Calendars · Lunisolar

At its core, Bazi (the Four Pillars) translates the instant of a person's birth into a set of Stem-Branch coordinates:

The moment of birth (year, month, day, hour) → conversion into Stem-Branch (the Four Pillars) → conversion into the relationships among the Five Elements

That “conversion” depends on calendrical rules at every step:

The key conclusion: Bazi rests on the skeleton of the solar calendar (the solar terms), not on the skeleton of the lunar calendar (the Moon). The lunar month affects only leap months and festivals; it has no bearing on casting a Bazi chart. This is where beginners go wrong most often.

1.2.1The fundamental difference between three calendar types

The traditional Chinese calendar — called the “Lunar Calendar” today and the “Xia calendar” or the “almanac” in older times — is a lunisolar calendar:

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  The “lunar” part: the months are laid out by the synodic month. The first day of the month is the new moon, and around the fifteenth comes the full moon. This served the tides, fishing and folk festivals directly.

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  The “solar” part: the 24 Solar Terms were brought in, so that the calendar kept pace with the Sun and could guide the farming year.

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  How the two are reconciled: by the leap month. Twelve synodic months come to ≈ 354.37 days, about 10.88 days short of the tropical year, so a whole month is lost roughly every three years. Hence the rule “one leap month in three years, two in five, seven in nineteen”.

1.2.2Key astronomical constants

1.2.3Seven leap months in nineteen years: the most remarkable discovery of ancient Chinese calendrics

19 tropical years ≈ 235 synodic months (235 = 12 × 19 + 7). In other words, insert seven leap months into nineteen years and the solar and lunar counts line up almost exactly.

In the West this rule is called the Metonic cycle, after the Greek astronomer Meton, who proposed it in 432 BCE. China's Spring and Autumn Annals already records “seven leap months in nineteen years” (6th century BCE): two civilisations discovered the same rule independently.

Ancient calendar-makers refined the leap cycle into more precise periods:

1.3.1High antiquity: reading the skies to give the seasons (c. 2000–771 BCE)

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  The Book of Documents, “Canon of Yao”: “He commanded Xi and He, in reverent accord with the august Heaven, to compute and delineate the sun, the moon and the stars, and respectfully to give the people the seasons.” The passage records a method of deciding the spring equinox, the summer solstice, the autumn equinox and the winter solstice by the “four culminating stars of the middle months” (Niao, Huo, Xu and Mao) — the earliest idea of “fixing the solar terms by astronomy”.

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  Shang oracle bones: they already carry a complete Stem-Branch day count, along with records of solar and lunar eclipses. Stem-branch day reckoning has run without a break from the Shang down to the present day — the longest continuously used day-counting system in the world, unbroken for more than three thousand years.

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  The Zhou dynasty: the winter solstice was determined by the gnomon shadow method. At the Dengfeng observatory site near Luoyang, the Duke of Zhou's shadow-measuring platform survives as physical evidence of this tradition. The Rites of Zhou records that “the shadow at the solstice is one foot five inches”.

1.3.2The Warring States: the six ancient calendars (c. 5th–3rd century BCE)

The “six ancient calendars” are six pre-Qin calendar systems: the Yellow Emperor calendar, the Zhuanxu calendar, the Xia calendar, the Yin calendar, the Zhou calendar and the Lu calendar.

They share three features:

• 1.

  All used the quarter-day calendar (a year = 365 and 1/4 days)

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  All took seven leap months in nineteen years as the leap cycle

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  They differed chiefly in which month they “fixed as the opening” — that is, which month was treated as the start of the year

Fixing the opening month (the three first-months):

When Confucius said “follow the seasons of Xia” (Analects, “Duke Ling of Wei”), he was arguing for the Yin opening of the Xia calendar, because it fitted the farming year best. The calendar is still “fixed at Yin” today: the first month is the Yin month.

The Zhuanxu calendar was the only one of the six ancient calendars to be formally adopted by the Qin (Qin used the Zhuanxu calendar, with the tenth month, fixed at Hai, as the start of the year — the historical reason behind “the tenth month as the opening of the year”).

1.3.3The Han dynasty: the beginning of calendrics as a science

The Taichu Calendar (104 BCE) — the first Chinese calendar to survive with its full text intact, and a landmark:

Those involved: the Grand Astrologer Sima Qian, the fangshi Tang Du, Luoxia Hong, the calendar official Deng Ping and others. Emperor Wu examined it himself.

The Santong Calendar (c. 7 BCE) — Liu Xin's revision of the Taichu Calendar, furnished with astronomical data to make a complete system. It was the first Chinese calendar with a complete theoretical framework, and the first theoretical work to join “tones and calendar” (music theory and calendrics) into one. It is the calendar set out in the Book of Han, “Treatise on Harmonics and Calendrics”.

The Qianxiang Calendar (206) — by Liu Hong. It was the first to introduce the idea that the Moon moves at varying speed (faster at perigee, slower at apogee), and it gave the first form of an algorithm for the true new moon. Its influence on the history of Chinese calendrics was profound.

1.3.4From the Northern and Southern Dynasties to the Sui and Tang: towards precision

Precession is the westward drift of the vernal equinox caused by the wobble of the Earth's axis, which completes one turn in about 25800 years. Zu Chongzhi's discovery of precession and his introduction of a correction for it was a landmark in the history of Chinese calendrics, nearly a thousand years ahead of Europe.

1.3.5Yuan and Ming: the summit of Chinese calendrics

The Shoushi Calendar (1281) — compiled by Guo Shoujing, Wang Xun, Xu Heng and others; the highest achievement in the history of Chinese calendrics:

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  It fixed the year at 365.2425 days (exactly the same as the Gregorian calendar in use today)

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  Yet the Shoushi Calendar came a full 300 years earlier than the Gregorian

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  It abolished the accumulated years since the epoch (no longer forcing a computation back to a notional “calendar epoch”)

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  It used the “method of finite differences” (third-order interpolation) to compute the positions of the Sun and the Moon

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  Its observational basis: Guo Shoujing directed a “survey of the four seas”, setting up 27 observing points across the country, from the far north in Siberia to the far south in the South China Sea (near the Paracel Islands)

The Datong Calendar (1368) — revised by Liu Ji in the Ming; in effect the Shoushi Calendar under a new name, and in use for more than 270 years.

1.3.6Ming and Qing: Chinese and Western astronomy collide

The Chongzhen Lishu (1634) — directed by Xu Guangqi with the participation of missionaries such as Johann Adam Schall von Bell. It introduced the Tychonic system, along with Western trigonometry and spherical astronomy: China's first large-scale adoption of Western astronomical methods.

The Shixian Calendar (1645) — formally promulgated in the Qing. Its key reforms:

The fixed-term method bears directly on charting: the solar terms are no longer evenly spaced, so the boundary dates of the Month Pillar shift, which is why the “moment a term begins” has to be accurate to the minute.

1.3.7Today: a national standard

“Calculation and Promulgation of the Chinese Calendar” (GB/T 33661-2017) — drafted by the Purple Mountain Observatory in 2017 and implemented in 2018. It is China's first national standard for the Chinese calendar, and it lays down:

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  The rules for laying out calendar dates (including the rules for inserting leap months)

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  The rules for reckoning years, months, days and hours by Stem-Branch

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  The rules for determining the 24 Solar Terms and the zodiac animals

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  The way days, months and years are numbered

An important consequence: the standard expressly fixes Beijing time — “standard time of the eighth eastern time zone” — as the basis for computing new moons and solar terms. This means that anyone charting from another time zone must apply a time-zone correction.

1.4.1What the Stem-Branch system is

The Heavenly Stems (ten): Jia, Yi, Bing, Ding, Wu, Ji, Geng, Xin, Ren, Gui. The Earthly Branches (twelve): Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu, Hai

Stems and branches combine — a yang stem with a yang branch, a yin stem with a yin branch — giving 10 × 12 / 2 = 60 combinations, the “60 Jia-Zi cycle”.

Two hypotheses about the origin of the stems and branches (scholars have yet to settle the question; both are set out here even-handedly):

The two are not in conflict; each may have been the basis for naming at a particular stage. The prevailing view: the stems stand for the qi of Heaven (the advance of time) and the branches for the substance of Earth (direction in space); together they form a “coordinate of space and time”.

1.4.2The ten Heavenly Stems and their attributes

A mnemonic verse: Jia and Yi, Wood of the East; Bing and Ding, Fire of the South; Wu and Ji, Earth of the Centre; Geng and Xin, Metal of the West; Ren and Gui, Water of the North.

1.4.3The twelve Earthly Branches and their attributes

Three points that trip people up:

• 1.

  A branch's Yin-Yang does not agree with the Yin-Yang of its element. Si and Wu both belong to Fire, yet Si is yin and Wu is yang (by the odd-even order of their positions) — while the Bing Fire hidden inside Si is yang fire. This is the traditional notion of “yin in substance, yang in use”.

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  The Hidden Stems in a branch are ranked as Principal, Middle and Residual Qi. Yin, for example, hides Jia, Bing and Wu: Jia is the Principal Qi (the dominant one), Bing the Middle Qi, Wu the Residual Qi. Strength follows that order.

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  Chen, Xu, Chou and Wei are the “four storehouses” (all Earth), the storehouses of Water, Fire, Metal and Wood respectively: Chen is the storehouse of Water, Xu of Fire, Chou of Metal and Wei of Wood.

1.4.4The strength tiers of the Hidden Stems in a branch

Example: Shen (Metal) hides Geng, Ren and Wu

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  Geng = Principal Qi (Metal, the same element as Shen)

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  Ren = Middle Qi (the middle spirit of the Shen–Zi–Chen Water combination)

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  Wu = Residual Qi (Earth left over from the Wei month)

1.4.5The full table of the 60 Jia-Zi cycle

The rule of calculation: the stems cycle through 10 and the branches through 12, the two advancing in step. For the nth combination, the stem index = (n-1) mod 10 and the branch index = (n-1) mod 12.

A memory aid: every tenth entry has the same stem, every twelfth the same branch.

1.4.6The Emptiness of a decade

Grouped by stem, the 60 Jia-Zi fall into “decades” of ten:

The pattern: the two branches that no stem in a given decade can reach are that decade's “Emptiness”. The Jia-Zi decade begins at Jia-Zi; it uses all ten stems and ten branches (Zi through You), and the remaining Xu and Hai are the Emptiness.

What it means in the destiny arts (the traditional account): Emptiness is a position that is “empty and not solid”; it indicates that things come to nothing or that strength falls short, and it also carries the more detached reading that “emptiness brings clarity”. In LiuYao, the Emptiness of the decade is an important basis for judgement.

1.4.7The Melodic Element table for the 60 Jia-Zi

The Melodic Element system takes the 60 Jia-Zi two at a time (one stem and one branch to a single Melodic Element), giving thirty in all. The method derives from ancient music theory (the matching of the Five Elements with the five notes and the twelve pitches). It once dominated the study of fate before the Song, and after the Song it was gradually replaced by the “regular Five Elements”, but it is still widely used in matchmaking and feng shui.

The Melodic Element verse (standard version):

Jia-Zi and Yi-Chou, Metal in the Sea; Bing-Yin and Ding-Mao, Fire in the Furnace; Wu-Chen and Ji-Si, Wood of the Great Forest; Geng-Wu and Xin-Wei, Earth by the Roadside; Ren-Shen and Gui-You, Metal of the Sword's Edge. Jia-Xu and Yi-Hai, Fire on the Mountain Top; Bing-Zi and Ding-Chou, Water in the Ravine; Wu-Yin and Ji-Mao, Earth on the City Wall; Geng-Chen and Xin-Si, Metal of White Wax; Ren-Wu and Gui-Wei, Wood of the Willow. Jia-Shen and Yi-You, Water in the Spring; Bing-Xu and Ding-Hai, Earth on the Roof; Wu-Zi and Ji-Chou, Thunderbolt Fire; Geng-Yin and Xin-Mao, Wood of Pine and Cypress; Ren-Chen and Gui-Si, Long Flowing Water. Jia-Wu and Yi-Wei, Metal in the Sand; Bing-Shen and Ding-You, Fire at the Foot of the Mountain; Wu-Xu and Ji-Hai, Wood of the Plain; Geng-Zi and Xin-Chou, Earth on the Wall; Ren-Yin and Gui-Mao, Gold Foil Metal. Jia-Chen and Yi-Si, Fire of the Covered Lamp; Bing-Wu and Ding-Wei, Water of the Heavenly River; Wu-Shen and Ji-You, Earth of the Great Post Road; Geng-Xu and Xin-Hai, Metal of Hairpins and Bracelets; Ren-Zi and Gui-Chou, Wood of Mulberry and Silkworm Thorn. Jia-Yin and Yi-Mao, Water of the Great Stream; Bing-Chen and Ding-Si, Earth in the Sand; Wu-Wu and Ji-Wei, Fire in the Heavens; Geng-Shen and Xin-You, Wood of the Pomegranate; Ren-Xu and Gui-Hai, Water of the Great Sea.

How to remember the Melodic Element sequence: taking the pairs in order (Jia-Zi and Yi-Chou → Bing-Yin and Ding-Mao), the elements run Metal → Fire → Wood → Earth → Metal, and vary after two rounds… In fact the whole sequence is a six-part cycle: “Metal, Fire, Wood, Earth, Metal; Fire, Water, Earth, Metal, Wood; Water, Earth, Fire, Wood, Water; Metal, Fire, Wood, Earth, Metal; Fire, Water, Earth, Metal, Wood; Water, Earth, Fire, Wood, Water”. There is no need to memorise it — consult the table.

1.5.1Why True Solar Time is needed

In setting the Hour Pillar, Bazi uses local True Solar Time, not clock time (Beijing time). The reasons:

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  Difference in longitude: Beijing time is set at 120° E. Urumqi (about 87.6° E) lies about 32.4° away from that meridian, giving a solar time difference of about 129 minutes (2 hours 9 minutes). Chart a person from Urumqi by Beijing time and the Hour Pillar will often be wrong.

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  The equation of time: because the Earth's orbit is an ellipse, and because of the obliquity of the ecliptic, the true solar day differs from the mean solar day by up to ±16 minutes.

1.5.2Conversion in three steps

Step one: longitude correction (local mean solar time)

Local mean solar time = standard time + (local longitude − standard longitude) × 4 minutes

Example: Urumqi (87.6° E), Beijing time 12:00 — correction = (87.6 − 120) × 4 = −129.6 minutes ≈ −2 hours 10 minutes; local mean solar time ≈ 09:50

Step two: equation-of-time correction

True Solar Time = local mean solar time + the equation of time

The equation of time varies with the season, from a maximum of +16 minutes (early November) to a minimum of −14 minutes (mid-February). For exact values, consult an astronomical almanac, or use this approximation:

Equation of time (minutes) ≈ 9.87·sin(2B) − 7.53·cos(B) − 1.5·sin(B)
where B = 360° × (N − 81) / 364, and N is the day of the year

Step three: determining the double-hour

Whichever double-hour interval the converted True Solar Time falls into is the Hour Pillar.

1.5.3The special case of the Zi hour: early Zi and late Zi

A day holds twelve double-hours, but 23:00–01:00 straddles two calendar days, and the schools disagree:

A practical recommendation: state both, or say plainly which school you follow. Most charting software defaults to the late-Zi view — that is, the day changes at 23:00.

1.6.1Luoxia Hong (c. 156–87 BCE)

Who he was: a Western Han astronomer and calendar-maker, courtesy name Changgong, a native of Langzhong in Ba commandery (modern Langzhong, Sichuan). One of the principal creators of the Taichu Calendar.

His work:

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  During the Yuanfeng era of Emperor Wu (110–104 BCE) he was recommended to the capital by a fellow townsman, Qiao Long, and worked with Deng Ping, Tang Du and others to draw up the new calendar.

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  He proposed “the first month as the start of the year” (that is, fixing the opening at Yin), and formally brought the 24 Solar Terms into the calendar — a system that lasted more than two thousand years.

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  He built an “armillary sphere” (the Luoxia Hong armillary), which he used to observe the stars directly.

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  He devised the “Tong Qi Lü” method, an early technique of approximating fractions.

His standing: he is honoured as the “father of Chinese astronomy and calendrics”. In 2004 the International Astronomical Union named asteroid 16757 “Luoxia Hong”. A memorial hall to him stands in Langzhong, Sichuan.

His link to the destiny arts: without the Taichu Calendar the solar terms would not have entered the calendar, and there would be no Bazi Month Pillar bounded by solar terms. It is fair to say that the skeleton of every chart cast rests on Luoxia Hong's calendar.

1.6.2Zhang Heng (78–139)

Who he was: an Eastern Han astronomer, mathematician and man of letters, courtesy name Pingzi, a native of Xi'e in Nanyang (modern Nanyang, Henan).

His work:

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  He wrote the Lingxian (“Spiritual Constitution”), a systematic account of the spherical-heaven theory of the cosmos, in which he set out an infinite universe: “the bound of space has no limit, the end of time has no end”.

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  He made an “armillary sphere” — a water-driven celestial globe turned by a clepsydra, which demonstrated the motions of the heavens automatically.

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  He made the “seismoscope” (houfeng didong yi), the world's earliest instrument for detecting earthquakes.

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  In the Lingxian he correctly explained the cause of lunar eclipses (the Earth blocking the sunlight) and measured the angular diameters of the Sun and the Moon.

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  He was the most important astronomical theorist after the Taichu Calendar, arguing that the spherical-heaven theory should replace the flat-heaven theory.

His link to the destiny arts: the spherical-heaven model Zhang Heng established gave later calendars a correct framework for celestial motion, and it is the intellectual basis of the idea of a “celestial sphere with its ecliptic”.

1.6.3Zu Chongzhi (429–500)

Who he was: an astronomer and mathematician of the Northern and Southern Dynasties, courtesy name Wenyuan, a native of Qiu county in Fanyang (modern Laishui, Hebei).

His work:

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  Mathematics: he pinned pi between 3.1415926 and 3.1415927, a world record that stood for nearly a thousand years, and gave the approximate ratio 22/7 and the close ratio 355/113.

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  Calendrics: he compiled the Daming Calendar (promulgated in 510), with two breakthroughs:

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  First to introduce precession: he showed that the winter-solstice point is not fixed, shifting by 1 degree in about 45 years and 11 months

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  A reformed leap cycle: from “7 leap months in 19 years” to “144 leap months in 391 years”, a great gain in precision

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  He was the first person in history to bring precession into the Chinese calendar, a reform that lifted its accuracy by an order of magnitude.

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  He also improved machines such as the south-pointing chariot, the thousand-li boat and the water-powered trip-hammer mill.

His standing: he is named together with Zhang Heng as “Zhang and Zu”, the emblem of the scientific peak of the Northern and Southern Dynasties.

1.6.4Yi Xing (683–727)

Who he was: a Tang dynasty monk and astronomer, secular name Zhang Sui, a native of Changle in Weizhou (modern Nanle, Henan).

His work:

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  He took monastic vows under the name Yi Xing, studied Tantrism under Subhakarasimha and Vajrabodhi, and became an important figure in Chinese Esoteric Buddhism.

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  At the order of Emperor Xuanzong he directed the reform of the calendar, compiling the Dayan Calendar (promulgated in 728), the most precise calendar of the Tang.

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  His innovations:

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  He used “quadratic interpolation on unequal intervals” to compute the position of the Sun, a large gain in precision over earlier generations

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  He organised a “meridian survey”: observers at 13 sites across the country measured the altitude of the pole star and the length of the noon shadow, yielding “351 li and 80 paces of north–south distance correspond to 1 degree of polar altitude” — the world's first measurement of a meridian arc

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  He used the “nine zones” shadow method to handle noon shadows at different latitudes

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  With Liang Lingzan he built a “water-driven bronze armillary” (one of the world's earliest forerunners of the mechanical clock), which struck the hours automatically.

His standing: one of the greatest organisers of observation in the history of Chinese astronomy. Joseph Needham called his work “an important event in the history of science”.

1.6.5Guo Shoujing (1231–1316)

Who he was: a Yuan dynasty astronomer, hydraulic engineer and mathematician, courtesy name Ruosi, a native of Xingtai in Shunde (modern Xingtai, Hebei).

His work:

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  With Wang Xun and Xu Heng he compiled the Shoushi Calendar (promulgated in 1281).

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  He fixed the tropical year at 365.2425 days, exactly matching today's Gregorian calendar, 300 years ahead of Europe.

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  He directed the “survey of the four seas”: 27 observing stations were set up across the country, from Tiele in the north (roughly modern Siberia) to the South China Sea in the south (near the Paracel Islands) — a scale never seen before.

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  He created thirteen instruments, among them the abridged armilla, the tall gnomon, the pole-observing instrument, the armillary globe, the exquisite instrument, the upward-viewing instrument, the standing-revolving instrument, the truth-verifying instrument, the shadow definer, the sighting table, the eclipse instrument, the star-dial timekeeper and the azimuth table.

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  He pioneered shadow measurement with the tall gnomon together with the “shadow definer”, raising the precision of shadow measurement to about one tenth of a day.

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  In the Shoushi Calendar he abolished “accumulated years since the epoch” and took observation directly as the basis.

His standing: the greatest astronomer and instrument-maker in Chinese history. In 1970 the International Astronomical Union named a crater on the far side of the Moon “Guo Shoujing”; in 1977 asteroid 2012 was named “Guo Shoujing”.

A saying of his: “The root of a calendar lies in observation, and for observation no instrument comes before the gnomon and the armilla.”

1.6.6Johann Adam Schall von Bell (Tang Ruowang, 1592–1666)

Who he was: a German Jesuit missionary and astronomer whose Chinese name was Tang Ruowang, courtesy name Daomo.

His work:

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  He reached China in 1622 and took part in compiling the Chongzhen Lishu under the direction of Xu Guangqi.

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  In the early Qing he directed the revision of the Shixian Calendar, promulgated in 1645. *He was the first to adopt the fixed-term method in an official Chinese calendar*, fixing the 24 Solar Terms by solar longitude.

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  He served as director of the Imperial Astronomical Bureau, the first foreigner in Chinese history to hold that post.

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  He introduced Western astronomical instruments, the telescope and spherical trigonometry.

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  In his later years he was imprisoned in the “calendar dispute” (impeached by Yang Guangxian) and died in 1666. He was rehabilitated in the Kangxi era.

His link to the destiny arts: the fixed-term method makes solar-term dates drift, which bears directly on pinning down the exact “moment a term begins” for the Month Pillar. Here lies one methodological source of the precision of modern charting software.

1.6.7Liu Hong (c. 130–196) and the Qianxiang Calendar

An Eastern Han astronomer, courtesy name Yuanzhuo, a native of Mengyin in Taishan (modern Mengyin, Shandong). In the Qianxiang Calendar he was the first to point out that the Moon does not move at a uniform speed (fast at perigee, slow at apogee), set out the theory of “the Moon's varying speed”, and gave an algorithm for the true new moon. He also proposed methods for predicting solar and lunar eclipses. He is called “the founder of the true-new-moon method in ancient China”, and his influence on later calendars was immense.