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Mostly, these are inherited from a system first enunciated in ''Jyotish Vedanga'' (one of the six adjuncts to the Vedas , 12th to 14th century BC), standardized in the '' Surya Siddhanta '' (3rd century) and subsequently reformed by astronomers such as Aryabhata (499), Varahamihira (6th century) Bhaskara (12th century), and Fatehullah Shirazi (16th century). There are differences and regional variations abound in these computations, but the following is a general overview. Yes Day The Hindu calendrical day starts with local sunrise. It is allotted five "properties", called ''anga''-s. They are: # the ''tithi'' active at sunrise # the ''vaasara'' or weekday # the ''nakshatra'' in which the moon resides at sunrise # the ''yoga'' active at sunrise # the ''karana'' active at sunrise. Together these are called the ''panchānga''-s where ''pancha'' means "five" in Sanskrit . An explanation of the terms follows. Tithi The (anticlockwise) angular distance between the sun and moon as measured from the earth along the Ecliptic (circle on the sky in which the sun, moon and planets seem to move) can vary between 0° and 360°. This is divided into 30 parts. Each part ''ends'' at 12°, 24° etc. The time spent by the moon in each of these parts (i.e. the time taken for the angular distance to increase in steps of 12° starting from 0°) is called one ''tithi''. The month has two ''paksha''-s or fortnights. The first 15 ''tithi''-s constitute the bright fortnight or ''shukla paksha'' and the next 15 ''tithi''-s constitute the dark fortnight or ''krishna paksha''. ''tithi''-s are indicated by their ''paksha'' and ordinal number within the ''paksha''. The 15th ''tithi'' of the bright fortnight (full moon) is called ''pūrnimā'' and the 15th ''tithi'' of the dark fortnight (new moon) is called ''amāvāsyā''. The ''tithi'' in which the moon is at the time of sunrise of a day is taken to be the ''tithi'' for the day. Vaasara The weekdays are as usual seven. They are (starting from Sunday): # Indu vāsara # Soma vāsara # Mangala vāsara # Budha vāsara # Guru vāsara # Shukra vāsara # Shani vāsara There are many other variations of these names, using other names of the celestial bodies of the Sun, Moon, Mars, Mercury, Jupiter, Venus and Saturn. The word ''vāsara'' means "weekday". In common language, the word 'vaasara' is replaced by 'vaara', so Friday is 'Shukravaara' etc. Nakshatra The ecliptic is divided into 27 Nakshatra s, which are variously called lunar houses or Asterisms . These reflect the moon's cycle against the fixed stars, 27 days and 7¾ hours. Nakshatra computation appears to have been well known at the time of the Rig Veda (2nd–1st millennium BC). The starting point for this division is the point on the ecliptic directly opposite to the star Spica called ''Chitrā'' in Sanskrit. (Other slightly-different definitions exist.) It is called ''Meshādi'' or the "start of Aries ". The ecliptic is divided into the ''nakshatra''s eastwards starting from this point. The ''nakshatra''-s with their corresponding regions of sky are given below, following {Link without Title} 's Appendix: Astronomy. As always, there are many versions with minor differences. The names on the right-hand column give roughly the correspondence of the ''nakshatra''-s to modern names of stars. Note that ''nakshatra''-s are (in this context) not just single stars but are segments on the ecliptic characterised by one or more stars. Hence you will find many stars mentioned for one ''nakshatra''. An additional 28th intercalary nakshatra, Abhijit (alpha, epsilon and zeta Lyrae - Vega - between Uttarasharha and Sravana), is required to compensate for the sidereal month being eight hours more than 27 days. Unlike the 13°20' range of the 27 proper nakshatras, Abhijit spans 4°14' to reflect the extra span of 7¾ hours. The ''nakshatra'' in which the moon lies at the time of sunrise of a day is the ''nakshatra'' for the day. Yoga First, the angular distance along the ecliptic of any object on the sky, measured from ''Meshādi'' (as defined above) is called the longitude of that object. When the longitude of the sun and the longitude of the moon are added, they produce a value ranging from 0° to 360°. (Values greater than or equal to 360° must be reduced to less than 360° by subtracting 360°.) This is divided into 27 parts. Each part will now equal 800' (where ' is the symbol of the Arcminute which means 1/60 of a degree.) These parts are called the ''yoga''-s. They are labeled: # Vishkambha # Prīti # Āyushmān # Saubhāgya # Shobhana # Atiganda # Sukarman # Dhriti # Shūla # Ganda # Vriddhi # Dhruva # Vyāghāta # Harshana # Vajra # Siddhi # Vyatīpāta # Varigha # Parigha # Shiva # Siddha # Sādhya # Shubha # Shukla # Brāhma # Māhendra # Vaidhriti Again, minor variations may exist. The ''yoga'' that is active during sunrise of a day is the ''yoga'' for the day. Karana A ''karana'' is half of a Tithi . To be precise, a ''karana'' is the time required for the angular distance between the sun and the moon to increase in steps of 6° starting from 0°. (Compare with the definition of a tithi above.) Since the ''tithi''-s are thirty in number, one would expect there to be sixty ''karana''-s. But there are only eleven. There are four "fixed" ''karana''-s and seven "repeating" ''karana''-s. The four "fixed" ''karana''-s are: # Kimstughna # Shakuni # Chatushpād # Nāgava The seven "repeating" ''karana''-s are: # Bava # Bālava # Kaulava # Taitula # Garajā # Vanijā # Vishti (Bhadrā)
The ''karana'' active during sunrise of a day is the ''karana'' for the day. Month and year of the solar calendar Now that the days are defined, we shall speak of how the solar calendar reckons its months and year. As has been previously noted, the sun is observed to travel along the ecliptic. The ecliptic is now divided into twelve parts called ''rāshi''-s, starting from the point of ''Meshādi'' defined above and moving eastwards. The names of the rāshis correspond to those in the West, and may indicate a common Sumerian origin. Greek astronomical interchange, as in the ''Romaka Siddhanta'', also led to a degree of homogenization. This table lists the rāshis along with their zodiac equivalents: The day on which the sun transits into each ''rāshi'' before sunset is taken to be the first day of the month. In case the sun transits into a ''rāshi'' after a sunset but before the next sunrise, then the next day is the first day of the month. (Minor variations on this definition exist.) The days are then labeled 1, 2, 3…. till the first day of the next month. Thus we get twelve months with varying lengths of 29 to 32 days. This variation in length occurs because the earth's orbit around the sun is an ellipse, but also because of some variability in the transit point falling before or after sunrise. The months are named by the ''rāshi'' in which the sun travels in that month. The new year day is the first day of the month of ''Mesha''. Currently, it occurs around April 15 on the Gregorian Calendar . This is the structure of the Hindu solar calendar. Months of the lunisolar calendar When a new moon occurs before sunrise on a day, that day is said to be the first day of the lunar month. So it is evident that the end of the lunar month will coincide with a new moon. A lunar month has 29 or 30 days (according to the movement of the moon). The ''tithi'' at sunrise of a day is the only label of the day. There is no running day number from the first day to the last day of the month. This has some unique results, as explained below: Sometimes two successive days have the same ''tithi''. In such a case, the latter is called an ''adhika tithi'' where ''adhika'' means "extra". Sometimes, one ''tithi'' may never touch a sunrise, and hence no day will be labeled by that ''tithi''. It is then said to be a ''tithi kshaya'' where ''kshaya'' means "loss". Naming lunar months There are twelve lunar month names: # Chaitra # Vaishākha # Jyaishtha # Āshādha # Shrāvana # Bhādrapada # Āshwina # Kārtika # Mārgashīrsha # Pausha # Māgha # Phālguna Determining which name a lunar month takes is somewhat indirect. It is based on the ''rāshi'' into which the sun transits within a lunar month, i.e. before the new moon ending the month. There are twelve ''rāshi'' names, there are twelve lunar month names. When the sun transits into the ''Mesha rāshi'' in a lunar month, then the name of the lunar month is ''Chaitra''. When the sun transits into ''Vrishabha'', then the lunar month is ''Vaishākha''. So on. The Sanskrit grammatical derivation of the lunar month names ''Chaitra'' etc is: the (lunar) month which has its central full moon occurring at or near the ''nakshatra Chitrā'' is called ''Chaitra''. Similarly, for the ''nakshatra''-s ''Vishākhā'', ''Jyeshthā'', ''(Pūrva) Ashādhā'', ''Shravana'', ''Bhādrapada'', ''Ashvinī'' (old name ''Ashvayuj''), ''Krittikā'', ''Mrigashīrsha'', ''Pushya'', ''Maghā'' and ''(Pūrva/Uttara) Phalgunī'' the names ''Vaishākha'' etc are derived. The lunar months are split into two pakshas of 15 days. The waxing paksha is called shuklapaksha, ''light half'', and the waning paksha the krishnapaksha, ''dark half''. There are two different systems for making the lunar calendar:
Extra months When the sun does not at all transit into any ''rāshi'' but simply keeps moving within a ''rāshi'' in a lunar month (i.e. before a new moon), then that lunar month will be named according to the first upcoming transit. It will also take the epithet of ''adhika'' or "extra". For example, if a lunar month elapsed without a solar transit and the next transit is into ''Mesha'', then this month without transit is labeled ''adhika Chaitra''. The next month will be labeled according to its transit as usual and will get the epithet ''nija'' ("original") or ''shuddha'' ("clean"). that an ''adhika māsa'' (month) is the first of two whereas an ''adhika tithi'' is the second of two. An ''adhika māsa'' occurs once every two or three years (meaning, with a gap of one or two years without ''adhika māsa''-s). Lost months If the sun transits into two ''rāshi''-s within a lunar month, then the month will have to be labeled by both transits and will take the epithet ''kshaya'' or "loss". There is considered to be a "loss" because: if the sun had transited into only one ''raashi'' in a lunar month as is usual, there would have been two separate months labeled by the two transits in question; but now there is only one month labeled by both transits! For example, if the sun transits into ''Mesha'' and ''Vrishabha'' in a lunar month, then it will be called ''Chaitra-Vaishaakha kshaya''. There will be no separate months labeled ''Chaitra'' and ''Vaishākha''. A ''kshaya māsa'' occurs very rarely. Known gaps between occurrence of ''kshaya māsa''-s are 19 and 141 years. The last was in 1983. Jan-15 through Feb-12 were ''Pausha-Māgha kshaya''. Feb-13 onwards was ''(adhika) Phālguna''. Special Case: If there is no solar transit in one lunar month but there are two transits in the next lunar month,
This is a very very rare occurrence. The last was in 1315. Oct-08 to Nov-05 were ''adhika Kārtika''. Nov-06 to Dec-05 were ''Kārtika-Māgashīrsha kshaya''. Dec-06 onwards was ''Pausha''. Religious observances in case of extra and lost months Among normal months, ''adhika'' months, and ''kshaya'' months, the earlier are considered "better" for religious purposes. That means, if a festival should fall on the 10th ''tithi'' of the ''Āshvayuja'' month (this is called Vijayadashamī ) and there are two ''Āshvayuja'' months caused by the existence of an ''adhika Āshvayuja'', the first ''adhika'' month will not see the festival, and the festival will be observed only in the second ''nija'' month. However, if the second month is ''āshvayuja kshaya'' then the festival will be observed in the first ''adhika'' month itself. When two months are rolled into one in the case of a ''kshaya māsa'', the festivals of both months will also be rolled into this ''kshaya māsa''. For example, the festival of Mahāshivarātri which is to be observed on the fourteenth ''tithi'' of the ''Māgha krishna paksha'' was, in 1983, observed on the corresponding ''tithi'' of ''Pausha-Māgha kshaya krishna paksha'', since in that year, ''Pausha'' and ''Māgha'' were rolled into one, as we mentioned above. Year of the lunisolar calendar The new year day is the first day of the ''shukla paksha'' of ''Chaitra''. In the case of ''adhika'' or ''kshaya'' months relating to ''Chaitra'', the aforementioned religious rules apply giving rise to the following results:
Another kind of lunisolar calendar There is another kind of lunisolar calendar which differs from the former in the way the months are named. This section describes the differences involved, and may be skipped if the article is already too complicated for the reader. It is only included for completeness. When a full moon (instead of new moon) occurs before sunrise on a day, that day is said to be the first day of the lunar month. In this case, the end of the lunar month will coincide with a full moon. This is called the ''pūrnimānta māna'' or "full-moon-ending reckoning", as against the ''amānta māna'' or "new-moon-ending reckoning" used before. This definition leads to a lot of complications:
It must be noted, however, that none of these above complications cause a change in the day of religious observances. Since only the name of the ''krishna paksha''-s of the months will change in the two systems, festivals which fall on the ''krishna paksha'' will be defined by the appropriate changed name. That is, the Mahāshivarātri , defined in the ''amānta māna'' to be observed on the fourteenth of the ''Māgha krishna paksha'' will now (in the ''pūrnimānta māna'') be defined by the ''Phālguna krishna paksha''. Correspondence of the lunisolar calendar to the solar calendar A Lunisolar Calendar is always a calendar based on the moon's celestial motion, which in a way keeps itself close to a Solar Calendar based on the sun's (apparent) celestial motion. That is, the lunisolar calendar's new year is to kept always close (within certain limits) to a solar calendar's new year. Since the Hindu lunar month names are based on solar transits, and the month of ''Chaitra'' will, as defined above, always be close to the solar month of ''Mesha'', the Hindu lunisolar calendar will always keep in track with the Hindu solar calendar. Year numbering The epoch (starting point or first day of the first year) of the current era of Hindu calendar (both solar and lunisolar) is BCE 3102 January 23 on the Proleptic Gregorian Calendar (i.e. the Gregorian Calendar extended back in time before its promulgation from 1582 October 15 ). Both the solar and lunisolar calendars started on this date. After that, each year is labeled by the number of years elapsed since the epoch. This is a unique feature of the Hindu calendar. All other systems use the current ordinal number of the year as the year label. But just as a person's true age is measured by the number of years that have elapsed starting from the date of the person's birth, the Hindu calendar measures the number of years elapsed. As Of May 18, 2005 , 5106 years have elapsed in the Hindu calendar, so this is the 5107th Hindu calendar year. Note that the lunisolar calendar year will usually start earlier than the solar calendar year. Other systems of numbering the Hindu years can be read about at the Samvat article. Year names Apart from the numbering system outlined above, there is also a cycle of 60 calendar year names, which started at the first year (at elapsed years zero) and runs continuously: # Prabhava # Vibhava # Shukla # Pramoda # Prajāpati # Āngirasa # Shrīmukha # Bhāva # Yuvan # Dhātri # Īshvara # Bahudhānya # Pramāthin # Vikrama # Vrisha # Chitrabhānu # Svabhānu # Tārana # Pārthiva # Vyaya (the current Hindu year 2006-2007 CE carries this name) # Sarvajit # Sarvadhārin # Virodhin # Vikrita # Khara # Nandana # Vijaya # Jaya # Manmatha # Durmukha # Hemalambin # Vilambin # Vikārin # Shārvari # Plava # Shubhakrit # Shobhana # Krodhin # Vishvāvasu # Parābhava # Plavanga # Kīlaka # Saumya # Sādhārana # Virodhikrit # Paritāpin # Pramādin # Ānanda # Rākshasa # Anala # Pingala # Kālayukti # Siddhārthin # Raudra # Durmati # Dundubhi # Rudhirodgārin # Raktāksha # Krodhana # Kshaya Eras Hindu mythology speaks of four eras or ages, of which we are currently in the last. The four are: # Krita Yuga or Satya Yuga # Tretā Yuga # Dvāpara Yuga # Kali Yuga They are often translated into English as the golden, silver, bronze and iron ages. ( Yuga means era or age.) It is believed that the ages see a gradual decline of Dharma , wisdom, knowledge, intellectual capability, life span and emotional and physical strength. The epoch provided above is the start of the ''Kali Yuga''. The ''Kali Yuga'' is 432,000 years long. The ''Dvāpara'', ''Tretā'' and ''Krita (Satya) Yuga''-s are said to be twice, thrice and four time the length of the ''Kali Yuga'' respectively. Thus they together constitute 4,320,000 years. This is called a ''Chaturyuga''. An interesting comparison can be made to Hesiod 's Ages Of Man Gold, Silver, Bronze, Heroes, and Iron from Greek Mythology . A thousand and a thousand (i.e. two thousand) ''chaturyuga''-s are said to be one day and night of the creator Brahmā . He (the creator) lives for 100 years of 360 such days and at the end, he is said to dissolve, along with his entire Creation, into the Eternal Soul or '' Paramātman ''. A different view of the timespan of a yuga is given by Swami Sri Yukteswar Giri , the Guru of Paramahansa Yogananda . This is detailed in his book, The Holy Science . According to this view, the chaturyuga spans a much lower timespan, on the order of thousands of years, and moves cyclically. According to calculations given in the book, the most recent yuga change was in 1800, when the Earth passed from Kali Yuga to Dvāpara Yuga. We are in an ascending spiral right now, and will pass into the Tretā Yuga in a few centuries. According to the book, the quality of human intellect depends on the distance of the Sun from the galactic core and other powerful stars. In the book, the core of the galaxy is called ''Vishnunābhi'', or the navel of Vishnu . The closer the Sun is to it, the more energy the Solar System receives, and the greater is the level of human spiritual and overall development. History The Hindu Calendar descends from the Vedic times. There are many references to calendrics in the Veda s. The Vedānga (adjunct to Veda) called Jyautisha (literally, "celestial body study") prescribed all the aspects of the Hindu calendars. After the Vedic period, there were many scholars such as Āryabhata (5th century), Varāhamihira (6th century) and Bhāskara (12th century) who were experts in Jyautisha and contributed to the development of the Hindu Calendar. The most widely used authoritative text for the Hindu Calendars in the ''Sūrya Siddhānta'', a text of uncertain age, though some place it at 10th century. The traditional Vedic calendar used to start with the month of agrahayan (agra=first + ayan = travel of the sun, equinox) or Mārgashirshe. This is the month where the Sun crosses the equator, i.e. the Vernal Equinox . This month was called mārgashirshe after the fifth nakshatra (around lambda orionis). Due to the Precession of the earth's axis, the vernal equinox is now in Pisces, and corresponds to the month of chaitra. This shift over the years is what has led to various calendar reforms in different regions to assert different months as the start month for the year. Thus, some calendars (e.g. Vikram) start with Chaitra, which is the present-day month of the vernal equinox, as the first month. Others may start with Vaisakha (e.g. Bangabda ). The shift in the vernal equinox by nearly four months from agrahaayana to chaitra in sidereal terms seems to indicate that the original naming conventions may date to the fourth or fifth millennium BC, since the period of precession in the earth's axis is about 25,800 years. Regional variants The Indian Calendar Reform Committee, appointed in 1952 (shortly after Indian independence), identified more than thirty well-developed calendars, all variants of the ''Surya Siddhanta'' calendar outlined here, in systematic use across different parts of India. These include the widespread ''Vikrama'' and ''Shalivahana'' calenders and regional variations thereof. An entirely different solar calender is used in Tamil Nadu and Kerala . Vikrama and Shalivahana calenders The two calendars most widely used in India today are the ''Vikrama'' calendar followed in North India and the Shalivahana or ''Saka'' calender which is followed in South India and Maharashtra . Both the ''Vikrama'' and the ''Shalivahana'' eras are lunisolar calenders, and feature annual cycles of twelve lunar months, each month divided into two phases: the 'bright half' (''shukla'') and the 'dark half' (''bahula''); these corrospond respectively to the periods of the 'waxing' and the 'waning' of the moon. Thus, the period beginning from the first day after the New Moon and ending on the Full Moon day constitutes the ''shukla paksha'' or 'bright half' of the month; the period beginning from the day after the full moon until and including the next new moon day constitutes the ''bahula paksha'' or 'dark half' of the month. The names of the 12 months, as also their sequence, are the same in both calenders; however, the new year is celebrated at separate points during the year and the "year zero" for the two calenders is different. In the Vikrama calender, the zero year corrosponds to 56 BC, while in the Shalivahana calender, it corrosponds to 78 AD. The Vikrama calender begins with the month of ''Kartika'' (Oct/Nov) and the Deepavali festival marks the new year. The Shalivahana calender begins with the month of ''Chaitra'' (March/April) and the Ugadi / Gudi Padwa festivals mark the new year. Another little-known difference between the two calenders exists: while each month in the ''Vikrama'' calender begins with the 'dark half' and is followed by the 'bright half', the opposite obtains in the ''Shalivahana'' calender. Thus, each month of the ''Vikrama'' calender ends with the full moon and the new month begins on the day after that, while the no-moon day brings each month of the ''Shalivahana'' calender to a close. National calenders in south Asia A variant of the ''Shalivahana'' Calendar was reformed and standardized as the Indian National calendar in 1957. This official calender follows the ''Shalivahana'' calender in beginning from the month of '' Chaitra '' and counting years with 78 AD being Year Zero . It features a constant number of days in every month (with leap years). The Bengal Calendar, Bangabda (introduced 1584), is widely used in eastern India. A reformation of this calendar was introduced in present-day Bangladesh in 1966, with constant days in each month and a leap year system; this serves as the national calendar for Bangladesh . Nepal follows the Vikram calendar. The same month names and roughly the same periods apply to a number of Buddhist calendars in Sri Lanka , Tibet and other areas. Corrospondence between calenders As an indicator of this variation, 'Whitaker Almanac' reports that the the Gregorian year 2000 AD corresponds, respectively with: #Year 6001 in the Kaliyuga calendar; #Year 2544 in the Buddha Nirvana calendar; #Year 2057 in the Vikram Samvat calendar; #Year 1922 in the Saka calendar; #Year 1921 (shown in terms of 5-yearly cycles) of the Vedanga Jyotisa calendar; #Year 1407 in the Bengali San calendar; #Year 1176 in the Kollam calendar. Further reading
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