Chandas — Vedic Metre

The three most important Rigvedic metres are Trishtubh, Gayatri and Jagati; together they account for the large majority of its verses. The Brahmanas link Gayatri with Agni and the morning soma pressing, Trishtubh with Indra and the midday pressing, and Jagati with the Vishvedevas and the evening pressing. Actual verses often have a syllable more or fewer than the ideal count, and the tradition has terms for such variations (nichrit for one short, bhurij for one extra). Longer metres beyond Jagati, such as Atijagati and Shakvari, also occur.

The Anushtubh deserves special mention. Its four lines of eight syllables evolved into the shloka, the verse form of the Ramayana, the Mahabharata, the Bhagavad Gita, the Puranas and most of classical Sanskrit literature. Tradition credits Valmiki with the first shloka, spoken in grief on seeing a hunter kill one of a pair of birds.

Pingala and the Chandahshastra

The foundational work of the discipline is the Chandahshastra (also called the Chandas Sutra) of Pingala, a sutra text in eight chapters that covers both Vedic and later metres. Its date is uncertain; it is commonly placed in the last centuries BCE. Pingala introduced a compact notation that is still used: the symbols la and ga for single light and heavy syllables, and eight ganas, each naming one of the eight possible groups of three syllables (L = laghu, G = guru):

With eight ganas plus la and ga, any classical metre can be described in a few letters. Students remember the system with the mnemonic ya-mā-tā-rā-ja-bhā-na-sa-la-gāḥ, in which each gana's syllable pattern can be read off from the syllable that names it and the two that follow.

Mathematics in Chandas

Binary patterns

Because every syllable is either light or heavy, a line of n syllables has 2ⁿ possible patterns. Pingala gives procedures — prastara (listing all patterns in order), nashta (recovering the pattern at a given position), uddishta (finding the position of a given pattern) and sankhya (counting the patterns) — that are equivalent to working with binary numbers, with light and heavy syllables playing the role of the two digits. His rule for computing 2ⁿ uses repeated halving and squaring, the same idea as the modern fast-exponentiation method. Pingala did not, of course, write numbers in base 2, but the structure of his procedures is binary.

Meru Prastara

A further question is how many patterns of n syllables contain exactly k heavy syllables. Pingala's text contains a brief rule on this, and the tenth-century commentator Halayudha explains it with a triangular figure called the Meru Prastara ("arrangement like Mount Meru"). Each number is the sum of the two above it — the array known in Europe since the seventeenth century as Pascal's triangle:

For example, the row 1 4 6 4 1 shows that among the 16 possible four-syllable patterns, one has no heavy syllable, four have one, six have two, four have three and one has four.

Counting by matras

Later prosodists working on metres measured by matras (where a light syllable counts 1 and a heavy one 2) asked how many patterns add up to a given total. The answer is the sequence 1, 2, 3, 5, 8, 13, 21…, in which each term is the sum of the two before. It was described by Virahanka (between the sixth and eighth centuries), and later by Gopala and Hemachandra in the twelfth century — before Leonardo of Pisa (Fibonacci) published it in Europe in 1202.

Why Chandas matters

Chandas gave the Vedic tradition a check on the integrity of its texts, a framework for musical recitation, and a vocabulary for describing poetry that shaped all of classical Sanskrit literature and the prosody of many Indian languages. It also shows how the careful study of a sacred text could lead to genuinely new mathematics. Chandas is closely linked to Shiksha, which defines syllable length, and to the musical chanting of the Samaveda.

Frequently asked questions