Hindu Calendar 4 of 5

 Different Kinds of Months

The periodic movement of the Moon generates the month / Maas.

The lunar motion is complex, and more so, when it is considered with the motions of the Sun and the Earth, hence, there are many different possible definitions of the month. The length of the month is different for all. These months are

• Synodic
• Sidereal
• Anomalistic
• Draconic/ Nodal
• Tropical

 The Panchang considers the length of all the different months for various purposes, such as calculating tithi, Adhik Maas, the position of nodes (Rahu and Ketu), Eclipses, type duration, location, etc. A synodic month is used for general purposes in Panchang. It considers a mean length of 29.53 days. The actual time between lunations may range from about 29.27 to about 29.83 days.

The beginning of a solar month, Solar Sankranti has many variants (as explained in the previous blog).

So when does a Lunar month begin? Two systems are being followed (this is observed right from the Vedic days). The two systems are known as

Amanta In this system, the lunar month is counted from New Moon to New Moon.

Purnimanta In this system, the month is counted from full Moon to full Moon.

Both systems were prevalent during the Vedic period.

Simple, as compared to conventions on solar month.

The waxing phase of the moon is called " शुक्ल पक्ष, and the waning phase is called कृष्ण पक्ष, in both types of the month 

Naming of the months

In ancient times, the months were named according to the prevailing season. Later, these were rechristened nakshatra names to correspond with the same seasons.

 Ancient Vedic name         Modern name

1. Madhu                            Chaitra
2.  Madhava                       Vaisakha
3. Sukra                               Jyeshtha
4.  Suchi                              Ashadha
5. Nabhas                           Sravana
6. Nabhasya                       Bhadrapada
7. Isha                                 Asvina
8. Urja                                 Karttika
9. Sahas                              Margasirsha
10.  Sahasya                         Pausha
11. Tapas                              Magha
12. Tapasya                          Phalguna

Madhu is "honey", "sweet spring". Madhava. "The sweet one". Sukra and Suchi both mean "bright". Nabhas, the rainy season. Nabhasya, "vapory", "rainy", ish or isha, 'draught" or "refreshment", "fertile". Urja, "strength", "vigour". Sahas strength". Sahasya means "strong". Tapas  , "mortification", "pain", "fire". Tapasya, "produced by heat", "sadhana ". All are Vedic words.

This goes to show that during Vedic times, the year accounting was tropical, ie, season-based.

The sidereal name "Chaitra” came into use about 2000 BCE.

The Sidereal names were derived from the nakshatras. The full-moon tithi (Purnima), on which the moon becomes full when near the nakshatra Chitra, was called Chaitra; the lunar month that contained the Chaitra Purnima was called Chaitra, and so on. See the diagram. The observer is at the centre of the circle. When he sees the full moon in the Chitra Nakshatra, the sun is near the equinox, or the start point of the zodiac, which is also called the beginning of the year. This is how the months got their names. It is easier to observe the position of the full moon than the sun.

However, the full moon does not occur in the same nakshatra every year. Hence, a group of nakshatras was allotted to each month for naming.

Names of lunar months, based on, grouping, of the nakshatra.

Grouping of Nakshatra                               Modern Month Names

• चित्रा ,स्वाति                                                        चैत्र
• विशाखा अनुराधा                                                वैशाख
•  ज्येष्ठा ,मूल                                                          ज्येष्ठ 
• पूर्व आषाढा,  उत्तर आषाढा                                आषाढ  
•  श्रवण ,धनिष्ठा                                                       श्रावण 
• शततारका , पूर्व भाद्रपदा/ उत्तर भाद्रपदा/         भाद्रपद
•  रेवती, अश्विनी,  भरणी                                         अश्विन
• कृत्तिका , रोहिणी                                                 कार्तिक
• मृगशिर, आर्द्रा                                                      मृगशीर्ष
• पुनर्वसु, पुष्य                                                         पौष
• पुष्य , मघा                                                            माघ 
  
• पूर्व फाल्गुनी ,उत्तर फाल्गुनी, हस्त                      फाल्गुन 

By about 1400 BCE, and the introduction of the Rashi system the solar Sankranti was used to denote Lunar months in which the full moon occurred. Most names remained the same. However, some solar calendars changed their names to Rashi's names.

The first month of the year depended upon the type of zodiac used; hence Vaishakh was the first month for the solar year, and Chaitra was the first month for the Lunar year. So, those who follow the solar year start their year from the month of Vaishakh, and those who follow the lunisolar year start the year from the Chaitra month.

The general rule of naming the lunar months to correspond with the solar year is that the amanta month in which the Mesh Sankranti or entrance of the sun into the zodiac sign Mesh, or Aries, occurs in each year is to be called Chaitra, and so on in succession.

The names of the month prevalent today in various parts of India are given in the table

Corresponding Names of Solar Months in Different Places
First Month of the Year is in Capitals
Sun Sankranti	BENGAL/ ODISHA	ASSAM	TAMIL NADU	KERALA
MESH	BAISAKH	BAHAG	CHITTIRAI	MEDAM
VRISHABH	Jyestha	Jeth	Vaikasi	Edavam
MITHUN	Ashadh	Ahar	Ani	Midhunam
KARAK	Shravan	Seon	Adi	Karkitakam
SIMHA	Bhadra	Bhad	Avani	CHINGAM
KANYA	Ashwin	Ahin	Puratassi	KANNI
TULA	Kartika	Kati	Aippasi	Thulam
VRISHIK	Agrayahana	Aghon	Kartikai	Vrischikam
DHANU	Pausha	Poha	Margalj	Dhanu
MARAK	Magha	Magh	Tai	Makaram
KUMBH	Phalgun	Phagun	Masi	Kumbham
MEEN	Chaitra	Chait	Panguni	Meenam

क्षय तिथि and अधिक तिथि 

Tithi, its definition, and accounting as current tithi are explained in Hindu Calendar 2 of 3 and Hindu Calendar 3 of 4

क्षय तिथि

To continue with the same example (as given in part 3), if the sunrise is at 0623 h on 10 January and the चतुर्थी  तिथि finishes at 0947 h, then the tithi for 10 January is चतुर्थी तिथि.

 If the Panchami tithi ends after sunrise (0634 h) on 11 January, then it will be Panchami tithi.

However, if पंचमी तिथि finishes before sunrise on 11 January, say by 0620 h, then  षष्ठी तिथि will be current at sunrise on 11 January. So tithi for 11 January will be षष्ठीतिथि. There will be no पंचमी तिथि, as पंचमी तिथि has lapsed and is not counted.

In short, a tithi on which the Sun does not rise is expunged! That is kshya क्षय तिथि. 

अधिक तिथि 

In the same example above, if the Panchami tithi finishes after sunrise on 11 January, say at 0821 h, and on 12 January, it finishes at 0700 h, then 12 January will still be Panchami, as per the current tithi rule. 

In short, on a तिथि on which the Sun rises twice, the तिथि is repeated. This is अधिक तिथि.

Generally, there are thirteen क्षय तिथि and seven अधिक तिथि in twelve lunar months.

The day on which no tithi ends or a तिथि is repeated is regarded as inauspicious.

  अधिक मासand क्षय मास

The aspect of अधिक मास and  क्षय  मास is peculiar to Luni solar calendars. The process of intercalary month adjustment is to synchronise with the solar calendar and seasons. A lunar year has 354 days, and a solar year has 365 days, a difference of 11 days in a year. Hence, in about 30 months, one month is added as an intercalary month to synchronise. 

अधिक मास

The length of a solar month                                           Length of a Lunar Month

Maximum    31 d 15 h 28 m                                          29 d 19 h 30 m

Minimum     29 d 7 h 38 m                                            29 d 7 h 20 m

When the length of the Solar month is greater than the lunar month, then, in this condition, a second Lunar month starts in the same solar month. or the lunar month completes between two sankrantis. Then this is अधिक मास.

Simply put, the lunar month where there is no transition of the Sun from one rashi to another is अधिक मास. 

Click on the link to see अधिक मास animation. Adhik Maas

क्षय मास

When the length of the Lunar month is greater than the solar month and in the lunar month, where there are two sankrantis/ transistions of the Sun in two rashis, then that month is क्षय मास. This occurrence is not so frequent.

Click on the link to see क्षय मास animation.  Kshay Maas

The adhik and kshya maas and its insertion, for synchronisation, is done on a real-time basis, unlike in the Gregorian calendar, where  1 day is added in February only.

Naming of Adhik/ Kshay Maas

 The insertion of an additional / expunged month has to be at a proper location and named correctly for identification without affecting the time of religious rites, seasons, etc.

Different rules were framed by various teachers. This resulted in variance in practice and caused confusion.

काल तत्व विवेचन - It is a treatise on the rules for the naming of months and times, seasons suitable for the performance of religious rites, and is attributed to sage Vyasa. 

The celebrated astronomer Bhaskaryacharys (1150 CE) used these rules, which were further modified by 1600 CE and are still used today.

Click on the link to see the naming of  अधिक मासand क्षय मास Month names in two systems

Brahma Siddhant and Surya Siddhant give out the detailed process of naming the intercalary months for both Amanta and Poornimanta systems.

The lunar month in which no Sankranti occurs is called Adhik, but the month in which the Sankranti actually occurs is called Nija, which means true or regular month. Examples: Adhik Shravan and Nij Shravan.

See the link Naming

Some Interesting Pecularities.

• During the Vedang period, the intercalary months, primarily adhik maas, were determined based on the mean motions of the sun and moon; hence, no kshay or decayed month could occur.
• However, around 1100 CE, the apparent motions of the new-moon-ending lunar month and the different solar months, as obtained from Siddhantic rules, were used. By these calculations, a क्षय मासoccurred.
• In a 19-year cycle, intercalations generally occur in 3,5,8,11,14,16, and 19th years
• A month becomes intercalary at an interval of 19 years and afterwards gives way to the month preceeding it , rarely to the following one.
• From 300 CE to 1900 CE    मृगशीर्ष , पौष  and माघ were never intercalary.
• The last kshaya mas was माघ in 1983 CE, and the next will be in पौश 2124 CE.
• Poornimanta has a slightly different system of intercalation of the naming of months.

Date Format 

Gregorian calendar 

Today, the date can be written in various formats, such as 

• DD/MM/YYYY, 
• YYYY/MM/DD, 
• MM/DD/YY 

and many more combinations of D, M and Y.

Hindu calendar

The format is 

•  Month / Paksh / Tithi/Samvatsar/ Year of era (Saka, Vikram Samvat, Kollam, Bengal San, etc). 
• Year of Era/ Samvatsar/Month/ Paksha/Tithi. (This format was found in most of the inscriptions found in excavations)

Month Paksh tithi - पौष शुक्ल अष्टमी ( bright half) माघ  कृष्ण अष्टमी (dark half )

A date mentioned in ancient texts is 

 Shalivahan Saka 1602 Raudra SamvatSar Chitra Shuddha Purnima.

                  Era/ Year/Samvatsar Name/Month/Tithi

This date corresponds to the Gregorian calendar-27 March 1680 CE (Full Moon day)

The Gregorian date of 14 March 2025 CE corresponds to 

Saka 1946 Krodhi Phalgun Shukla Poornima

Vikram Samvat 2081 Pingla Phalgun Shukla Poornima 

......................................................... The next blog is on Eras and various dates 

________________________________________________________________________

References:-

1.  Bhartiya Jyotish Shastra-SB Dixit
2. The Indian Calendar-Robert Sewell and SB Dixit
3. Cowasjee Patells Chronology
4. The book of Eras- Gen A Cunningham
5. Calendar Reforms Committee Report 
6. Ancient Indian Astronomy -RN Iyengar
7. The Calendars of India- VK Mishra
8. Video credits from " Vedic Astrology through Animations"

 

 

 

 

 

 

Hindu Calendar -3 of 5

 Framing a Calendar/ पंचांग

पंचांग is a comprehensive document that includes a civil calendar, a religious calendar, an ephemeris, an almanac, and other religious and ritual information.

To make a पंचांगor a calendar, certain aspects are required to be adhered to like

• Correct lengths of astronomical month and year
• Civil year and months should have an integral number of days, no fractions
• The starting days of a month and a year have to be defined.
• Days and months must correspond to seasons.
• For continuous dating, an era is required and should be defined
• Civil Day needs to be defined and distinguished from Astronomical Day
• A system of adjustment for lunar months is required.

Both, the sun, the moon, and to some extent Jupiter, are used as time-markers, and therefore precise knowledge of their motion, position and apogees in the zodiac are essential for the correct calculation of a तिथि,नक्षत्र, करणfor the formulation of an accurate पंचांग.

Though the Hindu Year is mentioned as a solar year, it is actually a Sidereal year with lunar months (see Vedic Period 2). Its length has been taken as per the various siddhantas, which are corrected/updated periodically. The length of the year, as given out by सूर्य आर्य, राजमृगांक (ब्रह्म) सिद्धांत  is used for the calculation of the calendars/ पंचांग.

There are only three schools of astronomers known; one is called the सौर-पक्ष-, followers of the presentसूर्य सिद्धांत  another is called the आर्य पक्ष, who follow the first आर्यसिद्धांत and the third is called the ब्रह्मपक्ष following Rajamriganka, which is a work based on work of Brahmagupt’s corrected version of ब्रह्मसिद्धांत. (This work is not in use now). These three schools seem to have been established around 1042 CE. Though some karanas and सिद्धांत were composed at a later period and were used for making a पंचांग.

All siddhantas and Karana works were corrected around 1500 CE. The corrected versions are still being followed in the respective regions.

The length of the year, as calculated by all of them is, nearly, the same. However, they differ in other elements.

The first आर्यसिद्धांत is the authority in Tamil Nadu, Kerala and some areas of Southern India

ब्रह्मपक्षis the authority in parts of Gujarat and western parts of northern India. 

सूर्य सिद्धांत is the standard authority in Bengal, eastern areas, and the rest of India and also the prevailing authority in India for many centuries past down to the present day.

Contents of पंचांग

The zodiac forms the reference point for fixing the position of any planet or star in the sky. Since it encircles the earth, it is comprised of 360 degrees. The 27  नक्षत्र being evenly placed on it each have a span of 13°20’ arc. 12 Zodiac signs/ राशी are also evenly placed on it, each having a span of 30°. Both are assumed to start from the fiducial point “First Point of Aries”. The राशी चक्रstarts from मेष राशि/ Aries and नक्षत्र starts fromअश्विनी.

The Hindu Zodiac, used for this purpose, is of two types Sidereal and the other is  Tropical, ie, निरयन and सायन. Most पंचांग are based on the Sidereal ( निरयन) system.

1.  निरयन (Sidereal Zodiac): It considers the zodiac to begin from a fixed point in the background of stars, usually a nakshatra. It is primarily used in Vedic astrology, giving importance to the fixed nakshatra for horoscope calculations. 

2. सायन (Tropical Zodiac): It considers the zodiac to begin from the vernal equinox, or the First Point of Aries, which aligns marking the beginning of spring in the northern hemisphere. It is related to the seasons.

अयनांश is the difference between the starting points of the two zodiacs. Its value changes due to the precession of equinoxes. For the current year, this value is mentioned in the respective Panchang. 

संक्रांति. It is the point of time when the sun leaves one zodiac sign and enters another is called a संक्रांति. The period between one संक्रांति and another, or the time required for the sun to pass completely through one राशी/zodiac sign, is called a सौरमास, or solar month. Twelve solar months make one solar year. A संक्रांति on which a solar month commences takes its name from the sign-name of that month.

Types of Calendars/Years.

 Solar These calendars are based on the yearly motion of the Sun, which could be either sidereal or tropical. Indian solar calendars followed in Assam, Bengal, Tripura, Haryana, Punjab, Orrisa, Tamil Nadu Kerala, etc. have sidereal year as the year length of their calendars.

Roman, French, Egyptian, and Gregorian calendars are solar calendars where the tropical year is used as the year length.

 Lunar Lunar calendar is based on the monthly cycle of phases of the Moon i.e. synodic month and has no relation with the yearly motion of the Sun. Islamic Hejira Calendar is a pure lunar calendar.

 Luni-Solar These calendars consider both the monthly motion of the Moon and the yearly motion of the Sun. Indian calendars used in Andhra Pradesh, Gujrat, Maharashtra, Karnataka, Bihar, Kashmir, Madhya Pradesh, Rajasthan, and Uttar Pradesh are lunisolar calendars.

Jews and Babylonian calendars are lunisolar calendars.

Conventions Followed in the Panchang.

The time calculated from the various time markers does not synchronize with the standard civil or Solar day and month. This creates challenges for daily activities and religious rituals. Therefore, certain conventions have been developed for religious observances and civil practices.

संक्रांति Rule

As a general rule the beginning of the solar month as occurring, civilly, is considered at sunrise. However, there is a twist and a vast variation to this simple rule, depending upon the type and version of Siddhant followed.

• The Orissa rule: The month begins on the same day as the संक्रांति.
• The Tamil rule: The month begins on the same day as the संक्रांति if the संक्रांति falls before sunset. Otherwise, the month begins on the following day.
• The Kerala rule: The month begins on the same day as the संक्रांति if the संक्रांति occurs before aparahna. Otherwise, the month starts on the following day. (Aparahna is the time at 3/5th duration, for the period, from sunrise to sunset. For example, if the times of sunrise and sunset are 6am and 6pm, the aparahna is [(3/5) x (18 – 6) + 6] am = 1.12pm.)
• The Bengal rule: When Sankranti takes place between sunrise and midnight on that day, the month begins on the following day. If it occurs between midnight and sunrise, the month begins on the third day. (In some special circumstances, there are some deviations from this rule.)

A case of unity in diversity even in heavens!

 तिथि, सौर दिवस

The beginning of the तिथि occurs any time of the day and does not coincide with the Solar day. Hence, as a general rule, for civil and ordinary religious purposes, the tithi current at sunrise of the solar day gives its name and numeral to that day and is coupled with its weekday. For example, if the sunrise is at 0623 h on 10 January and the चतुर्थी  तिथि finishes at 0947 h, then the tithi for10 January is चतुर्थी तिथि.

Now here is the twist again!

 Some religious ceremonies, rituals, and festivals are ordained to be performed at a particular tithi and time of day. Therefore, as a general rule, the tithi current for that specific solar day or weekday cannot be considered for the festival/ ritual mentioned, regardless of the current tithi.

Hence, a festival is celebrated/ observed a day earlier or later. 

For example, Holi is celebrated on the last full moon day of the Hindu calendar. That  is  फागुन/फाल्गुन/पूर्णिमा . As per the Gregorian calendar, this day corresponds to 14 March 2025, because the Poornima tithi ( Poornima Tithi starts From 1035h on 13 Mar 2025 to 1223h on 14 Mar 2025) was current at sunrise of 14 th March 2025. So as per the general rule, quoted above, 14th March is  फाल्गुन पूर्णिमा and Holi should be celebrated on 14th March 2025.

However, the twisting moment is 

Ritual rules state that Holika Dahan should be performed on the night of फाल्गुन पूर्णिमा, this condition of, particular tithi and time of day, is satisfied on 13th March and not on 14th March 2025 (Poornima is over by sunset on 14 Mar 2025). Hence Holika Dahan on 13th March and Dhulivandan on 14 March 2025.

Lengthy treatises have been written, on this subject, laying down what should be done under all such circumstances.

निर्णयसिंधु is one such authority on these matters. It is used in most places in India.

 It is amazing, how our Vedic people could calculate and lay down rules for such complex motions of the Sun and moon and their accounting for day-to-day functioning.

 

The next blog is titled “ Adhik Maas, Kshya, and Adhik Tithi, names of the Solar and Lunar months.”

 

 ______________________________________________________

References:-

1.  Bhartiya Jyotish Shastra-SB Dixit
2. The Indian Calendar-Robert Sewell and SB Dixit
3. Cowasjee Patells Chronology
4. The book of Eras- Gen A Cunningham
5. Calendar Reforms Committee Report 
6. Ancient Indian Astronomy -RN Iyengar
7. The Calendars of India- VK Mishra

 

 

Hindu Calendar-2 of 5

 Measurement of time 

One of the most striking features of the Hindu calendar system is its intricacy. It offers a multidimensional method of structuring time, combining information about lunar days, solar days, lunar months, solar months, the Sun's and the Moon's movements in relation to stellar constellations, and other astronomically defined time spans. This makes the Hindu calendar vastly more complex than the Western calendar, which is built around only two basic units of time: solar days and solar years.

The Flux of Time is apparently, without a beginning or end, but it is cut up periodically by several natural phenomena,

• The ever-recurring alternation of daylight and night defined a day
• The recurrence of the moon's phases, defined as a month
• The recurrence of seasons, defined as a year

It is this recurring phenomenon which is used to make a calendar.

In the Vedic period, they observed and used these very natural phenomena to record the passage of time.  My blog Vedic Period 2  explains

Day

The time from sunrise to sunrise gives us a natural solar day or a Savana day. The Jews Babylonians and Muslims/ Hijri calendars calculate from sunset to sunset. Gregorian calendars calculate from midnight to midnight.

The mean solar day is used for calendar purposes, as the length of a solar day is variable.

A sidereal day is a period between two successive transits of a fixed star, and by the astronomical definition, it is the transits of the first point of Aries.(The First Point of Aries is a fiducial Point)

A solar day is longer than a sidereal day.

Indian calendars use ‘तिथि’ to denote a lunar day. This is specific to the Indian calendar/Panchang and is nowhere seen in other calendars. तिथि will be explained in detail later.

Month

A month, known as Chandra mana or masa, is primarily a lunar phenomenon. Its duration is defined as the time elapsed between two lunations, which can be from the new moon to the new moon or from the full moon to the full moon. The average length of a mean synodic period is taken to be approximately 29.5 days. This month is further divided into two halves, referred to, as paksha, and into 30 segments known as Tithis.

Year

There are three types of years

Solar/Tropical Year –It is, the time taken by the Earth to move from equinox to equinox or tropics or season to season. Indian calendars call it ‘Varsha’ which also denotes the rainy season.

Sidereal Year- It is, the time taken by the Earth to make one revolution around the Sun with respect to a fixed star.

Anomalistic Year- It is, the time taken by the Earth to make one revolution from Aphelion to Aphelion (Aphelion-furthermost point from the Sun) or Perihelion to Perihelion. (Perihelion -the nearest  point from the Sun)

The sidereal year is greater than Solar/Tropical Year. These years are considered for calendar purposes.

For divisions of day month and year during the Vedic period see the blog Vedic Period 2

The primary aspect of any calendar is to measure the correct duration of a year. Once the duration is ascertained, the other time units are calculated accordingly.

The length of the year, as counted in Vedic and later in the Vedang period was 360 and 366 days. It was later corrected during Arya Sidhant period to 365d 6h 12m and then later adjusted to the modern value of 365d 5h 48 m. The sole aim of correction is to keep the calendars in sync with the actual positions on the ecliptic and the seasons. 

Elements and Definitions

पंचांग

This calendar is highly comprehensive, integrating various elements such as ephemeris data, rituals, and both astronomical and astrological information. It has developed over time to adapt to evolving needs and may exhibit slight variations depending on the region.

 As the name suggests it is composed of 5 elements पंच अंग = पंचांग. These elements are

•  वार् 
• तिथि 
• नक्षत्र
• योग
• करण 

The earliest calendar mentioned only तिथि and नक्षत्र. Other elements were added later on. 

वार्

A natural solar day called ‘Savan divas’ सवन दिवस'

The nakshatra names were used to name the 'days' during the Vedic period. Thus when the moon is expected to be found in the मघा नक्षत्र(Alpha Leonis). The day would be called the मघा day. However, this system was discontinued later.

The present name and order of the days were borrowed from the Chaldeans and introduced in Hindu astronomy around 500 BCE. A वार् begins at sunrise, and seven वार् compose a week.

Some common names of these days are

• Sunday- आदि,आदित्य,रवि,अहस्कर,अर्क,अरुणा,भट्टारक,अहरपति,भास्करः,ब्रध्णः,भानु
• Monday. सोम , अबज, चन्द्र, चन्द्र, इन्दु, निष्पति, क्षापकर,
• Tuesday.  मंगल, अंगारक, भौम, महिसुता ,रोहितांग.
• Wednesday.बुध ,बौध, रौहिनेय, सौम्या
• Thursday. गुरु, अंगिरस, बृहस्पति, धीषण, सुरचार्य, वाचस्पति.
• Friday.. शुक्र ,भार्गवं, भृगुं ,दैत्यगुरुं, काव्यं ,उसनानि, कवि
• Saturday. शनि, सौरी, मंद

The solar day (savan divas) is further divided as,

• 60 Ghatikas = 1divas /1 solar day.
• 1 Ghatika =60 Pal=24 Minutes
• 1 Pal=60 Vipal=24 Seconds
• 1 Vipal=60 Prativipal=0.4 Second        

 For more on day division see Vedic Period 2

तिथि

To put it in simple words, a तिथि is a lunar day, and it relates to the Hindu lunar calendar. It is the exact point of time when the moon, moving eastwards from the sun after the अमावस्या, leaves the sun behind by 12 degrees, is the first तिथि, called  प्रथमा or प्रतिपदा and so on till the complete synodic revolution of the moon or one lunation occupying 30 तिथि for the 360 degrees to denote 1 lunar month. Since, however, the motions of the sun, earth and the moon are always varying in speed the length of a तिथि constantly alters.

• The greatest length is 26 h 6m 24s
• The least length is 21 h 34m 24s. 
• An average or mean length of 23h 37m 28.09s is considered for calendric purposes.

The तिथि1 to 15 are named Pratipada, Dwitiya,Tritiya ….Poornima / Amavasya (Full or New Moon)

 नक्षत्र 

This is specific to the Hindu calendar, like Tithi. There are 27 Nakshatra along the ecliptic. Each nakshatra occupies 360/27= 13 deg 20 min of space along the ecliptic. The equal division is for ease of calculation. In actuality,  नक्षत्र  occupies a varying space ranging from 12 to 18 degrees, approximately. Because of the variable motions of the Moon, the Sun and Earth, the time the Moon takes to traverse one nakshatra ranges from 

• A maximum length of  26h 32m 24s. 
• A minimum length of 22h 22m 24s 
• The mean length of Moon nakshatra is taken as 24h 17m 9.3s

The system of starting the list of nakshatra from Ashwini came into vogue around the seventh century BCE. For details on नक्षत्र  see blog Vedic Pd 4

योग

Astronomically, a योग corresponds to 13 degrees and 20 minutes—being the sum of the Longitudes of the Sun and the Moon. That is, it is the time during which the Sun and the Moon together cover 13 degrees and 20 minutes of space. But there is no direct astronomical phenomena corresponding to it. There are 27 योग in number. The concept of योग arose sometime around 700 CE and became an integral part of  पंचांग only after around 700 CE.

करण

A करण being half a tithi, or the time during which the difference of longitudes of the Sun and Moon are increased by 6 degrees. There are 60 करण in a lunar month. There are seven करण in a series of eight cycles—a total of 56—every month, from the second half of शुक्ल प्रतिपदा(1st) to the end of the first half of कृष्ण पक्ष चतुर्दशी (14th). The other four करण are respectively from the second half ofकृष्ण पक्ष चतुर्दशी(14th) to the end of the first half of शुक्ल प्रतिपदा.

योग and करण are NOT used for calendric purposes but only for Astrological purposes.

 

 ..................to be continued with the construction of calendars, dating and Era's

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References:-

1.  Bhartiya Jyotish Shastra-SB Dixit
2. The Indian Calendar-Robert Sewell and SB Dixit
3. Cowasjee Patells Chronology
4. The book of Eras- Gen A Cunningham
5. Calendar Reforms Committee Report 
6. Ancient Indian Astronomy -RN Iyengar
7. The Calendars of India- VK Mishra