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In page Roman calendar:

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These Pythagorean-based changes to the Roman calendar were generally credited by the Romans to Numa Pompilius,[1] Romulus's successor and the second of Rome's seven kings, as were the two new months of the calendar.[5][6][a] Most sources thought he had established intercalation with the rest of his calendar.[citation needed] Although Livy's Numa instituted a lunar calendar, the author claimed the king had instituted a 19-year system of intercalation equivalent to the Metonic cycle[9] centuries before its development by Babylonian and Greek astronomers.[b] Plutarch's account claims he ended the former chaos of the calendar by employing 12 months totalling 354 days—the length of the lunar and Greek years—and a biennial intercalary month of 22 days called Mercedonius.[7][8]