Vedic Calendar

The nature of reality is pulsing. Life is breathing; the heart is beating; the day and night are turning out our experience. Pulsation requires the interplay of two forces. Śiva and Śākti, the Mother and Father, the Sun and Moon, create the pulsation which is the basis of all manifest existence. The Chinese call this force of opposites the Yin–Yang. In Sanskrit, it is called the Yugamaka – the couple, the pair, or the polarities. The Sun and Moon are the visible representatives of this Yugamaka, and they create time that pushes all things forward – the trees to bud, the flowers to bloom, and the bees to pollinate.

Through the movement of the Sun and Moon, all time cycles come into existence. The western Gregorian calendar, set in place by the pope of the Catholic Church, is not based on natural time. The Vedic calendar, used throughout millennia in India, is the mapping of the visible heavenly movements that are observed with astronomy. The Vedic calendar is a pulsating dance of the two divine luminaries that create a luni-solar calendar.

Vedic Calendrical Systems

The three basic astronomical cycles are the day (based on the rotation of the Earth on its axis – seen as the movement of the Sun); the month (based on the revolution of the Moon around the Earth – creating phases relative to the Sun); and the year (based on the movement of the Earth around the Sun – seen as the Sun’s change in position in the sky and against the stars). As the Sun rises and sets, it creates the days; and the Moon waxes and wanes, creating the months. The Earth–Sun cycle creates the year, which is divided into twelve lunations by the Moon. In these cycles are harmonics – numerical songs that create a matrix in which consciousness takes embodiment.

It would seem easy to calculate a calendar, but complexity arises because the year is not made of an integral number of days or an integral number of months. The harmonic is deeper, richer, and more complex. Different cultures have used very different calendars and ways of rectifying this. Even in India, throughout the millennia there have been various systems utilized, and various places to start within a cycle.

To begin understanding the basics of Vedic timekeeping we must understand the calculation of lunar months and solar years, which have within them solar months and lunar years. The solar months are considered the hinges, on which the doors of the lunar months move. What is a door without hinges, or hinges without a door? The Sun and Moon work together to create a luni-solar calendar that integrates the male and female, Śiva and Śakti, prakāśa and viśrama, or the pumping and resting of the heartbeat.

The lunar cycle divides the year into twelve harmonics. The year then resonates to this harmonic of twelve, and divides itself into twelve solar months. Like dancers, they move together. Time and its units are not man-made – they are man-observed. The divisions of time are divine harmonics that were recognized by the ancients.

Synodic Month (Lunation)

The Sun gains 1 degree per day, while the Moon gains 13 degrees per day; they are both moving. The more rapidly moving Moon is chasing the slower and more steadily moving Sun. The synodic month is the period in which the Moon gains one complete revolution over the apparent or visible motion of the Sun; or 360 degrees over the Sun (not just moving 360 degrees in the zodiac). The moment of New Moon (amāvāsyā) is the moment when the Sun and Moon have the same longitude. When the Sun and Moon have the same longitude, they enter union (saṁgata), known as syzygy, or the New Moon conjunction.

The time from one New Moon to the next New Moon is approximately 29.5 days, according to Sūrya Siddhānta it is 29.530587946 days. Modern calculation is 29.530588853 which is the same for the first six decimal places. The ancient Vedic astronomers calculated the length of the lunation to nine decimal places to insure precision of calculations over thousands of years. The modern and Vedic difference would amount to a variation of about 1 hour and 11 minutes in 5,000 years.

The mean New Moon occurs every 29.530587946 days (29 days, 12 hours, 44 minutes, 3 seconds) but the actual New Moon does not recur at exactly this interval. The mean motion is the average motion which is a constant, while the actual or true motion is what is actually happening and has fluctuations. The Moon may be fast or slow according to its elliptical motion at the time of becoming new and this anomaly needs to be taken into consideration[1].

The anomaly is based upon the anomalistic month of 27.5546 days (according to the Sūrya Siddhānta) where the Moon will repeat its pace according to its position. The siddhāntas gives charts of the Moon’s anomaly for precise calculation of the exact moment of new moon. In 1600 A.D. the Vedic Astronomer Gaṇeśa Daivajïa added a correction raising the annual increase of the Moon’s anomaly 2 seconds and decreasing the length of the anomalistic month from 27.5546 to 27. 55459797. The precision is needed to calculate the new Moon which also needs to take into account the anomaly of the Sun’s pace (the earth’s elliptical motion around the Sun).

The moment of the New Moon conjunction marks the beginning of the lunar month and the end of the previous month. This calculation is called amānta months (which is used in most places in India today). The Ṛgveda talks about the Sun and Moon cycles, and says that the Moon, as she invigorates (pyāyana) herself after having been drunk (prapiba) by the gods, gives shape (ākṛti) to the months (māsa). The Moon wanes, having had her light drunk by the gods; and then after the New Moon conjunction, which starts a new lunar month, grows in light and strength again.

[There is an ancient system called Pūrnimānta months which calculates the months from full moon to full moon, which is used in a few places in India.]

Solar Year:

The solar year is based upon the Sun’s 365-day motion through the zodiac as perceived from Earth. There are two types of solar year: the tropical year and the sidereal year. It is this difference between these two types of year that creates a variation between the stars and the seasons ( ayanāṁśa).

The tropical year is 365 days, 5 hours, 48 minutes and 45.2 seconds (365.2422408 days), while the sidereal year is 365 days, 6 hours, 9 minutes and 9.8 seconds. The difference between the tropical (seasonal) and sidereal (stellar) year is about 20 minutes. These 20 minutes creates the ayanāṁśa, the portion (aṁśa) of variation between the stars and the equinox (ayana).

The tropical year is the period of time from one vernal equinox to the next which according to modern calculations is 365.2422408 days. The utility of the tropical solar year is for starting the seasons at the same time every year. The Gregorian calendar is presently based upon the Sun’s motion only and therefore utilizes the tropical year.

The sidereal year is the period of time wherein the Sun passes through all twelve signs of the zodiac and returns to 0 degrees Aries (Meśa saṅkrānti). The length of solar year according to the Sūrya Siddhānta is 365.258756484 days; modern data lists it as 365.256363051 days.

The anomalistic solar year takes into account the difference of speed of the Sun at different times of the year when the Sun is farthest and nearest to the earth. This varying pace is needed for calculation of the exact point of new moon and the precise time of sunrise. The Vedic calendar utilizes the sidereal solar year (with the correction for the Sun’s anomaly) as it is based upon the location of the luminaries during the new Moon and at Sunrise.

Interaction of Solar and Lunar Months

Saṅkrānti is the time when the Sun enters a new sign and is within its zero-degree placement there. As the sidereal solar year begins with Meṣa saṅkrānti (entry into Aries), this is also the first solar month. A solar month is based upon the motion of the Sun through each of its signs, and is related to the energy of the Sun (Jaiminīya Brāhmaṇa II.77). The second month begins with 0° of Taurus (Vṛṣabha saṅkrānti). As the Sun’s velocity varies, a solar month will have either 29, 30 or 31 days.

• Saṅkrānti is the Sun changing signs of the sidereal zodiac. The solar day of Saṅkrānti starts the new sidereal solar month. There were a number of different variations to this calculation in ancient India. In the southwestern part of India (ancient Malabar region), if the Sun changed signs before 1pm (18 ghaṭikas) then that was the Saṅkrānti day; and if it changed after, then the next day was utilized. In Tamil Nadu, if the Saṅkrānti happens before sunset (30 ghaṭikas) they use that day, while after sunset they use the next day. In Bengal, they use the day that has Saṅkrānti before midnight (45 ghaṭikas). In Odisha, the Saṅkrānti day was whatever solar day the Sun changed signs. (Vedic day is sunrise to sunrise.) This would have ancient calendars in different kingdoms starting on different days. For those who use Pope Gregor’s tropical calendar, this is of little importance; but in ancient times, this changed the beginning of the month and could have large implications with adhika and kṣaya months.
• Being that I do not calculate adhika months, I utilize the 1pm (18 ghaṭikas) rule in the Vedic calendar that I publish. When the Sun has just changed signs, work is less effective. I use the analogy that if you install a fence on Saṅkrānti, you realize the next day that it is in the wrong place, and have to repeat the work. In this way, it is better to refrain from work that day (and you can do so free of guilt as it would be unproductive anyway). My nickname for Saṅkrānti is “beach day” – as it’s better to go to the beach. I use the 1pm rule to ensure that the day you take off is the day where the Sun is zero degrees for the largest number of normal working hours.
• It ancient times the Saṅkrānti day held religious importance. In astrology the charts of each Saṅkrānti are used to predict elements of the country’s politics. For example, Libra Saṅkrānti is the time to predict the country’s finances.

Sankrānti is the time while the Sun is within its zero degree. Even though this is clear, the actual day the month begins has different variations in different parts of the country. The moment of sankrānti is the same all over India but the corresponding month for civil purposes is not the same all over India. For example, some use the day that the Sun is in its 0 degree at sunrise, while others will use the day if the Sun enters 0 degrees before Sunset. Other parts will take the day even if it changes signs in the night time. There are a few other rules in different parts of the country which can often change which day is considered the first day of the solar month. In this way, there is a large amount of variation within different regions of India, which creates a hard time calling something standard and actually being proper. So we can generalize that the sankrānti is the first day of the solar month, though we must understand that detailed calculations will have variations according to tradition. These variations are also found in the naming of the solar months.

The solar months are considered the hinges, and the synodic lunar months the doors, of the Vedic calendar. The lunar month has its name determined by a New Moon conjunction occurring relative to a particular saṅkrānti. Vedic and Hindu rituals, festivals and vratas are determined according to the lunar month (the door); but that door is determined based upon the solar month (the hinge that opens the door).

The solar months are generally named from the lunar month, which is named from the nakṣatra where the Moon was most likely full. This is why the name of the lunar month correlates with a nakṣatra opposite the sign. If the Full Moon is in Chitrā, the New Moon conjunction will most likely be in Aries.

In the diagram below you will notice that the month of Chaitra begins at the new Moon before Meśa sankrānti (in the previous solar year), while the next month (Vaiśākha) begins in the new Moon before Vṛṣabha sankrānti.

Innermost circle is the solar months. Middle circle is lunar month named according to the New Moon conjunction. Here the lunar month starts in the middle, but it may start anywhere within the sign.

The lunar month is named according to the solar month in which it has its New Moon conjunction. Presently, in India, it is the sidereal solar year beginning with Aries that determines the entire lunar year. In the ancient calendar text, Vedāṅga Jyotiṣam, the mutual relation of solar and lunar months is kept from tropical Saṅkrāntis, starting at the winter solstice.

• In the table, you will notice that the month of Caitra (lunar New Year) begins at the New Moon conjunction before Meṣa Saṅkrānti (in the previous solar year); while the next month (Vaiśākha) begins in the New Moon conjunction before Vṛṣabha Saṅkrānti. There were over 30 different calendars before Indian Independence, which named the sidereal solar months differently. Bengali solar months were named from the lunar month after Saṅkrānti, while the Tamil solar months are named from the lunar month before. They have the same names but refer to different times. In the amānta system, the lunar month is determined/named based on the solar month of the Full Moon opposition. The Full Moon names the solar month, and the solar month determines the lunation order. The Malayalam and Odiya months were named according to the signs of the zodiac. In my Vedic Calendar, we utilize the names associated with the signs of the zodiac.
• In the Vedāṅga Jyotiṣam, the lunar months seem to be calculated according to tropical solar signs: v.14–15 discuss the two ayana; v.16 discusses 12 lunar months (made of pakṣas); v.17–18 discuss viṣuva (equinox); v.33 links nakṣatra calculation to the ayana; v.34 defines tropical solar months, sidereal solar months, synodic months, and nakṣatra months; v.40 discusses rectifying lunar months to the seasons (ṛtuśeṣa); v.41 discusses the winter solstice in Śravaṇa (dating the text to between 1500 and 500 BCE, being that the present winter solstice is in Mūla); interestingly v.41 also mentions the use of the Ascendant (prāgvilagna).
• In Bali, the Department of Religion decided, instead of having an irregular Adhika māsa, to ensure that Śiva Ratri would always fall in January (after winter solstice). If it occurred in December, then they would add an Adhika māsa. This generally keeps Śiva Rātri as the first Caturdaśī (approximate day before the New Moon conjunction) after the winter solstice. In India, the procession of the sidereal zodiac has Śiva Rātri generally falling on the second Caturdaśī after winter solstice. This is because calculations are according to āgamas written when the sidereal dates aligned with the tropical indications to have Śiva Rātri as the longest night, Caturdaśī.

When a standard All-India calendar was being created in 1952–7, the Calendar Reform Committee recommended that the luni–solar months be linked to the tropical months. This suggestion was not followed, since the calendar had been linked to the sidereal months for approximately one millennium. The Indian government instead created a tropical solar calendar with months named after the classical sidereal nakṣatra months, which was not accepted by most Indians. The committee named as the “Review of Committee on Indian Calendar and Positional Astronomy” met in 1986 to make new recommendations, which were not followed. Finally, new recommendations in 2004 were accepted to make the solar months coincide with the sidereal zodiac signs.

The luni–solar calendar is a type of cosmic attunement that connects us to an organic time. It is the interaction of the solar year with the lunar cycles that determines intercalary months, which allows the lunar months to align with the seasons. This is a dance between the Sun and Moon, as well as between fire and water. This dance is the balance we aim to achieve in ourselves between the male and female polarities.

• We also see the interplay between the elements in the Chinese luni-solar calendar. Hexagram 49 in the I Ching is called Lake above Fire. Thomas Cleary translates: “There is fire in a lake, changing. Thus do superior people make a calendar and clarify the seasons.” This indicates the interaction of the Sun and Moon, fire and water, and the balancing that is required in a luni–solar calendar, which aligns one to the year (which is a symbol of time). Too much water will put out fire; too much fire will turn the lake to mist. The Islamic calendar is too much water – their festivals follow only the Moon and they move through the seasons. The Gregorian calendar is too much fire, and there is no relationship with the Moon.

Broken Hinges and Missing Doors

The first day of the lunar New Year is Chaitra Śukla Pratipadā. The calculation of the month of Chaitra is the New Moon conjunction before Meśa sankrānti. It is therefore the Solar year beginning with Aries which determines the entire lunar year. It is also the solar year which determines the intercalary months which allows the lunar years to have consistency.

In general new moon conjunctions and sankrāntis occur alternately, therefore each door has its own hinge.

Normally, the Sun and Moon interrelate equally, but Adhika and Kṣaya are when they do not. An Adhika māsa is two lunations in one Saṅkrānti (two Moons in one Sun) and a Kṣaya māsa is two Sankrānti in one lunation (two Suns in one Moon). An Adhika tithi is when there are two days in one tithi (two Suns in one Moon); whereas a Kṣaya tithi is when there are two tithi in one day (two Moons in one Sun). The solar month names the lunar month, while the lunar day names the solar day. The Sun names the Moon’s month; the Moon names the Sun’s day.

Adhika Māsa

There may occasionally be a shorter lunation that does not have a Saṅkrānti. This makes two New Moon conjunctions within one solar month. In order for this to happen, the New Moon conjunction needs to happen right after Saṅkrānti, and the second New Moon conjunction will happen just before the next Saṅkrānti.

This additional lunation becomes the intercalated lunar month called an Adhika māsa. In this case both lunar months will take the same name. The first month is Adhika (additional, abundant, intercalated); and the second month is Nija (innate, native). For example, there could be an adhika Śrāvaṇa māsa and a nija Śrāvaṇa māsa. Most traditions utilize the natural (nija) month for standard festivals. Adhika months ordinarily occur once every three years.

Kṣaya Māsa

Rarely, there is a longer lunar month that has two Saṅkrānti. When this happens a lunar month is suppressed, as there is no hinge for the door to turn on. This suppressed month is called a lost month (kṣaya māsa). The Kṣaya month is very rare, while the intercalary month happens about once every three years. These variations are the key for keeping the solar and lunar cycles in harmony, and thereby allowing a functional luni–solar calendar.

A kṣaya māsa requires the New Moon conjunction to start just before a Saṅkrānti, and end just after the next Saṅkrānti, so that a solar month loses the ability to name a lunar month. Only the three months of Mārgaśirṣa, Pauṣa, and Māgha (Siddhāntaśiromaṇi of Bhāskarācārya says only Kārtika, Mārgaśirṣa, Pauṣa) can be kṣaya, because they are the three lunar months that turn on 29 days each. This is caused by the Sun at its perihelion, presently somewhere during January 2^nd to 4^th, when it moves the fastest through a sign, (the apsidal line precesses through the zodiac at about one degree every 372  years). The kṣaya māsa runs with the next month simultaneously, and so is also called a yugalibhūtamāśa, or paired month. A kṣaya masa happens about once every 141 years (sometimes 122 years because of a Metonic cycle of variation).[4] The last kṣaya māsa was in 1983.

The intercalary month was utilized from ancient Vedic times. Ṛg Veda 1.25.8 says that the Sage Dhṛtavrata knows the twelve months and the month that is being created. Here we see twelve natural lunar months and the Adhika māsa that is created by the cycle. The Yajurveda Vājasaneyisaṁhitā 22.30 worships the intercalary year (Saṁsarpa), the Moon (Chandra), the lights/stars (Jyotiṣa), the intercalary month (Malimluca) and the Sun (divāpati).

The Ṛgveda says the Sun and Moon move proceeding and following each other, because of Māyā, like two children playing round the sacrifice (10.85.18). Time is seen according to the Sun’s movement because it is steady and constant each year; it beholds all existence (viśvānyanyo bhuvanābhicaṣṭa); while the lunar months move all over the place like the emotions constantly fluctuating, yet they create the moment (ṛtūṁranyo vidadhajjāyate). The Vedic calendar keeps stability with the Sun, like the ātman keeps an individual centered. The individual happenings are guided by the Moon, like the emotions fluctuating across the mind.

The results of being born in the different lunar months are listed in Janardan Harji’s Mānsagarī. Someone born in the month of Caitra is likely to be happy, perform good works, be egotistical, have bloodshot eyes, deal with anger, and have a changeable love life. Someone born in the lunar month of Vaiśākha is likely to be a pleasure-seeker (bhogī), wealthy, of good disposition (su-citta), playful, handsome, and a favorite of the opposite sex. Those born in the month of Jyeṣṭha will enjoy going abroad, will have a good mind (subhacitta), be wealthy and long-lived, and have good intelligence. Birth in the month of Āśāḍha gives sons and grandsons; Śrāvaṇa gives equanimity in good or bad times; while Bhādrapada makes one soft-spoken but talkative, and always delightful. Āśvina has good qualities; is happy, poetic, wealthy and desirous. Those born in the month of Kārttika are harsher with tough personalities, and are often involved in trade. Mārgaśirṣa will have lots of friends, be soft-spoken, and helpful to others. Those born in the lunar month of Pauṣa are said to be intense and brave. Māgha birth indicates good intelligence, bravery and harsh speech; while Phalguna birth indicates a fair complexion, good wealth, education and comforts, as well as vacationing to foreign places. Birth in an Adhika māsa is said to make one spiritual, virtuous, and unconcerned with worldly matters; while birth on a Kṣaya māsa is said to make one ignorant, poor and diseased.

Intercalary Month (Adhika Māsa)

The kṣaya month happens only once or twice a century as an astronomical rule. The intercalary month happens about once every three years. It is the key for keeping the solar and lunar cycles in harmony and thereby allowing a functional luni-solar calendar.

The intercalation is how the lunations (Moon) are wedded to the year (Sun); and it is this wedding that keeps the lunations in tune with the seasons. To understand the mathematical harmonics more deeply, we shall calculate the first six years of Kali Yuga to see the actual functioning of the intercalary month. According to Sūrya Siddhānta, Kali Yuga began on midnight between the 17^th and 18^th of February 3102 B.C. (Caitra Pratipad).

At the end of the first sidereal year and beginning of the second, 12 synodic months had passed and 10.891701134 days of the next lunation.

Śuddhi is the time between the moment of each New Moon conjunction and the subsequent Saṁkrāṇti, also seen as the time gained by the luni–solar calculation over the solar. When this time (śuddhi) attains the length of a full lunation, then there is an entire lunation without a Saṁkrānti. This lunar month has no hinge to turn on and becomes Adhika. No election times (muhūrta) are given during this month (marriages, business openings, moving into a new home, etc.). The śuddhi (relation between the lunation and solar month) has a regular 19-year cycle (minus 2 hours); 228 solar months (19 x 12) is equivalent to 235 lunations. This inherent 19-year luni–solar cycle is called the metonic cycle by Greek and modern astronomers.

So, at the end of the first sidereal year and beginning of the second, 12 synodic months had passed and 10.891701134 days of the next lunation.

At the end of the second year, 12 synodic months had passed and 21.783402268 days of the next lunation.

By the next year there were 12 lunations plus 32.6751034 days. This is actually 32.6751034 days so we subtract a lunation of 29.530587946 days which is therefore 13 lunations and 3.144515454 days of the next lunation.

Again we can see that since there were 10.891701134 days of the next lunation in the previous solar year, the next lunation starts 18.638886812 days into the year (not 29.530587946 days, as in the previous year, which began on the new moon conjunction). Each year the New Moon conjunction will start 18.638886812 days later. At the end of the second year we have 18.638886812 days multiplied by 2, which is 37.277773624 days. This amount of time is more than one lunation, and therefore we subtract 29.530587946, and have 13 lunations, with the next New Moon conjunction happening 7.747185678 days into the month.

Beginning of the Year (Varṣa-Praveśa)

There are various beginnings of the year (varṣa-praveśa) for various purposes just as there are various types of years for different purposes: the calendar year for dating, the civil (sāvana) year for government related work, the seasonal year for agriculture, the fiscal year for financial books and taxes, the academic year for education, etc. The astronomical New Year is Meśa saṅkrānti. The lunar New Year is the New Moon before that, Chaitra Pratipada. Divali, the New Moon of Āśvina, is the fiscal New Year (similar to April 15^th in the USA).

Makara saṅkrānti is the New Year for many dating systems, and shares the same astronomical roots as the Gregorian New Year. Makara Saṅkrānti is generally in the middle of January and marks the Dakṣiṇāyana – the Sun moving towards the Southern Hemisphere (relating to the Winter Solstice and the lengthening of the days). Karka Saṅkrānti is approximately the middle of July and it is not celebrated because it marks the Sun moving towards the Northern Hemisphere, the start of Uttarāyaṇa (relating to the Summer Solstice) where the days get shorter and the nights longer.

The Solar calendar has been used for civil purposes (work days, government planning, business), while the lunar calendar and tithis are used for religious purposes. The lunar months utilize tithis, while the solar month utilizes days of the week. The overall calendar is luni-solar because it is regulated by the movements of the Moon but it is made to fit in the divisions of the Solar year. The National Calendar of India is prepared by the India Meteorological Department and published annually in The Indian Astronomical Ephemeris.

A calendar is more than merely a device for the numbering of days. All calendars are directly bound to the ever-recurring cycles of nature, most commonly manifested in the rotation of the earth and its cosmic influences; their underlying purpose is to help man adjust to these cycles and the forces that permeate them by achieving rhythmic flow of natural events. Ultimately this brings a sense of harmony with the Universe.

-José A. Argüelles

Other Calendrical Systems

Luni-solar calendars are used by the Hindus, Buddhists, Tibetans, Chinese, Mongolians, Koreans, and Hebrews. The Japanese used a luni-solar calendar till 1873. The Babylonian calendar (derived from the Sumerian calendar), the Greek Calendar, the pre-Islamic calendar, and the pre-Christian Germanic calendar were all luni-solar.

Islamic

The Islamic calendar is completely lunar and has no relation to the position or movement of the Sun. The twelve lunar months regress through the seasons over a cycle repeating every 33 years. The month begins with the first visibility of the crescent Moon after conjunction, though a lunar calendar of approximation is used for civil purposes in Muslim countries.

Hebrew

The Hebrew calendar is luni-solar and starts its first month (Nisan) on the first lunation after the spring equinox. The names of the months are the same as the Babylonian names. The calendar was originally observational based upon the first sighting of the crescent Moon but in the fourth century AD it became a fixed-arithmetic luni-solar calendar. This Hebrew calendar uses the 19 year Metonic cycle with 12 common years and 7 intercalary years (which are 3, 6, 8, 11, 14, 17 and 19^th year of the Metonic cycle). Utilizing the Metonic cycle instead of direct astronomical calculation allowed Hebrews in different countries to follow the same months and festival days, but it creates a slight variation from the Vedic months when the adhika māsa are added. There are three different moments the Vedic calendar can add an adhika māsa, but the Hebrew luni-solar calendar only adds the adhika māsa before the spring equinox. In the chart below, the adhika māsa of the Vedic and Hebrew calendars are marked in yellow, and the light red months are moments the two calendars do not correspond.

Julian and Gregorian

The West used the Julian calendar which replaced the Roman calendar in 46 BCE. It was introduced by Julius Caesar according to the astronomer Sosigenes of Alexandria. The first year of the Julian calendar marked the first new moon after the winter solstice as January 1st and never changed it again.

Some say Caesar shackled the months to the solar year as the Hellenic calendar was luni-solar. But the intercalation was manipulated for political purposes, like not inserting a month when opposition was in power and putting too many intercalary months when supporters were in power.

The Julian calendar used a 365.25 day sidereal solar year with a leap day every four years, which creates an excess of .00776 days, and thereby over long periods of time misaligns itself with the seasons. Originally the winter solstice was on December 25th of the Julian calendar, but without the correct use of the leap year, by 1581 CE it fell on December 11th. Easter is the first Sunday after the first full moon following the spring (vernal) equinox but was slowly Easter, meant to symbolize spring’s rebirth, was gradually sliding out of spring.

In 1582, Pope Gregory dropped out 10 days to rectify the Easter drift hereby creating the Old Style Gregorian calendar. The British Parliament dropped out another 11 days in 1752 making the New Style calendar. The modern western calendar now uses the tropical solar year along with the leap year to avoid such a recurrence. From its foundation one can see that it was originally based upon a luni-solar calendar but has become a tropical solar calendar in its present state. The variance in the days of the month originally corresponded to the anomaly of the Sun and its motion through the signs of the zodiac. The Gregorian calendar has presently become the internationally accepted civil calendar.

Conclusion

There are many variations throughout India based on the region/kingdom and time period. What is more important for the practitioner than the details of each calculation are the general concepts of the Sun and Moon creating a system of time together. There are 12 solar signs based on 12 lunations. The Full Moon names the solar signs. The lunar month is named by the solar sign containing the New Moon conjunction. This interaction makes a luni–solar calendar.

The dynamics of the calendar are fundamental to how we look at time and how we calculate it. The Vedic calendar comes from watching the cycles of the Sun and Moon, and then expressing the natural cycles in these observations. The stars turning in the year and the lunations are already present; the human mind is just watching them and giving them names. We watch the dance of the Sun and the Moon, and see how all the festivals and times of worship are guided by this clock. And when we look deeper, we see that this dance is a movement of consciousness, in the sky above and in our personal experience.

[1] This irregularity (or anomaly) is called eccentricity of orbit and the correction to be applied to it is called the equation of the center. The mean and actual positions are the same at 0° (perigee) and at 360° (apogee).

[2] The correlating Gregorian date is slowly moving with procession. I give an example here of the time period when the tropical and sidereal zodiacs coincided (290 to 295 CE) and the present time period (2015 to 2020 CE). The example is for the New Moon conjunction of Caitra:

[3] prāṇīye varṣa etasmi-nkārtikādiṣu dakṣataḥ || Tantralokā 6.122||

pitāmahāntaṁ rudrāḥ syu-rdvādaśāgre'tra bhāvinaḥ |

[4] Metonic Cycle (or Enneade Caeteris)

There are a few other cycles that interact with the normal luni-solar calculations that a good astrologer should be aware of. If a New Moon starts on the beginning of the year, it will take 235 lunar months till the New Moon starts again at the beginning of the year. This is an approximation rounded to 6,940 days with an error of 2 hours each cycle (one full day every 219 years). This cycle was recorded and named after the Greek astronomer Meton of Athens in 432 B.C. and is used by calendar makers. In general, adhika months happen seven times in this nineteen year cycle. The Metonic Cycle was the basis of the Greek calendar and is retained in the Hebrew calendar. The cycle is an approximation and still needs rectification over large periods of time, as it is not an exact orbital resonance.

References

Argüelles, José A., Introduction to I Ching: Taoist Book of Days, Calendar Diary 1975 by Khigh Alx Dhiegh.

Arkasomayaji, Dr. D. trans., Siddhāntaśiromaṇi of Bhāskarācārya. Rashtriya Sanskrit Vidyapeetha, Tirupati (2000).

Chattejee, S. K. Indian Calendric System. Publications Division of the Ministry of Information and Broadcasting, Government of India, New Delhi, (2006).

Dhiegh, Khigh Alx. I Ching: Taoist Book of Days, Calendar Diary 1975. Shambala, Berkeley, (1974).

Eiseman, Fred B. Bali: Sekala and Niskala: Volume I: Essays on Religion, Ritual, and Art. Periplus Editions Ltd., New York, NY (1992).

Mishra, Dr. Suresh Chandra. Vedanga Jyotisham: Akhilananda Bhashyopetam. Ranjan Publications, New Delhi, 2005.

Pillai, Swamikannu, and L. D. Dewan Bahadur. Indian chronology (solar, lunar and planetary: a practical guide): The interpretation and verification of tithis, nakshatras horoscopes and other Indian time-records BC I to AD. Asian Educational Services, New Delhi (1982).

Pillai, Swamikannu. Panchanga and Horoscope or the Indian Calendar and Indian Astrology: Astronomically Considered in the Light of First Principles with Numerous Practical Examples . Asian Educational Services, New Delhi (1996).

Saha, M. N., and N. C. Lahiri. Report of the Calendar Reform Committee. Council of Scientific and Industrial Research, New Delhi, 1955.

Sewell, Robert, Sankara Balkrishna Dikshit, and Robert Schram. The Indian calendar: with tables for the conversion of Hindu and Muhammadan into AD dates, and vice versâ Vol. 289. Originally by S. Sonnenschein & Co., 1896. Reprint by Motilal Banarsisass Publishers, Delhi (1996).

Subbarayappa, Bidare V., and K. Venkateswara Sarma. Indian astronomy: a source-book, based primarily on Sanskrit texts. Nehru Centre, Bombay (1985).

Further Resources

The Indian Astronomical Ephemeris, utilized by the Indian Government’s India Meteorological Department http://www.packolkata.gov.in/history.php