Agni Purāṇa
333 - Description of metres having equal characteristics in the alternate quarters
This chapter corresponds to Pingala ch. V, sutras 32-45.
Agni said:
1. The metre Upachitraka (consists of) three sas, la, and two gas (in the first quarter), three bhas and two gas (in the second) (and the third and the fourth like the first and second). Drutamadhya is said to have three bhas and two gas (in the first quarter), na, two jas and ya (in the second quarter) (and the third and fourth like the first and second quarters).
2. Vegavati has three sas and ga (in the first quarter), three bhas and two gas (in the second). Bhadravirāț has ta, jas, ra and gas (in the first quarter), and ma, sa, ja and two gas (in the second quarter).
3. (When the first quarter) has sa, ja, sa and ga and (the second quarter) has bha, ra, na and two gas it is Ketumati. Akhyāniki has two tas, ja and two gas (in the first quarter) and ja, ta, ja and two gas (in the second quarter).
4. Viparītākhyāniki has ja, ta, ja and two gas (in the first quarter) and ta, ta, ja and two gas (in the second quarter). Hariņapluta2 has three sas, la and ga (in the first quarter), na, bha, bha and ra (in the second quarter).
2. The Purâna wrongly gives Harimavallabha.
5-6. Aparavaktra3 consists of two nas, ra, la and ga (in the first quarter) and na, ja, ja and ra (in the second quarter). (Puspitägrå1 has two nas, ra and ya (in the first quarter) and na, ja, ja, ra and ga (in the second quarter). Yavamati2 has ra, ja, ra and ga (in the first quarter) and ja, ra, ja and ra (in the second quarter). Sikhả consists of twentyeight (short letters) and a long syllable at the end (in the first quarter) and thirty letters and a long syllable at the end in the second quarter. (The third and fourth quarters are also similar.) (The metre) Khañja has got the characteristics reversed. Metres of similar characteristics (in the four quarters) are described now.
3. The Purāṇa reads Aparikramam.
1. The Puråna reads Puspitā.
2. The Purāṇa reads Panamati.
Summary of chapter 335 of the Agni Purāṇa is as follows:
The combinatorial science of metres (chandas) is elaborated through the prastāra method — the systematic expansion of all possible metrical variants. Agni explains the Meru-prastāra, which arranges the variants of an n-syllable pāda in a triangular grid corresponding to the mathematical structure of Pascal's triangle, revealing the deep connection between Sanskrit prosody and number theory. The formulae for calculating the total number of variants (saṃkhyā), the position of a given variant (naṣṭa), and the variant at a given position (udddiṣṭa) are set out. This teaching establishes chandas as both an aesthetic science and a form of sacred mathematics rooted in the structure of language itself.
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