Dynasty Islamic Calendar
7.12.2006 [latest revision 7.9.2009]
is a rough and incomplete translation of
beginning of the description of the Islamic calendar in the
the Ming Dynasty. The calendar has a solar Persian calendar and an
calendar. The formulas for determining the
leap years and days of the week are interesting.
The description continues with astronomical tables. I have
not translated this
part but I have made an attempt to understand how solar
tables themselves are missing
from my main source and apparently all mainland Web sites that I have
The Chinese term for the calendar
回历法 Huíhui lìfǎ, where Hui is the normal
post-1949 term for Chinese speaking Muslims, formerly known as Dungans
“Islamic Calendar”, by King Mahama of the
Modina, which is situated on 24.5 degrees northern latitude, 107
to the west, about 8000 Chinese miles from
Yunnan. The beginning of the era is Kaihuang
in the Sui Dynasty, which is the year of the establishment of the
country. At the beginning of the Hongwu reign period [Jan. 23
1368–Feb. 5, 1399], this book was
obtained in the Yuan capital. In the autumn of the fifteenth year
Emperor said that the Westerners were best in predicting astronomical
phenomena, and China did not have their system of coordinates for the
celestial bodies. He ordered the Hanlin Academicians Li Chong and Wu
Bozong to translate the book with the Muslim master Sheikh Ma.
The method does not use intercalary months. A year has 365 days. The
year is divided into 12 signs of the Zodiac, which have leap days, so
that 128 years have 31 leap days. 354 days form a lunar year with 12
months which can have leap days.
There are 11 leap days in 30 years. In
years the lunar and the solar years coincide again. These are the main
points of this calendar.
are different opinions of
the leap year cycle of Persian calendars. This is a relatively early
source which clearly describes a very elegant and accurate mathematical
calendar with a 128-year leap year cycle.
prime factors of 1941
are 3 and 647. It is unclear what relevance it has to the calendar.
107° degrees east of Medina is in the Pacific Ocean east of
The passage mentions older Western calendars, which have mistakes. The
Muslim astronomer use books from their own countries and dust board.
Dust board presumably refers to calculations with Arabic numerals.
积年 起西域阿喇必年， 隋开皇己未。
Numbering the years starts from the western Alabi year, Kaihuang ji-wei
(599 AD) in the
Sui Dynasty. By Hongwu jia-zi (1384 AD) it is 786.
beginning of the Islamic lunar calendar is 23 years too early because
786 has been taken
to mean Chinese years (with intercalary months) instead of Islamic
lunar years. The correct date is
Friday, 16th July, 622 AD (Julian).
This error has persisted until modern times.
The solar calendar starts in 599 AD, 786 solar
years before 1384 AD (Shi
Peipei). This fits the formula in the text.
用数 天周度三百六十。 每度六十分，每分六十秒，微纤以下俱准此。 宫十二。 每宫三十度。 目周分一千四百四十，时二十四， 每时六十分。
刻九十六。 每刻十五分。 宫度起白羊，节气首春分，命时起午正。 午初四刻属前日。
The circle of heaven is divided into 360 degrees. Each degree has 60
each minute sixty seconds. These are also used for coordinates. There
are 12 signs of the Zodiac,
each of them 30 degrees. The day has 1440
minutes, 24 hours of 60 minutes, 96 quarters,
each of them 15 minutes. The signs of the Zodiac start from Aries, on
equinox. Hours are counted from noon.
The four quarters before noon belong
to the previous day.
It is traditional in the Persian calendar to round the times to the
nearest midnight. (Heydari-Malayeri).
This is equivalent to having integral days from noon to noon, a system
that was also followed by Ptolemy.
of the week
1. Sunday, 2. Monday, 3. Tuesday, 4. Wednesday, 5. Thursday,
6. Friday, 7. Saturday. The sexagenary
cycle is not used.
The names are names
Moon, and the planets named after elements, Fire (Mars),
Water (Mercury), Wood (Jupiter), Gold (Venus), Earth (Saturn). These
names are still
used for the days of the week in Japanese.
Qi Zheng Tuibu gives the Persian names which are also ordinal with the
counting starting from Sunday.
The signs of the Zodiac
Aries 0, Taurus 1,
Aries 0, because a sign is also an angle measure, 30°. This
to be so in Persian astronomical tables.
days of the signs of the Zodiac
These twelve signs are known
as immovable months. Each period of 365 days is a year. In a leap year
Pisces has an extra day and the year contains 366 days.
is different from the pre-1925 Persian calendar described by Birashk,
in which Gemini had 32
days instead of Cancer. The duration of these periods should change
from year to year and
with precession. Some sources say the pre-1925 solar months
astronomically determined. Afghanistan uses the names of the signs of
the Zodiac for months and they are known in Tajik as well.
duodecimal cycle is used in Chinese but
I have omitted it from the translation.
Libra has 31 days in the version of the text I have used as my main
and hollow months
Odd numbered months are full, even numbered ones hollow. These are so
called movable months. A full month has 30 days, a hollow one 29. Each
354 days is a period of twelve months. When a month is a leap
month a day is added to the twelfth month to make a period of 355
is no attempt to use the
original Arabic names of the months in Chinese, but Qi zheng tuibu
gives the Persian names as well. These are used for the solar months in
present Persian calendar.
The apogee calculated for 622 AD.
These values are for 16th
July, 622 AD (Julian). However, in the
astronomical tables the accumulated change is -10°40′28″
at epoch and 0° in the year 660, so the values are actually for
this year, AD 1262. The actual longitude of solar apogee is
Ming History and the astronomical tables give the following values of
mean longitudes and mean motion for
July, 622 AD (Julian).
1440 lunar years
From the above table one can
calculate a more accurate value of the
daily increments. 30 lunar years are 10631 days.
In earlier versions
the above passage was
unfortunately confused and had imcomprehensible mistakes. I hope it is
the case of linear functions, the Ming History only
describes how the tables are made, but Qi Zheng Tuibu has the tables
written out. There
are different tables of the mean motion for cycles of thirty
from epoch and jumping direct to year 600, as well as for
months, both solar and lunar, and days.
The values derived from the
tables are more accurate than the ones given by the Ming History.
Huihui Lifa gives instructions for adding or subtracting the smallest
units at certain intervals, leap seconds and thirds. There
are obvious mistakes in the tables. Digits may be missing and carried
numbers added a few lines too late.
I will attempt to
calculate the solar longitude at epoch. First, 1′4″
is subtracted from the mean solar longitude. There are different
theories about this (Chen Jiujin, Shi
To get the mean anomaly,
subtract the longitude of the solar
from the mean solar longitude.
At epoch it is 116°4′15″
The mean anomaly is used as the index to get the equation of centre.
Chen Jiujin (1989) states that the eccentricity is 0.0351295, but this
does not generate the maximum value of 2°0′47″
at 92°. The following Excel function generates values that
at most one second from the table in Qi Zheng Tuibu within the first 92
F2 mean anomaly
In the table for the equation of the centre in Qi Zheng Tuibu, the
value for 37° is 1°10′41″.
To make interpolation easy the table also gives the difference from the
next value, 1′39″
above Excel formula).
This is subtracted from the mean solar longitude. The solar longitude
at epoch is
114°52′55″, which is reasonably
close to the
given by Calendrica.
Yunli has made the same calculation and arrived at 114°51′53″.
It seems that the correction of 1′4″
has not been included in his calculation.
include the day of the week, which can be used to tie the system to the
real world. Year one has Friday, which is 16th
July, 622 AD
(Julian). The next year in the
table for every thirty years has 1 Sunday, which is the first day of
the year 601 AH. In the yearly, monthly and daily tables the day
indicated is an increment, although the name of the planet is included.
Thus, the first year in the yearly table has 4 Wednesday, which means
an increment of 4 days (modulo 7) after the 354 days of the first year
of the cycle. Similarly, the first month has 2 Monday, a two day
increment after a 30-day month. The daily table adds 1 Sunday, 2 Monday
The text says that these should take to the first of Aries, but I
cannot see how this is possible since the increments clearly take us to
the current day.
求宫分闰日 无〔 宫？〕之馀日。
置西域岁前积年，减一，以一百五十九乘之， 一百二十八年内，闰三十一日故以总数乘。 内加一十五，
以一百二十八屡减之，馀不满之数，若在九十七已上， 闰限。 其年宫分有闰日，已下无闰日。於除得之数内加五， 宫分立成起火三，故须加五。
the leap day for the signs of the Zodiac.
(Extra day in a sign of the Zodiac) Take the years accumulated before
the Western year, subtract one,
multiply it with 159 (there
years in 128 years, so you multiply with the total). Add 15 to it
(earlier error) to
find the leap year. Repeatedly subtract 128. If the remainder is above
97 (intercalation), it is a leap year. Then add 5 to the quotient of
the above division
(because the starting point is Tuesday, one has to add 5). Divide by 7
and the remainder is the day of the week of the first day of
Aries. (For a leap year add 1.)
passage has two functions
which find whether a solar year is a
leap year and what is the day of the week of the first day of the year.
Leap year rule
following Excel function determines whether
the solar year YS, is a leap year:
The year is a leap year if the remainder is greater than 96.
The rule creates a
128-year cycle which consists of the subcycles of
29+3*33 years. Each subcycle begins with four common years followed by
97 is the smallest remainder that defines a leap year. Because
97+31=128, this means that the accumulated error carried over from
previous years amounts to one full day. The error is checked at the
beginning of the year, in other words, the formula finds out how much
was left over after the previous year.
The number 15, called leap
constant by Shi Yunli,
should mean the fractional days accumulated before the beginning of the
era, in this case 15/128 of a day, 2h48'45". Since days are from noon
to noon, the spring equinox occurred at 14h48'45" at the beginning of
the calendar. However, in the following formulas where we know the
longitude better the leap constant has
no relation to the actual time of the spring equinox.
The rule described in
passage is a typical
rule of the Persian calendar,
but it checks the beginning of the year and also calculates the day of
the week. Another rule
one by Abdollahy in Encyclopedia Iranica s.v. Calendars:
using the fractional part of the division
of the remainder. The fractional part should be <0.24. With a
calculator it would be easier to use the fractional part.
To check the end of
the year the
function should be written =IF(MOD((YS-1)*159+26;128)>96;"leap";"common"
uses a 2820-year cycle.
The following Excel function agrees
with his tables:
occurred at 5h48'45" after noon on the first day.
The remainder has to be greater than or equal to 2820-683=2137.
Day of the week
second rule keeps track of
of the week at the starting point of the era. This Excel
function does it correctly:
This is 5, Thursday, if YS is 1.
In both formulas the multiplier 159=128+31. The first number keeps
track of the day of
the week, the second number takes care of the leap years. The 15 in the
formulas is the excess fractions of a day accumulated before the
beginning of the calendar, 15/128 days.
求月分闰日 朔之馀日。 置西域岁前积年，减一，以一百三十一年乘之， 总数乘。 内加一百九十四， 闰应。 以三十为法屡减之，馀在十九已上，
the leap day for the lunar months
(Extra day before the new moon) Take the years accumulated
the Western year, subtract one, multiply
it with 131 (multiply
total). Add 194 to it (earlier error). Repeatedly subtract 30. If the
remainder is above
19 (intercalation), it is a leap year. Divide the quotient of
the above division by 7 and the remainder is the day of the week of
of the first month.
This passage also
has two functions, which generate a standard mathematical Islamic
This function determines whether a year is a leap year:
The fractional part should be >0.6 if decimals are used.
Day of the week
This function calculates the day of the week of the first day of the
The first day of the first year (AD 622) is correctly 6, Friday, if YL is 1.
The total that is used to multiply means 4*30+11. Since the length of a
common year is 354 days the day of the week advances by 4 every common
year and the integral part of the quotient changes accordingly.
194=6*30+14 sets the first day of the first year of the era at
6, Friday. The accumulated error is 14/30 days. In
calendar it is 15/30.
In Qizheng tuibu there is a passage which is of
Chinese leap months (with 121 years
between Yuan jia-zi (1324 AD) and
jia-zi (1384 AD))
”Take the years from Yuan 甲子 (1324 AD), subtract one, add 137
multiply with 123. Add 10 and divide by 334. If the remainder is above
211, the year is a Chinese leap year. If the remainder is below 211,
the year is not a Chinese leap year. If the remainder is above 211,
subtract it from 334, multiply the difference by 4 and divide by 41.
The quotient is the Chinese leap month.
”If the result [rounded up?] is one, it is the
month, if it is two, it is the second month etc.”
The years are confused. 121 years before Hongwu jia-zi is before
the Yuan dynasty rule in China.
According to this formula, there are 123 leap years in 334 years. 334
is the length of a twelfth of the solar year in units of
time suitable for the accuracy of the calculation. The lunar
is 123 units shorter. This figure is equivalent to the epact of the
Gregorian calendar. The solar year is 4008 units long and the lunar
year 3885 units. The
ratio 3885:4008 is the ratio of the lunar year to the solar year,
although it is not exactly the ratio obtaining in the Huihui lifa. If
divided by 12 the result is 10.25=41/4, the monthly
dividing 334-remainder with 10.25 indicates in how many months an extra
month fits into the solar year. This means the formula relies on the
mean sun and the mean moon. The Chinese gave up the mean moon at
beginning of the Tang dynasty, about 619 (Aslaksen).
Alternatively, the solar year is 12 123/334= 4131/334
lunations but the ramifications of this idea are not yet clear. The ratio of the lunar year to the solar
year is 4008:4131.
It is difficult to anchor
this scheme in time. The 123/334 formula produces an endless cycle of
Metonic cycles with new moons that drift slowly towards the end of the
solar year. At 334-year intervals the last new moon moves from
February to January. This corresponds to the solar equation in the
The remainder refers to the time before the the last possible new moon
(or alternatively the time elapsed from the end of the lunar year). The
remainder 0 means the last possible date and 333 the first possible
A somewhat fruitful approach is to compare these cycles to the Metonic
cycle in the Gregorian calendar. The pattern of
remainders and leap years fits an epoch with golden
number 3 and epact 24 in the 14th or 15th century according to the
Gregorian calendar. This is based on the idea that the last possible
date of the New Year is near 20th February, which has epact 9.
According to Calendrica the switch of the new moon from
February to January takes place in 1423 which would place the
epoch on 1351. The next switch is in 1890 while the formula predicts
1757 so there is some latitude in the choice of the epoch.
The pattern of leap years produced by the formula fits the present
Chinese calendar for the years 1900-1918 as well, although an
calendar may have exceptions to regular patterns.
A1 Year AD
B1 Years from 1351
F1 Leap month
G1 Golden number
The number of leap years before the current year can be found with the
Since the length of a lunar month is known it should be possible to
find the date once the epoch is known.
Supposing the epoch is the new moon in February AD 1351 we can find its
Julian date of lunar epoch 1948440
Initial value at lunar epoch: 14/30=168/360
750 years: 750*10631/30=12*750*10631/360
11 months: (11*10631/30)/12=11*10631/360
Days elapsed from lunar
Chinese New Year AD 1351: 266100+1948440=2214540
This date is two days after Calendrica's Chinese New Year because the
Islamic tradition requires that the new moon should be visible.
Besides, the day is the first day of the month, not the last day of the
previous month. This is probably a mistake in most of my formulas.
Starting from this day any Chinese New Year can be calculated with the
following Excel formulas.
B1 years elapsed from 1351
C1 Leap years from 1351
E1 JD in integers
F1 Golden number
C2=TRUNC((B2*123+161)/334) [perhaps FLOOR is needed]
E2=TRUNC(D2) [to be
pasted on Calendrica; perhaps FLOOR is needed]
The golden number is useful for studying the cycles. I have checked the
years 2009–2028. All the dates are on the correct new moon, with
the Chinese dates usually two days earlier. Calendrica's arithmetic
Islamic new moons sometimes differ from the Ming formula.
A remarkable thing is that for the years AD 10000–10018 the
agreement is almost as good. The date is even better because it is
usually the same as the Chinese New Year. Only year 10001 (and 10020,
golden number 8) starts a month earlier according to the Ming formula.
The month in question is a leap 12th according to Calendrica while the
Ming formula places the leap month two months later.
This is not bad for a little formula from the Ming dynasty meant for
human computers who did their calculations on a sand board.
加次法 置积日， 全积并
减月闰内加三百三十一日， 己未春正前日。 以三百五十四 一年数
除之，馀数内减去所加三百三十一，又减二十三， 足成一年日数。 又减二十四， 洪武甲子加次。 又减一， 改应所损之一日。 为实距年 己未至今
得数。又法：以气积 宫闰并通闰为气积 内减月闰， 置十一，以距年乘之，外加十四，以三十除之，得月闰数。
Start with the total number of elapsed days (based on elapsed days and
leap days). Subtract the number of
lunar leap days, add 331 to reach the beginning of the era (spring
of AD 599). Divide it with
354 (the number of days in a year). Subtract from the remainder the 331
that was previously added. Subtract 23 (to a full year). Subtract 24
attain the year 1384. Subtract 1 once more to compensate for the lost
The result is the difference between AD 599 and the present day.
Another method: From the accumulated number of solar leap years and
general leap years subtract the number of lunar leap years.
multiply it by the difference in years, add 14, divide by 30 and you
get the number of leap years.) Divide by 354. Subtract 24
addition to Hongwu jia-zi, then subtract 23 and subtract one for the
lost day. (To
calculate general leap days, take 11 and multiply it by the difference
in years. For calculating solar leap years, see above.)
unclear. Shi Yunli thinks
it is a
very confusing later
probably by Tang Shunzhi 唐顺之 while Tao Peipei thinks that the author is
Huang Baijia 黄百家, an editor of the Ming Histories. The passage is made
clear by the Nanjing manuscript.
What I translate（with
‘epacts’ means something like ‘adding
and means the numbers that have to be added to the solar
year to get the lunar year. They resemble the epact in the Gregorian
calendar, but there are separate numbers for the year, month and day,
which are separately added to the solar date.
The formula for calculating the number of lunar leap years is clear:
Shi Yulin gives the
corresponding function for solar leap years:
These refer to a period of years starting from the epoch. If the period
starts from another year, the remainder has to be adjusted. For
instance, if we want to count the number of lunar leap years
during the 24 years preceding and including 1 AH (with the remainder
14), we will have to find the remainder for the first year. We can use
the formula =MOD(14-11*23;30). The remainder is 1 and the number of
leap years is INT((11*24+1)/30)=8.
The formula in the
has strange numbers, 331, 23, 24 and 1. The Nanjing manuscript has an
makes clear that the figure 24 refers to years, while the
other figures are days. The numbers are not really explained in Tao
Peipei's article, although
it is shown that the above formulas give a correct result. The number 8
is regarded as
an error and it is said that 331 is very close to 339. Tao
points out that the lunar new year preceding the epoch of the solar
calendar is 339 before 1st
Aries 599 AD and the following one is 15 days later.
The other numbers have an explanation. 331+15=354, equal to a common
lunar year. Adding 331 moves the
beginning of the period to a date 8 days short of the previous lunar
new year (not the spring equinox as the text says). This will ensure
that the leap days
of the 24-year period are not counted twice. Then we move back to the
original beginning by subtracting the 331 again, and move forward 15+8
days to a point eight days after the lunar new year, again taking care
not to count the leap days twice.
Hopefully the following
arrangement will clarify the relations
between the times.
the period of
24 years has 9 leap years and the error is corrected at the end by
It is not clear why such a complicated procedure is followed. It may be
connected to a traditional algorithm.
Moving towards the preceding lunar year is totally unnecessary since at
this point lunar leap years are counted and the year in question is a
common year. The second method simply moves to the following lunar new
year, plus 8.
The example of the Nanjing manuscript shows how to calculate
the epacts corresponding to 21st March, 1629, the spring equinox
procedure calculates the number of days up to the day preceding the
spring equinox. There are 1030 solar years (1629-599) containing
1030*365 days, plus 249 73/128 leap days, altogether 376199 73/128
days. Then the lunar leap days are calculated, first for 1030 lunar
years, resulting in 378 4/30 days.
Interestingly, the lunar leap days are subtracted in two stages. First
376199-378+331=376152, the total number of days from the lunar new year
prceding the solar epoch minus part of the lunar leap days. The
resulting number of days is divided by 354 to get the number of years
and remaining days, 1062 204/354 years. A preliminary epact is 1062
years 204 days – 331 days – 23 days – 24
– 1 day = 7 years 203 days (Tao Peipei 2003).
This is then corrected by removing the lunar leap days. The formula is
=MOD((Y-1)*11+14;30). This makes two days, so the correct epacts are 7
years 6 months 24 days. These are added to the spring equinox.
In the example a date 93 days into the year is required. These days
be separately added.
Proceding in two stages may be connected to the way the leap days in
the 24 lunar days are taken into account.
The duration of a period in years or days are easy to calculate when
the accumulated error and length of the year are known. The
accumulated error is
necessary to keep the leap years in the correct places. The formulas
not mentioned in the Ming dynasty history.
The number of days before the solar year Ys can be calculated
with the Excel
leap constant and the length of the year is known, the leap year fall
in their correct places.
If DS is the number of
days, the number of full solar years before the current year can be
calculated from =INT((DS-15/128)/(365+31/128)).
The number of days in
lunar calendar before
year YL can be calculated
with the Excel
If DL is the number of
days, the number of full lunar years before the current year can be
calculated from =INT((DL-14/30)/(354+11/30)).
Converting between the solar and lunar calendar
To convert between the Hui solar and Hijra calendar it is necesary to
days since the beginning of the calendars. If you start from the Hui solar
year, you can use the function
=INT(((Ys-1)*(365+31/128))+15/128). Then subtract the
difference of the Hui
solar and Hijra years from
difference between the solar and lunar calendars is 8520 days.
let's check 5th
December, 2006 (Julian day 2454075), full moon
the Gregorian calendar around the time of the writing of these lines.
The year is
The 1st of Aries
is Monday, 20st March ( Julian day 2453815),
the 79th day of the Gregorian
year (2*30+1-2+20=79; it
to count the days above or below 30
separately). The 5th of December is the 339th day of the Gregorian
year (11*30+6-2+5=339) and the 261st day of the Hui solar
year (339-78=261). Before
beginning of the year there have been INT((1407*(365+31/128))+15/128)=513895 full days and the 5th
of December is
the 513895+261=514156th day
from the epoch of
the solar calendar.
Using the formula YL=INT((DL-14/30)/(354+11/30)) we get
14/30+1426*(354+11/30)=505327 days. 505375-120-505327=309 days into the
lunar months make 10*10-5=295 days. You can also use the
function =TRUNC(309/29.5). Subtract
this from 309 to get the
of the eleventh month, 1427 AH, and the day after full moon.
Checking this on the
Calendrical Calculations applet, we see that the
date is correct.
These formulas can be used to find the epacts that can be added to the
epoch of the solar calendar.
If the Julian day is known, the following functions may be used to
convert to the Hui calendar.
A1 Julian Day
B1 elapsed full solar years
C1 elapsed full days
before the beginning of the solar year
days in the solar year
preceding full years
E1 elapsed full lunar
F1 elapsed full days before the beginning
of the lunar year
days in the lunar year
H1 day of the week
G1=A1-F1-1948439 (for epact
1939920 Thursday, solar epoch
1948440 Friday, lunar epoch
I have calculated the longitude with the following Excel formulas:
A1 Julian day
B1 mean longitude
C1 change of apogee
E1 mean anomaly
F1 equation of centre
G1 true longitude
H1 day of the week
The longitudes can be displayed in degrees, minutes and seconds by
dividing with 24 and displaying the result in hours, minutes and
The History of the Ming Dynasty decribes two calendars from the 14th
century, a Persian mathematical solar clendar with the year starting on
the 1st of Aries, and a conventional
Islamic mathematical lunar
calendar starting 8520 days later on Fridayday, 16th July, 622 (Julian).
The solar calendar has years of 365 31/128 days and an accumulated
15/128 days at the starting point of the calendar. There is a leap year
whenever the accumulated error reaches one full day. This can be
calculated from the Excel formula
The weekday of the first day of year YS can be calculated
from the Excel
This places the
beginning of the first year on a Thursday. This is different from the
modern Persian calendar, which has the 1st of Aries on a Friday.
The lunar calendar has years of 354 11/30 days with an accumulated
error of 14/30 days at the starting point. There is a leap year
accumulated error reaches one full day. This can be calculated from the
Excel formula =IF(MOD((YL-1)*131+194;30)>18;"leap";"common").
The weekday of the
day of year YL can be calculated
from the Excel
=MOD(INT(((YL-1)*131+194)/30);7). This places the
beginning of the
first year on a Friday.
Fake Leap Months in the Chinese
Calendar:From the Jesuits to 2033.
Nikolaus A. Iranische
Nasir ed-Din Tusi has lists
of early leap years according to
the Maliki calendar. They reveal no pattern of cycles.
A Comparative Calendar of the Iranian, Muslim Lunar,
Christian Eras for Three Thousand Years. Persian Studies Series,
No. 15. Mazda Publishers,
This book may not be fully trustworthy. The 1925 law
says nothing about the 2820-year cycle, and the pre-1925 months were
astronomically determined (Roozbeh Pournader, personal communication).
Richard. A Modern Almagest: An
version of Ptolemy's Almagest.
An excellent site which is reasonably close to the format of the
Heydari-Malayeri, M.: A
concise review of the
(transl. and annotated by G. J. Toomer, London 1984)
Some glitches with MacOS 10.2.3. With MacOS 10.4.11 Safari refreshes
the window three times before showing the result.
No. 6 - Fung Kam Wing - 香港科技大學圖書館善本書室開幕 ...
Chinese and Muslim contacts
A very detailed entry but not very clear on eras and early leap year
Calendar -- from Eric Weisstein's World of Astronomy
Ma Zhaozeng. Converting between
the Islamic, Gregorian
This text uses decimal numbers for conversion.
There are numerous versions of this text, but I have not found one
which contains the original tables.
There are numerous versions online. The text is from this one, but
because of the numerous mistakes the Academica Sinica version has also
been used. This version has no tables.
The Islamic calendar description is on pages 744–880 of this
version the Ming History. Starting from page 516 there is some history
and comparison of calendars. The tables start on page 775. The site is
hard to use.
Aubin. Notule sur les
l’astronomie islamiques en Chine
IV of Kūshyār ibn Labbān's Jāmic Zīj: An Arabic Astronomical Handbook
by an Eleventh-Century Iranian Scholar / - [S.l.] : [s.n.],
Doctoral thesis Utrecht University
of Chinese Calendars,
Sonmyong-ryok and Susi-ryok by Koryo Scholars
This has some traditional terms.
Korean Adaptation of the Chinese-Islamic Astronomical Tables. Arch.
Hist. Exact Sci. 57 (2003) 25–60.
This paper, a freely downloadable copy of which was found only after I
uploaded the first version of the page.
Tao Peipei. Study on the Huihui Lifa Collected by Nanjing Library.
Studies in the History of Natural Sciences, 2003
Vol.22 No.2 P.117-12
The library copy
has a full description of the method to calculate the time
interval between the solar and lunar calendars. This paper can be
downloaded for a few cent from http://club.cqvip.com.
A short description which includes the Arabic names of the months
The same in a better format:
七政推步 Qi zheng tuibu (ISBN：
A fuller edition of the
calendar with astronomical tables.
Unfortunately this is a facsimile edition with many pages illegible.
回万年历 A modern Islamic calendar for sale.
Mentions a few other names.
Linshan: Islamic observatories
Chen Jiujin: A detailed explanation of the principles of the lunar and
solar eclipses in the Hui calendar
Studies In The History of Natural Sciences, Vol. 9 No. 1 (1989),
Chen Jiujin: The calculation of the sun and the moon and geometric
models of their motions in the Hui calendar
In The History of Natural Sciences, Vol. 8 No. 3 (1989),
Yi: A study on the geometrical model explaining the movement of
planets in Islamic calendar
Studies In The History of Natural Sciences, vol. 10 No. 3 (1991),
Time and Date of Vernal Equinox
Hermetic Systems: Dates and Times of Equinoxes and Solstices