मल मास - Adhik Masa / अधिक मास / Kshay Masa / क्षय मास

 मल मास - Adhik Masa / अधिक मास / Kshay Masa / क्षय मास 

Adhik masa refers to the extra month in Hindu Lunar Calendar. It is composed of two words Adhik means extra and Mas means month. A year with an Adhik masa will mean that it has 13 months instead of the usual 12 months. This s unique concept in Hindu calendar for bridging of the lunar and solar calendars. The Adhik masa appears only in calendars that consider it. Hence, the local / regional calendars that are followed in Tamil Nadu, Kerala, Orissa, Bengal and Assam will not have them since they follow the Solar Calendar. Another name of this month is Mal Maas or Purushottam Maas. This month is dedicated to Lord Vishnu.
As per the Indian Calendar system, there are two calendars i.e. Lunar and Solar. A lunar month consists of about 29.5 days long whereas Solar month is 30 or 31 days.
In the lunar calendar, there are 354 days in a year and in the solar calendar there are 365 days and 6 minutes in the year. Hence, there is a difference of 11 days, 1 hour, 31 minutes and 12 seconds between the both.

Season are according to Solar months and Festivals are celebrated according to Lunar months. To remove the abnormality and correlate both Luni-Solar year was formed.
So, in the three years’ time {every 32 months, 16 days and 8 Ghati as per Vasishtha Siddhanta (the treatise of Vasishtha)} the difference increases to about one month. So, to match the two calendars one extra month is added. This thirteenth month of the lunar calendar is termed as Adhik Maas. Adhik Maas adopts the name of the month that follows Adhik Maas.
In a Luni Solar month there is one New Moon (Amavasya) and one Full Moon (Purnima). But if in any Lunar month there are two Sankrantis then this is reckoned as Extra month. And on the other hand, if no Sankranti occurs between two new moons then this becomes Kshay month

यस्मिन मासे न संक्रांति: संक्रांतिद्वयमेव वा मलमास: स विज्ञेयो मासे त्रिंशत्तमे भवेत् ||
असंक्रान्ति मसोअधिमास: स्फुटः स्यात द्विसंक्रान्ति मासः क्षयाख्या कदाचित ||

“When two Amavasya fall in a Solar month (between two consecutive Sankrantis) there will be two Lunar months of that Solar month”
In case there are two Sankrantis in a Lunar month (from one Amavasya to another Amavasya) then a Lunar month of the name of Solar month which is between two Sankrantis is missed. Kshaya Masa can happen only in Margashirsha, Kartika, Pausha and Magha. (November to February). This month is added when the Amavasya and Surya Sankranti coincide. It happens only when Amavasya ends few Minutes/Hours earlier than the Sankranti. Kshaya masa occurs in 19 / 122 /or 144 years as per Bhaskara-II in “Siddhant Shiromani”. In the year 1983 Pausha and Magha were rolled into one causing loss of one month. In case of kshay month festivals of that month are also rolled into one month. For example, in1983 Shivaratri was on Chaturdashi Tithi of Magha Krishna Paksha was observed on the corresponding Tithi of Pausha-Magha Kshay Krishan Paksha.

There are Three types of Mala Masa:

1. Samanya: If in a year Adhik mas happens but no Kshaya mas. This is called Samanya.
2. Sansarp:
3. Mallimlucch:
Reason for Mala Masa: When Sun is near to Earth its angular velocity increases and it moves faster. Its during early January
When Sun is farthest from Earth, its angular velocity is slower. It happens in early July. This is the reason for Solar months are shorter from November to February than the Lunar months.

Example of Extra month /Adhik Mas

In 2013 Hindu calendar, there is an Adhik Maas or an extra month. This Adhik Maas is from August 13, 2013 to September 16, 2013 as per North Indian Calendar. Hence, this extra month is also known as Adhik Bhadrapada Mas.
In 2015 this Adhik Maas is from June 3, 2015 to July 2, 2015 as per North Indian Calendar. Hence, this extra month is also known as Adhik Ashada Mas.

Paksha In Adhik Mas

And before that in year 2007 there were two Jyeshtha. We call them first and second Jyeshtha. There are four Pakshas in two months. First Jyeshtha commences from Krishna Paksha.

It is followed by Shukla Paksha of 1st Jyeshtha, then Krishna Paksha of 2nd Jyeshtha and finally Shukla Paksha of 2nd Jyeshtha. The Krishna Paksha of 1st Jyeshtha and Shukla Paksha of 2nd Jyeshtha is considered true or pure Jyeshtha month. The remaining two Pakshas i.e. Shukla Paksha of 1st Jyeshtha and Krishna Paksha of 2nd Jyeshtha comprise to make extra month which is known as Adhik Masa or Mal Masa. No auspicious ceremony except meditation or spiritual activity is performed during this Adhik Masa.

Since new moon is falling in Taurus sign twice, therefore there are two Jyeshtha months this year.

Note: (This type of system is available in Luni-Solar calendar of Northern India only. Gujarati calendar is also based on Luni-Solar motion but in this calendar month begins from Shukla Paksha. Therefore, in Gujarati calendar the first month itself is extra or Adhik or Mal Masa and 2nd month is considered pure or shuddh month. Muslim calendars are also based on lunar motion but in this calendar, there is no extra month (Adhik Masa) and for this reason this calendar moves faster slowly. If the month of Ramjaan was falling in August in 2006 than it shall fall in July in 2007 now. This type of shifting of month or extra month is not there in Luni-Solar or Solar calendars.)

Calculation of Adhik Masa:

The earth revolves around the Sun and completes one circle in 365.2564 days (365 days 6 hours 9 minutes & 12.96 seconds) whereas Moon takes 29.5306 (29 days 12 hours 44 minutes & 3.84 seconds) days from new moon (Amavasya) to next new moon. 

According to this 

No. of days in a Lunar month =29.5306. 

No. of days in 12 months = 29.5306x12=354.3672 days.

The difference between one year of earth & 12 Lunar months is 10.8992 days = 11 days.

Therefore, every year lunar months comes 11days earlier but in 3 years this difference reaches up to 33 days, which is more than one month. We call this as Adhik Masa.

Adhik Mas in last few years

Generally new moon (Amavasya) falls once between two Sankrantis that is Sun's transit into next sign. 

Minimum value of two Sankrantis is 29 days 10 hours and 48 minutes and maximum value is 31 days 10 hours and 48 minutes 

Whereas the minimum value of two new moons 29 days 5 hours 54 minutes and 14 seconds and the maximum value of two new moons 29 days 19 hours 36 minutes and 29 seconds. 

Therefore, it happens very rarely that no new moon falls between two Sankrantis. 

This generally happens after 19 years, or after 141 years, and sometimes after 65, 76 or 122 years. 

This type of situation is termed as Kshaya Masa. This is possible only during small signs like Scorpio, Sagittarius and Capricorn. 

This implies Kshaya Masa can happen during Margashirsha, Pausha and Magha only because in all other months the duration of Sankranti of Sun is more than lunar month.

Whenever Kshay Masa is there certainly there shall be two Adhik Masa one before and one after Kshay Masa. Following Kshay Masa happened in last over one thousand years

In 1982-83 there was no Amavasya during the Solar month of Magha, as a result Lunar month Magha was a Kshaya (Lost) Month. But this year has two Adhik Masa (Ashwin & Falgun) to compensate the Kshaya Masa. 

यस्मिन चांद्रे न संक्रान्ति सो अधिमासो निगह्यते, तत्र मंगल कार्याणि नैव कुर्यात कदाचन् ।

यस्मिन मासे द्वि संक्रान्ति क्षयः मासः स कथ्यते, तस्मिन शुभाणि कार्याणि यत्नतः परिवर्जयेत।।

How To find Mal Mas

Multiply the Shalivahana Shaka Samvat year by 12 and divide by 19. If remainder is 9 or less than 9 then that will be a mal mas.

Shalivahan Shaka Samvat X 12 = Remainder =9 or >9

 19

And to calculate which number of month will be a Mal mas: 

If remainder of above calculation is 5 or more than 5 then subtract 1 from that and count from Chaitra that month will be a Mal mas.

Sun moves faster in the months of Kartika (Scorpio), Margashirsha (Sagittarius) and Pausha (Capricorn) therefore Sun takes lesser time than Moon to cover these three months.

Months from Chaitra to Ashwin only can be a Adhik mas (sometimes it can be Falgun).

Just as there is the lunar year with the extra month (Adhik Maas), so there is a lunar year with a reduced month, with only eleven months in the particular lunar year. The lunar year with eleven months is very rare. It occurs once in 140 years or once in 190 years.