The saṃyoga-meru: A combinatorial tool in the Saṅgīta-ratnākara

IF 0.5 3区哲学 Q3 HISTORY & PHILOSOPHY OF SCIENCE

Historia Mathematica Pub Date : 2024-03-01 DOI:10.1016/j.hm.2024.02.003

G Sreeram, Aditya Kolachana

引用次数: 0

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.

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萨迦瑜伽髓：萨迦摩尼宝典》中的组合工具

Śārṅgīta-ratnākara（《音乐的海洋》）（约公元 1225 年）是 13 世纪的一部梵文音乐学著作。Saṅgīta-ratnākara 的第五章对所有可能的节奏（tālas）进行了总体分析，这些节奏可以通过组合一组称为 tālāṅgas 的基本节奏成分而获得。在这里，Śārṅgadeva 描述了 "组合表"（saṃyoga-meru）的构造，这是一种工具，可将特定持续时间内通过组合不同 tālāṅgas 子集的元素而获得的可能 tālas 总数列表。在本文中，我们将讨论圣十字加德瓦在构建 "saṃyoga-meru "时所采用的数学原理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Historia Mathematica 数学-科学史与科学哲学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

72 days

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.