The Hebrew calendar used today cycles every 19 years. The intercalation of seven additional months for each 19 years yields 235 lunar months, which are almost equivalent to 19 solar years. The intercalary month of We-Adar is inserted in the 3rd, 6th, 8th, 11th, 14th, 17th and 19th years of the lunar cycle.

Scientific dating the Elephantine papyri reveals that the Hebrew calendar used in the 5th century BC was under development. The intercalation of 7 months in 19 years did occur based on the 19 year cycle between the moon and sun. This is a natural occurrence. However, the use of an intercalary month was not fixed. For example, the Chronological Calendar for King Artaxerxes' reign in the 5th Century BC added only one intercalary month for 7 years. If you choose to investigate this phenomenon, review the Hebrew calendar column for years 1 to 7. You will find that it was only in the 7th year that Jewish New Year (Tishri 1) jumped forward from August 24, 460 BC to September 12, 459 BC.