Lunar calendar or crescent moons and others employing detailed calculations. Since each lunation is approximately days (29 days, 12 hours, 44 minutes, 3 seconds, or days), it is common for the months of a lunar calendar to alternate between 29 and 30 days. Since the period of twelve such lunations, a lunar year, is only 354 days, 8 hours, 48 minutes, 34 seconds ( days), purely lunar calendars lose around 11 days per year relative to the Gregorian calendar. In purely lunar calendars like the Islamic calendar, the lack of intercalation causes the lunar months to cycle through all the seasons of
Callippic cycle unrounded Metonic cycle (within a few seconds per year). If it is considered as 940 lunations less one day then the Callippic mean year will be shortened by of a day (18 minutes 57 seconds), making it grossly too short, and it will also grossly drift ahead with respect to the mean lunar cycle at the rate of of a day (1 minute 31 seconds) per lunar month. If the cycle length is truncated to 27,758 days then the mean year is 365 days 5 hours 41 minutes 3 seconds, or almost 8 minutes too brief per year, and it