Tarikh-e Elm, 8(2009), pp.19-44

History and Provenance of the “Chinese” Calendar
in the Zīj-i Īlkhānī
Yoichi Isahaya
Doctoral Student at the University of Tokyo, research fellow at the Japan Society for the
Promotion of Science, and visiting fellow at the Institute for the History of Science,
University of Tehran
amirsahibqiran@yahoo.co.jp(received: 02/08/2010-accepted: 20/09/2010)

Abstract
This article sheds light upon a “Chinese” calendar described in the Zīj-i Īlkhānī. In
previous studies, some characteristics of the calendar were ascribed to the “Uighurs”
However, I will show that it was not originally associated with the Uighur. This “Chinese”
calendar was brought to Iran by the Chinese Taoist Fu Mengchi who accompanied his
ruler Hülegü. Fu Mengchi informed Nasīr al-Dīn Tūsī of the Chinese calendrical system,
which Tūsī described in his Zīj-i Īlkhānī. Soon afterward, the calendar was included in thezīj of Muhyī al-Dīn Maghribī, because it was only used among the Mongol ruling classand their Buddhist servants, who were called Uighur. Muhyī al-Dīn labeled the “Chinese”
calendar the “Chinese-Uighur” calendar, and this title was repeated in subsequent zījes.
Therefore, modern scholars have regarded the calendar as a product of the Uighurs.
However, the title “Uighur” attached to the calendar in later zījes does not reflect thecharacteristics of the calendar, but rather the circumstances in which it was utilized.
Key words: Zīj-i Īlkhānī, Nasīr al-Dīn Tūsī, Uighur, “Chinese” calendar, Fu Mengchi

1. Introduction
This article sheds light upon the “Chinese” calendrical system described in
the Zīj-i Īlkhānī by Nasīr al-Dīn Tūsī (1201–1274). The Mongols created avast transcontinental empire in the 13th century. Under their auspices,various commodities, ideologies, and technologies were disseminated across20/Tarikh-e Elm, 8(2009)

Eurasia (Allsen). Therefore, aspects of cross-cultural contact in this period
have attracted scholars of various disciplines. Among the elements of thiscross-cultural exchange, knowledge of astronomy was one of the first to beheld in high esteem by great historians of science such as George Sarton andJoseph Needham. These scholars noted that a Chinese astronomer, who has
been called Fu Mengchi, had an academic acquaintance with Tūsī, apolymath representative of the Muslim world in the thirteenth century(Sarton, 1005; Needham with Wang, 218). Although Fu Mengchi has been
widely acknowledged, his personage has been cloaked in a dense fog.
His scarce but clear vestige is the “Chinese” calendar in the Zīj-i Īlkhānī(compiled ca. 1271), which was subsequently recorded in later zījes(astronomical handbooks) with a few modifications. Analysis of the“Chinese” calendar in various zījes began in the first half of the nineteenth
century (Ideler) and has been conducted for a number of astronomical
handbooks. For example, it was scrutinized by Itaru Imai in the Zīj-i Sultānī
compiled ca. 1445, by Edward S. Kennedy in the Zīj-i Khāqānī compiled ca.
1420, and by Benno van Dalen et al. in the Zīj-i Īlkhānī. These studies havealready clarified the calendar’s mathematical structure to a great extent.
Despite these great achievements, there remain a few points on whichsome further elucidations are in order, particularly concerning thecharacteristics of the calendar and its designation as “Uighur.” According toprevious studies, the calendar had some different characteristics from not
only the official contemporary Chinese calendar but also from any othercalendar adopted by the successive Chinese dynasties. Its peculiarities havebeen attributed to the influence of the Uighurs (Kennedy, 435; van Dalen
2002, 336; van Dalen et al., 111), who had famously played an importantrole in the nascent period of the Mongol empire and surely contributed to
the Mongol acceptance of the Chinese calendar (Bazin, 402-403). Present
recognition of the calendar is well reflected in a statement by Benno van

History and Provenance of the…/21

Dalen, who produced a series of fruitful works on the astronomical contacts
between Iran and China in this period (slightly adjusted):“The Chinese-Uighur calendar, which is of lunisolar type, was a mixture of
the official Chinese calendar of the Jin dynasty, which was defeated by the
Mongols in 1215, and certain elements from “unofficial” Chinese calendars.
One of the latter may have been the calendar used by the Uighurs, whostarted to serve the Mongol administration around 1210” (van Dalen 2004,
17, n. 2).

In the Zīj-i Īlkhānī, however, there is no reference to the Uighurs, eventhough in later sources the term appears not only in descriptions of thecalendrical system, but also in the title Tarikh-i Khitā wa Uighūr (ChineseUighur Calendar). These indications, as I will show, evidence of Uighur
influence cannot be found in the contents of the “Chinese” calendar of the
Zīj-i Īlkhānī. As previous studies suggest (Imai, passim), the calendar is anamalgam of various elements found in several Chinese calendars, not only
the official one. The two cores of this amalgam are closely associated with
the Jin dynasty (1115–1234), which dominated northern China immediately
before the Mongols. Specifically, they are the Zhong xiu Da ming li1(Revised Great Enlightenment Calendar) and the Fu tian li (Heavenly
Agreement Calendar) (van Dalen et al., 129).
The personal background of Fu Mengchi is not related to the Uighurs
either, but, instead, to northern China. The title given to Fu Mengchi,sīngsīng, means “Taoist master,” as is well known among scholars who
research Chinese sources of this period. In the early period of the Mongol
empire, a Taoist sect known as the Quan-zhen jiao (Integral Realization
Sect?) established a strong base over northern China, support of the Mongol

1. It is worthwhile remarking on the Chinese word “li,” usually translated as “calendar.” Li not only stood fora general system by which the beginning, length, and subdivision of a year were fixed, it also indicated analmanac dealing with solstices; the length of days, months, and years; the motion of the sun and moon;planetary revolution periods, and the like (Needham, 9).

22/Tarikh-e Elm, 8(2009)

court. Also, the Hülegü family had their own fief in Chinese territories, inwhich a decree was issued concerning Taoists (Takahashi, 33-34).
Whereas there is no evidence for Uighur influence, we thus see thatstrong connections to northern China can be found in Fu Mengchi’s
personal background and in his “Chinese” calendar. The available clues leadto the assumption that he was more affiliated with northern China than withthe regions further west, the land of Uighurs.
In scrutinizing Fu Mengchi and his calendar, it will be necessary to makea slight adjustment in our understanding of the cross-cultural contacts of theMongol period. Before going into details, it is useful to remark on calendars
and astronomical activities in the Mongol period in general?
2. Historical BackgroundBy 1206, Temüjin completed the task of forcefully unifying the tribes ofMongolia. In that year, following a decision of the quriltai (the council oftribal chiefs), he was acknowledged as khan of the consolidated TurkoMongol tribes1 and took the new title Chinggis Khan (Morgan, 1986, 63).
Within a short period after that, he and his successors would create a huge
empire across Eurasia.
Since ancient times, the Turko-Mongols had appreciated solar motion notdirectly, by astronomical observations or calculations, but indirectly,
through its effects on vegetation, in a way suitable to their pastoral economy(Bazin, 119). In the official Chinese history of the sixth-century dynasty it isstated that“ [Turks] do not know the succession of years, and only count it based on thegrass turning green” (Ling & De, 910; Bazin, 118).

The Mongols seem to have adopted the Chinese calendric system throughcontacts with the Jin dynasty around 1201 (Bazin, 402). Despite the
1. The term “Turko-Mongols” is used because, concerning the tribes of Mongolia in the twelfth century, it isby no means clear in all cases which were Turkic and which Mongol (Morgan, 1986, 56).

History and Provenance of the…/23

disharmony between the astronomically-determined beginning of theChinese year and the Turko-Mongolian nomadic tradition, according towhich the year starts at the beginning of spring, the Mongols accepted theChinese calendar (Melville, 84).
Therefore, at first, the Mongols continued to use the Revised Great
Enlightenment Calendar of the Jin dynasty. Xu Ting, who was the Sungambassador to the Mongolian court in 1237, reported that he encountered
the Chinese calendar being used in the Mongol court. Upon inquiry, thecalendar was identified as that made by Yelü Chucai (1190-1244), who
accompanied Chinggis Khan on several campaigns and was famous as thechief “Chinese” advisor of the early Mongol rulers (Allsen, 165-166). In
Chinggis’s military expedition to the west, Yelü Chucai compiled a calendar
which took into account the difference in geographical longitude between
Samarqand and mainland China. This was the Xi zheng geng-wu yuan li(Western Expedition Calendar with Epoch Year Geng-Wu [i.e., 1210]).
With the exception of the small correction due to the difference in
geographical longitude, it is identical to the Revised Great Enlightenment
Calendar. He also wrote the Ma da ba li1, which was based on the “methodsof western regions”. After the eastern Muslim lands had been annexed to the
Mongol empire and Chinese territories had been put under direct Mongol
rule, Muslim astronomers came to these territories. In 1267, the most
famous of these astronomers, Jamāl al-Dīn (fl. 1267-91)2, compiled andsubmitted the Wan nian li (Myriad Years Calendar) to Qubilai, the de facto
first emperor of the Yuan dynasty (1271–1368), which constituted theeastern part of the Mongol empire. Qubilai promulgated it to a limited

1. The meaning of this term is yet to be determined (Allsen, 165).
2. Without doubt, Jamāl al-Dīn initiated the most significant phase in the history of West Asian astronomy in
Yuan China. His activities in China are crucial to any consideration of astronomical exchange in this period(Allsen, 166; van Dalen, 2002, 336, 340-341).

24/Tarikh-e Elm, 8(2009)

extent. Unfortunately, the contents of both the Ma da ba li and the Myriad
Years Calendar are currently unknown (Yabuuchi, 1997, 11-12).
Although, in this way, the project for calendrical reform had beenongoing since the time of Chinggis Khan, it made rapid progress after Linan, the capital of the Southern Song dynasty, was occupied in 1276. That is
because afterward, it was possible to make use of not only northern Chinese
astronomical achievements -from the Jin to the Yuan dynasties- but also
southern ones, and to carry forward the reform on this integrated
astronomical accumulation. In 1280, a year after Qubilai finally defeated theSouthern Song dynasty and reunified China under one rule, the new Shoushi li [be consistent in rendering Chinese words in pinyin; until now you had
not yet used any hyphens, from here on you start doing it in some cases but
not all] (Season-Granting Calendar) was compiled, and almanacs based on it
were widely distributed beginning the following year (Yamada, 179;
Yabuuchi, 1997, 13). It was by far the most accurate calendar in the
tradition of Chinese mathematical astronomy and continued to be used foralmost 400 years1; although calendar reform was also conducted in thefollowing Ming dynasty (1368–1644), that dynasty’s calendar, the Da tongli (Great Concordance Calendar), was very similar to the Season-Granting
Calendar (van Dalen, 2002, 340).
Meanwhile, in the 1250s, a brother of Qubilai, Hülegü, led extensive
military campaigns in the Middle East. By taking Baghdad in 1258, heended the Abbasid caliphate. He reigned over Iran and Iraq from 1256 to1265 and founded the Ilkhanid dynasty (1256–1336; van Dalen, 2002, 329).
The first aim of Hülegü’s campaign was to exterminate the Ismā‘īlīs, a goal
he achieved along with “releasing” Tūsī, who resided in their fortress.
Under the Ilkhanid patronage, the Maragha observatory was established, and1. For the structure of the Season-Granting Calendar and the astronomical reforms that underlie its
compilation, we can refer to Nathan Sivin’s work (Sivin).

History and Provenance of the…/25

Tūsī became its director. He compiled an astronomical handbook titled Zīj-iĪlkhānī at the observatory, shortly before his death in 1274. Because various
human and material resources were concentrated at Maragha, a range ofhighly significant research was done there, and the achievements of scholars
who were active at the Maragha observatory had a lasting effect on theastronomical output of future generations, up until the European
Renaissance (Saliba, 2006, 367-368).
3. Historical Sources concerning Fu Mengchi
We have only a faint idea of who Fu Mengchi was. There are four known
primary sources concerning him:
1. “Tārīkh-i Chīn” (“History of China”)1, a section/chapter? inJāmi‘ al-Tawārīkh, by Rashīd al-Dīn Hamadānī
2. Tārīkh-i Banākatī, by Dāwūd b. Muhammad Banākatī
3. Tanksūq-nāma
4. “Tārīkh-i Khitā,” in Zīj-i Īlkhānī, by Nasīr al-Dīn Tūsī.
Among these sources, Rashīd al-Dīn’s “Tārīkh-i Chīn” and the history by
Banākatī refer directly to Fu Mengchi by name. The latter is an abridged
version of the former; thus, its statements do not provide any new
information concerning Fu Mengchi (Banākatī, 338). Furthermore, thedescription concerning him in the Tanksūq-nāma, which is a translation of a
Chinese medical text, is also based on Rashīd al-Dīn’s “History of China”(Rashīd al-Dīn, Tanksūq-nāma, 16)2 Rashīd al-Dīn’s statement in “Tārīkh-i
Chīn,” in Jāmi‘ al-Tawārīkh, is, therefore, the most direct and original
1. The second part of the Jāmi‘ al-Tawārīkh is dedicated to world history, including the history of the biblicalprophets, Muhammad, the emergence of Islam, the caliphates and major sultanates, a history of the Mongolian
and Turkic peoples, the rise of the Chinggisid dynasty, and separate accounts of the Chinese, Indians, Jews,
and Franks. The first part of the history of China in this work provides general information on the populationand certain aspects of Chinese culture, such as its calendar (Allsen, 83, 91).
2. Koichi Haneda elucidates the provenance of the work (Haneda).

26/Tarikh-e Elm, 8(2009)source concerning the Chinese sage, Fu Mengchi; the following passage
represents Rashīd al-Dīn’s reference to him in the “History of China”.
“In the time when the Qanate, or sovereignty all over the world, came to
Mönke Qan’, he dispatched his own brother Hülegü Khan, son of Tolui Khan,son of Chinggis Khan, to the land of Iran, and the sovereignty of theseregions was established on him [Hülegü Khan]. Chinese philosophers,
astrologers, and physicians gathered to his presence. Since he reigned withperfect intelligence, ability, and enthusiasm for all sciences, he ordered ourlord, the prominent teacher of mankind, and the most distinguished amongcontemporaries, Khwāja Nasīr al-Dīn al-Tūsī -may God have mercy upon
him- to build an observatory and compile an astronomical handbook after his
majestic name”.

For the reason that Hülegü Khan had seen their [Chinese] astrologers,
known the astrological rules according to their methods, and accustomed
himself to them, he [Hülegü Khan] ordered Khwāja Nasīr al-Dīn tointroduce their [Chinese] calendar and astrological rules and to incorporate
these contents into the astronomical handbook that he would compile insuch a way that, in compiling calendars, their dates and calculations of theiryears could be also added to our calendars according to the methods andtechnical terms that they had. Then, he [Hülegü Khan] ordered a Chinese,
whose name was Fu Mengchi, known as sīngsīng -namely, a sage -to
explain whatever points he knew about their calendar and astrology toKhwāja Nasīr al-Dīn and to learn astronomy from Khwāja Nasīr al-Dīn. In
two days, Khwāja Nasīr al-Dīn acquired whatever he [the Chinese sage]
knew in this field and incorporated it into the Zīj-i Īlkhānī that hecompiled.
However, that Chinese scholar could not acquire more scientific profit
from Khwāja. That scholar knew some of their methods for calculating thedates relative to astrological choices and orders to some extent, [but] he was
not quite familiar with how to apply an astronomical handbook or
understand celestial movements and their details. No matter the place orHistory and Provenance of the…/27

time, it is rare to find a perfect scholar familiar with these kinds ofknowledge. Below, it shall be said what the aforementioned scholar
explained and what was mentioned in the Zīj-i Īlkhānī (Rashid al-Dīn, Wan
ed., 83-85; idem, Rawshan ed., 5-6; Jahn, 21-22)1.
According to Rashīd al-Dīn, the Chinese man who explained the Chinese
calendrical and astrological knowledge to Tūsī was named Fu Mengchi(QWMHY)2 and held the title sīngsīng, which Rashīd al-Dīn explained as“sage” (‘ārif; Boyle, 253, n. 4). Even though scholars have not identified
this Chinese sage with a historical personage up to now, it has been wellknown that the title sīngsīng is the transliteration of the Chinese xiansheng.
Whereas Western scholars grasped this word as having a more generalized
1. I would like to thank Mohammad Bagheri for his assistance in translating Persian sources. However,needless to say, I am responsible for all mistakes. The following Persian text from the “History of China” isbased on Muhammad Rawshan’s edition.
‫ ﺑﺮادر ﺧﻮﯾﺶ ﻫﻮﻻﮔﻮﺧﺎن ﺑﻦ ﺗﻮﻟﻮی ﺧﺎن ﺑﻦ ﭼﯿﻨﮕﮕﯿﺰ ﺧﺎن را ﺑﻪ اﯾﺮان زﻣﯿﻦ‬،‫ و در زﻣﺎﻧﯽ ﮐﻪ ﻧﻮﺑﺖ ﻗﺎآﻧﯽ و ﭘﺎدﺷﺎﻫﯽ روی زﻣﯿﻦ ﺑﻪ ﻣﻮﻧﮑﮑﺎﻗﺎآن رﺳﯿﺪ‬...
ِ‫ و ﭼﻮن ﭘﺎدﺷﺎﻫﯽ ﺑﻐﺎﯾﺖ ﺑﺎ ﮐﻤﺎل‬،‫ اﻃﺒّﺎی ﺧﺘﺎی در ﺑﻨﺪﮔﯽ وی ]ﺟﻤﻊ[ آﻣﺪه ﺑﻮدﻧﺪ‬...‫ از ﺣﮑﻤﺎ و ﻣﻨﺠّﻤﺎن و‬،‫ ﭘﺎدﺷﺎﻫﯽ اﯾﻦ ﻣﻤﺎﻟﮏ ﺑﺮ وی ﻣﻘﺮّر ﺷﺪ‬،‫ﻓﺮﺳﺘﺎد‬‫ ﻓﺮﻣﻮد ﺗﺎ رَﺻَﺪ‬- ‫ رﺣﻤﺔ ﷲ ﻋﻠﯿﻪ‬- ‫ ﻣَﻮﻻﻧﺎ ﺳﻌﯿﺪ اﺳﺘﺎد اﻟﺒﺸﺮ اﻓﻀﻞ اﻟﻤﺘﺄﺧّﺮﯾﻦ ﺧﻮاﺟﻪ ﻧﺼﯿﺮاﻟﺪﯾﻦ اﻟﻄّﻮﺳﯽ را‬،‫ﻋﻘﻞ و ﮐﻔﺎﯾﺖ ﺑﻮد و ﻣُﻬَﻮﱠس ﺟﻤﻠﻪ ﻋﻠﻮم‬،‫ و زﯾﺠﯽ ﺑﻪ ﻧﺎم ﻫﻤﺎﯾﻮن او ﺗﺄﻟﯿﻒ ﮐﻨﺪ‬،‫ﺳﺎزد‬‫ ﻓﺮﻣﻮد ﺗﺎ ﺧﻮاﺟﻪ ﻧﺼﯿﺮاﻟﺪﯾﻦ‬،‫ و اﺣﮑﺎمِ ﻧﺠﻮﻣﯽ ﺑﺮ ﻗﺎﻋﺪۀ اﯾﺸﺎن داﻧﺴﺘﻪ و ﺑﺪان ﻣﻌﺘﺎد ﺷﺪه‬،‫ و ﺑﻪ ﺟﻬﺖ آﻧﮑﻪ ﻫﻮﻻﮔﻮ ﺧﺎن ﻣﻨﺠّﻤﺎن اﯾﺸﺎن را دﯾﺪه ﺑﻮد‬...
‫ ﺗﺎرﯾﺦ و ﺣﺴﺎب ﺳﺎﻟﻬﺎی اﯾﺸﺎن را‬،‫ ﭼﻨﺎﻧﮑﻪ ﺑﻪ وﻗﺖِ اﺳﺘﺨﺮاجِ ﺗﻘﻮﯾﻢ‬،‫ و آن ﻣﻌﻨﯽ را در زﯾﺠﯽ ﮐﻪ ﻣﯽﺳﺎزد ﺑﯿﺎرد‬،‫ﺗﺎرﯾﺦ و ﻗﻮاﻋﺪ ﻧﺠﻮﻣﯽ اﯾﺸﺎن ﻣﻌﻠﻮم ﮔﺮداﻧﺪ‬،‫ و ﺷﺤﺼﯽ ﺧﺘﺎﯾﯽ را ﮐﻪ ﻧﺎم او ﻗﻮﻣﯿﺤﯽ ﺑﻮد و ﻣﻌﺮوف ﺑﻪ ﺳﯿﻨﮕﺴﯿﻨﮓ ﯾﻌﻨﯽ ﻋﺎرف‬.‫ﻧﯿﺰ ﺑﻪ ﻣﻮﺟﺒﯽ و ﻣﺼﻄﻠﺤﯽ ﮐﻪ دارﻧﺪ ﺑﻪ ﺗﻘﻮﯾﻤﻬﺎی ﻣﺎ اﺿﺎف ﺗﻮان ﮐﺮد‬‫ و‬،‫ﻓﺮﻣﻮد ﺗﺎ از ﺗﺎرﯾﺦ و ﻧﺠﻮﻣﻬﺎی اﯾﺸﺎن ﺑﻪ ﻧُﮑَﺖ ﻫﺮآﻧﭽﻪ ﺑﺮآن وﻗﻮف دارد ﺑﺎ ﺧﻮاﺟﻪ ﻧﺼﯿﺮاﻟﺪّﯾﻦ ﺗﻘﺮﯾﺮ ﮐﻨﺪ و ﻋﻠﻢِ ﻧﺠﻮم از ﺧﻮاﺟﻪ ﻧﺼﯿﺮاﻟﺪّﯾﻦ ﺑﯿﺎﻣﻮزد‬.‫ ﺧﻮاﺟﻪ ﻧﺼﯿﺮاﻟﺪّﯾﻦ ﺑﻪ ﻣﺪت دو روز ﺗﻌﻠﯿﻢ ﮐﺮد و ﺑﻪ زﯾﺞ اﯾﻠﺨﺎﻧﯽ ﮐﻪ ﺳﺎﺧﺖ درآورد‬،‫ﻫﺮآﻧﭽﻪ او را از آن ﻗﺴﻢ ﻣﻌﻠﻮم ﺑﻮد‬‫ و ﺑﺮ آﻧﭽﻪ‬،‫ وآن ﺣﮑﯿﻢ ﺣﺴﺎبِ ﺗﺎرﯾﺦ ﺑﻌﻀﯽ اﺧﺘﯿﺎرات و اﺣﮑﺎم اﯾﺸﺎن ﻣﯽداﻧﺴﺖ‬.‫ اﻣّﺎ آن ﺣﮑﯿﻢ ﺧﺘﺎﯾﯽ زﯾﺎدت ﺑﻬﺮه ای ﻋﻠﻤﯽ از ﺧﻮاﺟﻪ ﻧﺘﻮاﻧﺴﺖ ﯾﺎﻓﺖ‬...
‫ ﻫﺮﭼﻪ در ﻫﺮ اﻗﻠﯿﻤﯽ و ﻫﺮ ﻋﻬﺪی ﺣﮑﯿﻤﯽ ﮐﺎﻣﻞ ﮐﻪ ﺑﺮ ﭼﻨﺎن ﻋﻠﻮم واﻗﻒ ﺗﻮاﻧﺪ‬.‫ و دﻗﺎﯾﻖ آن زﯾﺎدت وﻗﻮﻓﯽ ﻧﺪاﺷﺖ‬،‫ﻋﻤﻞ زﯾﺞ و ادراک ﺳَﯿﺮ ﺳﺘﺎرﮔﺎن ﺑﺎﺷﺪ‬.‫ و در زﯾﺞ اﯾﻠﺨﺎﻧﯽ ﻣﺬﮐﻮر ]در آﻣﺪ[ اﯾﻦ ﻣﻘﺪار اﺳﺖ ﮐﻪ ﯾﺎد ﮐﺮده ﻣﯽﺷﻮد‬،‫ آﻧﭽﻪ آن ﺣﮑﯿﻢِ ﻣﺬﮐﻮر ﺗﻘﺮﯾﺮ ﮐﺮد‬.‫ ﺑﻨﺎدر ﯾﺎﻓﺖ ﺷﻮد‬،‫ﺑﻮد‬
2. Although the Chinese sage is provisionally called Fu Mengchi in this article, there is a long history ofattempting to identify him that began at the end of the seventeenth century. In 1689, Müller reconstructed thisname as FUMNJI from the Tārīkh-i Banākatī and vocalized it as Fau Munjī (Boyle, 253, n. 4). Later,d’Ohsson represented it as Fao-moun-dji, relying on Müller (d’Ohsson, 265). Needham introduced the theory
by a modern Chinese scholar that it could be represented Fu Meng-chi (Needham with Wang, 375). Morerecently two Chinese scholars have reconstructed it as Fu Man-tzu, with a question mark (Zhou & Gu, 830; cf.
Allsen, 162).

28/Tarikh-e Elm, 8(2009)

meaning, as in, for example, “teacher” or “master” (Jahn, 21-22; Allsen162), it should be more concretely interpreted as “Taoist master,” inconsideration of the contemporary Chinese context. For example, from partsof a Chinese decree issued to a Taoist temple dated to 1238, it is clear thatthe term was used to represent a Taoist master“…a decree to instruct any provincial and urban darughachi (resident
commissioner), governor, and darughachi administrating artisans in the landsof the Han people. In [our] words, in the temples of Buddhist monks (heshang), the churches of Christian priests, the Taoists’ temples of Taoist
masters (xiansheng), and the mosques of imams, representative persons
who pray to Heaven shall not be disturbed by laymen or subject to any duties
or payments. [Religious] broken or old establishments shall be repaired. They
shall pray for [our] long lives and recite scripts in our names. Whosoever
should disobey our words, whatever kind of persons are they, shall beslain…” (Takahashi, 20).

In this statement, there is a clear distinction between religious sects, andTaoist masters are expressed as xianshengs. Buddhist monks (heshengs) also
appear in Rashīd al-Dīn’s “History of China” in the form of khūshāng
Although the history of Chinese people derives from far ancient times,
and the numbers of their years and cycles [are derived] in the way that they
already explained to Khwāja Nasīr al-Dīn, there is a historical work inwhich names of their sovereigns are described in detail and the foundationof accounts is established, and which becomes famous among Chinese
people in this time, and is so accurate and certain that all scholars andintellectuals rely on it. It is a work that three reliable scholars compiled intheir collaboration, one of whom is named Fūhīn Khūshāng -Fūhīn is his
proper name, and Khūshāng represents his attribution, specifically,
bakhshī- and comes from the city of Tāy‘ānjūy (Tai-an zhou) (Rashid alDīn, Wan ed., 86-87; idem, Rawshan ed., 8; Jahn, 24)1.
1. ‫ ﻟﮑﻦ ﺗﺎرﯾﺨﯽ ﮐﻪ‬،‫ ﺑﻤﻮﺟﺒﯽ ﮐﻪ ﭘﯿﺶ از اﯾﻦ ﺑﺎ ﺧﻮاﺟﻪ ﻧﺼﯿﺮاﻟﺪﯾﻦ ﺗﻘﺮﯾﺮ ﮐﺮدهاﻧﺪ‬،‫ﻫﺮﭼﻨﺪ ﺗﺎرﯾﺦ اﻫﻞ ﺧﺘﺎی ﻋﻈﯿﻢ ﻗﺪﯾﻢ اﺳﺖ و ﻋﺪد ﺳﺎﻟﻬﺎ و ادوار اﯾﺸﺎن‬‫ و ﺗﺎرﯾﺨﯽ درﺳﺖ و ﻣﺨﻘﱠﻖ‬،‫ و ﺑﻨﯿﺎد ﺣﮑﺎﯾﺎت ﺑﺮ آن ﻧﻬﺎده و درﯾﻦ وﻗﺖ ﻣﯿﺎن اﻫﻞ ﺧﺘﺎی ﺷﻬﺮﺗﯽ دارد‬،‫اﺳﺎﻣﯽ ﭘﺎدﺷﺎﻫﺎن آﻧﺠﺎ در آن ﻣﺸﺮوح و ﻣﻔﺼﻞ اﺳﺖ‬History and Provenance of the…/29

As shall be explained later, bakhshī denoted Buddhists in thecontemporary Persian sources (Doerfer, 271-277); therefore, Buddhists andTaoists were clearly recognized as distinct in Persian as well as Chinesesources. The above excerpt shows that Fu Mengchi adhered to Taoism.
Thus, we have seen that Fu Mengchi, a Taoist master, came to Iran aspart of Hülegü’s expedition and informed Tūsī of Chinese astronomical
knowledge, which came to be a part of Tūsī’s Zīj-i Īlkhānī1. In fact, asection of the Zīj-i Īlkhānī’s first chapter, which concerns various calendars
and eras in the zīj, focuses on the Chinese calendrical system called “Tārīkhi Khitā”2. We will now discuss this section in detail.
4. The “Chinese” Calendar in the Zīj-i Īlkhānī
4.1. Chinese Calendars

In Chapter 3, the personage of Fu Mengchi has been clarified as much as
possible. Now, after some general remarks on the “Chinese” calendar, thecontents of his calendar are scrutinized. Although the “Chinese” calendar
was also described in the various Persian and Arabic zījes of the following‫ ﻓﻮﻫﯿﻦ اﺳﻢ‬،‫ ﯾﮑﯽ از ﻧﺎم ﻓﻮﻫﯿﻦ ﺧﻮﺷﺎﻧﮓ‬.‫ ﮐﺘﺎﺑﯽ اﺳﺖ ﮐﻪ آن را ﺳﻪ ﺣﮑﯿﻢ ﻣﻌﺘﺒﺮ ﺑﻪ اﺗﻔﺎق ﺳﺎﺧﺘﻪ اﻧﺪ‬،‫ ﺗﻤﺎﻣﺖ ﺣﮑﻤﺎ و داﻧﺎﯾﺎن ﺑﺮ آن اﻋﺘﻤﺎد ﮐﺮده‬،[‫]اﺳﺖ‬.‫ و از ﺷﻬﺮ ﺗﺎی ﻋﺎن ﺟﻮی ﺑﻮده اﺳﺖ‬،‫اﺳﺖ و ﺧﻮﺷﺎﻧﮓ ﺻﻔﺖ ﯾﻌﻨﯽ ﺑﺨﺸﯽ‬1. Although the accepted view is that Fu Mengchi worked at the Maragha observatory (e.g., Sayɪlɪ, 1960, 205207), this does not have a solid foundation: to my best knowledge, there are no sources that prove the fact.
Referring to research by Mamedbeili, John Boyle states that the Chinese astronomer’s name is mentioned in a
Tehran manuscript of Mu’ayyad al-Dīn ‘Urdī’s treatise on the instruments of the Maragha observatory, Risālafī Kayfiya al-Arsād (Boyle, 253, n. 4); however, Muhammad Tarbīyat, on whom Mamedbeili relies in thisregard (Mamedbeili, 194), does not bring evidence to show the existence of Fu Mengchi at the Maragha
observatory, despite referring to the manuscript (Tarbīyat, 377-378). It is possible that Fu Mengchi’s
acquaintance with Tūsī was a personal one. I would like to thank Benno van Dalen for providing me with therelevant pages of Mamedbeili’s monograph.
2. The word Khitā originally referred to a nomadic people who dominated a vast area in northern China fromthe tenth century and established the Liao Dynasty (916–1125). By the Mongol period, the Turko-Mongols
and the Western people used Khitā to refer to northern China and its inhabitants. The Russian word, Китай,representing China, is derived from it (Isahaya, 2009, 171).

30/Tarikh-e Elm, 8(2009)

periods, almost all the descriptions were based on that in the Zīj-i Īlkhānī.
For the following information on the general description of the “Chinese”
calendar, I have mainly relied on an article by van Dalen (van Dalen, 2002,
334-335)1.
The “Chinese” calendar shares basic characteristics with calendars
officially adopted in successive Chinese dynasties, which were lunisolar;
therefore, lunar months and solar years are compounded to keep pace withlunations and solar motion. In addition, the calendar employed an abstract
duodecennial cycle of “twelve branches,” in conjunction with a decennialseries of “ten trunks,” to derive a sexagenary cycle for denoting years anddays (Melville, 83).
Each month starts with the day of a new moon and consists of 29 or 30
days. To determine the day of the new moon, at first, the time of the mean
new moon is calculated from the average length of a lunation; in the
Chinese calendrical system in the Zīj-i Īlkhānī, this length is taken to be
29.5306 days. To obtain the time of the true new moon, the time of themean new moon is corrected by means of the solar and lunar equations,whose maximum values are 0.1840 days and 0.3844 days, respectively. The
period of the solar equation corresponds to the solar year, but that of thelunar equation, called the anomalistic month, which is, specifically, 27.5556
days long, is somewhat smaller than a lunar month.
1. More details can be found in an article by van Dalen et al. (van Dalen et al., 1997). Note that among
many extant manuscripts of the Zīj-i Īlkhānī, the following three, all of which were copied shortly after thetime of compilation are utilized in this article.
1. British Library Ms. Or. 7464; This manuscript was produced/copied at Maragha in 676
AH/1277–78, only three years after Tūsī’s death, and includes the “longer” introduction,
which does not appear in any other manuscripts (Boyle). On the assumption that thismanuscript well preserves the form of the original, it is taken as the basic text.
2. Bibliothéque nationale de France, Ms. Ancien fonds persan 163 ; This is also quite an earlymanuscript and, according to notes on the manuscript (Tūsī, Paris Ms. 2r, 3r), the copyist wasa son of the author, Asīl al-Dīn b. Nasīr al-Dīn (d. 715 AH/1315; Richard, 179).
3. Dār al-Kutub al-Misrīya, Ms. Dār al-Kutub Mīqāt Fārsī 1; This manuscript was copied at
Maragha in 692 AH/1293 (King, 203).

History and Provenance of the…/31

The solar year in this calendar starts around the time when the sun passes
through the halfway point of the zodiacal sign Aquarius; it has a length of
365.2436 days and is divided into twenty-four equal parts, called qi. The
beginning of the first month is calculated on the basis of the starting point of
the second division of the solar year, the Yu-shui; practically, the first month
immediately precedes the entrance of the sun into the zodiacal sign Pisces.
An ordinary year consists of twelve lunar months (354 or 355 days), but, toconform to the solar year, the calendar requires insertion of a leap monthevery second or third year. The leap month is that which includes only one
starting point of a solar division (all other months include two starting
points).
Although Fu Mengchi’s calendar basically relied on the official Chinese
calendrical system, it differed in several respects from the Chinese model.
4.2. Fu tian li (Heavenly Agreement Calendar)

As mentioned above, Fu Mengchi’s calendrical system has a number ofcharacteristics that are rather atypical for an official Chinese calendar. They
are summarized by the following four points.
1. Use of a point different than the winter solstice to prescribe thesolar year.
2. Use of a parabolic interpolation scheme for the solar equation.
3. Use of a peculiar value of the anomalistic month (27.5556
days).
4. Use of decimal notation to represent the fraction of a day
instead of specific denominators (cf. van Dalen, 2002, 335).
In regard to the first point, the Zīj-i Īlkhānī reads as follows:“Fifth Section, on knowing the beginnings of the divisions of the solar year
which occur in each year
Whenever we want to know the beginning of each of the twenty-four
divisions in a given year, we must know which day and double-hour chāghfell, [or will fall,] on the beginning of the Līchun (Li-chun; the first division)

32/Tarikh-e Elm, 8(2009)
in the proceeding and following year in a sexagenary cycle. We call it “thestarting point of the division of a year,” which is called “kījū” (qi-shou) in the
Chinese language” (Tūsī, London Ms. 5v; idem, Paris Ms. 7r; idem, Cairo
Ms. 6r)1.

This passage shows that the Li-chun was regarded as the starting point forcomputation of the divisions of the solar year, qi-shou, in the Zīj-i Īlkhānī.
Under the Chinese tradition, the Dong-zhi (winter solstice) was taken as thestarting point. This rule was first changed in the Fu tian li (Heavenly
Agreement Calendar) compiled by Cao Shi-wei during the Jian-zhong era(780–783) of the Tang dynasty (618–907). In regard to the Fu tian li, the
New Standard History of the Five Dynasties offers the following passage:
During the Jian-zhong era, the mystic Cao Shi-wei first changed the oldmethods. This calendar, which set the fifth year of the Xian-qing era (600AD) as the start of the epoch and the Yu-shui as the starting point of theyear, was named the Heavenly Agreement Calendar. [However,] it was used
only among the people under the name of civil calendar (xiao-li) (Ou Yang,
670; Yabuuchi, 1982, 2).
As Yabuuchi noted, in the above passage “the starting point of the year”
should be corrected to “the starting point of the division of the solar year”(Yabuuchi, 1982, 4). Therefore, the use of a different point from the wintersolstice to set the start of the solar year commenced with the Heavenly
Agreement Calendar, and the “Chinese” calendar in the Zīj-i Īlkhānī
followed this precedent.
Next, we address the use of a parabolic interpolation scheme for the solar
equation. Although the contents of the Heavenly Agreement Calendar were
unknown for a long time, a small fragment entitled “Futenreki nitten sa
rissei” (the table of the Heavenly Agreement Calendar concerning the solar
1. ‫ ﻫﺮﮔﺎه ﮐﻪ ﺧﻮاﻫﯿﻢ ﮐﻪ ﻣﺒﺪأ ﻫﺮ ﻗﺴﻤﯽ از اﻗﺴﺎم ﺑﯿﺴﺖ و ﭼﻬﺎرﮔﺎﻧﻪ در‬،‫ در ﻣﻌﺮﻓﺖ ﻣﺒﺎدی اﻗﺴﺎم ﺳﺎﻟﻬﺎی ﺷﻤﺴﯽ ﮐﻪ واﻗﻊ ﺑﺎﺷﺪ در ﻫﺮﺳﺎل‬،‫ﻓﺼﻞ ﭘﻨﺠﻢ‬‫ﺳﺎﻟﯽ ﻣﻌﯿﻦ ﺑﺪاﻧﯿﻢ ﺑﺎﯾﺪ ﮐﻪ در ﯾﮏ ﺳﺎل ﭘﯿﺶ از آن ﺳﺎل ﯾﺎ ﺑﻌﺪ از آن داﻧﺴﺘﻪ ﺑﺎﺷﯿﻢ ﮐﻪ ﻣﺒﺪأ ﻟﯿﭽﻦ در ﮐﺪام روز و ﭼﺎغ ﺑﻮده اﺳﺖ از دور ﺳﺘﯿﻨﯽ و ﻣﺎ‬.‫آﻧﺮا اﺻﻞ اﻗﺴﺎم ﺳﺎل ﻣﯽ ﺧﻮاﻧﯿﻢ و آﻧﺮا ﺑﻠﻐﺖ ﻗﺘﺎﯾﯿﺎن ﮐﯿﺠﻮ ﻣﯽﺧﻮاﻧﻨﺪ‬History and Provenance of the…/33

equation) was found at the Tenri Library, Japan, in March 1963. From this,it was proved that the data were all given by the following formula:y = (182 – x) x/331
Then, the parabolic interpolation scheme utilized in the table had the samebase as that of the “Chinese” calendar in the Zīj-i Īlkhānī:
y = (2/9) x (182–x) (Kennedy, 438).
In contrast to the former formula, in which the values were denoted in
Chinese degrees, the solar equation is here expressed in terms of the fractionof a day of lunar elongation. This method had also never been found in
Chinese calendars prior to the Heavenly Agreement Calendar (Nakayama,451). It subsequently succeeded to the official calendars in the Song period
and eventually was used in the Season-Granting Calendar in the Yuan
dynasty, extended to third-order formulas (Chen).
In regard to the third point, the value of the anomalistic month (27.5556
days) utilized in the “Chinese” calendar in the Zīj-i Īlkhānī is, as Itaru Imai
properly stated, quite inaccurate, and this inexact value is rare in Chinese
calendars (Imai, 33). Although Edward Kennedy remarked that theapproximate value 248/9 ≈ 27.5556 days originated in Babylonia (Kennedy,441), according to Kiyoshi Yabuuchi it was also adopted in an official
Chinese calendar, the Qin tian li (Veneration for Heaven Calendar) usedfrom 958 to 963, which imitated the Heavenly Agreement Calendar(Yabuuchi, 1963, 95).
Finally, the adoption of decimal notation to represent the fraction of a day
was unusual. The fractions of a day used to mark the constants of Chinese
calendars were, in general, denoted with specific denominators; for instance,
the lengths of a year and month were represented as 365 1274/5230 and 29
2775/5230, respectively, in the Revised Great Enlightenment Calendar. In
1. In this formula, y is the solar equation and x is the mean solar anomaly, both expressed in Chinese degrees.
The aforementioned formula reflects revisions made by Ikkei Suzuki to the original version introduced by
Shigeru Nakayama (Suzuki, 72-73; Nakayama, 451).

34/Tarikh-e Elm, 8(2009)

the “Chinese” calendar described in Islamic sources?, decimal notation was
substituted for this specific notation, and a common denominator of 10,000
was adopted. According to Yabuuchi, it was another way in which the
Heavenly Agreement Calendar “first changed the old methods.” This new
method was also adopted in the Season-Granting Calendar (Yabuuchi, 1982,
5).
Based on the evidence of these four points, it is clear that the “Chinese”
calendar in the Zīj-i Īlkhānī had strong similarities with the Heavenly
Agreement Calendar. Except for that denoted by the first point, theseelements common to both calendars are devices to simplify computation.
This is one reason that the Heavenly Agreement Calendar was not officiallyadopted and was instead called a “civil calendar” -significant digits are
sometimes lost when these devices are used. However, the Heavenly
Agreement Calendar was adopted as a text for the examination of the
Astronomical Bureau in the Jin and Yuan dynasties, even though it was a“civil calendar” (Yamada, 119-125). This may explain why the “Chinese”
calendar in the Zīj-i Īlkhānī also inherited its simplifying elements.”
When we consider that a good number of bureaucrats of the Jin dynasty
escaped into the Taoist sects, particularly into the Integral Realization, after
the fall of the dynasty (Kubo, 167), it is likely that Fu Mengchi, thetransmitter of the amalgamated calendar, was one of them. In any case, the“unofficial” elements of his calendar were all derived from the tradition of
the Chinese calendars since the Tang period, and there is no evidence of
Uighur participation, as suggested by van Dalen, who said, “it is therefore
tempting to conjecture that the above-mentioned characteristics of theChinese-Uighur calendar that stem from unofficial Chinese calendars derivefrom the original calendar of the Uighurs” (van Dalen, 2002, 336). Although
the actual contents of the calendar utilized in the Mongol period by the
Uighurs, who usually had their own calendar basically corresponding with
the Chinese one, have not become well known, the transliteration into

History and Provenance of the…/35

Persian script of a cycle in the Zīj-i Īlkhānī called “the fourth cycle” (dawr-ichahārum), which consists of twelve elements for divination, was somewhat
different from the transliteration into Uighur script of the same cycle in adocument from 1202 (Bazin, 286-288). Also, the dates of an [to be able towrite “the” you need to specify it more] Uighurian text written in Brahmi
script from 1277 agreed with those of the official Chinese calendar (Bazin,306-308). Therefore, it is natural to consider that the “Chinese” calendar in
the Zīj-i Īlkhānī was brought by a Taoist scholar from Chinese territories
and had little connection with the contemporary Uighurs.
Incidentally, it has been suggested that Cao Shi-wei, the compiler of the
Heavenly Agreement Calendar, came to China from the “western regions,”
which included the land of the Uighurs. This is because his family name,Cao, was attached to the people who came from a city of Sogdiana in theTang period, and it was stated in some Chinese sources that the Heavenly
Agreement Calendar was based on Indian methods (Yabuuchi 1982, 3-4).
Although Yabuuchi took a prudent attitude to this assumption, there is astrong possibility that Cao Shi-wei came from Sogdiana1 because it is wellknown that many Sogdians came to China in the Tang period andpropagated Manichaeism, and these Manichaeans, in particular, brought
new astrological and calendrical elements into China (Lieu, 232).
In this sense, it is possible that the “Chinese” calendar in the Zīj-i Īlkhānī
is the epitome of cultural traffic between East and West. Some elements ofthe calendar were supposedly transmitted from the western regions into
China through Sogdian Manichaeans in the eighth century and then,conversely, from China into Iran by the Chinese Taoist (Fu Mengchi) in thethirteenth century.

1. Sogdiana covered territories around Samarkand, Bukhara, Khujand, and Kesh in modern Uzbekistan. The
name “Cao” was specifically attached to the people from the city of Kabudan.

36/Tarikh-e Elm, 8(2009)

5. Turkic Elements in the Calendar
Finally, it is necessary to consider why the calendar in the Zīj-i Īlkhānī hasbeen thought to have a relationship with the Uighurs. As mentioned above,
the analysis of the “Chinese calendar” described in zījes commenced withthat of a zīj authored after the Zīj-i Īlkhānī, specifically, Ulugh Beg’s Zīj-i
Sultānī (compiled ca. 1445), in which the Chinese calendrical systemderived from Fu Mengchi was given the title of “Chinese-Uighur” calendar(Sédillot, 314). The first zīj in which the term Uighur appeared is the Adwār
al-Anwār madā al-Duhūr wa al-Akwār (ca. 1275) by Muhyī al-Dīn alMaghribī (Muhyī al-Dīn, 11v)1, who also worked in the Maragha
observatory and who compiled this zīj over a period of several years after
Tūsī’s zīj was completed (Saliba 1983, 391-392). There is no doubt thatMuhyī al-Dīn referred to the statements of Tūsī concerning the Chinese
calendrical system, since the contents of their zījes scarcely differed despite
the difference of language: Muhyī al-Dīn’s zīj was in Arabic and Tūsī’s wasin Persian. Adding the term “Uighur” was likely connected to observation ofwhich groups utilized the “Chinese” calendar in Iran. It is probable that, in
those days, this calendar was properly used only among the ruling classcentered upon Mongol royalty and among Buddhist monks protected in theearlier period of the Ilkhanate. This is reflected in the statements of the Zīj-iĪlkhānī:“Exordium
On describing calendars used in this period
The calendar which our sovereigns use is the calendar of the Chinese andTurkic peoples. Those used in our regions are Roman, Arabian, and Persian
calendars, and a new calendar was established by Sultan Malikshāh. Astral

1. I express deep appreciation to Benno van Dalen for informing me of this matter.

History and Provenance of the…/37
scholars take these calendars into consideration” (Tūsī, London Ms. 17r;
idem, Paris Ms. 5r; idem, Cairo Ms. 3v)1.

From this passage, it is clear that the “Chinese” calendar was utilized among“our [Mongol] sovereigns and Turks (including a few Chinese),” not byother people in Iran. Furthermore, the following statements appear in thesection on the festivals of various calendars.
“Seventh Division
Concerning famous days in each calendar
The sovereigns of the Mongols celebrate New Year’s Day as well as the firstday of each month and the birthday of the sovereign. Buddhist monks
practice bājāq for three days each month. That is their fasting. They differ inthe days, one day earlier or later. On the last days of the months and in the
Jaqshābāt month (the twelfth month of the “Chinese” calendar), several days
are also those of bājāq, in which they practice religious observances and eat
decided foods” (Tūsī, London Ms. 23v; idem, Paris Ms. 18v; idem, Cairo Ms.
23r)2

This passage is devoted to the explanation of the “famous days” of the“Chinese” calendar. By these statements, it is made clear that, in Iran,people who utilized this calendar were Mongol rulers and the Buddhist
monks who served them. In fact, according to Charles Melville, the events
recorded in the “Chinese” calendar all concern the activities of the Mongol
ruling class or persons closely attached to the ruling elite in thecontemporary Persian chronicles (Melville, 85). Moreover, it is worthwhile
noting that the term bakhshiyān, which denoted Buddhist monks, became
synonymous with “Uighur” in the course of Mongol domination in Iran
(DeWeese, 82-83, n. 22). Muhyī al-Dīn Maghribī came from the western
1. ‫ ﺗﺎرﯾﺨﯽ ﮐﻪ ﭘﺎدﺷﺎﻫﺎن ﻣﺎ ﺑﮑﺎر ﻣﯽدارﻧﺪ ﺗﺎرﯾﺦ ﻗﺘﺎﯾﯿﺎن و ﺗﺮﮐﺎﻧﺴﺖ و آﻧﭻ در وﻻﯾﺘﻬﺎء ﻣﺎ ﺑﮑﺎر‬،‫ﻣﻘﺪﻣﻪ در ذﮐﺮ ﺗﺎرﯾﺨﻬﺎﺋﯽ ﮐﯽ درﯾﻦ وﻗﺖ ﺑﮑﺎر ﻣﯽدارﻧﺪ‬.‫ﻣﯽدارﻧﺪ ﺗﺎرﯾﺦ روﻣﯿﺎن و ﺗﺎرﯾﺦ ﻋﺮﺑﯿﺎن و ﺗﺎرﯾﺦ ﻓﺎرﺳﯿﺎن ﺑﺎﺷﺪ و ﺗﺎرﯾﺨﯽ ﻣﺤﺪث ﮐﻪ ﺳﻠﻄﺎن ﻣﻠﮑﺸﺎه ﻧﻬﺎده اﺳﺖ و ﻣﻨﺠﻤﺎن اﯾﻦ ﺗﺎرﯾﺨﻬﺎ اﻋﺘﺒﺎر ﮐﻨﻨﺪ‬2. ‫ ﭘﺎدﺷﺎﻫﺎن ﻣﻐﻮل اول روز ﺳﺎل ﻧﻮ ﺟﺸﻦ ﻣﯽﮐﻨﻨﺪ و اول ﻫﺮ ﻣﺎﻫﯽ و روز وﻻدت ﭘﺎدﺷﺎه وﻗﺖ ﻫﻢ ﭼﻨﯿﻦ و‬،‫ﻓﺼﻞ ﻫﻔﺘﻢ در اﯾﺎم ﻣﺸﻬﻮر از ﻫﺮ ﺗﺎرﯾﺨﯽ‬‫ﺑﺨﺸﯿﺎن در ﻫﺮ ﻣﺎه ﺳﻪ روز ﺑﺎﺟﺎق ﻣﯽ ﮐﻨﻨﺪ و آن روزۀ اﯾﺸﺎﻧﺴﺖ و در ﺗﻘﺪﯾﻢ و ﺗﺄﺧﯿﺮ ﺑﻌﻀﯽ از آن روزﻫﺎ ﺑﯿﮏ روز ﻣﯿﺎن اﯾﺸﺎن ﺧﻼﻓﺴﺖ و آﺧﺮ ﻣﺎﻫﻬﺎ و‬.‫در ﻣﺎه ﺟﻘﺸﺎﺑﺎط ﭼﻨﺪ روز ﻫﻢ ﺑﺎﺟﺎق ﺑﺎﺷﺪ و در ﺑﺎﺟﺎق ﻋﺒﺎدت ﮐﻨﻨﺪ و ﻃﻌﺎﻣﻬﺎء ﻣﻌﯿّﻦ ﺧﻮرﻧﺪ‬38/Tarikh-e Elm, 8(2009)

Muslim world and had probably never been farther east than Baghdad andMaragha (Ridawī, 232-237). Therefore, for him, Uighur was not a term
representing the people who dwelt in the western region of China, butinstead described the Buddhist monks serving the Mongol rulers who
utilized their peculiar calendar, which he called the “Chinese-Uighur”
calendar in his zīj. Originally, the calendar that Fu Mengchi taught to Tūsī
had no relationship to the Uighurs, but it eventually became known as the“Chinese-Uighur’s” as a reflection of the political situation in Iran.
There are several Turkic words in the calendar in the Zīj-i Īlkhānī; forinstance, the names of years and months are described in both Chinese andTurkic, and a Turkic technical term concerning the solar equation also
appears (Mercier, 50). However, this fact does not mean that the Uighur—aTurkic people—had anything to do with the creation of the calendar. As
Louis Bazin properly stated, from the middle of the thirteenth century, theTurkophonic regions were under Mongol domination. The Mongols, who
had been influenced by the Turkic culture, in particular the Uighur culture,since the nascent growth of their empire, mingled further with it as they
advanced to the western regions. Eventually, the Mongolian language wasonly imposed on the eastern regions of the empire that depended directly on
the Yuan dynasty, that is, present-day Inner and Outer Mongolia and theirborder lands. In more western regions, where Mongolic people haveremained even up to the present day, the Mongol ruling elites linguisticallyturkicized themselves through several generations, although preserving theirown customs and faith to the blood of Chinggis (Bazin, 403). As a result,the “Chinese” calendar was practiced in Turkic form in Iran,1 so it was
1. Most Turkic people also utilized the “Chinese” calendar, but in the skeletal and simplified form. In the Zīj-iĪlkhānī, it is stated that “Turks curtail the (sexagenary) cycle to a duodecennial one and count it in theirlanguage. Their calendrical measure (qayd-i tārīkh-i īshān) is not known” (Tūsī, London Ms. 5v; idem, Paris
Ms. 7r; idem, Cairo Ms. 6r). Finally, this “Turkic” calendar was assimilated into Persian calendrical customs
and the year has commenced on Persian New Year, Nawrūz, since the Timurid period (Isahaya 2008).

History and Provenance of the…/39

natural to insert Turkic words into the description of the “Chinese” calendar
in the Zīj-i Īlkhānī.

Muhyī al-Dīn, 11v1
1. It is possible to see Uyghur words on this page, with which the description of the “Chinese” calendar
begins.

40/Tarikh-e Elm, 8(2009)

6. Conclusion
On the basis of a range of evidence, the nature of the “Chinese” calendar hascome to light. It was brought to Iran by the Chinese Taoist Fu Mengchi who
accompanied his ruler Hülegü. He informed Tūsī of the calendar, which
Tūsī described in the Zīj-i Īlkhānī. The Chinese calendrical system was thenincluded in the zīj of Muhyī al-Dīn Maghribī in the period immediately
thereafter, and it was practiced only among the Mongol ruling class andtheir Buddhist servants, who were called “Uighur.” In reflecting on thissocial situation, Muhyī al-Dīn labeled the “Chinese” calendar as the“Chinese-Uighur” calendar, and this title succeeded to the later zījes, one ofwhich became the first focus for analysis of the “Chinese” calendar. Thus,
the calendar was attributed to the Uighurs, who surely played an importantrole in the nascent period of the Mongol empire.
It is natural that there are similarities between the Heavenly Agreement
Calendar, the “Chinese” calendar in the Zīj-i Īlkhānī, and the SeasonGranting Calendar, as several previous studies have noted (e.g., Imai, 37;
Nakayama, 452), because, as clarified in this article, these calendars were allused or compiled in accordance with the same intellectual foundation,
namely, that of China during the late Jin and early Yuan periods.
Studies on the Mongol empire have made remarkable progress (Jackson;
Morgan 2004), and historical studies on science in this period have also
advanced,1 but the results of both have not necessarily reflected upon eachother. It would give me great pleasure if this work served, even if only in asmall way, to bridge the gap between these fields.

1. One of the representative researchers is, of course, Benno van Dalen, on whose works this study greatly
relied.

History and Provenance of the…/41

Acknowledgements
In addition to Dr. Benno van Dalen, I sincerely appreciate the help of Dr.
Michio Yano and Dr. Ryoko Watabe, who kindly offered me access toprecious manuscripts. This work is supported by a Grant-in-Aid for theJapan Society for the Promotion of Science Fellows (09J10434).
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