Mongolian Calendar




Mongolian Calendar

Mongolian Calendar

Как исчисляется

Тюрко-монгольский календарь представляет собой попытку установить определенную связь между лунным месяцем и солнечным годом. В основу этого соотношения было положено то наблюдение, которое в свое время было сделано в древней Греции Метоном и к которому монголы пришли независимо от него: наблюдение о том, что 19 солнечных лет содержат 235 полных лунных месяцев. Исходя из этого, тюрко-монгольская календарная система предусматривала в пределах каждого девятнадцатилетнего периода чередование 12 простых годов (по 12 месяцев) и 7 годов удлиненных (по 13 месяцев). 12 Месяцев х 12 + 13 месяцев х 7 = 235 месяцев.

Шестидесятилетние монгольские циклы считаются от 1027 г., который и является начальным годом тюрко-монгольской системы летосчисления ("рабчжуном"), занимая четвертое порядковое место в первом цикле (см. таблицу XXV). Поскольку 1027 г. по тюркомонгольской номенклатуре был годом огня и зайца, постольку все дальнейшие хронологические даты приводятся тоже в циклах (кругах) огня и зайца. Когда например, говорят: "второй цикл (круг) огня и зайца"; то значит, что речь идет о втором шестидесятилетнем периоде по тюрко-монгольской эре, т. е. от 1027 г. (рабчжуна), который носил название огня и зайца и был четвертым по счету в исходном цикле.

Так, например, в грамоте ханши Тайдулы в. кн. Семену Ивановичу имеется дата: "свиного лета осмого месяца в пятый ветха". Год свиньи в княжение Семена Ивановича Гордого (1341--1353) имел место только один раз 1). По современной эре это -- 1347 г. В лунном цикле 1347 г. занимает 17 место (1347:19 = 70 и 17 в остатке). Январское новолуние для года с порядковым номером 17 приходится на 16 января, а с поправкой на 4 для XIV в. -- на 12 января 2). Следовательно, монгольское новогодие падает уже на февраль, именно (учитывая поправку) -- на 10 число 2). Восьмой месяц начинается 5 сентября 2), а вторая (ветхая) его половина через 15 дней, т. е. 20 сентября, 5 день второй (ветхой), половины -- 24 сентября 1347 г.



Olli Salmi 29.12.2009 (First version uploaded 25.7.2009)



Years in the Mongolian calendar are
designated by two terms, an element or colour (usually not both) and an
animal. It is very easy to find these for a given Gregorian year.



1. To get the number of the element or colour subtract 3 from the
year (AD) and
take the last digit and find the element in the table.
Odd numbers are male
and even numbers female. Mongolian has a different form for the colour
of female animals.

2. Next divide the same number by 12.
The remainder is the number of the animal. (0=12=pig). This is
easy to calculate mentally but you can deduce the remainder
from the decimal part on your calculator. Add 1 to the first decimal up
to .50, add 2 if its more, from .58 upwards.



Let's check the year 1192. Subtract 3 and you get 1189. The last digit
is 9, so
the year is black/water, male. When you divide 1189 by 12
you get 29 and a remainder of 1. So it's the year of the
Black Mouse or Water Mouse.


Махбод
Element
Өнгө Colour Жил Year
1 valign="undefined">木 модон
wood
xml:lang="zh" lang="zh">хөх blue 1 子鼠 хулгана
mouse
2 lang="zh">хөх xml:lang="zh" lang="zh">өгчин 2 丑牛 үхэр

cattle

3
гал fire
улаан red 3 寅虎 бар tiger
4 улаа lang="zh">гчин 4 卯兔 туулай

hare

5 valign="undefined">土 шороо
earth
шар yellow 5 辰龙 луу
dragon
6 шара lang="zh">гчин 6 巳蛇 могой
snake
7
төмөр iron
цагаан white 7 午马 морин
horse
8 цагаа lang="zh">гчин 8 未羊 хонин
sheep
9
усан water
хар black 9 申猴 бичин
monkey
10 хара lang="zh">гчин 10 酉鸡 тахиа
fowl
11 戌狗 нохой dog
12 亥猪 гахай pig





The historical 60-year Mongolian-Tibetan cycle (жар) starts with the
year of
the Red Hare in 1027. To find the cycle subtract 1026 and divide by 60.
The quotient indicates how many full cycles have elapsed. The next
integer is the current cycle. The remainder gives the number of the
year in the cycle.



The rest of this page is under construction. It has speculation and may
contain grave
errors of misunderstanding or carelessness. Information is rather
scarce.



The Mongolian calendar is a reformed version of the href="http://www.rabten.eu/calendar.pdf">Tibetan calendar, known
as Төгс буянт (Tögs buyant, Very Virtuous) in
Mongolian. According to Berzin and L. Terbish (Урианхан

Лхасрангийн Тэрбиш) the calendar was reformed
by Сүмбэ хамба Ишбалжир (Sümbe hamba Ishbaljir 1704-1788, href="http://www.tbrc.org/kb/tbrc-detail.xq?RID=P339&wylie=n">Sum-pa
mkhan-po Ye-shes dpal-‘byor). It has
940
months in 76 years (365.2422*76=27758.4 and
29.5306*940=27758.7, the decimals are wrong in the source). Years can
have 353, 354, 355, 383, 384 or 385
days. The orbit of Jupiter takes 12 years (11.862 years) and Saturn 30
years (29.458). The
rules
for determining the date of the New Year are not clear. It may fall on
the same date as the Chinese New Year, or a day
later, but also a month later than these dates.



Since the Tibetan calendar has 804 months in 65 years we should
substitute 76/940 (=19/235) for every occurrence of 65/804 in the
Tibetan formulas in order to get the dates of the Mongolian calendar.
However,
Berzin indicates there are differences in the epoch. It is not clear
what
they are in numbers.



940 months in 76 years means 28 leap years in as many years. Both
numbers are divisible by 4 and the result is four cycles of 19 years,
which coincide nicely with the Metonic cycle (or 76 years corresponds
to the Calippic cycle). This is clear in the list
of Buryat New Years. Consequently the intercalary months should occur
with the same intervals as the Hebrew
calendar. In effect this means that the calendar
has only a 19 year cycle over all. The length of the year is 12 28/76 =
12 7/19 lunar months.



If we designate the year with Y and the remainder with R, the Buryat
leap year can be found with the formula adapted from the href="Huili.html">Islamic calendar of the Ming Dynast href="Huili.html">y described in Qizheng tuibu style="font-family: monospace;">
七政推步.
If the remainder R from the division
[(Y+16)*28]/76 is larger than or equal to 48 (which is 76-28), the year
is a leap year. I would expect the leap months to occur in months 9, 6,
2,11, 7, 4 and 12, but unfortunately there is no information to check
this. Besides, if the available information is correct, the pattern is
different before 1960 ([(Y+5)*28]/76), which would indicate that there
are not precisely 940 months in 76 years.



In the 20th century, the Mongolian New Year is a month earlier
than the Tibetan New Year in four years of the 19 years of the
cycle.  The dates
differ, which may be caused by the different rate of
the sun's movement. The Mongolian
reform was published in 1747 (the first year of cycle XIII). Berzin
says the new calendar was started in 1786
and the starting point of the calculations is the 40th year of the 60
year cycle, which presumably is cycle XIII, that is 1786. If we just
substitute the Metonic cycle for the Tibetan leap year rule, the dates
seem to fall on correct new moons. No days have to be taken away,
unlike in
the Gregorian reform, but to make the longitude of the sun correct, the
intitial values have to be revised. It is irrelevant from which point
the
calculations
start as long as the initial values are correct. If the
calendar is to be useful for agriculture or cattle breeding, it needs
to follow the sun.


The dates in
a Tibetan calendar are numbered so that a day is 1/30 of
the orbit of the moon with full moon occurring on the 15th. This means
that there may be dates missing
or two days may have the same number. Mongolia also has followers of
the Yellow system, which numbers days consecutively. As far as I have
been able to ascertain, it is the Chinese calendar imposed by Manchus
on the Mongolians.



The length of the month in the Tibetan calendar, 167025/5656 days, is
quite near the correct value. With this length of the month the
Mongolian solar year is 365.2467338 days, which means about four and a
half days too long in a millennium when compared with the tropical year
(365.24219 days). Better values could be reached by 123 leap years in
334 years (12 123/334 months ≈ 365.2420804 days (about one day
too
short in 10000 years), 12 253/687 months ≈
365.2422091 days, or 12 882/2395 months ≈ 365.2421911 days. Of
these 123/334 was used by the formula for Chinese leap years in the
Islamic calendar mentioned above.





Links and references



Монгольско–русский словарь/Монгол орос толь, Москва 1957. The
information (pp. 712–715) is in tables with the elements in
columns and animals in rows. The cycles are listed.



Henning, Edward: Kalacakra and the Tibetan Calendar.Columbia University
Press, 2006.



JANSON,
SVANTE : 

TIBETAN CALENDAR MATHEMATICS

http://www.math.uu.se/~svante/papers/calendars/tibet.pdf



Л.Тэрбиш: Монгол зурхайн цаглабарын уламжлал хийгээд
өнөөгийн байдлын талаар уншигч танаа учирлах нь The main source because
it has numerical information. A long
description of
the development. Terbish
is widely mentioned on Mongolian pages about the calendar.

The people mentioned:

Гармаваа Ранжүндорж (rang 'byung rdo rje)  /rtsis gun btus pa/

Цүрпүваа (mtshur phu ba )  Жамьяандондов-одсэр

Пүгваа (phug ba) Лхүндэвжамц

Дэсрид Санжаажамц (sde srid sangs rgyas rgya mtsho) /rtsis gzhung
be dur dkar po/

Сүмбэ ханбо Ишбалжир /rtsis gzhung dge ldan rtsis gsar)/

“Цагаан биндэръяа” хийгээд
Лувсанданзанжанцан(1639-1704) (1789)

 Дэчингалавын сүмийг байгуулан “Цагийн Хүрдэний Язгуур
үндэс” (1806)

http://www.tsahimurtuu.mn/main/200901201512.htm

href="http://dayarmongol.com/index.php?option=com_content&task=view&id=2979">http://dayarmongol.com/index.php?option=com_content&task=view&id=2979



Alexander Berzin, Tibetan Astro Science: 2 History and the
TibetanCalendar. 1986.

href="http://www.berzinarchives.com/web/en/archives/study/tibetan_astrology_medicine/astrology/tibetan_astro_sciences/tibetan_astro_science_02.html">http://www.berzinarchives.com/web/en/archives/study/tibetan_astrology_medicine/astrology/tibetan_astro_sciences/tibetan_astro_science_02.html



MONGOLIAN NEW YEAR - TSAGAAN SAR

href="http://mayaguais.blogspot.com/2008/02/mongolian-new-year-tsagaan-sar.html">http://mayaguais.blogspot.com/2008/02/mongolian-new-year-tsagaan-sar.html
Useful information on the history.



http://en.wikipedia.org/wiki/Tsagaan_Sar
A set of dates for New Years. It is not clear if these are from the
official list of dates calculated
by the Gandantegchinlen Monastery. I haven't been able to find the
official list, “Жаран жарны цаг тооны бичиг” (1207-гоос
4626 он дуусталх 3600 жил
)



http://ru.wikipedia.org/wiki/Сагаалган Another
set of dates for the day before New Year (битүүн), different from the
above (for
Buryat New Year?). Thre is a link to this page from the English
Wikipedia page.



http://www.olloo.mn/modules.php?name=News&file=print&sid=87603
A list of New Years for 112 years. This page seems to be written by
Terbish, so this may be the official list. The second 2003 is a typo
and should be deleted. The pattern changes in 1960 but the list is not
long enough to determine how often that happens. An important reference.



http://tuurug.banjig.net/mongol/index.php?b_type=cal


href="http://tuurug.banjig.net/mongol/index.php?b_type=cal&jil=2009&sar=07">http://tuurug.banjig.net/mongol/index.php?b_type=cal&jil=2004&sar=03

href="http://tuurug.banjig.net/mongol/index.php?&b_type=cal&jil=2009&sar=03">http://tuurug.banjig.net/mongol/index.php?&b_type=cal&jil=2009&sar=07

Online Mongol calendar, only for a couple of months, but changing the
URL you can find more. Lots of mistakes, missing lunar day numbers,
missing months, dates ind descending order. An important reference if
the rest is correct. Leap months are not indicated.



href="http://mongolulamjlal.blog.banjig.net/index.php?page=3&tag=%D0%A6%D0%B0%D0%B3+%D1%82%D0%BE%D0%BE%D0%BD%D1%8B+%D0%B1%D0%B8%D1%87%D0%B8%D0%B3">http://mongolulamjlal.blog.banjig.net/index.php?page=3&tag=%D0%A6%D0%B0%D0%B3+%D1%82%D0%BE%D0%BE%D0%BD%D1%8B+%D0%B1%D0%B8%D1%87%D0%B8%D0%B3



mongγolčud-un odun orun jiruqai-yin uqaγan-u teüke
("Монголчуудын одон орон зурхайн ухааны түүх")

http://www.onongol.com.cn/?product-772.html
A history of of the astronomy and calendar of the Mongols. In Uyghur
script Mongolian. From what I gather there is nothing on the reformed
Mongolian calendar.



Jacqueline Hobbs: Sumpa Khenpo in Amdo

http://jacquelinehobbs17.blogspot.com/search/label/5%20-%20Sumpa%20Khenpo%20in%20Amdo



http://www.kalacakra.org/calendar/tiblist.htm
The dates for the current year of the historical calendars agree with
the official calendar from
Dharamsala.



http://en.wikipedia.org/wiki/Losar

A set of dates for the Tibetan New Year. At the beginning of the same
lunation as the Mongolian ones but the date may differ. This may been
that the epoch is rather recent but the corrected movement of the sun
generates different dates.



href="http://mongolianphoto.blogspot.com/2008/02/blog-post.html">http://mongolianphoto.blogspot.com/2008/02/blog-post.html

New Year dates from 1900 to 2009. Same as in Wikipedia but the dates
differ from the Buryat list, although the same new moon is meant.
Neatly arranged in 19-year cycles. From 1959 onward a different pattern
of leap years is followed. I presume 2000 is a typo, probably for
2000.02.06.

http://blogportal.bugdeeree.mn/uzeh.jsp?temdeg=264
A page with a link to a copy of the preceding.



href="http://wiki.ecm-outsourcing.com/index.php?title=%3F%3F%3F%3F%3F%3F_%3F%3F%3F%3F%3F%3F_%3F%3F%3F%3F%3F%3F_%3F%3F%3F%3F_%3F%3F%3F%3F">http://wiki.ecm-outsourcing.com/index.php?title=ЦАГААН_САРУУД_ХЭДЭНД_БОЛЖ_БАЙВ

A list that differs for a few dates from the above. href="http://www.olloo.mn/modules.php?name=News&file=print&sid=87603">



http://www.mongolnews.mn/unuudur.php?n=15980
The table of the elements in a nicer format.

href="http://www.olloo.mn/modules.php?name=News&file=article&sid=84914">

http://www.olloo.mn/modules.php?name=News&file=article&sid=84914
Terbish about missing days. Alas, in Mongolian.

href="http://www.olloo.mn/en/modules.php?name=News&file=comments&pid=&sid=763&op=Re">http://www.olloo.mn/en/modules.php?name=News&file=comments&pid=&sid=763&op=Re

Terbish in English about missing days.



href="http://www.newswire.mn/index.php?option=com_content&task=view&id=180&Itemid=66">http://www.newswire.mn/index.php?option=com_content&task=view&id=180&Itemid=66
Controversy over the date of the New Year: the Mongolian calendar
places the New Year on ‘black wind days’, which is bad.
[Link dead 29.12.2009]

http://www.qppstudio.net/publicholidays2009/mongolia.htm Controversy
over the date of the New Year: the Mongolian calendar avoids the New
Year on ‘black wind days’, which would be bad.



http://www.people.com.cn/GB/guoji/1031/2266673.html
Controversy about
the date of the New Year. Some think the precise and scientific Chinese
calendar should be used instead of the tradition Tibetan calendar.
Terbish thinks it would be disrespectful of Mongolian science and
traditions. In Chinese.



href="http://www.montsame.mn/index.php?option=com_news&task=news_detail&tab=200903&ne=101">http://www.montsame.mn/index.php?option=com_news&task=news_detail&tab=200903&ne=101
The news item about the official dates of the New Year.

http://www.mongolia-web.com/content/blogcategory/16/56/



href="http://www.men-tsee-khang.org/calendar/calendar_2009/index2.htm">http://www.men-tsee-khang.org/calendar/calendar_2009/index2.htm

Official Tibetan calendar from Dharamsala





http://mm.httpcn.com/Mingli/Clock/ZangLi.shtml
List of the years of each sixty-year cycle and months in one year. In
Chinese.



http://mongol.cri.cn/21/2005/11/24/43@55450.htm
Ishbaljir was an Oirat



http://xvv.blogmn.net/20930/ units
for measuring time

href="http://setgeliinjiguur-bunje.blogspot.com/2008/09/blog-post_7628.html">http://setgeliinjiguur-bunje.blogspot.com/2008/09/blog-post_7628.html

Measures of time

1 хоног (24 hours) = 60 мөч

1 мөч = 60 чинлүүр

1 чинлүүр = 6 амьсгал

1 амьсгал = 67 агшин

1 агшин = 707 дэнс





Double hours:

Монгол тооллийн цаг

1. Хулгана- 23.40-1.40

2. Yхэр- 1.40-3.40

3. Бар- 3.40-5.40

4. Туулай- 5.40-7.40

5. Луу- 7.40-9.40

6. Могой цаг- 9.40-11.40

7. Морь- 11.40-13.40

8. Хонь- 13.40-15.40

9. Бич- 15.40-17.40

10. Тахиа- 17.40-19.40

11. Нохой- 19.40-21.40

12. Гахай- 21.40-23.40

href="http://www.legendtour.ru/rus/mongolia/informations/tsagaan_sar.shtml">

http://www.legendtour.ru/rus/mongolia/informations/tsagaan_sar.shtml
In Russian. The Mongolian calendar was made official in 1911 instead of
the Chinese yellow calendar. During the years of repression the
Mongolian New Year was celebrated as a feast of livestock breeders.



href="http://himalaya.socanth.cam.ac.uk/collections/journals/bot/pdf/bot_1992_02_02.pdf">http://himalaya.socanth.cam.ac.uk/collections/journals/bot/pdf/bot_1992_02_02.pdf
A short biography of Sümbe hamba Ishbaljir, including the full
name of his astronomical work.

href="http://trinity.village.virginia.edu/THDLDictionary/internal_definitions/public_term/38797?list_view=true&mode=browse">http://trinity.village.virginia.edu/THDLDictionary/internal_definitions/public_term/38797?list_view=true&mode=browse
Another name of the work.

href="http://libris.kb.se/hitlist?q=zper:%22%5ESum%20pa%20mkhan%20po%20Ye%20shes%20dpal%20%CA%B9byor%5E%22&p=1&m=10&d=libris&f=browse">http://libris.kb.se/hitlist?q=zper:%22%5ESum%20pa%20mkhan%20po%20Ye%20shes%20dpal%20%CA%B9byor%5E%22&p=1&m=10&d=libris&f=browse



His collected works are available at Uppsala University Library.



http://harada.ru/news-view-65.html
Kalmyk kalendar. Nothing on the
mathematics. The New Year was earlier in the autumn. In Russian.



http://baike.baidu.com/view/2698973.html
An illustrated article on Sum-pa mkhan-po, in Chinese. There are
several Chinese forms of his name.

伊希巴拉朱尔

松巴堪布也摄班珠尔

松巴堪布·益希环觉尔

松巴堪布益西班觉

松巴堪布伊希巴勒珠尔



http://unn.people.com.cn/GB/14799/21813/9697082.html
Officially Tibetan
calculations are still done on a sand board.

href="http://www.iwf.de/iwf/res/mkat/others/bp/04000024049910000000.pdf">http://www.iwf.de/iwf/res/mkat/others/bp/04000024049910000000.pdf



href="http://www.tsahimurtuu.mn/main/200802051343.htm?quicktabs_4=1&quicktabs_3=1">http://www.tsahimurtuu.mn/main/200802051343.htm?quicktabs_4=1&quicktabs_3=1
Interview of an astrologist.



href="http://www.archives.gov.mn/index.php?option=com_content&task=view&id=100&Itemid=302">http://www.archives.gov.mn/index.php?option=com_content&task=view&id=100&Itemid=302

Calendar history from the National Archives






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