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S. Khalid Shaukat
Ancient Calendars: All ancient calendars were lunar calendars. The practice of starting a month at the first sighting of a new moon was observed not only by Romans but by Celts and Germans in Europe and by Babylonians and Hebrews in the Lavant. The new moons were sighted after either 29 or 30 days. If clouds obscured vision on the 29th day, that month was declared to have 30 days. This is still done for the Islamic Calendar.
When human civilization excelled in agriculture, there was a need for having a calendar that repeats the seasons so that it would help sowing and harvesting on repeated calendar dates. This calendar was established based on rotation of the earth around the sun. Early estimates of this rotation was 360 days, so the first solar calendar was invented having 12 months of 30 days each. Some civilizations invented a lunisolar calendar which basically had lunar months based on new crescent moons but were adding days or a month to be decided by priests/rabiis wherever and whenever they felt to satisfy social and religious needs to keep their calendar in phase with seasons. This practice of adding days or a 13th month was called "Intercalation".