |
| 5. wu-chen | 20. gui-wei | 35. wu-xu | 50. gui-chou |
| 6. ji-si | 21. jia-shen | 36. ji-hai | 51. jia-yin |
| 7. geng-wu | 22. yi-you | 37. geng-zi | 52. yi-mao |
| 8. xin-wei | 23. bing-xu | 38. xin-chou | 53. bing-chen |
| 9. ren-shen | 24. ding-hai | 39. ren-yin | 54. ding-si |
| 10. gui-you | 25. wu-zi | 40. gui-mao | 55. wu-wu |
| 11. jia-xu | 26. ji-chou | 41. jia-chen | 56. ji-wei |
| 12. yi-hai | 27. geng-yin | 42. yi-si | 57. geng-shen |
| 13. bing-zi | 28. xin-mao | 43. bing-wu | 58. xin-you |
| 14. ding-chou | 29. ren-chen | 44. ding-wei | 59. ren-xu |
| 15. wu-yin | 30. gui-si | 45. wu-shen | 60. gui-hai |
6.1 Rules
There is no specific initial epoch for counting years. In historical records, dates were specified by counts of days and years in sexagenary cycles and by counts of years from a succession of eras established by reigning monarchs.
The sixty-year cycle consists of a set of year names that are created by pairing a name from a list of ten Celestial Stems with a name from a list of twelve Terrestrial Branches, following the order specified in Table 6.1.1. The Celestial Stems are specified by Chinese characters that have no English translation; the Terrestrial Branches are named after twelve animals. After six repetitions of the set of stems and five repetitions of the branches, a complete cycle of pairs is completed and a new cycle begins. The initial year (jia-zi) of the current cycle began on 1984 February 2.
Days are measured from midnight to midnight. The first day of a calendar month is the day on which the astronomical New Moon (i.e., conjunction) is calculated to occur. Since the average interval between successive New Moons is approximately 29.53 days, months are 29 or 30 days long. Months are specified by number from 1 to 12. When an intercalary month is added, it bears the number of the previous month, but is designated as intercalary. An ordinary year of twelve months is 353, 354, or 355 days in length; a leap year of thirteen months is 383, 384, or 385 days long.
The conditions for adding an intercalary month are determined by the occurrence of the New Moon with respect to divisions of the tropical year. The tropical year is divided into 24 solar terms, in 15o segments of solar longitude. These divisions are paired into twelve Sectional Terms (Jieqi) and twelve Principal Terms (Zhongqi), as shown in Table 6.1.2. These terms are numbered and assigned names that are seasonal or meteorological in nature. For convenience here, the Sectional and Principal Terms are denoted by S and P, respectively, followed by the number. Because of the ellipticity of the Earth's orbit, the interval between solar terms varies with the seasons.
Reference works give a variety of rules for establishing New Year's Day and for intercalation in the lunisolar calendar. Since the calendar was originally based on the assumption that the Sun's motion was uniform through the seasons, the published rules are frequently inadequate to handle special cases.
The following rules (Liu and Stephenson, in press) are currently used as the basis for calendars prepared by the Purple Mountain Observatory (1984):
(1) The first day of the month is the day on which the New Moon occurs.
(2) An ordinary year has twelve lunar months; an intercalary year has thirteen lunar months.
(3) The Winter Solstice (term P-11) always falls in month 11.
(4) In an intercalary year, a month in which there is no Principal Term is the intercalary month. It is assigned the number of the preceding month, with the further designation of intercalary. If two months of an intercalary year contain no Principal Term, only the first such month after the Winter Solstice is considered intercalary.
(5) Calculations are based on the meridian 120o East.
The number of the month usually corresponds to the number of the Principal Term occurring during the month. In rare instances, however, there are months that have two Principal Terms, with the result that a nonintercalary month will have no Principal Term. As a result the numbers of the months will temporarily fail to correspond to the numbers of the Principal Terms. These cases can be resolved by strictly applying rules 2 and 3.
| Term* | Name | Sun's Longitude | Approx. Greg. Date | Duration | |
| S-1 | Lichun | Beginning of Spring | 315 | Feb. 4 | |
| P-1 | Yushui | Rain Water | 330 | Feb. 19 | 29.8 |
| S-2 | Jingzhe | Waking of Insects | 345 | Mar. 6 | |
| P-2 | Chunfen | Spring Equinox | 0 | Mar. 21 | 30.2 |
| S-3 | Qingming | Pure Brightness | 15 | Apr. 5 | |
| P-3 | Guyu | Grain Rain | 30 | Apr. 20 | 30.7 |
| S-4 | Lixia | Beginning of Summer | 45 | May 6 | |
| P-4 | Xiaoman | Grain Full | 60 | May 21 | 31.2 |
| S-5 | Mangzhong | Grain in Ear | 75 | June 6 | |
| P-5 | Xiazhi | Summer Solstice | 90 | June 22 | 31.4 |
| S-6 | Xiaoshu | Slight Heat | 105 | July 7 | |
| P-6 | Dashu | Great Heat | 120 | July 23 | 31.4 |
| S-7 | Liqiu | Beginning of Autumn | 135 | Aug. 8 | |
| P-7 | Chushu | Limit of Heat | 150 | Aug. 23 | 31.1 |
| S-8 | Bailu | White Dew | 165 | Sept. 8 | |
| P-8 | Qiufen | Autumnal Equinox | 180 | Sept. 23 | 30.7 |
| S-9 | Hanlu | Cold Dew | 195 | Oct. 8 | |
| P-9 | Shuangjiang | Descent of Frost | 210 | Oct. 24 | 30.1 |
| S-10 | Lidong | Beginning of Winter | 225 | Nov. 8 | |
| P-10 | Xiaoxue | Slight Snow | 240 | Nov. 22 | 29.7 |
| S-11 | Daxue | Great Snow | 255 | Dec. 7 | |
| P-11 | Dongzhi | Winter Solstice | 270 | Dec. 22 | 29.5 |
| S-12 | Xiaohan | Slight Cold | 285 | Jan. 6 | |
| P-12 | Dahan | Great Cold | 300 | Jan. 20 | 29.5 |
In general, the first step in calculating the Chinese calendar is to check for the existence of an intercalary year. This can be done by determining the dates of Winter Solstice and month 11 before and after the period of interest, and then by counting the intervening New Moons.
Published calendrical tables are often in disagreement about the Chinese calendar. Some of the tables are based on mean, or at least simplified, motions of the Sun and Moon. Some are calculated for other meridians than 120o East. Some incorporate a rule that the eleventh, twelfth, and first months are never followed by an intercalary month. This is sometimes not stated as a rule, but as a consequence of the rapid change in the Sun's longitude when the Earth is near perihelion. However, this statement is incorrect when the motions of the Sun and Moon are accurately calculated.
6.2 History of the Chinese Calendar
In China the calendar was a sacred document, spopnsored and promulgated by the reigning monarch. For more than two millennia, a Bureau of Astronomy made astronomical observations, calculated astronomical events such as eclipses, prepared astrological predictions, and maintained the calendar (Needham, 1959). After all, a successful calendar not only served practical needs, but also confirmed the consonance between Heaven and the imperial court.
Analysis of surviving astronomical records inscribed on oracle bones reveals a Chinese lunisolar calendar, with intercalation of lunar months, dating back to the Shang dynasty of the fourteenth century B.C. Various intercalation schemes were developed for the early calendars, including the nineteen-year and 76-year lunar phase cycles that came to be known in the West as the Metonic cycle and Callipic cycle.
From the earliest records, the beginning of the year occurred at a New Moon near the winter solstice. The choice of month for beginning the civil year varied with time and place, however. In the late second century B.C., a calendar reform established the practice, which continues today, of requiring the winter solstice to occur in month 11. This reform also introduced the intercalation system in which dates of New Moons are compared with the 24 solar terms. However, calculations were based on the mean motions resulting from the cyclic relationships. Inequalities in the Moon's motions were incorporated as early as the seventh century A.D. (Sivin, 1969), but the Sun's mean longitude was used for calculating the solar terms until 1644 (Liu and Stephenson, in press).
Years were counted from a succession of eras established by reigning emperors. Although the accession of an emperor would mark a new era, an emperor might also declare a new era at various times within his reign. The introduction of a new era was an attempt to reestablish a broken connection between Heaven and Earth, as personified by the emperor. The break might be revealed by the death of an emperor, the occurrence of a natural disaster, or the failure of astronomers to predict a celestial event such as an eclipse. In the latter case, a new era might mark the introduction of new astronomical or calendrical models.
Sexagenary cycles were used to count years, months, days, and fractions of a day using the set of Celestial Stems and Terrestrial Branches described in Section 6.1. Use of the sixty-day cycle is seen in the earliest astronomical records. By contrast the sixty-year cycle was introduced in the first century A.D. or possibly a century earlier (Tung, 1960; Needham, 1959). Although the day count has fallen into disuse in everyday life, it is still tabulated in calendars. The initial year (jia-zi) of the current year cycle began on 1984 February 2, which is the third day (bing-yin) of the day cycle.
Western (pre-Copernican) astronomical theories were introduced to China by Jesuit missionaries in the seventeenth century. Gradually, more modern Western concepts became known. Following the revolution of 1911, the traditional practice of counting years from the accession of an emperor was abolished.