{"title":"The saṃyoga-meru: A combinatorial tool in the Saṅgīta-ratnākara","authors":"G Sreeram, Aditya Kolachana","doi":"10.1016/j.hm.2024.02.003","DOIUrl":null,"url":null,"abstract":"<div><p>The <em>Saṅgīta-ratnākara</em> (Ocean of Music) of Śārṅgadeva (c. 1225 CE) is a 13th century text on musicology in Sanskrit. The fifth chapter of the <em>Saṅgīta-ratnākara</em> deals with a general analysis of all possible rhythms (<em>tāla</em>s) which can be obtained by combining a set of basic rhythmic components known as <em>tālāṅga</em>s. Here, Śārṅgadeva describes the construction of the <em>saṃyoga-meru</em> (Table of Combinations), a tool that tabulates the total number of possible <em>tāla</em>s of a given duration which are obtained by combining elements of different subsets of <em>tālāṅga</em>s. In this paper, we discuss the mathematical rationale employed by Śārṅgadeva in the construction of the <em>saṃyoga-meru</em>.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0315086024000053/pdfft?md5=1e9ed71e46f5239130c59d4c493d2de7&pid=1-s2.0-S0315086024000053-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Historia Mathematica","FirstCategoryId":"98","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0315086024000053","RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"HISTORY & PHILOSOPHY OF SCIENCE","Score":null,"Total":0}
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Abstract
The Saṅgīta-ratnākara (Ocean of Music) of Śārṅgadeva (c. 1225 CE) is a 13th century text on musicology in Sanskrit. The fifth chapter of the Saṅgīta-ratnākara deals with a general analysis of all possible rhythms (tālas) which can be obtained by combining a set of basic rhythmic components known as tālāṅgas. Here, Śārṅgadeva describes the construction of the saṃyoga-meru (Table of Combinations), a tool that tabulates the total number of possible tālas of a given duration which are obtained by combining elements of different subsets of tālāṅgas. In this paper, we discuss the mathematical rationale employed by Śārṅgadeva in the construction of the saṃyoga-meru.
期刊介绍：
Historia Mathematica publishes historical scholarship on mathematics and its development in all cultures and time periods. In particular, the journal encourages informed studies on mathematicians and their work in historical context, on the histories of institutions and organizations supportive of the mathematical endeavor, on historiographical topics in the history of mathematics, and on the interrelations between mathematical ideas, science, and the broader culture.
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