The lunar calendar adds one extra month every third year. This extra month is known by various names: Adhik Maas, Mal Maas, Purushottam Maas, Malimmacha. This is the thirteenth month of the lunar calendar.
Just as there is the lunar year with the extra month (Adhik Maas), so is there a lunar year with a diminished or reduced month, with only eleven months in the year. The lunar year comprising of eleven months only is very rare indeed. It occurs once in 140 years or once in 190 years. But the extra month or Adhik Maas comes every third year. Adhik Maas adopts the name of the month that follows adhik Maas.
Whenever Sankranti does not fall within one month then Adhik Maas occurs. When there are two Sankrantis within one month then it becomes the lunar year with one reduced month (11 months in the year).
Vasishtha Siddhanta (the treatise of Vasishtha) mentions that Adhik Maas or the extra lunar month occurs after every 32 months, 16 days and 8 Ghadis (a Ghadi is a period of 24 minutes and 60 Ghadis equal 24 hours).
It is a fact that the solar year is made up of 365 days and about 06 minutes and the lunar year is made up of 354 days. Thus both the solar and the lunar years have gaps of 11 days, 1 hour, 31 minutes and 12 seconds. As this gap increases each year, it approximates in three years to one month.