The Chinese Lunisolar Calendar

The calendar that fixes the date of the Chinese new year, of the Qingming observance and of the almanac’s seasonal advice is lunisolar: its months are lunar and its year is held in step with the sun. Four separate mechanisms do that work, and they are routinely run together into one. A counting cycle labels days and years. A conjunction opens a month. A division of the solar year into twenty-four parts tracks the seasons. A rule joining the last two decides when a thirteenth month is inserted.

Only the third and fourth of these have anything to do with measuring the sky.

A counting cycle, not a division of the sky

Two series are paired: ten heavenly stems, tiāngān 天干, and twelve terrestrial branches, dìzhī 地支, in fixed interlock, giving a cycle of sixty. The short form is gānzhī 干支. The earliest surviving Chinese documents, from the mid second millennium BCE, already use a cycle of sixty to count off days, and a single series of ten or of twelve would have been too short to be useful for that ^{1 p. 69}. With the formation of a single empire in the third century BCE, and so a single chronology, scribes began applying the same series to years as well ^{1 p. 70}.

How far back the day-count runs without interruption is an open question. Sivin puts it plainly: there is some uncertainty about whether the day-count has been continuous since the oldest written records of about 1450 BCE, and what can be relied on is that both the year and the day counts are unbroken from the earliest comprehensive astronomical system, around the beginning of the Common Era ^{1 p. 70}.

Months begin at a conjunction

A month begins with the new moon, meaning the instant of conjunction; a first sighting of the crescent plays no part. Because a month boundary is an instant, the civil date it falls on depends on the meridian to which the computation is referred, so a meridian has to be named. The modern rule names Beijing, and distinguishes two conventions at the same place: the local mean time of 116 degrees 25 minutes east for dates before 1929, and the eight-hour zone after it ².

Twenty-four divisions of the solar year

Since a lunar month tracks nothing seasonal, the seasons are carried by a separate solar structure. The qi 氣 were twelve equal divisions of the tropical year, a solar counterpart of the month, each about 30.4 days long. Each was cut in half, into a nodal term, jiéqì 節氣, just after the node dividing one qi from the next, and a medial or principal term, zhōngqì 中氣, between the nodes. The set of twenty-four takes its usual name from the halves ^{1 p. 79}. Later and current usage names the whole set of twenty-four with the word for the nodal half, which is how the 2006 national inventory enters it ³.

The names of the terms, from Enthronement of Spring through Grain Rains to Greater Snow, describe a climatic and agricultural year, and specifically that of north central China rather than of the whole territory any later dynasty governed ^{1 p. 79}.

The leap month

Twelve lunar months fall about eleven days short of a solar year, so a thirteenth has to be inserted from time to time, and the question is which month gets doubled. The classical answer used the principal terms: a month containing no zhōngqì became the intercalary month. Sivin records this as a subsidiary rule that treatises mention because it was classical, without necessarily using it ^{1 p. 81}.

The rule now in force is the classical one with a qualification attached. In a year running to thirteen months between one eleventh month and the next, the leap month is the first of those months that contains no principal term ². The unqualified form no longer suffices on its own, and the reason is the subject of the next section.

Mean terms and true terms

The twenty-four terms have been two different mathematical objects at different periods, under one name.

In the Season Granting system, the reform of 1280 whose treatise survives in full, the qi of the civil calendar were mean terms: equal divisions of the tropical year, so equal intervals of time. The system also computed a corrected qi, referred to the sun’s apparent position, but that entered as part of the solar theory rather than as the basis of the calendar ^{1 p. 395}.

The gap between the two is substantial, and the 1280 system measured it. Its Four Standard Points are the beginnings of corrected terms and coincide with the apparent equinoxes and solstices. The vernal Standard Point precedes the beginning of the mean term Vernal Division by 2.4 tu, the system’s maximum equation of centre. So the apparent sun crosses the equator 88.9 days after the winter solstice, at the halfway point in angle between the solstices, and enters the mean term Vernal Division 2.4 days later, at the halfway point in time ^{1 p. 411}.

That is the same distinction this site draws at a cross-quarter day, arrived at from the other end of Eurasia and about seven centuries earlier: the angular midpoint of a season and its temporal midpoint are different instants, and neither is a worse definition of a middle than the other. See Cross-Quarter Days, where all three defensible datings of a station are set out, and Solstices and Equinoxes for the instants the midpoints are measured between. The cause is identical in both traditions: the sun’s apparent motion along the ecliptic is not uniform, because the Earth’s orbit is eccentric ⁴.

The difference between a European cross-quarter day and a Chinese solar term is what each tradition did with the discrepancy. In Britain and Ireland the calendar dates were fixed and the astronomical midpoints are a modern refinement. In China the two definitions were both computed inside one official system for centuries, kept apart by function, and then swapped: the calendar moved from the mean terms to the true ones.

The system that made the swap was compiled under Jesuit direction and adopted when the Qing took Beijing. Sivin dates the official use of the Temporal Pattern system, Shíxiàn lì 時憲曆, from 1644 to 1742, and describes its treatise as a hybrid of Chinese content with European content that was already going out of date in Europe ^{1 pp. 52-53, 234}. Martzloff’s survey of the canons that computed the calendar runs from 104 BCE and stops at 1644 for the same reason: what follows is a different object ⁵.

The terms are now true terms, dìngqì 定氣 rather than píngqì 平氣: equal divisions of ecliptic longitude, fifteen degrees apart, with the twelve principal terms falling at multiples of thirty ². Because the sun’s apparent speed varies, equal steps in longitude are unequal steps in time, so the intervals between successive principal terms differ, and the placement of leap months is no longer evenly distributed across the year ⁴. The published national standard specifies the computational model for the current rule and the precision it must reach ⁶.

One phrase, twenty-four solar terms, therefore names equal divisions of time on one side of the seventeenth century and equal divisions of solar longitude on the other. A conversion table that treats them as one thing will be wrong about one of them.

A calendar with a standards number

The material on this page is inventoried, inscribed and standardised, and each of those acts has a retrievable document behind it.

State Council notice Guofa 2006 no. 18, of 20 May 2006, promulgated the first national inventory of intangible cultural heritage in ten categories and 518 items. Item 516, coded IX-68 under folk custom, is the twenty-four solar terms of the lunisolar calendar, entered against the China Agricultural Museum ³. In 2016 the same body of knowledge was inscribed on the UNESCO Representative List as element 00647 ⁷. In 2017 the arrangement rules, the computational model, the required precision and the conditions of promulgation were issued as GB/T 33661-2017, effective 1 September of that year ⁶.

The calendar and divination are two subjects, not one

This distinction matters more than it looks, and getting it wrong is the most common fault in outside accounts.

The state that inventories, inscribes and standardises the calendar does not extend the same standing to divination. During the Nanjing decade the Nationalist government pursued campaigns against a range of practices it classified as superstition, and calendar reform belonged to the same politics ⁸. In the present, practitioners of fate calculation argue for their own legitimacy in borrowed registers: as moral counsel, as traditional culture, as psychological work, as an academic subject ⁹. Over the same decades the calendar acquired an inventory entry, a UNESCO inscription and a standards number ³⁷⁶.

Two things follow for a reference work written from outside. The argument about the standing of divination is a domestic one, conducted in Chinese, under Chinese law, by people whose livelihoods are in it ⁹; a foreign encyclopedia is not a party to it and has no standing to adjudicate it. And a page that runs the calendar and divination together as one topic misdescribes both, since one of them has a standards number and the other is the subject of a live dispute about whether it may be practised for money.

Where this page sits

The institution that computed the calendar, the prohibition on interpreting the sky outside it, and the trial of the man who ran it under the Qing are treated at The Astronomical Bureau and the Calendar Case. The arrival in Tang Chang’an of the Hellenistic material this site follows westward is at Eastward Transmission of Hellenistic Astral Material.