calendars used by Hindus on the Indian subcontinent
A page from the Hindu calendar 1871-72
Hindu calendar is a collective term for the various lunisolar calendars traditionally used in the Indian subcontinent. They adopt a similar underlying concept for timekeeping, but differ in their relative emphasis to moon cycle or the sun cycle and the names of months and when they consider the New Year to start. Of the various regional calendars, the most studied and known Hindu calendars are the Shalivahana Shaka found in South India, Vikram Samvat (Bikrami) found in North and Central regions of India, Tamil calendar used in Tamil Nadu, and the Bengali calendar used in the Bengal – all of which emphasize the lunar cycle. Their new year starts in spring. In contrast, in regions such as Kerala, the solar cycle is emphasized and this is called the Malayalam calendar, their new year starts in autumn, and these have origins in the second half of the 1st millennium CE. A Hindu calendar is sometimes referred to as Panchanga (पञ्चाङ्ग).
The ancient Hindu calendar conceptual design is also found in the Jewish calendar, but different from the Gregorian calendar. Unlike Gregorian calendar which adds additional days to lunar month to adjust for the mismatch between twelve lunar cycles (354 lunar days) and nearly 365 solar days, the Hindu calendar maintains the integrity of the lunar month, but insert an extra full month by complex rules, every few years, to ensure that the festivals and crop-related rituals fall in the appropriate season.
[The current year] minus one,
multiplied by twelve,
multiplied by two,
added to the elapsed [half months of current year],
increased by two for every sixty [in the sun],
is the quantity of half-months (syzygies).
— Rigveda Jyotisha-vedanga 4 Translator: Kim Plofker
Time keeping was important to Vedic rituals, and Jyotisha was the Vedic era field of tracking and predicting the movements of astronomical bodies in order to keep time, in order to fix the day and time of these rituals. This study was one of the six ancient Vedangas, or ancillary science connected with the Vedas – the scriptures of Hinduism. The ancient Indian culture developed a sophisticated time keeping methodology and calendars for Vedic rituals.
David Pingree has proposed that the field of timekeeping in Jyotisha may have been "derived from Mesopotamia during the Achaemenid period", but Yukio Ohashi considers this proposal as "definitely wrong". Ohashi states that this Vedanga field developed from actual astronomical studies in ancient India. The texts of Vedic Jyotisha sciences were translated into the Chinese language in the 2nd and 3rd centuries CE, and the Rigvedic passages on astronomy are found in the works of Zhu Jiangyan and Zhi Qian.
Timekeeping as well as the nature of solar and moon movements are mentioned in Vedic texts. For example, Kaushitaki Brahmana chapter 19.3 mentions the shift in the relative location of the sun towards north for 6 months, and south for 6 months.