Tabular Islamic calendar

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The Tabular Islamic calendar (Arabic: التقويم الهجري المجدول, romanized: altaqwim alhijriu almujadwal) is a rule-based variation of the lunar Hijri calendar. It has the same numbering of years and months, but the starting moment of each months is determined by arithmetical rules rather than by lunar crescent observation or astronomical calculations. It was developed by early Muslim astronomers to provide a predictable time base to calculate the positions of the Moon, Sun, and planets. It is now used by historians to convert an AH date into a Western calendar date when no other information (like the day of the week) is available. Its era is the Hijri era.

Each year has 12 months for a total of 354 or 355 days, approximating a lunar year. The odd numbered months have 30 days and the even numbered months have 29 days, except in a leap year when the 12th and final month Dhu al-Hijjah has 30 days.

Virtually all Muslims in the Sunni Islam tradition use the lunar Hijri calendar for religious purposes. This depends in principle on actual observation of the first crescent of the new moon (hilal), to declare the beginning of each month. (The Umm al-Qura calendar, which uses astronomical calculations to identify the day of first crescent independently of weather conditions, is widely used in practice.) Apart from a sect in India and Pakistan (who use this tabular calendar directly), the tabular calendar is employed only to approximate the date (because dates predicted by the tabular Islamic calendar can occur one or two days too early or too late compared to the observational calendar).

Intercalary schemes

30-year cycle

In its most common form there are 11 leap years in a 30-year cycle. Noting that the average year has 354+11⁄30 days and a common year has 354 days, at the end of the first year of the 30-year cycle the remainder is 11⁄30 day. Whenever the remainder exceeds a half day (15⁄30 day), then a leap day is added to that year, reducing the remainder by one day. Thus at the end of the second year the remainder would be 22⁄30 day which is reduced to −8⁄30 day by a leap day. Using this rule the leap years are year number 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 and 29 of the 30-year cycle.

If leap days are added whenever the remainder equals or exceeds a half day, then all leap years are the same except 15 replaces 16 as the sixth long year per cycle.

The Ismaili Tayyebi community delays three leap days by one year: the third to year 8, the seventh to year 19 and the tenth to year 27 in their 30-year cycle. There is another version where, in addition, the fourth leap day is postponed to year 11 and the last leap day is in the last year of the 30-year cycle.

The mean number of days per month in the 30-year cycle is 29.53056 days, or 29d 12h 44m. Six months of 29 days and six with 30 days, plus 11 days of the leap years. (29 days × 6 months + 30 days × 6 months) × 30 years + 11 leap days = 10,631 days and 10,631 / 360 = 29.53056 (360 is number of months in 30 years). And this is approximately how long it takes for the Moon to make full lunar cycle.

Microsoft's Kuwaiti algorithm is used in Windows to convert between Gregorian calendar dates and Islamic calendar dates. There is no fixed correspondence defined in advance between the algorithmic Gregorian solar calendar and the Islamic lunar calendar determined by actual observation. As an attempt to make conversions between the calendars somewhat predictable, Microsoft claims to have created this algorithm based on statistical analysis of historical data from Kuwait. According to Rob van Gent, the so-called "Kuwaiti algorithm" is simply an implementation of the standard Tabular Islamic calendar algorithm used in Islamic astronomical tables since the 11th century.

Overview of various 30-year leap cycles
Origin or usage Long lunar years (nth/30) Gap till next long year
#1#2#3 #4#5#6#7#8#9#10#11 #1#2#3 #4#5#6#7#8#9#10#11
Kūshyār ibn Labbān, Ulugh Beg, Taqī ad-Dīn Muḥammad ibn Maʾruf 2571013151821242629 323 323 3 323 3
al-Fazārī, al-Khwārizmī, al-Battānī, Toledan Tables, Alfonsine Tables, Microsoft "Kuwaiti algorithm" 2 5 7 10 13 16 18 21 24 26 29 323 3 323 32 3 3
Muḥammad ibn Fattūḥ al-Jamāʾirī of Seville 2 5 8 10 13 16 18 21 24 26 29 3 323 323 323 3
Fāṭimid / Ismāʿīlī / Ṭayyibī / Bohorā calendar, Ibn al-Ajdābī 2 5 8 10 13 16 19 21 2427 29 3 323 3 323 323
Ḥabash al-Ḥāsib, al-Bīrūnī, Elias of Nisibis 2 5 8 11 13 16 19 21 24 2730 3 3 323 323 3 32

8-year cycle

Tabular Islamic calendars based on an 8-year cycle (with 2, 5 and 8 as leap years) were also used in the Ottoman Empire and in South-East Asia. The cycle contains 96 months in 2835 days, giving a mean month length of 29.53125 days, or 29d 12h 45m.

Though less accurate than the tabular calendars based on a 30-year cycle, it was popular due to the fact that in each cycle the weekdays fall on the same calendar date. In other words, the 8-year cycle is exactly 405 weeks long, resulting in a mean of exactly 4.21875 weeks per month.

120-year cycle

In the Dutch East Indies (now Indonesia) into the early 20th century, the 8-year cycle was reset every 120 years by omitting the intercalary day at the end of the last year, thus resulting in a mean month length equal with that used in the 30-year cycles.

See also

Notes

  1. ↑ Most Muslims in the Shia Islam tradition use the solar Hijri calendar based on astronomical observation of the spring Equinox in the northern hemisphere.
  2. ↑ The Dawoodi Bohra, a religious denomination within the Ismā'īlī branch of Shia Islam

References

  1. ↑ Kennedy, Edward Stewart (1956). "A Survey of Islamic Astronomical Tables". Transactions of the American Philosophical Society. 46 (2): 17.
  2. ↑ Dershowitz, Nachum; Reingold, Edward M. (2008). "6. The Islamic calendar". Calendrical Calculations (Third ed.). Cambridge: Cambridge University Press. p. 82–87. ISBN 9780521885409. OCLC 144768713.
  3. ↑ "Hijri Dates in SQL Server 2000". Microsoft.com. Archived from the original on January 8, 2010.
  4. ↑ Kriegel, Alex; Trukhnov, Boris M. (2008). SQL Bible. Indianapolis, IN: Wiley. p. 383.
  5. ↑ Robert Harry van Gent (December 2019). "Online Calendar Converters Based on the Tabular Islamic Calendar". Mathematical Institute, Utrecht University. Retrieved 15 November 2020. It can easily be demonstrated that the so-called 'Kuwaiti Algorithm' was based on the standard arithmetical scheme (type IIa) which has been used in Islamic astronomical tables since the 8th century CE.
  6. ↑ Ian Proudfoot, Old Muslim Calendars of Southeast Asia (Leiden: Brill, 2006 [= Handbook of Oriental Studies, Section 3, vol. 17]).
  7. ↑ Gerret Pieter Rouffaer, "Tijdrekening", in: Encyclopaedie van Nederlandsch-Indië (The Hague/Leiden: Martinus Nijhoff/E.J. Brill, 1896–1905), vol. IV, pp. 445–460 (in Dutch).

Literature