Chinese calendar

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Chinese Calendar of 2017
A page of the Chinese calendar

The traditional Chinese calendar (official Chinese name: Rural Calendar (農曆; 农历; Nónglì; "farming calendar"),[a] alternately Former Calendar (舊曆; 旧历; Jiùlì), Traditional Calendar (老曆; 老历; Lǎolì), or Lunar Calendar (陰曆; 阴历; Yīnlì; "yin calendar")) is a lunisolar calendar which reckons years, months and days according to astronomical phenomena. It was first developed during the Qin Dynasty[citation needed], and is currently defined by GB/T 33661-2017 Calculation and promulgation of the Chinese calendar, which the Standardization Administration of China issued on May 12, 2017.

China now officially uses the Gregorian calendar, but the traditional Chinese calendar still governs traditional activities in China and in overseas Chinese communities, such as the Chinese New Year. It lists the dates of traditional Chinese holidays, and guides people in selecting the most auspicious days for weddings, funerals, moving, or beginning a business.

As with Chinese characters, different variants of this calendar are used in different parts of the Chinese cultural sphere. Korea, Vietnam, and the Ryukyu Islands adopted the calendar completely, where it evolved into Korean, Vietnamese, and Ryukyuan calendars, respectively. The main difference from the traditional Chinese calendar is the use of different meridians, which leads to some astronomical events—and the calendar events based on those—falling on different dates. The traditional Japanese calendar also derived from the Chinese calendar based on a Japanese meridian, however its official use in Japan was abolished in the early 20th century[citation needed]. Calendars in Mongolia and Tibet have absorbed elements from the traditional Chinese calendar, but they are not direct descendants of it.

In this calendar, days begin and end at midnight. Months begin on the day with the new moon. Years begin on the second or third new moon after the winter solstice. The solar terms govern the start and end of each month. Written versions in ancient China[when?] would include information like the stem – branch of the year and names of each month, including leap months when needed. For each month, there would be characters for if the month was long (, containing 30 days) or short (, containing 29 days); the stem-branches for the first, eleventh, and 21st days; and the date, stem-branch, and time of the solar terms.

Structure[edit]

General[edit]

Definitions of elements in the traditional Chinese calendar:

  • Day, the time from one midnight to the next.
  • Month, the time from one new moon to the next. These synodic months are about 29 ​1732 days long.
  • Date, when a day occurs within the month. Days are numbered in sequence from 1 – 29 or 1 – 30.
  • Year, the time of one full revolution of Earth around the sun. This is measured from the first day of spring (lunisolar year) or the winter solstice (solar year). A year is about 365 ​31128 days.
  • Zodiac, ​112 year, 30° on the ecliptic. A zodiac is about 30 ​716 days. The Chinese zodiac is 45° away from the Western zodiac[citation needed].
  • Solar term, ​124 year, 15° on the ecliptic. A solar term is about 15 ​732 days.
  • Calendar month, when a month occurs within the year. The months are numbered according to the zodiac number[citation needed] and some months may be repeated.
  • Calendar year, when it is agreed that one year ends and another begins. In this calendar, the year starts on the first day of spring, defined as the day on which the second (sometimes third) dark moon after winter solstice falls. A calendar year is 353 – 355 days or 383 – 385 days long.

The Chinese calendar is lunisolar, similar to the Hindu and Hebrew calendars.

7 Luminaries, Great Bear (Ursa Major), 3 Enclosures, 28 Mansions[edit]

The movements of the Sun, the Moon, Mercury, Venus, Mars, Jupiter, and Saturn are the key references for calendar calculations. These are known as the seven luminaries.

  • The distance between Mercury and the sun is within 30°, which is the sun's height at chénshí (辰時) or 08:00-10:00, so Mercury was sometimes called the "chen star" (). More commonly, it is called the "water star" (水星).
  • Venus appears at dawn and dusk, so the Venus is called the "bright star" (啟明; 启明) or "long star" (長庚; 长庚).
  • Mars looks like fire and occurs irregularly, so Mars is called the "fire star" (熒惑; 荧惑 or 火星). Mars is in charge of punishment in Chinese culture. When Mars is close to Antares (心宿二), it is a sign of bad luck and can forebode the death of the emperor or the ousting of the chancellor (荧惑).
  • The period of Jupiter's revolution is about 11.86 years, so Jupiter is called the "age star" (歲星; 岁星), since 30° of Jupiter's revolution is about a year on Earth.
  • The period of Saturn's revolution is about 28 years, so Saturn is called the "guard star" (鎮星). This means that Saturn guards one of the 28 mansions every year.

The Big Dipper is regarded as the compass in the sky, and the handle's direction decides the season and solar month.

The stars are divided into Three Enclosures and 28 Mansions according to their locations in the sky relative to Ursa Minor at the centre. Each mansion is named with a character that describes the shape of the principal asterism it contains.

The moon moves through about one lunar mansion per day, so the 28 mansions were also used to count days. In the Tang Dynasty, Yuan Tiangang (袁天罡) matched the 28 mansions, seven luminaries and yearly animal signs, yielding combinations such as “horn-wood-flood dragon” ().

Codes[edit]

Several coding systems are used for some special circumstances in order to avoid ambiguity, such as continuous day or year count.

Codes in Chinese calendar and timekeeping
Stem-branches Heavenly stems Earthly branches
Wu Xing Stem, branch Wu Xing Stem -gēng (​110 of day) Wu Xing Branch -shí (dual hour) -yuè (month)
metal 1, 1 9, 9 7, 5 1, 7 9, 3 7, 11 wood 1 jiǎ 19:12 yīgēng 1 water 00:00 Shíyīyuè (SYY) 十一月
2, 2 10, 10 8, 6 2, 8 10, 4 8, 12 2 21:36 èrgēng 2 soil chǒu 02:00 Làyuè (LAY) 臘月
fire 3, 3 1, 11 5, 1 3, 9 1, 5 5, 7 fire 3 bǐng 0:00 sāngēng 3 wood yín 4:00 Zhēngyuè (ZNY) 正月
4, 4 2, 12 6, 2 4, 10 2, 6 6, 8 4 dīng 2:24 sìgēng 4 mǎo 6:00 Èryuè (ERY) 二月
wood 5, 5 9, 7 7, 3 5, 11 9, 1 7, 9 soil 5 4:48 wǔgēng 5 soil chén 8:00 Sānyuè (SNY) 三月
6, 6 10, 8 8, 4 6, 12 10, 2 8, 10 6 7:12 morning 6 fire 10:00 Sìyuè (SIY) 四月
water 3, 1 1, 9 9, 5 3, 7 1, 3 9, 11 metal 7 gēng 9:36 ante (midmorning) 7 12:00 Wǔyuè (WUY) 五月
4, 2 2, 10 10, 6 4, 8 2, 4 10, 12 8 xīn 12:00 noon 8 soil wèi 14:00 Liùyuè (LUY) 六月
soil 7, 7 5, 3 3, 11 7, 1 5, 9 3, 5 water 9 rén 14:24 post (late afternoon) 9 metal shēn 16:00 Qīyuè (QIY) 七月
8, 8 6, 4 4, 12 8, 2 6, 10 4, 6 10 guì 16:48 evening 10 yǒu 18:00 Bāyuè (BAY) 八月
11 soil 20:00 Jiǔyuè (JUY) 九月
12 water hài 22:00 Shíyuè (SHY) 十月

Time system[edit]

Explanatory Chart for Chinese time

China has used the Western hour-minute-second system to divide the day since the Qing dynasty[1]. Before then, several systems of dividing the day were used depending on the era. Systems using multiples of twelve and ten were popular since they could be easily counted and aligned with the celestial stems and earthly branches.

In both old systems and the modern one, days begin and end at midnight although, colloquially, people refer to days beginning at dawn.

Week[edit]

As early as the Bronze Age Xia dynasty, days were grouped into nine- or ten-day weeks, called xún (). [2] Months were divided into 3 xún. The first 10 days was the early xún (上旬), the middle 10 days was the mid xún (中旬), and the last 9 or 10 days is the late xún (下旬). Japan adopted this pattern, though the 10-day-weeks were called jun (). In Korea, it was called sun (,).

The structure of xún lead to work holidays being every five or ten days. During the Han dynasty, officials of the empire were legally required to rest every five days (; , from 休沐; xiūmù; "wash rest")[citation needed], which allowed these breaks to happen twice a xún and 5–6 times a month. This was changed to every 10 days in the Tang dynasty[citation needed]. The name of these breaks was changed to huan (; , again meaning "wash").

Grouping days into sets of ten is still used today in referring to specific natural events. Three Fu (三伏), a period of 29–30 days which are the hottest of the year, is a term reflecting that it lasts for three xún.[3] After the winter solstice, people traditionally count off 9 sets of 9 days (or 9 late xún) to figure out when winter ends.[4]

The seven-day week was adopted from the Hellenistic system by the 4th century CE, although by which route is not entirely clear. It was again transmitted to China in the 8th century by Manichaeans, via the country of Kang (a Central Asian polity near Samarkand).[5][b][c] It is the most predominantly used system in modern China.

Month[edit]

Months are defined by the time between new moons, which averages to 29 ​1732 days. Instead of using half-days to balance the months with the lunar cycle, every other month of the year has 29 days (short month, 小月) and the rest have 30 (long month, 大月). Years start on a long month and alternate short-long-short-long until the year ends.

A 12-month-year using this system has only 354 days. Using only 12 months per year would cause significant drift from the tropical year. To fix this, traditional Chinese years alternate a 13-month-year every other year. The 13-month version has the same alternation of long and short months, but adds a 30-day month at the end of the year. Years with 12 months are called common years, and years with 13 months are called long years.

Though most of the above rules applied until the Tang Dynasty, different eras used different systems to keep the lunar and solar years aligned. For example, the synodic month of the Taichu calendar was 29 ​4381 days. The 7th century Wùyín Yuán Calendar of the Tang dynasty was the first to determine month length by the real synodic month, instead of using the cycling method. Since then, month lengths have been determined by observation and prediction, with few exceptions.[d]

The days of the month are numbered beginning with 1, and the day's number is always written with two characters.

  • Days 1 to 10 are written with the Chinese numeral of the day number, preceded by the character Chū (). For example, Chūyī (初一) is the 1st day of the month, and Chūshí () is the 10th.
  • Days 11 to 20 are written as regular Chinese numerals. For example, Shíwǔ (十五) is the 15th day of the month, and Èrshí (二十) is the 20th.
  • Days 21 to 29 are written with the character Niàn (廿) before the characters for 1 through 9. For example, Niànsān (廿三) is the 23rd day of the month.
  • Day 30, for months that have it, is written as the regular Chinese numeral Sānshí (三十).

As a convention, history books use days of the month as numbered with the 60 stem-branches. For example:

Tiānshèng (天聖) 1st year, Èryuè (二月), Dīngsìrì (), Set the portrait of the Great Chris and Pope in the Hongqing Palace of the southern capital. - Volume ix: Biographic Sketches of Pope Ren, History of Song Dynasty.[citation needed]

Because astronomical observation is used to determine month lengths, dates on this calendar correspond to moon phases. The first day of each month is the new moon. In the 7th or 8th day of each month, the first quarter moon is visible in the afternoon and early evening. In the 15th or 16th day of each month, the full moon is visible all night. In the 22nd or 23rd day of each month, the last quarter moon is visible late at night and in the morning.

Since the beginning of the month is determined by the time when the new moon occurs, other countries using this calendar use their own time standards to calculate it. This results in deviations. For instance, the first new moon in 1968 was at UTC Jan 29 16:29. Since North Vietnam used the UTC+7 timezone to calculate their Vietnamese calendar, and South Vietnam used the longitude of Beijing to calculate theirs, North Vietnam started the holiday of Tết at Jan 29 23:29, while South Vietnam started it at Jan 30 00:15. Using this time difference allowed asynchronous attacks in Tet Offensive.[6]

Solar year and solar term[edit]

The solar year (; ; Suì) is the time between winter solstices. The solar year is divided further into 24 solar terms. In ancient China, solar terms were estimated as ​124 of the solar year, or about 15 ​732 days.[citation needed] Starting from the 17th century, when the Shixian Calendar of Qing dynasty was adopted, the solar year was determined by the real tropical year instead.[citation needed] The solar terms correspond to intervals of 15° along the ecliptic.

Different version of traditional Chinese calendar might have different average solar year length. One solar year of the Tàichū calendar from 1st century BC is 365 ​3851539—or 365.25016—days. A solar year of the 13th century Shòushí calendar is 365 ​97400—or 365.24250—days, the same as the Gregorian calendar. The additional 0.00766-day from the Tàichū calendar leads to a one-day shift every 130.5 years.

Couples of solar terms are climate terms, or solar months. The first of each couple is "pre-climate" (節氣; 节气; Jiéqì), and the second of the each couple is "mid-climate" (中氣; 中气; Zhōngqì). In the list below, the odd numbers are the pre-climates, and the even numbers are the mid-climates.

The intercalary (leap) months of the 19-year cycle, 1862 to 2108
Year mod 19 0 3 6 8 9 11 14 17
Leap month starts
after month
7/8 6/5 4 10 3/2 7/6 5 4/3
1862 8 5 4 10 6 5 3
1881 7 5 4 2 6 5 3
1900 8 5 4 2 6 5 2
1919 7 5 4 2 6 5 3
1938 7 6 4 2 7 5 3
1957 8 6 4 3 7 5 4
1976 8 6 4 10 6 5 3
1995 8 5 4 3 7 5 4
2014 9 6 4 2 6 5 3
2033 11 6 5 2 7 5 3
2052 8 6 4 3 7 5 4
2071 8 6 4 3 7 5 4
2090 8 6 4 2 7 5 4
  1. FTC 小寒 First Term of Cold Season
  2. STC 大寒 Second Term of Cold Season
  3. VC 立春 Vernal commence (start of spring)
  4. LTC 雨水 Last Term of Cold Season
  5. FTR 惊蛰 First Term of Rainy Season
  6. VE 春分 Vernal Equinox
  7. STR 清明 Second Term of Rainy Season
  8. LTR 谷雨 Last Term of Rainy Season
  9. SC 立夏 Summer commence
  10. FTG 小满 First Term of Growing Season
  11. STG 芒种 Second Term of Growing Season
  12. SS 夏至 Summer Solstice
  13. FTH 小暑 First Term of Hot Season
  14. STH 大暑 Second Term of Hot Season
  15. AC 立秋 Autumn Commence
  16. LTH 处暑 Last Term of Hot Season
  17. FTD 白露 First Term of Dew Season
  18. AE 秋分 Autumn Equinox
  19. STD 寒露 Second Term of Dew Season
  20. LTD 霜降 Last Term of Dew Season
  21. WC 立冬 Winter Commence
  22. FTS 小雪 First Term of Snowy Season
  23. STS 大雪 Second Term of Snowy Season
  24. WS 冬至 Winter Solstice
2017
Month Term 1 start
(in days after WS)
Start
time 1
Term 1
name
Term 2
start
Start
time 2
Term 2
name
End of
term 2
End
time
ws WS 0 18:44
0 8 14:53 FTC 15 11:55 STC 30 5:23
1 38 8:06 VC 44 23:34 LTC 59 19:31
2 67 22:58 FTR 74 17:32 VE 89 18:28
3 97 10:57 STR 104 22:17 LTR 120 5:26
4 126 20:16 SC 135 15:30 FTG 151 4:30
5 156 3:44 STG 166 19:36 SS 182 12:24
6 185 10:30 FTH 198 5:50 STH 213 23:15
i 214 17:45 AC 229 15:39
7 244 2:30 LTH 245 6:20 FTD 260 18:38
8 273 13:29 AE 276 4:01 STD 291 10:22
9 303 3:11 LTD 306 13:26 WC 321 13:37
10 332 19:42 FTS 336 11:04 STS 351 6:32
ws 362 14:30 WS 366 0:27

In general, there are 11 or 12 complete months—plus 2 incomplete months which border the winter solstice—in a solar year. The 11 mid-climates except the winter solstice are in the 11 or 12 complete months. The complete months are numbered from 0 to 10, and the incomplete months together are considered to be the 11th month.

The first month without a mid-climate is the leap month or intercalary month. Leap months are numbered using the character for "intercalary", rùn , then the name of the month they follow. In 2017, the intercalary month after month 6 was called Rùn Liùyuè, or "intercalary sixth month" (六月). When writing or using shorthand, it was referred to as 6i or 6+. The next intercalary month occurs in 2020 after month 4, so it will be called Rùn Sìyuè (四月) and 4i or 4+ will be used as shorthand.

Lunisolar year[edit]

The lunisolar year starts from the first spring month, called Zhēngyuè (正月; "capital month") and ends at the last winter month, called Làyuè (臘月; 腊月; "sacrificial month"). All other months are named for the month number. If a leap month falls after month 11—as it will in 2033—the 11th month will be Shíèryuè (十二月; "twelfth month") and the leap month will be Làyuè.

Years were numbered after the reign title in Ancient China, but the reign title was no longer used after the founding of PRC in 1949. People use the stem-branches to demarcate the years. For example, the year from February 8, 2016 to January 27, 2017 was a Bǐngshēn year (丙申), 12 months or 354 days long.

To Encode the date in the Chinese calendar, the flag of the intercalary month should be considered. For example, Run Liuyue 6, Dingyounian: 408-6i-06 (Timestamp: 40806106)

In Tang Dynasty, the earthly branches are used to mark the months for about 150 days (Dec, 761~May, 762).[e] At that time, the year starts from the month with Winter Solstice, and the month from Zhengyue to Layue are named as: Yinyue, Maoyue, Chenyue, Siyue, Wuyue, Weiyue, Shenyue Youyue, Xuyue, Haiyue, Ziyue, and Chouyue.

Estimate the Chinese date[edit]

  1. A month in the Chinese calendar is 29 or 30 days long, and a month in the Gregorian calendar is 30 or 31 days long (except for February). So, we may estimate the Chinese date if we know the bias between Layue 1st and January 1. In general, from Eryue/March, the Chinese date moves 1 day backward, after a month; the Chinese date moves a day forward after Zhengyue/February. If the bias is over 29 days, consider if there's an intercalary month before.
  2. The date of the solar term in the Gregorian calendar is more or less fixed. In general, the date of the solar term in the Chinese calendar can vary ±15 days around the fixed date. The first climate term is around the 1st of the corresponding month, and the middle climate term is around the 15th of the corresponding month.
  3. A solar year is about 365 ​14 days, and 12 lunar months are about 354 ​38 days. So the Chinese date moves about 11 days backward or 19 days forward.
  4. If the Chinese New Year is in January, there's an intercalary month in that year.
  5. The Chinese date is more or less fixed after 19 years (or 11 years occasionally) later. But dates near intercalary months always are tricky. The dates in the winter of the nominal year of Merton cycle are strange too, such as 2014+19n. There are 7 leap years in 19 years, but not always. The date of the Chinese New Year and the leap month not only move forward every eight years but also move slowly along with the 19-year cycle. For details see the table below.
Nineteen-year cycle for Chinese calendar
Cell: year mod 19 | Column: plus 8 mod 19 | Row: plus 11 mod 19
09 17 06 14 03 11 00 08 16 05 13 02 10 18 07 15 04 12 01
01 09 17 06 14 03 11 00 08 16 05 13 02 10 18 07 15 04 12
12 01 09 17 06 14 03 11 00 08 16 05 13 02 10 18 07 15 04
04 12 01 09 17 06 14 03 11 00 08 16 05 13 02 10 18 07 15
15 04 12 01 09 17 06 08 03 11 00 08 16 05 13 02 10 18 07
07 15 04 12 01 09 17 06 14 03 11 00 08 16 05 13 02 10 18
18 07 15 04 12 01 09 17 06 14 03 11 00 08 16 05 13 02 10
10 18 07 15 04 12 01 09 17 06 14 03 11 00 08 16 05 13 02
02 10 18 07 15 04 12 01 09 17 06 14 03 11 00 08 16 05 13
13 02 10 18 07 15 04 12 01 09 17 06 14 03 11 00 08 16 05
05 13 02 10 18 07 15 04 12 01 09 17 06 14 03 11 00 08 16
16 05 13 02 10 18 07 15 04 12 01 09 17 06 14 03 11 00 08
08 16 05 13 02 10 18 07 15 04 12 01 09 17 06 14 03 11 00
00 08 16 05 13 02 10 18 07 15 04 12 01 09 17 06 14 03 11
11 00 08 16 05 13 02 10 18 07 15 04 12 01 09 17 06 14 03
03 11 00 08 16 05 13 02 10 18 07 15 04 12 01 09 17 06 14
14 03 11 00 08 16 05 13 02 10 18 07 15 04 12 01 09 17 06
06 14 03 11 00 08 16 05 13 02 10 18 07 15 04 12 01 09 17
17 06 14 03 11 00 08 16 05 13 02 10 18 07 15 04 12 01 09
Leap years Common years
M02
M03
J21
J23
F19
F20
M02
M04
J22
J24
--
--
M03
M05
J24
J26
--
--
M04
M06
J25
J28
--
--
M05
M06
J26
J29
--
--
M06
M07
J28
J30
--
--
M06
M11
J30
F01
--
--
M08
M10

J31
F02
--
--
--
--
F02
F04
--
--
--
--
F03
F06
--
--
--
--
F05
F07
--
--
--
--
F07
F08
--
--
--
--
F08
F10
--
--
--
--
F10
F12
--
--
--
--
F11
F14
--
--
--
--
F13
F15
--
--
--
--
F14
F16
--
--
--
--
F16
F18
--
--
--
--
F18
F20
--
--
Earliest Leap months and dates of New Year's Day (M: Month | J: January | F: February) Latest

Graphical representation[edit]

A typical graphical representation of the Chinese calendar is the spring cattle diagram (; ), which help people calculate the date. In this diagram:

  1. The color of the cattle's head marks the Wu Xing element of the year's stem.
  2. If the cattle's mouth is closed, it is a yin year; if open, it is a yang year.
  3. The color of the cattle body marks the branch of the year.
  4. The color of the cattle tail marks the Wu Xing element of the stem for the first day of spring (立春).
  5. If the cattle tail is on the left, the first day of spring is a yang day; if on the right, it's a yin day.
  6. The color of the cattle's legs marks the branch of the first day of spring.
  7. If the cowherd stands ahead the cattle, the first day of spring is more than 5 days after the new year; if the cowherd stands behind the cattle, the first day of spring is more than 5 days before the new year; otherwise the difference between the new year and the first day of spring is within 5 days.

Age recognition in China[edit]

In China, age for official use is based on the Gregorian calendar. For traditional use, age is based on the Chinese calendar. For the first year from the birthday, the child is considered one year old. After each New Year's Eve, add one year. "Ring out the old age and ring in the new one (辭舊迎新; 辞旧迎新; cíjiù yíngxīn)" is the literary express of New Year Ceremony. For example, if one's birthday is Làyuè 29th 2013, he is 2 years old at Zhēngyuè 1st 2014. On the other hand, people say months old instead of years old, if someone is too young. It is that the age sequence is "1 month old, 2 months old, ... 10 months old, 2 years old, 3 years old...".

After the actual age (實歲; 实岁) was introduced into China, the Chinese traditional age was referred to as the nominal age (虛歲; 虚岁). Divided the year into two halves by the birthday in the Chinese calendar,[f] the nominal age is 2 older than the actual age in the first half, and the nominal age is 1 older than the actual age in the second half (前半年前虛兩歲,後半年虛一歲; 前半年前虚两岁,后半年虚一岁).[g]

Birthday issue[edit]

Just as it is awkward to define the birthday of someone born on the 29th of February in the Gregorian calendar, special rules are used for birthdays or other anniversaries during the intercalary month or on the 30th day.

  1. If someone was born in an intercalary month (except intercalary Shi'eryue), his birthday is in the common month (the month before the intercalary month).
  2. If someone was born in Shi'eryue, and Layue is the intercalary Shi'eryue, his birthday is in Layue (the last month of a year).
  3. If someone was born at 30th day of a month, his birthday is the last day of the month, i.e. the 30th day if that exists, or the 29th day if it does not.

Year number system[edit]

Era system

In the Ancient China, years were numbered from 1, beginning from the next year after a new emperor ascended the throne or the current emperor announced a new era name. The first reign title was Jiànyuán (建元; "era establishment", from 140 BCE), and the last reign title was Xuāntǒng (宣統; 宣统, from 1908 CE). The era system was abolished in 1912 CE, after which the Current Era or Republican era was used. The epoch of the Current Era is just the same as the era name of Emperor Ping of Han, Yuánshí (元始; "era beginning").

Stem-branches system

The 60 stem-branches were used to mark the date continually from Shang Dynasty. Before Han Dynasty, people knew the orbital period of Jupiter is about 4332 days, which is about 12*361 days. So, the orbital period of Jupiter was divided into 12 periods, which was used to number the year. The Jupiter was called as the star of age (嵗星; 岁星; suìxīng), and the 1/12 Jupiter orbital period was called as the age (; ; suì).

361 days is just 6 cycles of 60-stem-branches, so the stem-branches of the first day move forward one after each sui. The first day of each sui was called as the sui capital (太嵗; 太岁; tàisuì).

And the stem-branches of the taisui was used to mark the year. Obviously, there're two taisui in some year for the sui is shorter than solar rear. About after each 86 year, a taisui was leaped. The leaped of the sui was called as beyond the star (超辰; chāochén).

At the eastern Han Dynasty, the chaochen are abolished, and the 60 stem-branches are used to mark year continually without leap.

The Stem-branches year number system provided a solution for the defect of era system (unequal length of the reign titles)

Continuous year numbering

Occasionally, nomenclature similar to that of the Christian era has been used, such as[7]

Anno Huángdì (黄帝紀年), referring to the beginning of the reign of the Yellow Emperor, 2698+AD=AH
Anno Yáo (唐尧紀年), referring to the beginning of the reign of Emperor Yao, 2156+AD=AY
Anno Gònghé (共和紀年), referring to the beginning of the Gonghe Regency, 841+AD=AG
Anno Confucius (孔子紀年), referring to the birth year of Confucius, 551+AD=AC
Anno Unity (統一紀年), referring to the beginning of the reign of Qin Shi Huang, 221+AD=AU

No reference date is universally accepted. The most popular is the Christian Era, such as in "Today is gongli (GC) 1984 nian (year)... nongli (CC)...".

On January 2, 1912, Sun Yat-sen declared a change to the official calendar and era. In his declaration, January 1, 1912 is called Shíyīyuè 13th, 4609 AH which assumes an epoch (1st year) of 2698 BCE. This declaration was adopted by many overseas Chinese communities outside Southeast Asia such as San Francisco's Chinatown.[8]

In the 17th century, the Jesuits tried to determine what year should be considered the epoch of the Han calendar. In his Sinicae historiae decas prima (first published in Munich in 1658), Martino Martini (1614–1661) dated the ascension of the Yellow Emperor to 2697 BC, but started the Chinese calendar with the reign of Fuxi, which he claimed started in 2952 BCE. Philippe Couplet's (1623–1693) Chronological table of Chinese monarchs (Tabula chronologica monarchiae sinicae; 1686) also gave the same date for the Yellow Emperor. The Jesuits' dates provoked great interest in Europe, where they were used for comparisons with Biblical chronology.

Modern Chinese chronology has generally accepted Martini's dates, except that it usually places the reign of the Yellow Emperor in 2698 BC and omits the Yellow Emperor's predecessors Fuxi and Shennong, who are considered "too legendary to include".

Starting in 1903, radical publications started using the projected date of birth of the Yellow Emperor as the first year of the Han calendar. Different newspapers and magazines proposed different dates. Jiangsu, for example, counted 1905 as year 4396 (use an epoch of 2491 BCE), whereas the newspaper Ming Pao (明報; 明报) reckoned 1905 as 4603 (use an epoch of 2698 BCE). Liu Shipei (劉師培; 1884–1919) created the Yellow Emperor Calendar, now often used to calculate the date, to show the unbroken continuity of the Han race and Han culture from earliest times. Liu's calendar started with the birth of the Yellow Emperor, which he determined to be 2711 BC. There is no evidence that this calendar was used before the 20th century.[9] Liu calculated that the 1900 international expedition sent by the Eight-Nation Alliance to suppress the Boxer Rebellion entered Beijing in the 4611th year of the Yellow Emperor.

Calendric epoch

There is an epoch for each version of the Chinese calendar, which is called Lìyuán (曆元; 历元). The epoch is the optimal origin of the calendar, and it is a Jiǎzǐrì, the first day of a lunar month, and the dark moon and solstice are just at the midnight (日得甲子夜半朔旦冬至). And tracing back to a perfect day, such as that day with the magical star sign, there's a supreme epoch (Chinese: 上元; pinyin: shàngyuán). The continuous year based on the supreme epoch is shàngyuán jīnián (上元積年; 上元积年). More and more factors were added into the supreme epoch, and the shàngyuán jīnián became a huge number. So, the supreme epoch and shàngyuán jīnián were neglected from the Shòushí calendar.

Yuán-Huì-Yùn-Shì system

Shao Yong (邵雍 1011–1077), a philosopher, cosmologist, poet, and historian who greatly influenced the development of Neo-Confucianism in China, introduced a time system in his The Ultimate which Manages the World (皇極經世; 皇极经世; Huángjíjīngshì)

In his time system, 1 yuán (), which contains 12'9600 years, is a lifecycle of the world. Each yuán is divided into 12 huì (; ). Each huì is divided into 30 yùn (; ), and each yùn is divided into 12 shì (). So, each shì is equivalent to 30 years. The yuán-huì-yùn-shì corresponds with nián-yuè-rì-shí. So the yuán-huì-yùn-shì is called the major tend or the numbers of the heaven, and the nián-yuè-rì-shí is called the minor tend or the numbers of the earth.

The minor tend of the birth is adapted by people for predicting destiny or fate. The numbers of nián-yuè-rì-shí are encoded with stem-branches and show a form of Bāzì. The nián-yuè-rì-shí are called the Four Pillars of Destiny. For example, the Bāzì of the Qianlong Emperor is Xīnmǎo, Dīngyǒu, Gēngwǔ, Bǐngzǐ (辛卯、丁酉、庚午、丙子). Shào's Huángjíjīngshì recorded the history of the timing system from the first year of the 180th yùn or 2149th shì (HYSN 0630-0101, 2577 BC) and marked the year with the reign title from the Jiǎchénnián of the 2156th shì (HYSN 0630-0811, 2357 BC, Tángyáo 1, 唐堯元年; 唐尧元年). According to this timing system, 2014-1-31 is HYSN/YR 0712-1001/0101.

The table below shows the kinds of year number system along with correspondences to the Western (Gregorian) calendar. Alternatively, see this larger table of the full 60-year cycle.

Year in cycle s,b Gānzhī (干支) Year of the... CE[1] AR[1] HYSN[2] AH[3] Begins
27 7,3 gēngyín (庚寅) Metal Tiger 2010 99 0712-0927 4707 February 14
28 8,4 xīnmǎo (辛卯) Metal Rabbit 2011 100 0712-0928 4708 February 3
29 9,5 rénchén (壬辰) Water Dragon 2012 101 0712-0929 4709 January 23
30 10,6 guǐsì (癸巳) Water Snake 2013 102 0712-0930 4710 February 10
31 1,7 jiǎwǔ (甲午) Wood Horse 2014 103 0712-1001 4711 January 31
32 2,8 yǐwèi (乙未) Wood Goat 2015 104 0712-1002 4712 February 19
33 3,9 bǐngshēn (丙申) Fire Monkey 2016 105 0712-1003 4713 February 8
34 4,10 dīngyǒu (丁酉) Fire Rooster 2017 106 0712-1004 4714 January 28
35 5,11 wùxū (戊戌) Earth Dog 2018 107 0712-1005 4715 February 16
36 6,12 jǐhài (己亥) Earth Pig 2019 108 0712-1006 4716 February 5

1 As of the beginning of the Chinese year. AR=Anno the Republic of China
2 Timestamp according to Huángjíjīngshì, as a format of Huìyùn-Shìnián.
3 Huángdì era, using an epoch (year 1) of 2697 BC. Subtract 60 if using an epoch of 2637 BC. Add 1 if using an epoch of 2698 BC.

Phenology[edit]

The plum rains season is the rainy season during the late spring and early summer. The plum rains season starts on the first Bǐngrì after the Corn on Ear, and ends on the first Wèirì after the Moderate Heat.
The Sanfu days are the three sections from the first Gēng-day after the summer solstice. The first section is 10 days long, and named the fore fu (初伏; chūfú). The second section is 10 or 20 days long, and named the mid fu (中伏; zhōngfú). The last section is 10 days long from the first Gēng-day after autumn commences, and named the last fu (末伏; mòfú).
The Shujiu cold days are the nine sections from the winter solstice. Each section is 9 days long. The shǔjǐu are the coldest days, and named with an ordinal number, such as Sìjǐu (四九).

Festivals[edit]

In the Sinosphere, the traditional festivals are calculated using the date or solar terms, and are considered auspicious.

Traditional festivals in the Sinosphere
Festival English Define Original Define (Han Dynasty) Date of the following... Remark
Major traditional festivals on fixed date
臘日/腊日
Lari
0008
Sacrifice Day
Làyuè 8 The third Xuri (戌) after the Winter Solstice 2017-01-05
小年
Xiaonian
0023/0024
Preliminary Eve
Làyuè 23/24 23-officers,
24-civilians,
25-monks,
for convenience
2017-01-20
2017-01-21
the cleanup day before New Year's Week
除夕
Chuxi
0100
New Year's Eve
the last day of the year, Làyuè 29 or 30 2017-01-27 a statutory holiday
春節/春节
Chunjie
0101
New Year's Day
The first day of the year, Zhēngyuè 1 2017-01-28 a statutory holiday
上元
Shangyuan
0115
Shangyuan
Zhēngyuè 15 The first full moon of the year 2017-02-11 Also called as Yuanxiao (the night of the first full moon), an annual carnival in ancient China
上巳
Shangsi
0303
Outing Festival
Sānyuè 3 The first Siri (巳) of Sanyue 2017-03-30 a version of Qingmin Festival, The origin of Thailand water splashing festival
佛誕/佛诞
Fodan
0408
Buddha's Birthday
Sìyuè 8 2017-05-03 a statutory holiday in Hong Kong SAR
端午
Duanwu
0505
Dragon Boat Festival
Wǔyuè 5 The First Wuri (午) of Wuyue 2017-05-30 a statutory holiday
七夕
Qixi
0707
Star Festival
Qīyuè 7 2017-08-28 Ingenuity Maiden's Day
中元
Zhongyuan
0715
Ghost Festival
Qīyuè 15 The full moon at the mid-year 2017-09-05 the worship of ancestors
中秋
Zhongqiu
0815
Mid-Autumn Festival
Bāyuè 15 The full moon at the mid-autumn 2017-10-04 Reunion Day, a statutory holiday
重陽/重阳
Chongyang
0909
Climbing Festival
Jiǔyuè 9 2017-10-28 Regarded as Elder's Day in China

a statutory holiday in Hong Kong SAR

十月朝
Shiyue Chao
1001
Shiyue Worship
Shíyuè 1 The New Year's Day of Qin Calendar 2017-11-18 Issue Royal calendar (almanac) for the following year.
下元
Xiayuan
1015
Spirit Festival
Shíyuè 15 The first full moon in Qin calendar 2017-12-02 the worship of worthy
Major traditional festivals on solar term
立春
Lichun
Beginning of Spring The day that Spring commences
about February 4
Zhēngyuè 8
(February 3)
The day of the Stimulation of Agriculture
寒食
Hanshi
Cold Food Festival the 105th day after the Winter Solstice
about April 4
Sānyuè 7, 2017
(April 3)
The fast before the worship of ancestors at Qingming Festival.
清明
Qingming
Qingming Festival The day of the solar term of Bright and Clear
about April 5
Sānyuè 8, 2017
(April 4)
The day of the worship of ancestors, a statutory holiday
冬至
Dongzhi
Winter Solstice The day of the Winter Solstice
about December 21
Shíyīyuè 5, 2017
(December 22)
The node of the solar years
春社/秋社
Chunshe/Qiushe
Spring/Autumn Pray the fifth Wùrì (戊) after Spring/Autumn Commences March 21
September 23
a version of Spring/Autumn equinox
The traditional business festivals
開市/开市
Kaishi
0105
Opening Day
Zhēngyuè 5 In the old days, merchants used to open their stores from Zhēngyuè 5, and host a prayer service on that day. God of Wealth's Day, which the prayer service is called God of Wealth is Welcome.
頭牙/尾牙
头牙/尾牙
Touya & Weiya
0202/0016
First/Last Thanksgiving
Èryuè 2 / Làyuè 16 In the Ancient China, business owners hosted the Yaji rites (Chinese: 牙祭; pinyin: Yaji) at the 2nd and 16th day of each month from Eryue to Layue, to reward the local guardian god and their employees. The First/Last Thanksgiving rite is held on Èryue 2/Làyuè 16.

History[edit]

Earlier Chinese calendars[edit]

Before the Zhou dynasty, the Chinese calendars used a solar calendar.

The History of Chinese Calendar

According to Ancient Chinese literature, the first version was the five-phases calendar (五行曆; 五行历), which came from the tying knots culture. In the five-phases calendar, a year was divided into five phases which were expressed by five ropes. Each rope was folded into halves, and the day in the corner was the capital day (行御). They're three sections in each halves, and the Chinese Character of phase is the pictograph of the rope of the tying knots. The ten half-ropes were arranged into a row, and a man shape was engraved by the ropes. The part of man shape derived into 10 heaven stems. The days in each sections were recorded with 12 earthly branches. So, in the five-phases calendar, a year is fives phases or ten months, and a phase is six sections or 73 days. The remainder of each phases are marked in the Hetu, which is found in Song Dynasty.

The second version is the four-seasons calendar (四時八節曆; 四时八节历). In the four-seasons calendar, the days were counting by ten, and three ten-days weeks were built into a month. There were 12 months in a year, and a week were intercalated in the hot month. In the age of four-seasons calendar, the 10 heaven stems and 12 earthly branches were used to mark days synchronously.

The third version is the balanced calendar (調曆; 调历) a year was defined into 365.25 days, and the month was defined into 29.5 days. And after each 16 months, a half-month was intercalated. There half-months were merged into months later, and the archetype of the Chinese calendar was brought out in the Spring and Autumn ages.

Oracle bone records indicate that the calendar of Shang Dynasty were a balanced calendar, and the 12, 13, even 14 months were packed into a year roughly. Generally, the month after the winter solstice was named as the capital month (正月).[10]

Ancient Chinese calendars[edit]

Pre-Qin dynasty calendars[edit]

In Zhou dynasty, the authority issued the official calendar, which is a primitive lunisolar calendar. The year beginning of Zhou's calendar (周曆; 周历) is the day with dark moon before the winter solstice, and the epoch is the Winter Solstice of a Dīngyǒu year.

Some remote vassal states issued their own calendars upon the rule of Zhou's calendar, such as:

The epoch of the Lu's calendar (魯曆; 鲁历) is the winter solstice of a Gēngzǐ year.

During the Spring and Autumn period and Warring States period, Some vassal states got out of control of Zhou, and issues their own official calendar, such as:

Jin issued the Xia's calendar (夏曆; 夏历), with a year beginning of the day with the nearest darkmoon to the Vernal Commences. The epoch of Xia's calendar is the Vernal Commences of a Bǐngyíng year.
Qin issued the Zhuanxu's calendar (顓頊曆; 颛顼历), with a year beginning of the day with the nearest darkmoon to the Winter Commences. The epoch of Zhuanxu's calendar is the Winter Commences of a Yǐmǎo year.
Song resumed the Yin's calendar (殷曆; 殷历), with a year beginning of the day with the darkmoon after the Winter Solstice. The epoch of Yin's calendar is the Winter Solstice of a Jiǎyíng year.

These six calendars are called as the six ancient calendars (古六曆; 古六历), and are the quarter remainder calendars (四分曆; 四分历; sìfēnlì). The months of these calendars begin on the day with the darkmoon, and there are 12 or 13 month within a year. The intercalary month is placed at the end of the year, and called as 13th month.

The modern version of the Zhuanxu's calendar is the Chinese Qiang calendar and Chinese Dai calendar, which are the calendar of mountain peoples.

Calendar of the Qin and early Han dynasties[edit]

After Qin Shi Huang unified China under the Qin dynasty in 221 BCE, Qin's calendar (秦曆; 秦历) was promulgated. The Qin's calendar follows the rules of Zhuanxu's calendar, but the month order follows the Xia calendar. The months in the year are from the 10th month to the 9th month, and the intercalary month is called as the second Jiuyue (後九月; 后九月). In the early Han dynasty, the Qin calendar continued to be used.

Taichu calendar and the calendars from the Han to Ming dynasties.[edit]

Emperor Wu of the Han dynasty introduced reforms halfway through his administration. His Taichu or Grand Inception Calendar (太初曆; 太初历) introduced 24 solar terms which determined the month names. The solar year was defined as 365 385/1539 days, and divided into 24 solar terms. Each couples of solar terms are associated into 12 climate terms. The lunar month was defined as 29 43/81 days and named according to the closest climate term. The mid-climate in the month decides the month name, and a month without mid-climate is an intercalary month.

The Taichu calendar established the frame of the Chinese calendar, Ever since then, there have been over 100 official calendars in Chinese which are consecutive and follow the structure of Tàichū calendar both. There're several innovation in calendar calculation in the history of over 2100 years, such as:

In the Dàmíng Calendar released in Tiānjiān 9 (天监九年, 510) of the Liang dynasty, Zhu Chongzhi introduced the equation of equinoxes.
Actual syzygy method was adopted to decide the month from the Wùyín Yuán Calendar, which was released in Wǔdé 2 (武德二年, 619) of the Tang dynasty.
The real measured data was used in calendar calculation from Shòushí Calendar, which was released in Zhìyuán 18 (至元十八年, 1281) of the Yuan dynasty. And the tropical year is fixed at 365.2425 days, the same as the Gregorian calendar established in 1582,[11] and derived spherical trigonometry.[12][13][14]

Modern Chinese calendars[edit]

The Chinese calendar lost the status of the official statutory calendar in China in the beginning of the 20th century,[15] however it has been continually being used for various purposes.

Because the Republic of China adopted the UTC+8 timezone instead of using Beijing Mean Solar Time in 1928 CE, Chinese calendars produced in Mainland China have switched to use UTC+8 in the following year. However, the switch in time standard used in Chinese calendars has not been universally adopted in areas like Taiwan and Hong Kong, and some calendars were still follow the last calendar of Qing dynasty that was published in 1908. In 1978, this practice caused confusion on what date the 1978 Mid-autumn festival occur, and caused those areas to switch to the UTC+8-based Chinese calendar thereafter.[16]

Shíxiàn calendar[edit]

In the late Ming dynasty, Xu Guangqi and his colleagues worked out the new calendar based on western astronomical arithmetic. But the new calendar was not released before the end of the Ming dynasty. In the early Qing dynasty, Johann Adam Schall von Bell submitted the calendar to the Shunzhi Emperor. The Qing government released the calendar under the name the Shíxiàn calendar, which means seasonal charter. In the Shíxiàn calendar, the solar terms each correspond to 15° along the ecliptic. It meant the Chinese calendar can be used as astronomical calendar. However, the length of the climate term near the perihelion is shorter than 30 days and there may be two mid-climate terms. The rule of the mid-climate terms decides the months, which is used for thousands years, lose its validity. The Shíxiàn calendar changed the rule to "decides the month in sequence, except the intercalary month."

Current Chinese calendar[edit]

The version of the traditional Chinese calendar currently being used follows the rules of the Shíxiàn calendar, except that:

  1. The baseline is Chinese Standard Time rather than Beijing local time.
  2. Actual astronomical data is used rather than only theoretical mathematical calculations.

Proposals to optimize the Chinese calendar[edit]

To optimize the Chinese calendar, astronomers have released many proposed changes. A typical proposal was released by Gao Pingzi (高平子; 1888-1970), a Chinese astronomer who was one of the founders of Purple Mountain Observatory. In his proposal, the month numbers are calculated before the dark moons and the solar terms were rounded to the day. Under his proposal, the month numbers are the same for the Chinese calendar upon different time zones.

As the intercalary month is determined by the first month without mid-climate and the exact time when each mid-climate happen would vary according to time zone, countries that have adopted the calendar but calculate with their own time could vary from the one used in China because of this. For instance, the 2012 FTG happened in UTC May 20 15:15, which would translate to May 20 23:15 in UTC+8, making FTG the mid-climate for the fourth month of that traditional Chinese year [April 21 ~ May 20 in Gregorian calendar], but in Korea it happened in May 21 00:15 in UTC+9, and as new moon take place in May 21 in that month, therefore the month before that would only consist of the SC solar term, lacking mid-climate. As a result, the month starting at April 21 would be an intercalary month in Korean calendar, but not in Chinese Calendar, and the intercalary month in Chinese calendar would start in the month after, in the fifth month starting from May 21, which would only consist of the solar term STG, while the month in Korean Calendar would have both FTG and STG solar term in it.

Other practices[edit]

Among the ethnic groups inhabiting the mountains and plateaus of southwestern China, and those living in the grasslands of northern China, their civil calendars show a diversity of practice based upon their characteristic phenology and culture, but they are based on the algorithm of the Chinese calendar of different periods, especially those of the Tang dynasty and pre-Qin dynasty period.

See also[edit]

Notes[edit]

  1. ^ Despite the literal meaning of the word 農曆 as "farming calendar", this is a cultural/religious calendar, and only loosely based on agricultural traditions. It was first designated 農曆 by the newspapers of the mainland of China on 1 January 1968[citation needed], as part of the Socialist Education Movement. The traditional calendar was labelled with "", meaning "farming", and was regarded as part of the Four Olds to be eliminated. A more accurate translation of "農曆" is "rural calendar", since usage of the traditional Chinese calendar today is confined to rural areas (except when calculating the Chinese New Year). This is particularly ironic since the Gregorian calendar is more convenient for farming than the traditional Chinese calendar.[citation needed]
  2. ^ The 4th-century date, according to the Cihai encyclopedia,[year needed] is due to a reference to Fan Ning (範寧; 范宁), an astrologer of the Jin dynasty.
  3. ^ The renewed adoption from Manichaeans in the 8th century (Tang dynasty) is documented with the writings of the Chinese Buddhist monk Yi Jing and the Ceylonese Buddhist monk Bu Kong.
  4. ^ For instance, the 19th year in Wùyín Yuán Calendar was expected to have 4 consecutive long months if the real synodic method was used. Since this broke the traditional pattern of alternating long and short months, they reverted to using the cycling method to determine month length for that year.[citation needed]
  5. ^ 新唐書•本紀六 肅宗、代宗
    (上元)二年……,九月壬寅,大赦,去“乾元大圣光天文武孝感”号,去“上元”号,称元年,以十一月为岁首,月以斗所建辰为名。…。
      元年建子月癸巳[2],…。己亥[9],…。丙午[16],…。己酉[29],…。庚戌[30],…。[初一壬午大雪,十七冬至]
        建丑月辛亥[1],…。己未[9],…。乙亥[25],…。[初一辛亥,初三小寒,十八大寒]
    宝应元年建寅月甲申[4],…。乙酉[5],…。丙戌[3],…。甲辰[24],…。戊申[28],…。[初一辛巳,初三立春,十八雨水]
        建卯月辛亥[1],…。壬子[2],…。癸丑[3],…。乙丑[15],…。戊辰[18],…。庚午[20],…。壬申[22],…。[初一辛亥,初四惊蛰,十九春分]
        建辰月壬午[3],…。甲午[5],…。戊申[19],…。[初一庚辰,初五清明,二十谷雨]
        建巳月庚戌[1],…。壬子[3],…。甲寅[5],…。乙丑[16],…。大赦,改元年为宝应元年,复以正月为岁首,建巳月为四月。丙寅,…。[初一庚戌,初五甲寅立夏]。
  6. ^ The birthday is the day in each year that have the same date as the one on which someone was born. It is easy to confirm the birthday in the Chinese calendar for most people. But, if someone was born on the 30th of a month, his birthday is the last day of that month, and if someone is born in an intercalary month, his birthday is the day with the same date in the common month of the intercalary month.
  7. ^ The Gregorian calendar is a solar calendar and the Chinese calendar is a lunisolar calendar, and the birthday in the Chinese calendar is not same as in the Gregorian calendar always. so, there's a bias of +/-1 between the actual age in the Chinese calendar and in the Gregorian calendar. Thus, the nominal age in the Chinese calendar is 0~3 older than the actual age in the Gregorian calendar.

References[edit]

  1. ^ Sôma, Mitsuru; Kawabata, Kin-aki; Tanikawa, Kiyotaka (2004-10-25). "Units of Time in Ancient China and Japan". Publications of the Astronomical Society of Japan. 56 (5): 887–904. Bibcode:2004PASJ...56..887S. doi:10.1093/pasj/56.5.887. ISSN 0004-6264. 
  2. ^ 海上 (2005). 《中國人的歲時文化》. 岳麓書社. p. 195. ISBN 7-80665-620-0. 
  3. ^ 陳浩新. "「冷在三九,熱在三伏」". Educational Resources - Hong Kong Observatory. 
  4. ^ "【典故】冬至進入數九寒天 九九消寒圖蘊藏智慧 | 神傳文化 | 大紀元". Epoch Times. Retrieved 15 May 2018. 
  5. ^ "Days of the week in Japanese". CJVLang. Retrieved 15 May 2018. 
  6. ^ Mathematics of the Chinese calendar, pp. 29–30.
  7. ^ 《辽宁大学学报:哲社版》,2004/06,43~50页
  8. ^ Aslaksen, p.38.
  9. ^ Cohen (2012), p. 1, 4.
  10. ^ http://www.newsmth.net/bbsanc.php?path=%2Fgroups%2Fsci.faq%2FAstronomy%2Fbw%2Fall2%2Fbk37k%2FM.1275291864.z0&ap=353
  11. ^ Asiapac Editorial. (2004). Origins of Chinese Science and Technology. Translated by Yang Liping and Y.N. Han. Singapore: Asiapac Books Pte. Ltd. ISBN 981-229-376-0, p.132.
  12. ^ Needham, Joseph. (1959). Science and Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth. Cambridge University Press., reprinted Taipei: Caves Books, Ltd. (1986), pp. 109–110.
  13. ^ Ho, Peng Yoke. (2000). Li, Qi, and Shu: An Introduction to Science and Civilization in China. Mineola: Dover Publications. ISBN 0-486-41445-0. p. 105.
  14. ^ Restivo, Sal. (1992). Mathematics in Society and History: Sociological Inquiries. Dordrecht: Kluwer Academic Publishers. ISBN 1-4020-0039-1. p. 32.
  15. ^ 孙中山:“临时大总统改历改元通电”,载《孙中山全集》(第2卷),中华书局1982年版,页5。
  16. ^ Mathematics of the Chinese calendar, pp. 28.

Further reading[edit]

External links[edit]

Calendars
Calendar conversion
Rules