Festivals and vrats

A tithi is the time the Moon takes to move 12° further from the Sun in longitude. Thirty tithis make a lunar month: fifteen in the bright half from new moon to full, and fifteen in the dark half back to new moon. Because the Moon's speed varies, a tithi lasts anywhere from about 19 to 26 hours and rarely lines up with a civil day. The tithi running at sunrise is the one written against that day in the panchang, though many observances use the tithi at another time, such as midnight or moonrise.

A paksha is a lunar fortnight of fifteen tithis. Shukla paksha, the bright half, runs from the new moon to the full moon as the Moon waxes; Krishna paksha, the dark half, runs from the full moon back to the new moon as it wanes. Tithi names repeat in each paksha, so a date is only complete when the paksha is stated, as in 'Shravana Krishna Ashtami'. Many observances belong to one paksha only: Vinayaka Chaturthi to Shukla, Sankashti to Krishna.

Indian lunar months are counted in two ways. In the amanta system, used in Maharashtra, Gujarat, the South and in this engine, a month runs from new moon to new moon and the bright half comes first. In the purnimanta system of North India, a month runs from full moon to full moon, so the dark half comes first and carries the name of the following amanta month. The two systems agree on every bright-half date and differ only in the name given to the dark half; Janmashtami is Shravana Krishna 8 in amanta and Bhadrapada Krishna 8 in purnimanta, on the same night.

Twelve lunar months fall about eleven days short of a solar year, so roughly every 32 months an extra month is inserted to keep festivals in their seasons. A lunar month that contains no sankranti (the Sun's entry into a new rasi) is declared adhika, 'extra', and takes the name of the month that follows with the prefix adhika; the regular month is then called nija or shuddha. Festivals are kept in the nija month, not the adhika one. Rarely, a month holds two sankrantis and is dropped as a kshaya masa.

In the panchang a day begins at local sunrise, not at midnight. The tithi, nakshatra, yoga and karana written against a date are the ones running at that sunrise, and the weekday itself changes at sunrise. This is why the same date can show different tithis in Delhi and Chennai when a tithi ends between their sunrises, and why a panchang must be computed for a place. Observances that depend on another moment, such as midnight for Janmashtami or moonrise for Karwa Chauth, say so explicitly; sunrise is the default.

Because a tithi can be shorter or longer than a day, the sunrise-to-sunrise rule produces two irregularities. A kshaya (lost) tithi begins after one sunrise and ends before the next, so it never touches a sunrise and is skipped in the day count; the calendar then jumps, for example, from the 6th to the 8th. A vriddhi (grown) tithi spans two sunrises and is written against two consecutive days. Neither is an error; they are the ordinary result of fitting roughly 29.5 tithis into 29 or 30 civil days, and festival rules say which of the two days to take.