A decimal calendar contains either ten days per week, a multiple of ten days in a month, or ten months per year. Examples that have been adopted are the calendar of Romulus, the Egyptian calendar, the Alexandrian calendar, the Coptic calendar, the Ethiopian calendar, and the French Republican Calendar.
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The only calendar with a ten-month year was the calendar of Romulus adopted sometime after Romulus and Remus founded the city of Rome in 753 BC, when Romulus killed Remus. According to Roman writers, including Censorinus and Macrobius, it had ten of the twelve months in our modern calendar, March through December, but it only had 304 days in its year. The remaining days needed to form a solar year were winter days not assigned to any month. It only lasted until about 700 BC when King Numa, the successor of Romulus, added the winter months of January and February and rearranged the number of days in each month, creating the Roman calendar.
The Egyptian calendar of the first three millennia BC had twelve months of 30 days each, consisting of three ten-day weeks, plus five epagomenal days at the end of the year. The Alexandrian calendar, named for the city of Alexandria, is the Egyptian calendar with an additional sixth epagomenal or leap day added to the end of the year, as decreed in 25 BC by the Roman emperor Augustus five years after he conquered Egypt. The Coptic calendar is the Alexandrian calendar as adopted by the Coptic Church at the beginning of the fourth century. The Ethiopian calendar is the Alexandrian calendar as adopted by the Ethiopian Church during the fourth century. Both the Coptic and Ethiopian calendars are still used today.
The French Republican Calendar, which was introduced along with decimal time in 1793, was a modern version of the Egyptian/Alexandrian calendar. It consisted of a 12-month year, with each month consisting of three 10-day weeks, called décades, plus five or six sansculottides days at the end of the year. It was utilized as the official calendar of France for a period of twelve years, but was abolished by Napoleon on January 1, 1806.
The modern Gregorian calendar does not have either ten-day weeks or ten-month years, so a few decimal calendars have been proposed by individuals to create a more rational calendar. But none have gained any level of public acceptance, and the cost of any proposed conversion would far outweigh the savings that any might deliver.