The Tabular Islamic calendar (an example is the Fatimid or Misri calendar) is a rule-based variation of the Islamic calendar. It has the same numbering of years and months, but the months are determined by arithmetical rules rather than by observation or astronomical calculations. It was developed by early Muslim astronomers of the second hijra century (the 8th century of the Common Era) to provide a predictable time base for calculating the positions of the moon, sun, and planets. It is now used by historians to convert an Islamic date into a Western calendar when no other information (like the day of the week) is available.
It is used by some Muslims in everyday life, particularly in the Ismaili and Dawoodi Bohra communities and they believe that this calendar was developed by Ali. It is believed that when Ali drew up this calendar, the previous events of the earlier prophets also fell into line with this calendar. It is their belief that all Fatimid Imams and their Da'is have followed this tradition.
Each year has 12 months. 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 has 30 days.
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
: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.
The Ismaili Tayyebi community uses the following order of leap years in their 30-year cycle.
:2, 5, 8, 10, 13, 16, 19, 21, 24, 27 and 29
Apart from these, there is another version which orders the leap years as follows
:2, 5, 8, 11, 13, 16, 19, 21, 24, 27 and 30
The mean month is 29 191/360 days = 29.5305555... days, or 29d 12h 44m. This is slightly too short and so will be a day out in about 2500 years. The Tabular Islamic calendar also deviates from the observation based calendar in the short term for various reasons.
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