Home Music Theory, Mathematics, and Patterns of Innovation in the Saṅgītaratnākara
Article
Licensed
Unlicensed Requires Authentication

Music Theory, Mathematics, and Patterns of Innovation in the Saṅgītaratnākara

  • Alessandra Petrocchi EMAIL logo
Published/Copyright: August 18, 2018
Become an author with De Gruyter Brill

Abstract

This paper investigates the relationship between textuality and mathematics in the Saṅgītaratnākara, a Sanskrit work on music composed in the thirteenth century by Śārṅgadeva. Within the traditional Sanskrit knowledge system on musicology, the Saṅgītaratnākara can be regarded as a seminal work, given the commentaries it has inspired and the innovative features it contains. I shall explore some textual aspects which, in Medieval India, have contributed to establish the authority of this text and whose significance can be traced in later works. Among these are types of verbalization and mathematical procedures whose role, I shall argue, is entirely theoretical. In the Saṅgītaratnākara, calculations and diagrams underline an innovative language of musical speculation, as well as the relationship between theory and practice and the shaping influence of other śāstric traditions. The set of conventions which are based on a vocabulary and methods shared with other technical literatures, particularly prosody and mathematics, attests the variety of literary practices introduced by Śārṅgadeva. I shall argue that this text builds up a code whose aim and function are not necessarily musicological in character. Although orality clearly retains its special status as the archetype of learning, Śārṅgadeva’s contribution manifests the autonomy of literature on saṅgīta as an “art” which constitutes an independent sphere of activity, defining its own rules, and adhering to its own criteria of value.

Bibliography

Primary sources

Dattilam: a compendium of ancient Indian music. 1970. Introduction, translation, and commentary by Emmie te Nijenhuis. Leiden: Brill.Search in Google Scholar

Nṛtyaratnakośa of Kumbha. 1957. Edited by R.C. Parīkha and P. Shah. Jayapura: Sancālaka, Rājasthāna Purātattvānveshaṇa Mandira.Search in Google Scholar

Saṅgītadarpaṇa of Dāmodara. 1989. Edited by Vasudeva Sastri, K. Tañjāpurī: Tañjāpurī Mahārājā Śarabhojī Sarasvatīmahāl Granthālaya Kāryakariṇi Samitiḥ.Search in Google Scholar

Saṅgītadāmodara of Śubhaṅkara. 1960. Edited by Gauninath Sastri and Govindagopal Mukhopadhyaya. Calcutta: Sanskrit College.Search in Google Scholar

Saṅgītakalpalatikā of Haladharamiśra. 1984. Edited by Nilamadhab Panigrahi. Bhūvaneśvara: Oḍiśā Saṅgīta Nāṭaka Ekāḍemī.Search in Google Scholar

Saṅgīta-ratnākara of Śārṅgadeva. 1978–1989. Sanskrit text and English translation with comments and notes. English translation by R.K. Shringy; under the supervision of P. Sharma. 2 Vols. Delhi: Motilal Banarsidass.Search in Google Scholar

Saṅgītaratnākara of Śārṅgadeva: with Kalānidhi of Kallinātha and Sudhākara of Siṁhabhūpāla. 1943–1953. Edited by S. Subrahmanya Sastri. In 4 vols. Madras: Adyar Library.Search in Google Scholar

Saṅgītasamayasāra of Pārśvadeva. 1925. Edited by T. Gaṇapatiśāstrī. Trivandrum: Printed by the Superintendent Government Press.Search in Google Scholar

Saṅgītaśiromaṇi: A Medieval Handbook of Indian Music. 1992. Edited with introduction and translation by Emmie te Nijenhuis. Leiden; New York: E.J. Brill.Search in Google Scholar

Saṅgītopaniṣat-saroddhāraḥ of Sudhākalaśa. 1998. Edited and translated by Allyn Miner. Delhi: Indira Gandhi National Centre for the Arts in association with Motilal Banarsidass Publishers.Search in Google Scholar

Saṅgītopaniṣat-sāroddhāra: A Work on Indian Music and Dancing. 1961. Edited by Umakant Premanand Shah. Baroda: Oriental Institute.Search in Google Scholar

Srīmataṅgamunipraṇītā Bṛhaddeśī of Śrī Mataṅga Muni. 2 Vols. 1992–1994. Edited and translated by P. Sharma. New Delhi: Indira Gandhi National Centre for the Arts in association with Motilal Banarsidass Publishers, Delhi.Search in Google Scholar

Secondary sources

Beck, Guy L. (1993): Sonic Theology: Hinduism and Sacred Sound. Columbia, SC: University of South Carolina Press.Search in Google Scholar

Benedetti, Giacomo / Tonietti, Tito M. (2009): “Sulle antiche teorie indiane della musica. Un problema a confronto con altre culture”. Rivista di Studi Asiatici 4: 75–108.Search in Google Scholar

Brown, Charles P. (1869): Sanskrit Prosody and Numerical Symbols Explained. London: Trübner & Co.Search in Google Scholar

Datta, B. (1935): “Mathematics of Nemicandra”. The Jaina Antiquary 1.2: 25–44.Search in Google Scholar

Datta, B. / Singh, A. N. (1992): “Use of Permutations and Combinations in India”. Revised by K. S. Shukla. Indian Journal of History of Science 27.3: 231–249.Search in Google Scholar

Filliozat, Pierre-Sylvain (2004): “Ancient Sanskrit Mathematics: An Oral Tradition and a Written Literature”. In: History of Science, History of Text. Edited by Karin Chemla, Robert S. Cohen, Jürgen Renn et al. Dordrecht: Springer Netherlands, 137–157.10.1007/1-4020-2321-9_7Search in Google Scholar

Jairazbhoy, Nazir Ali (1961): “Svaraprastāra in North Indian Classical Music”. Bulletin of the School of Oriental and African Studies 24.2: 307–32510.1017/S0041977X0009145XSearch in Google Scholar

Katz, Jonathan (1983): “Indian Musicological Literature and Its Context”. Puruṣārtha 7: 57–75.10.4000/books.editionsehess.48574Search in Google Scholar

Kitada, Makoto (2012): The Body of the Musician: An Annotated Translation and Study of the Piṇḍotpatti-prakaraṇa of Śārṅgadeva’s Saṅgītaratnakara. New York: Peter Lang.10.3726/978-3-0351-0417-2Search in Google Scholar

Kulkarni, Amba (2008): “Recursion and Combinatorial Mathematics in Chandashastra”. Available online at: http://arxiv.org/pdf/math/0703658 (07/11/2015).Search in Google Scholar

Kusuba, Takanori (1993): Combinatorics and magic squares in India. A study of Nārāyaṇa Paṇḍita’s Gaṇitakaumudī. Chapters 13–14. Ph.D. Diss., Brown University, Providence, RI.Search in Google Scholar

Kusuba, Takanori / Plofker, Kim (2013): “Indian Combinatorics”. In: Combinatorics: Ancient & Modern. Edited by Robin J. Wilson & John J. Watkins. Oxford: Oxford University Press, 41–64.10.1093/acprof:oso/9780199656592.003.0002Search in Google Scholar

Nijenhuis, Emmie te (1977): Musicological Literature. Wiesbaden: Harrassowitz.Search in Google Scholar

Orsini, Francesca / Schofield, Katherine B. (eds.) (2015): Tellings and Texts: Music, Literature and Performance in North India. Cambridge, UK: Open Book Publishers.10.11647/OBP.0062Search in Google Scholar

Patte, Françoise (2012): “Rhythmes et algorythmes: Le génie mathématique indien”. In: Astronomie and Mathematics in India. Edited by Jean-Michel Delire. Peters: Leuven, 158–173.Search in Google Scholar

Petrocchi, Alessandra (2016): “The Bhūtasaṃkhyā Notation: Numbers, Culture, and Language in Sanskrit Mathematical Literature”. In: On Meaning and Mantras: Essays in Honor of Frits Staal. Edited by George Thompson and Richard K. Payne. Berkeley: California, Institute of Buddhist Studies and BCK America, 367–392.Search in Google Scholar

Plofker, Kim (2009): Mathematics in India. Princeton, NJ; Oxford: Princeton University Press.Search in Google Scholar

Rowell, Lewis E. (1992): Music and Musical Thought in Early India. Chicago; London: University of Chicago Press.10.7208/chicago/9780226730349.001.0001Search in Google Scholar

Shah, J. (2013): “A History of Pingala’s Combinatorics”. Available online at: http://www.northeastern.edu/shah/publications.html (05/10/2015).Search in Google Scholar

Sharma, Prem Lata (1970–1971): “Brihaddeśī of Mataṅga”. Indian Music Journal 6.1970: 54–58; 7.1971: 56–66.Search in Google Scholar

Sharma, Prem Lata (ed.) (1998): Śārṅgadeva and His Saṅgīta-ratnākara: Proceedings of the Seminar, Varanasi, 1994. Delhi: Sangeet Natak Akademi.Search in Google Scholar

Sridharan, R. / Sridharan, R. / Srinivas, M. D. (2010): “Combinatorial methods in Indian music: Pratyayas in Saṅgītaratnākara of Sārṅgadeva”. In: Studies in the History of Indian Mathematics. Edited by C. S. Seshadri. New Delhi: Hindustan Book Agency, 55–112.10.1007/978-93-86279-49-1_5Search in Google Scholar

Truschke, Audrey (2016): Cultures of Encounters: Sanskrit at the Mughal Court. New York: Columbia University Press.10.7312/columbia/9780231173629.001.0001Search in Google Scholar

Widdess, Richard (1995): The Rāgas of Early Indian Music: Modes, Melodies and Musical Notations from the Gupta Period to c.1250. Oxford: Clarendon Press.Search in Google Scholar

Wilke, Annette / Moebus, Oliver (2011): Sound and Communication: An Aesthetic Cultural History of Sanskrit Hinduism. Berlin; New York: De Gruyter.10.1515/9783110240030Search in Google Scholar

Published Online: 2018-08-18
Published in Print: 2018-08-28

© 2018 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Aufsätze – Articles – Articles
  3. Les manuscrits du sud de la vallée de l’Indus en écriture khojkī sindhī: état des lieux et perspectives
  4. Hell as “Eternal” Punishment? On the Depiction of Hell in Vīlhojī’s Kathā Gyāncarī
  5. Entwicklungen in der Darstellung Buddhistischer Erzählstoffe in Sri Lanka
  6. Mack the Knife and Knife-Black Dorothy Appositional Metaphoric Compounds: A Comparison and Contrast of the Varying Approaches in Sanskrit Treatises on Grammar and Poetics
  7. Music Theory, Mathematics, and Patterns of Innovation in the Saṅgītaratnākara
  8. Considerations About Traditions Influential in the Ahirbudhnyasaṃhitā
  9. Meanings Out of Rules. Definitions, Functions and Uses of Paribhāṣās in Śrautasūtras, Gṛhyasūtras, Vyākaraṇa, Mīmāṃsā and Vedānta
  10. A General Overview
  11. The paribhāṣās in the Śrautasūtras: Problems, Opportunities and Premises for an Investigation
  12. Towards a Methodology for Applying the paribhāṣās in the Kauśikasūtra (II)
  13. From Commentary to paribhāṣās: Kātyāyana and Patañjali vis-à-vis Vyāḍi
  14. The Role of paribhāṣās in Mīmāṃsā: Rational Rules of Textual Exegesis
  15. … And What about the Vedānta Paribhāṣā’s paribhāṣātva? Some hypotheses on the use of paribhāṣās in later Advaita Vedānta
  16. Meanings Out of Rules: The Editor’s Overview
  17. Rezensionen – Comptes rendus – Reviews
  18. Some More Notes on Siderits and Katsura’s Translation of Nāgārjuna’s Mūlamadhyamakakārikā
  19. Rezension – Compte rendu – Review
  20. Otter, Felix: Grundkurs Sanskrit: Eine Einführung in die Sprache der altindischen Erzählliteratur
Downloaded on 27.10.2025 from https://www.degruyterbrill.com/document/doi/10.1515/asia-2016-0003/html
Scroll to top button