Study on the Period of the Use of Datong-li in Korea
- Author: Lee Ki-Won, Ahn Young-Sook, Mihn Byeong-Hee, Lim Young-Ryan
- Organization: Lee Ki-Won; Ahn Young-Sook; Mihn Byeong-Hee; Lim Young-Ryan
- Publish: Journal of Astronomy and Space Sciences Volume 27, Issue1, p55~68, 15 March 2010
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ABSTRACT
It has been generally known that
Datong-li (a Chinese calendar in the Ming dynasty) was first introduced into Korea in the nineteenth reign of KingGongmin (1370) of the Goryeo dynasty and lasted to the third reign of KingHyeojong (1652) of the Joseon dynasty. This understanding is based on the records ofGoryeo-sa (History of the Goryeo dynasty) and ofSeoungwan-ji (Official book ofSeoungwan)/ Jeungbomunheon-bigo (Explanatory Notes of Library Document). To verify the period of the use ofDatong-li in Korea, we develop a Fortran code to calculate the calendar day byDatong-li and also investigate historical literatures and extant almanacs. As a result, we find the possibility thatDatong-li had been in use since 1389 at least. However, we cannot confirm whetherDatong-li was first enforced in 1370 or not. On the other hand, we confirm thatDatong-li was used until 1653 and reintroduced during the period from 1667 to 1669. Also, we find that previous studies had some errors in the sexagenary cycle of the real first day of a month. We think that this study will contribute to understanding the calendrical history of the Joseon dynasty.
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KEYWORD
calendrical methods (Datong-li , Shoushi-li , Shixian-li) , astronomical almanac , period (Goryeo dynasty , Joseon dynasty)
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Datong-li is a calendrical method of the Ming dynasty in China (1368 ∼ 1644) and there are two versions of 'Musin Datong-li ' made byLiu, Ji onEulmi Dongji in 13681) and 'Datong-lifatonggui' ' made byYuan, Tong in 1384 (Zhang 1971). Although there are slight differences between two calendars such as the fact that the epoch of the former is 1281 (Sinsa year) while that of the latter is 1384 (Gapja year), both are fundamentally the same calendrical methods based onShoushili (Lee 1996). It is known thatDatong-li began to be used in 1370, the 19th year of the reign of KingGongmin of the Goryeo dynasty (Jeon 1974, 1998, Lee 1996, Lee 1997b), based on the records ofGoryeo-sa etc. On the contrary, Yu (1982) and Lee (1988) infer thatDatong-li could not be adopted because the Goryeo dynasty was declining at that time.According to
Sangwi-go (Volume) ofJeungbo-munheon-bigo (Explanatory Notes of Literary Document) (King Sejong The Great Memorial Society 1978), the Joseon dynasty usedDatong-li from the beginning of the dynasty. However, the calculation methods such as solar/lunar eclipses and five planets were not known. Hence, KingSejong orderedIn-Ji Jeong, Cho Jeong , andHeum-Ji Jeong to study the methods, correctTaiyang-tonggui, Taiyin-tonggui and so forth, and compiledChiljeongsan-naepyeon (Yu et al. 1973; hereafter Naepyeon). Currently, the oldest available edition of Naepyeon is the one compiled bySun-Ji Yi andDam Kim in 1444 (Lee & Kim 1444). The series oftonggui books such asDatong-liri-tonggui, Taiyang-tonggui and Taiyin-tonggui etc compiled by the same authors were also preserved in theGyujanggak library. According to the work of Lee (1988), thesetonggui series became the basis of the compilation of Naepyeon. Naepyeon is basically the same line of calendrical method asDatong-li (therefore,Shoushi-li ). Moreover, the titles of currently available astronomical almanacs at that time are written asDatong-li (see Kim 2002, Jeong 2008).Shixian-li made by Adam Schall et al. became to be enforced in theChing dynasty of China from 1645 (Lee 1985). In Joseon, the calendar became effective from the 4th year of the reign of KingHyojong (1653) after over ten years efforts ofYuk Kim , the head of the Bureau of Royal Astronomy andSang-Beom Kim , a staff of the Bureau (King Sejong The Great Memorial Society 1978). Therefore, it is known thatDatong-li was used until 1652, the 3rd year of the reign of KingHyojong (Lee 1997a, Yu 1999, Lee 2008). In recent, Jeon (2002, 2004) pointed out thatShixian-li was introduced in 1654, i.e.,Datong-li was used until 1653, based on the records ofJoseon-Wangjo-Sillok (Annals of Joseon dynasty; hereafter Sillok) (also see, Ahn et al. 2000).As such, the introduction year or the period of the use of
Datong-li completely depended on literary records without any verification through astronomical almanac or calendrical calculation. In this paper, we develop a computer program to calculate calendar days byDatong-li and investigate the period of use ofDatong-li in Korea by the analysis of astronomical almanacs and records of old literatures. In section 2, the calculation of calendrical days byDatong-li was briefly explained and compared it with extantDatong-li almanacs. We discuss the introduction year and the period of the use ofDatong-li in sections 3 and 4, respectively. The literary records related toDatong-li were verified in section 5. Finally, we summarize in section 6.1)According to our calendrical calculation by Datong-li, the sexagenary circle of the winter solistice of 1367 (23 November) not 1368, is Eulmi
2. Calendrical day calculation by
Datong-li As mentioned earlier,
Shoushi-li ,Datong-li and Naepyeon are basically the same calendrical methods and differences between them are as shown in Table 1 (refer to Lee 1988). As shown in the table, Naepyeon is the same asDatong-liri-tonggui andMusin Datong-li except forXiaochangfa . We, therefore, refer to Naepyeon translated into Korean by Yu et al. (1973) in order to calculate calendrical days byDatong-li . There are two editions in Naepyeon: one is appended to the volume ofSejong in Sillok (hereafter Sillok edition) (King Sejong The Great Memorial Society 1990) and the other is compiled by Lee and Kim in 1444, printed withGabin fonts and preserved inGyujanggak library (hereafterGyujanggak edition) nowadays.Datong-ilri-tonggui compiled by the same authors (hereinaftertonggui edition) are also preserved inGyujanggak . The former, Sillok edition, was translated into Korean by Yu et al. (1973). In the course of calculating calendrical days, we checked constant values presented in these three editions and foundGyujanggak edition, in general, had relatively more errors than Sillok edition.Because the translated book by Yu et al. (1973) also contains calculation examples referring to the books of
Jeongmyoyeon-gyeosik-garyung (examples for the calculation of solar and lunar eclipses occurred in 1447) andGyeosik-chubobeob (calculation method for the solar and lunar eclipses), we will not describe detailed processes of calendrical day calculation in this paper. Instead, we will briefly mention on a few issues. First, the translated book is explaining that 'according toGyeosik-chubobeob , the difference between the lunar and solar movements (in unit of degree) should be divided in the process of obtaining the real first day from the mean first day of a month and this method is the same inDatong-li '. However, we found that when only the lunar movement was divided, the results were consistent with extant almanacs. Second, the method, adopting nowadays (refer to Korea Astronomy and Space Science Institute 2008) and mentioned in Naepyeon, was used in inserting a leap month. That is, we apply the intercalation method itself in the calculations of calendrical days differently with previous studies which were obtained the leap month information from historical documents. As a result, we find that all leap months were perfectly consistent with previously known leap months. Finally, whenXiaochang-fa was applied to calculate calendrical days, there were some disagreement on leap months. Thus, we do not useXiaochang-fa in this study.Table 2 is a list of
Datong-li almanacs of the Joseon dynasty period used in this study. In the table, 1, 2 and 3 columns are year, content of the almanacs and reference, respectively. At present, the oldest almanac isGyeongjin year (1580) which was designated as treasure no. 1319 and is currently stored in the National Folk Museum of Korea (Kim 2002).Datong-li almanacs are generally composed of a table of 24 seasonal subdivisions, a map showing the directions of evil spirits (hereafter,Yeonshinbangwi-do ), the calendrical day data of each month covering two pages (one for the 1st day ≫ 13th day and the other for the 14th day ∼ 29th/30th day), and the producers. From the almanac after 1604, the tables of 24 seasonal subdivisions and ofYeonshinbangwi-do are also recorded covering two pages. In Table 2, the signs of a and b represent the former and the latter part between two pages, respectively (in this study, we will not considerYeonshinbangwi-do andGiyeon [yearly] table). In the course of reviewingDatong-li almanacs, we found some parts of the almanac of 1601 in the almanac of 1604 compiled by Korea Mental Culture Research Institute (1994) (refer to Table 2). We also found some single pages of calendrical day from the archive ofJangseogak library: Januarya of 1595, yearly table of 1615, Julya /Augusta /Octobera of 1618 and February a of 1621.To verify calendrical calculations, we first compared our results with extant almanacs for the items of the dates and times of 24 seasonal subdivisions, sunrise and sunset times, the lengths of day and night times, the dates of the real first/last-quarter and so forth. All the data showed perfect consistency except for the sunrise time on August 28, 1607:
Myojeong 1 and 2Ke according to almanac and our calculation, respectively. This difference seems a typo in the almanac of 1607. Next, we compared our results with previous studies (Han 1987, 2001, Ahn, et al. 2009a) for day names as the sexagenary cycle (hereafter Iljin) of the real first day in each month and found generally matched well. However, there were differences in several days as shown in Table 3. In particular, Iljin of the real first day of February 1530 isSinyu andImsul according to Sillok and our calculation, respectively. In the case of the real first day of September 1597, Iljin isMuja in the volume of KingSeonjo while it isGichuk according to our calculation, the revised volume of KingSeonjo , almanac of the year andBaekjungryeok 2). In addition, Iljin of the real first day of September 1602 isGyeongsin in the volume of KingSeonjo , while it isGimi according to our calculation andBaekjungryeok . Lastly Iljin of the real first days of September and October of 1652 areGisa andGihae , respectively, according to our calculation and the almanac of the year. While Ahn et al. (2009a) identified the days asGyeongoh andGyeongja . For your information, Han (1997) pointed out that Iljin of the real first days of December 1437, December 1499, February 1548 and September 1592 in Sillok are obvious errors and thus attention should be paid when quoting Iljin from Sillok's records.2)An almanac contains brief calendrical data for long periods. This book is preserved in Gyujanggak (no. 7275) and the names of the producer and the year of production are unknown.
3. Introduction year of
Datong-li The argument that
Datong-li was introduced in the 19th year of the reign of KingGongmin (1370) is based on the records ofGoryeo-sa andJeungbo-munheon-bigo . The records ofGoryeo-sa on the 19th year of the reign of KingGongmin are as follows.On Gabin day, the emperor of Ming sent an envoy to deliver his letter relating to an investiture . . . . . . King went out to the outside of the castle to meet the envoy on arrival accompanying with officials. The letter read, "Jeon Wang, the king of Goryeo, has been . . . . . . Now, I am sending an envoy with a seal to install you as the king of the Goryeo dynasty . . . . . . I am also sending a Datong-li almanac and 10 rolls of embroidered silk carpet, you take them!" . . . . . .
Jun-Deuk Seong came back from the Ming country. The emperor sent an autograph letter stamped with the imperial seal and the letter read, . . . . . . Now, I am sending a king's official uniform, musical instruments, your retainers' uniforms and the Datong-li almanac of the 3rd year of Hongwu [author's note: 1370], you take them!". According to Sangwi-go of Jeungbo-munheon-bigo (King Sejong The Great Memorial Society 1978),
When Jun-Deuk Seong, an envoy of our country, was coming back from Ming in the 19th year of the reign on King Gongmin, the emperor of Ming granted a Datong-li almanac. [Gyobinggo read, "The emperor sent an envoy to deliver a royal order and then granted a Datong-li almanac.]
In the 19th year of the reign of King Gongmin, the emperor granted a Datong-li almanac and Jun-Deuk brought it . . . . . . . .
In the 19th year of the reign of King Gongmin, the emperor of Ming sent an envoy . . . . . . . and allowed to follow the traditional manners and customs. Then the emperor granted a Datong-li almanac and embroidered silk carpets . . . . . . . .
However, it will be correct to interpret the above records as indicating that just the
Datong-li almanac of 1370 was received from theMing dynasty rather than indicating thatDatong-li was used from the 19th year of the reign of KingGongmin . The grounds of this interpretation include, first, the fact thatDatong-li began to be enforced since 1368 in the Ming dynasty (Lee 1985). Thus it is too early, two years later, for the Goryeo dynasty to use the calendrical method even if the method is similar toShoushi-li . Second,Shoushi-li began to be used in the Goryeo dynasty since the reign of KingChungseon (1308-1313), about 20 years later, from the record that a newly madeShoushi-li almanac was received from theYuan dynasty in the 7th year of the reign of KingChungryeol (1281). Finally, Iljin of the real first day of August 1378 isGyeongja in the calculation byDatong-li , but, it isSinchuk in the calculation byShoushi-li . According to previous studies (e.g. Yang et al. 1999, Ahn et al. 2001, 2009b), Iljin of the day isSinchuk in Korea, China and Japan. We, therefore, think that it is difficult to conclude thatDatong-li was used from the 19th year of the reign of KingGongmin , solely based on the record that aDatong-li almanac was 'granted/taken'. Instead, we think that it is more reasonable to consider that aDatong-li almanac was received in 1370 like the case of receiving aShoushi-li almanac in 1281. Probably, those records might have been specially made because a new calendar,Shoushi-li , was made in 1281 and Datong-minli by MusinDatong-li , the almanac of the 3rd year ofHongwu (1370), was published in China.To verify the introduction time of
Datong-li in the Goryeo dynasty, we first examined the records of the dates of 24 seasonal subdivisions presented inGoryeo-sa . After the reign of KingChungseon , there were only two records: one is that theGihae day of November 1345 wasDaehan (Sever Cold) and another is that theGyeongin day of November 1389 wasDongji (Winter Solstice). First,Daehan is a seasonal subdivision belonging to December and there was noGihae day in December 1345. Sillok also has the record that prisoners with minor crime were released because it wasDaehan (a record on December 4 of the 29th year of the reign of KingSukjong ). This day was January 10, 1704 (in Gregorian calendar) and was notDaehan . Therefore, all of these records aboutDaehan should be translated as 'severe cold' not as a seasonal subdivision. In the case of 1389,Dongji was theGyeongin day of November according to our calculation byDatong-li . This result, of course, is the same in the calculation byShoushi-li . In conclusion, we think that it is difficult to conclude thatDatong-li was used from the 19th year of the reign of KingGongmin . IfDatong-li was really accepted in the Goryeo dynasty, on the other hand, it might have begun to be used since 1389 at least.4. Period of the use of
Datong-li 4.1 Verification using Iljin of 24 seasonal subdivisions recorded in Sillok/Ilgi
To verify until when the Joseon court used
Datong-li , we, first, examined the records regarding seasonal subdivisions from Sillok as did fromGoryeo-sa . Except for records with obscurity in interpreting, a total of 160 Iljin of seasonal subdivisions ranging from 1392 to 1654 are recorded in Sillok3) andSeungjeongwon-ilgi (Diary of the Royal Secretariat; hereafter Ilgi4)). There was one record of eachIpchun, Cheoseo, Ipdong andSoseol , two records ofDaeseol and 153 records ofDongji , the largest in numbers. Of the records ofDongji , the records performed the ritual atDongji were the most frequent. We compared the 160 Iljin with our calculations byDatong-li and found a good agreement in general includingDongji Iljin of 1653. However, we found six records showing disagreement and listed in Table 4. First, the records of 1445 and 1447 are the cases which Iljin are same but dates are different because of incorrect estimate of the dates of the real first day in the website of Sillok. While, the record of November 30, 1479 is translated as, "The 28th of this month isDaeseol , thus . . . . . . . " and the record of November 11, 1621 as, "This day wasDongji and an earthquake occurred, and thus . . . . . . " in Sillok. However, these should be translated as "A heavy snow came on the 28th of this month, and thus . . . . . . " and "An earthquake continued for a long time on this day, and . . . . " respectively. The record of November 29, 1468 reads, "Since it wasDongji, Euijeong-bu (State Council) and six departments dedicated inner and outer materials of clothes, and . . . . . . ". Considering this record, we cannot explain the cause for the inconsistency at this moment. Finally, from the record of November 13, 1654 (Gihae day) reading "SinceDongji already came close . . . . . . ", we can infer thatDongji was later than the 13th. According to the almanac of 1654, however,Dongji of this year was November 13.4.2. Verification by the comparison with extant almanacs
A direct way to investigate the period of the use of
Datong-li in the Joseon dynasty is to check the almanacs used at that time. To this end, we obtainedDatong-li almanacs of the 1650s amongYoon, Jeung 's Family collection from a private owner and examined them. Figure 1 shows the first pages of the almanacs of 1652, 1653 and 1654. As can be seen in the figure, however, the first page showing the name of the calendrical method and 24 seasonal subdivisions was tore off in most almanacs. In the case of the almanac of 1652, the part relating to the reign name of theChing dynasty was erased. According to the work of Jeon (2002), the Family ofYoon-Seok Hwang (a linguist in the middle of the Joseon dynasty) also had been used almanacs after cutting out the first page until in the later of 1760s. Therefore, the date, Iljin and time of 12 seasons5) were compared with the results of calendrical calculations.Table 5 shows the results of comparison between the calendrical calculation and the almanacs of 1653 and 1654. As shown in the table, whereas the almanac of 1653 shows exact agreement with the calculations for the date, Iljin and time in all 12 seasons, that of 1654 does for date and Iljin in several seasons. Meanwhile, the almanac shows completely difference in the time of 12 seasons. From this fact, we can know that
Datong-li was used until the 4th year of the reign of KingHyojong (i.e. 1653) in the Joseon dynasty.3)http://silok.history.go.kr 4)http://sjw.history.go.kr
5. Verification of records related to
Datong-li 5.1 Records regarding the reintroduction of
Datong-li In Sillok, a discussion and order of a king about the reuse of
Datong-li are recorded on a leap July 13, 1661 (the 2nd year of the reign of KingHyeonjong ) and on December 11, 1666 (5 years later), respectively. Also, the record of August 8, 1671 (the 12th year of the reign of KingHyeonjong ) reads,The birthday of the prince is August 15 of
Sinchuk year (1661). However, the calendar system was changed intoDatong-li inJeongmi year (1667) so the leap month ofSinchuk year is not July but October6). Given this fact, August should become September and thus the birthday of the prince was determined to be September through discussion with ministers. However, sinceShixian-li began to be used again in Gyeongsul year (1670), the birthday of the prince should be changed back to August . . . . . . .From above record, we can infer that
Datong-li was used from 1667 (Jeongmi year) to 1669 andShixian-li began to be used again from 1670 (Gyeongsul year). To verify this record, the date, Iljin and time of 12 seasons in the almanac of the years of 1667, 1668 and 1669 were compared with the results of the calculations byDatong-li as the same manner mentioned in section 4.2. Whereas the almanacs of 1668 and 1669 were completely consistent with the calculations byDatong-li , that of 1667 showed differences.6)
Shixian-li was used in 1661 and the leap month was July. However, according to calendrical calculations byDatong-li , the year of 1661 becomes to have a leap month in October.This means that
Shixian-li was used in 1667 andDatong-li did only in 1668 and 1669. In other word, our result suggests thatDatong-li began to be used again in 1668 not 1667. However, we can clear the mystery from both the record of KingHyeonjong regarding the discussion about the reason why the almanac of 1667 brought from theChing country was different from previous ones and the table of 24 seasonal subdivisions of the almanac of 1667. According to the record of December 10, 1666, theChing court decided to abolishShixian-li and useDatong-li again from 1667. In Joseon, however, the almanac by the old calendrical method (author's note:Shixian-li ) had been already distributed in time so the government tried to urgently print the almanac by new calendrical method (author's note:Datong-li ) and redistribute. But since the time was not enough, the king ordered to print and distribute a simple almanac. In the almanac of 1667, we found that the table of 24 seasonal subdivisions was corrected (see Figure 2) and confirmed that corrected dates and times were those byDatong-li . Therefore, it is inferred that the almanac we obtained is the one which was already distributed, that is, the almanac byShixian-li and the dates and times of 24 seasonal subdivisions were corrected on the base of the simple almanac byDatong-li . Another interesting fact is that there is a leap December in the almanac of 1669 (the leap December also becomes to exist in our calculation of calendrical days byDatong-li ). According to the study of Jeon (2002), theChing court informed the Joseon court that there would be no leap month in December 1669 and instead, there would be a leap month in February next year due to the reuse ofShixian-li from 1671. The almanac of 1670 was also already distributed in Joseon. This time the government just announced that there would be no leap month (record of April 11 1680, the 10th year of the reign of KingHyeongjong ). This fact is also can be verified from the fact that Iljin of January 1670 is the same as that of a leap December 1666 in almanacs of both years (refer to Figure 3).5.2 Records regarding the use of sunrise and sunset time of the Joseon dynasty
When obtaining the days of real first/last-quarter or real full-moon, one day is to be set back in
Datong-li or Naepyeon if the time is before the sunrise time of the day. Examples of this rule also appear in the record of Sillok. According to the record of April 18,1457 (the 3rd year of the reign of KingSejo ),In discussing the differences between
Tang 's and Joseon's almanacs with a vice director ofSeoun-gwan . . . . . . The determination of a real full-moon day differs from place to place due to the different time of sunrise/sunset in each place. In determining a real full-moon day of August, Tang 's court set back one day because the real fullmoon time is before the sunrise inTang 's country, while our court did not set back because its time is after sunrise in our country. As such, the ways to determine the real full-moon day are not the same. Please determine the real full-moon day as the 16th based on our almanac . . . . . . and announce it to the public. The king follows the vice director's request.Based on the calculation by
Datong-li , the summer solstice of 1457 is May 22 and the real fullmoon time of August is 2,428.05 min on the 16th day. This day is 83 days after the summer solstice and the sunrise time is 2,412.09 min according to the sunrise/sunset time presented in Naepyeon (i.e. sunrise/sunset time in Joseon). That is, the real full-moon time at that time is 15.96 min (2.29 min in the modern time) later than the sunrise time. Hence, the real full-moon day is the 16th without setting back to one day. To check whether this rule was also applied to other years or not, we examined the cases when the time of a real first/last-quarter or full-moon was before the sunrise time in the year of 1580. Of 10 cases, we found that all dates were determined by setting back one day in the almanac of the year. We also examinedDatong-li almanac of 1637 published in theMing country but preserved inGyujanggak 7). Based on the result, the dates, Iljin and times of 24 seasonal subdivisions showed perfect match with our calendrical calculation. However, the length of a day/night showed maximum 2Ke differences. In particular, the first-quarter time of February is 2629.6425 min on the 8th (73 days afterDongji of 1636 [November 25]) and the sunrise time of the day is 2,631.86 min by Naepyeon, and thus the first-quarter day should become the 7th by setting back one day. But, the almanac ofMing is writing as the 8th day.5)In the almanacs of the Joseon dynasty, the date, Iljin and time of 12 seasons (not 12 subdivisions) corresponding to the relevant month are recorded in the beginning part of each month except for a leap month (refer to Lee 2005).
In this paper, the period of the use of
Datong-li in Korea was studied. To this end, a program to calculate calendrical days byDatong-li was developed first and then compared our calculations with extant almanacs and previous studied to verify the program. As a result, we found that the dates, Iljin and times of 24 seasonal subdivisions, Iljin of real first days in months, the lengths of the months, leap months, and so forth show match well in general. On the other hand, in comparison of Iljin of a real first day in each month with previous studies, a total of 10 cases showed differences. Among them, three cases could be checked with extant almanac and all were consistent with the results of our calculation.With regards to the introduction year of
Datong-li , we analyzed the records relating to Iljin of 24 seasonal subdivisions fromGoryeo-sa and compared them with our calendrical calculations. However, it was difficult to conclude whetherDatong-li was actually used in Korea from the 19th year of the reign of KingGongmin or not. Nonetheless, we confirm thatDatong-li might have been used from about 1389 at least if it was actually used. On the other hand, we verified thatDatong-li was used until 1653 and again used for three years from 1667 to 1669 in Joseon. In addition, we found that there was a leap December in 1669, but it was not used becauseShixian-li became to be used again from the next year. Finally, we also verified that the records of Sillok indicating that if the time of the first/last-quarter or the full moon is before sunrise time, the day is determined by setting one day back.In conclusion, we think that this study will be very helpful to the studies on calendrical methods of the Joseon dynasty, particular studies on Iljin of real first days in months and the dates of 24 seasonal subdivisions during the period of the early Joseon dyansty.
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[Table 1.] Comparison between Shoushi-li, Datong-li and Naepyeon.
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[Table 2.] A list of Datong-li almanacs of the Joseon dynasty period used in this study.
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[Table 3.] Comparison of our calculations by Datong-li with a previous study for Iljin of the first day in each month.
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[Table 4.] Comparison of our calculations by Datong-li with the records of Sillok/Ilgi for 24 seasonal subdivisions.
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[Figure 1.] The first pages of the almanacs of Imjin year (1652), Gyesa year (1653) and Gaboh year (1654).
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[Table 5.] Comparison of our calculations by Datong-li with the almanacs for date, Iljin and time of 12 seasons.
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[Figure 2.] The almanac of 1667 where the dates and times of 24 seasonal subdivisions were corrected.
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[Figure 3.] Comparison between Iljin of the leap December 1669 and that of January 1670.
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