Kalpa — The Vedanga of Ritual

Shrauta Sutras: the great sacrifices

The Shrauta Sutras govern the solemn rituals based directly on shruti, the revealed Vedic texts. These are performed with three sacred fires — the garhapatya, ahavaniya and dakshinagni — and require several specialist priests: the hotri who recites Rigvedic verses, the adhvaryu who performs the actions with Yajurvedic formulas, the udgatri who sings Samavedic chants, and the brahman who supervises. The rituals range from the twice-daily agnihotra and the fortnightly new- and full-moon offerings (darsha-purnamasa) to the soma sacrifices such as the agnishtoma and the elaborate agnicayana, the building of a great brick fire altar. Several of these rituals are still performed by traditional families in Kerala, Andhra Pradesh, Karnataka and elsewhere. The timing of the new- and full-moon rites is one reason why Jyotisha developed alongside Kalpa.

Grihya Sutras: the household rites

The Grihya Sutras deal with rites performed by the householder at the domestic fire. Their best-known subject is the samskaras, the life-cycle ceremonies that sanctify a person from before birth to death: rites for conception and pregnancy, jatakarma at birth, namakarana (naming), annaprashana (first solid food), chudakarana (first tonsure), upanayana (initiation into Vedic study), vivaha (marriage) and antyeshti (funeral rites). The Grihya Sutras also describe daily and seasonal offerings, the reception of guests, house-building and ancestral rites (shraddha). Many features of a modern Hindu wedding — the sacred fire, the clasping of hands, the seven steps (saptapadi) — are described in these texts.

Dharma Sutras: conduct and law

The Dharma Sutras broaden Kalpa from ritual to the whole of life. The surviving works attributed to Apastamba, Gautama, Baudhayana and Vasishtha discuss the duties of students and householders, the stages of life, rules of purity and food, the duties of kings, inheritance, crime and penance. They are the forerunners of the later verse Dharmashastras such as the Manusmriti and the Yajnavalkya Smriti, and they are an important historical source for social life in ancient India.

Shulba Sutras: the geometry of the altar

Vedic altars had to be built in precise shapes — squares, circles, half-moons, even a falcon with outspread wings — and often with the same area as another altar of a different shape. The Shulba Sutras ("rules of the cord") explain how to lay them out with ropes and pegs. They are among the oldest mathematical texts of India. The Baudhayana Shulba Sutra states that the diagonal of a rectangle produces, by itself, the area produced separately by its two sides — the theorem now named after Pythagoras — and the texts use integer triples such as (3, 4, 5), (5, 12, 13) and (8, 15, 17). They give the approximation √2 ≈ 1 + 1/3 + 1/(3·4) − 1/(3·4·34) = 1.4142156…, correct to five decimal places, and methods for turning a square into a circle of approximately equal area and back. The principal Shulba Sutras are those of Baudhayana, Apastamba, Katyayana and Manava.

Kalpa in living practice

Kalpa is the Vedanga most visible in everyday Hindu life. Whenever a priest performs a wedding, an upanayana, a griha pravesha or an annual shraddha, the procedure ultimately goes back to a Grihya Sutra of his tradition, supplemented by later manuals (prayogas and paddhatis). The sankalpa recited at the start of such rites names the place and the exact moment — samvatsara, ayana, ritu, masa, paksha, tithi, vara and nakshatra — taken from the Panchangam. In this way Kalpa and Jyotisha still work together: Jyotisha supplies the time, Kalpa the procedure.

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