These Pythagorean-based changes to the Roman calendar were generally credited by the Romans to Numa Pompilius, Romulus's successor and the second of Rome's seven kings, as were the two new months of the calendar. Most sources thought he had established intercalation with the rest of his calendar. 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 centuries before its development by Babylonian and Greek astronomers. Plutarch's account claims he ended the former chaos of the calendar by employing 12months totaling 354days—the length of the lunar and Greek years—and biennial intercalary months of 22days.