Combinatorial Methods in Indian Music: Pratyayas in Saṅgītaratnākara of Sārṅgadeva

Six combinatorial tools (called pratyayas) have been in systematic use in India for the study of Sanskrit prosody (Chandas-śāstra) and these go back in time at least to Pingala (c. 300 BC?). Among these, three—prastāra (an enumeration rule for generating all the possible metrical patterns of a given class as a sequence of rows), uddiṣṭa (the process for finding, for any given metrical pattern, the corresponding row number in the prastāra) and naṣṭa (the converse of uddiṣṭa)—are found in Bharata’s Nāṭyaśāstra, in the chapter where prosody is discussed. Incidentally, the problem of placing Piṅgala and Bharata in the chronology of time still remains an unsettled question. The notion of pratyayas was perhaps discussed in other ancient texts of music also. However, the first extant text on music where the pratyayas are systematically dealt with, both in connection with patterns of musical phrases (tānas) and patterns of musical rhythms (tālas), is Saṅgītaratnākara of Śārṅgadeva (c.1225 AD). Nārāyaṇa Paṇḍita in his Gaṇitakaumudī (1356 AD) deals with some of these questions in a more general context, though his theory does not cover the kind of tāla-prastāra considered by Śārṅgadeva.