The concept of Adhikamasa or Inter-Calary Month

THE CONCEPT OF ADHIKAMASA OR INTER-CALARY MONTH

Inter-calary Month in June-July

The lunar year Pramadi has an Adhika or Mala Masa (16-5-1999 to 13-6-1999) and a Suddha or Nija Masa (13-6-1999 to 13-7-1999) in the lunar month of Jyeshta. The Adhika and Mala Masas testify to the highly scientific method of calendar-making in ancient India.

The scientific Hindu Calendar, formulated by ancient Indians, is based on the natural movements of the luminaries. They called the year varsha, meaning 'shower of rains' or time during which the annual seasons completed their course, taking into account the movements of the sun. The night, on which the Masa or month becomes Poorna or complete, based on the movements of the Moon, was called Pournamasi (Pournima). They were perhaps the first to try, as pioneers in calendar - making right from the vedic times, to fuse, rather successfully, the solar calendar into the lunar and form a luni-solar calendar.

Solar and Lunar Months

Two basic observations held sway over the effort of ancient Hindu calendar-making. The first was the apparent movement of the sun, causing the solar year, on its re-entry into the first of the twelve Rasis of the Zodiac, from where it started its annual sojourn and completed a cycle of seasons. The moment of entry of the sun into a zodiacal sign was called Samkranti, and Soura or Solar month. Likewise, the period of time between the appearance and reappearance of either the Full Moon or New Moon was called a Masa or Month.

Amanta and Pournimanta

For a solar month, the sun's ingress to the sign alone matters. Therefore, there is only one its kind. But as the lunar month is either reckoned with the end of amavasya or Pournami there are two kinds of them. These are namely the New moon ending and Full moon ending. Those months which end with an Amavasya or New moon are called Amanta and those which end with Pournima or Full moon are called Pournimanta. Both the modes of reckoning were in vogue since the Vedic times. Even now, Pournimanta lunar months are followed in some parts of India. Only the Amanta system is taken for calendaric calculations for determining Inter-calary month or Adhikamasa and decayed month or Kshayamasa. These Amanta lunar months commerce just at the moment of a New moon and end at the instant of the next New moon.

Twelve solar months based on the twelve Samkrantis or solar ingresses into each of the twelve signs of the Zodiac constitute one solar year. These solar months have varying periods of 30 to 32 days due to the vagaries of the movement of the sun, in relatio to the earth. It was found that the twelve lunar months, varying from 20 to 30 days, based on the occurence and re-occurence of either the Full moons or the New moons did not converge exactly with this solar year. The length of an solar year on an average is 365 days, 5 hours, 49 minutes (Surya Siddhanta takes this as 365 days, 6 hours and 13 minutes) and of a lunar month 29 days, 12 hours, 44 minutes. So 12 lunar months add to 354 days, 9 hours and lag behind the solar year by about 11 days (10.896 days) per year. It is evident then that in three years this difference itself will be more than thirty days resulting in a slide of a month in relation to the solar reckoning.

Sychronizing Months and Seasons

The religious calendar of the Hindus, as of many other faiths over the world, is lunar and is based on the Tithis or lunar days. If the lunar months are allowed to recede progressively, [this is allowed in the Islamic calendar] the seasonal festivals of any particular lunar month will get divorced from their association of their correct seasons. For the lunar months to move through all the solar months and to come back to their original position it may take about 321 years. In other words, the religious festivals will harmonize with the seasons once in about 321 years only. Therefore, there arose a need to synchronize the religious calendar with the calendar of seasons, mainly to prevent this problem of shift of festival days. It is only to avert this contingency the occasional introduction of inter-calary months in the lunar calendar was devisedby our ancients. When this recession of about 11 days per year gets accumulated to 30 days or one month, an inter-calary month is inserted in the lunar calendar to bring it back to its original position in relation to the seasons. Such extra months can come at regular intervals after every 32 and 33 solar months, alternately, to maintain the balance. This procedure was in vogue in the early period of Siddhantic astronomy. However, later the method adopted is different and is the determined on the basis of true motions of the Sun and the Moon.

The ancient Hindu concept of computation of time stems from the Mahayuga. In a Mahayuga there are 4,320,000 years, which contain 51,840,000 solar months or Souramasas and 53,433,336 lunar months or Chandramasas. So in a Mahayuga there will be 1,593,336 inter-calary or Adhikamasas in the lunar calendar. The pattern of occurence of the solar and lunar months can be expressed mathematically,as a continuous fraction based on the fact there are 33 lunar months for 32 solar months.

But the problem does not stop with this. For 423 solar months there will be 436 luner months, an additive of 13. If we take 1692 solar months or exactly 141 years, we get 52 additive months. On the basis of one per 32 years, the additive month must be 53 for 1696 years. It can be seen that an increase of 4 solar months has brought in another lunar month. So also for 1920 solar months only 59 Adhikamasas occur. As per the normal rules this must be be 60. Therefore, one month has to be reduced to make it 59. That is why the need to identify a Kshayamasas or surpressed month arises to offset the excess. This is done by just ignoring a count of a lunar month. Kshayamasas occur generally once in 141 years and again after 19 years, more frequently though they are possible in other intervals of 46, 65, 76 and 122 years.

The Extra Month

Adhikamasa is defined as that lunar month which does not have any solar ingress during its period. It other words Adhikamasa occurs when the sun's stay in a sign or Rasi is more than the duration of that lunar month. The rule is that the lunar month bears the same name as the solar month in which the initial New month occurs. When a lunar month is completely covered by a solar month or in other words when there are two moments of New Moons one at the commencement and other at the end of any solar month, two lunar months originate in the same solar month and both these lunar months derive the same name as per the above rule. So the lunar month that begins from the first New moon, so occuring, is deemed as an extra month and termed as Adhikamasa or Malamasa. The lunar month begining from the second New moon is called the real or pure, otherwise Nija or Suddha. Both these months bear the same name of the solar month and the first gets the prefix of Adhika and the next, Suddha.

In the current Pramadi year, in the solar month of Vrishabha two New Moons occur, causing two lunar months in the solar month. So the first lunar month is taken as Adhika. The first is Adhika Jyeshta and the second is the Nija Jyeshta.

It can thus be seen that an inter-calary month comes after two to three years in the normal course. Such Adhikamasas generally occur in the period from Chaitra to Bhadrapada as these solar months have a longer duration than the lunar months. No religious festivals are observed in these Malamasas or Adhikamasas.

The Suppressed Month

What is a Kshayamasa or suppressed month? At times, a lunar month can completely cover a shorter solar month. Then the Sun's stay in a Rasi will be less than the duration of a lunar month. This will result in two Samkramanas or solar ingress occuring in a particular lunar month. In such a contingency there will be no New moon in that particular solar month. Therefore, there will be no lunar month to be named after that solar month. Obviously this will create a gap in the sequence of names of the lunar months, missing out one name. This dropped out month is callled Kshayamasa or decayed month.

In such years when a lapsed month occur (this happens less frequently) there will be two inter-calary months or Adhikamasas, one before the Kshayamasa and the other after that, within a span of three months on either side. The inter-calary month occuring prior to the Kshayamasa is called Samsarpa and this is generally exempted from the injunctions of performance of religious festivals in that month, as attributable to normal Adhikamasa. The latter inter-calary month is called Amhaspati and this second Adhikamasa will be the correct Adhikamasa, as it occurs after 30 months of the previous Adhikamasa.

Though the average length of a lunar month is 29 days, 12 hours, 44 minutes, it actually varies from 29 days, 5 hours, 54 minutes to 29 days, 19 hours, 36 minutes depending on the position of the New moon of the lunar perigee (Surya Siddhanta gives the limits as 29 days, 6 hours, 18 months to 29 days, 19 hours, 6 months). as the months of Vrischika, Dhanus and Makara have their lengths between these two limits, only the lunar months of Margasira, pushya and Magha can become Kshaya more often than the other two and Magha, the least.

To summarise, a Malamasa or Adhikamasa occurs when there are two New Moons in a solar month creating a situation of absence of any solar ingress or Samkramana in that lunar month. For an Adhikamasa to occur, a solar ingress must take place just before a New Moon and the next ingress must be just after the next New Moon. Or in other words, a lunar month with no Samkrantis of the Sun occuring in it is called a suppressed month, Kshayamasa or Amhaspati.

A decayed month or Kshayamasa occurs when there is no New Moon in any solar month creating a situation of two solar ingresses or Samkramanas happening in that lunar month. For a Kshayamasa to happen the solar ingress must happen just after a New moon and the following solar ingress must take place before the ending of the next New Moon. In other words a lunar month will two Samlrantis of the Sun occuring in it is called a suppressed month, Kshayamasa or Amhaspati.

Much variance in computational factors is found in the different ancient astronomical treatises as regards the length of the solar year and the like. Different Siddhantas are followed in different regions of different people. The opinions expressed in various Sastriac texts are also in variance with regard to the observances of religious festivals. Therefore there is difference of opinion amongst scholars in determining some of these Adhika and Kshaya months. Only some of the basic principles have been discussed here to give the reader a general but clear idea about the subject, without going into the intricacies.

Blue Moon

Then what exactly is a Blue Moon? The 'Blue Moon' does't have anything to do with color. The second full moon that occurs within a given calendar month is called a Blue Moon. An ancient tradition calls the fourth full moon, in a season, as Blue Moon. Each of the four seasons in a year will have three months and usually three Full Moons. Each of these 12 Full Moons, of a year, has its own name in folklore, like "Harvest Moon," "Hunter's Moon" etc. When, however occassionally,a season got four Full Moons, it was called "Blue Moon", as there was no name for this occassional Full Moon. "Harvest Moon" is the Full Moon of Harvest time or more exactly, occuring just before the autumnal Equinox on about September 23. As the continuance of the moonlight after sunset was useful to farmers in northern latitudes, who usually harvest their crops, the name stuck. The Full Moon following the Harvest Moon, which exhibits the same phenomena in a lesser degree, is called the Hunter's Moon.

Arbitary Concept

It takes the Moon about on an average of 29 days, 12 hours, 44.05 minutes to circle the earth, once in its orbit. Occasionally therefore, two Full Moons can occur within a same calendar month. If a Full Moon occurs on the 1st or 2nd day of the month, there is a good chance for a second Full or Blue Moon by the end of that month. Such was the case in January 1999, when the Moon was the full on the 2nd and the 31st, making the second Full Moon on the 31st a 'Blue Moon'. On an average, this takes place once every two and a half years. This time, however, we did not have to wait so long for another Blue Moon which appeared in March 1999, with two Full Moons on the 2nd and the 31st of March. The next Blue Moon will be in November 2001, then in July 2004 and thereafter in 2007 June and so on. On an average, in a century, there will be 41 months, which can have two full moons. Therefore once in a blue moon actually means only once every two-and-a-half years, which is not a rare occurence either to justify its imort or undue excitement. To see two Blue Moons in one year, next, we have to wait until 2018. Once in a double Blue Moon, may be a better idiom then.

The Gregorian civil calendar is artificial and arbitary. There is nothing scientific or even significant in trying to identify a second Full Moon in a month of a civil calendar and give it a name. Full Moon and New Moon are natural phenomena and identifying their occurence twice in a solar month, a natural time division, will be more scientific and definable astronomically.

It can be seen that the Hindu calendar is natural, purposeful and scientific, sans sensations like Blue Moons. We must not leave our posterity oblivious to the attaiments of our ancestors in the fields of mant of these exact sciences. But for some in India, anything Indian is unscientific, be it mathematics, astronomy, positive sciences, astrology or even religion. For such agnostics, unless they try to understand the heritage of this great land of Bharata, the freedom they have gained at mid-night can never see the dawn.