Vedic Science International Multidisciplinary Peer-reviewed Journal 

Article  Information

Journal: Vedic Science
Volume: 2026 | Issue: 1 | Year: 2026
Pages: 39–47
DOI:  10.66718/0975-0312.vol.2026.issue1.4    
Received: 15 Feb. 2026
Accepted: 20 March, 2025
Published: 20 April, 2025

Chandas: The Magic and Mastery of Music and Mathematics

Sindhu Bhogal (Dharma Prabhakar), Veda Niketan & School of Vedic Studies, Arya Samaj South Africa, 87 Harbottle Rd, Sydenham, Durban, 4091, South Africa

Abstract

Pingala's Chandas Shastra has long been recognised as the foundational text of prosody. This study posits that beneath its taxonomic surface lies a profound achievement: the formal codification of a complete algorithmic system for combinatorial analysis, encoding five foundational concepts of discrete mathematics.

Through a rigorous analysis of the six Pratyayas (cognate rules) of the eighth chapter, the paper demonstrates that: (1) Naṣṭa and Uddiṣṭa provide complete algorithms for decimal-binary and binary-decimal conversion, establishing a fully realised binary numeral system with weighted positional values; (2) Ekadvyādi-laga-kriyā, implemented through the Varnic Meru, yields the binomial coefficients in a triangular array identical to Pascal's Triangle; (3) the extension to mātric metres generates the Fibonacci sequence through the recurrence Fₘ = Fₘ₋₁ + Fₘ₋₂; (4) Saṅkhyāna computes 2ⁿ in O(log n) steps via exponentiation by squaring, anticipating modern fast exponentiation; and (5) Adhvayoga provides the closed-form sum of the geometric series 2ⁿ⁺¹ - 2.

Pingala explicitly cites predecessors including Krauṣṭuki and Āśvalāyana, positioning himself as systematiser rather than originator. His achievement was rendering explicit the combinatorial logic implicit in Vedic oral tradition. These findings reposition ancient India as a wellspring of mathematical thought, where abstract structures emerged not from pure speculation but from the practical demands of Vedic verse.

Keywords

Pingala, Chandas Shastra, Sanskrit prosody, binary numbers, Pascal's Triangle, Fibonacci sequence, combinatorics, history of mathematics, ancient India, algorithms, exponentiation, geometric series, base conversion, binomial coefficients, oral tradition, Guru-Laghu, computational thinking, discrete mathematics.

References

Arya, Ravi Prakash (2022). Vedic Origin of Zero, Amazon Books, USA in collaboration with Indian Foundation for Vedic Scence.

Halsted, George Bruce (1912). On the Foundation and Technic of Arithmetic. Chicago: The Open Court Publishing Company.

Ifrah, Georges (2000). The Universal History of Numbers. John Wiley and Sons.

Sachau, E.C. 1964: Alberuni's India. Vol. 1. S. Chand & Company, Delhi.

How to cite this article

Bhogal, S.  (2026). Chandas: The Magic and Mastery of Music and Mathematics. Vedic Science, 2026 (1), 1–8.

https://www.ved.org/archives/VEDSC-202601-2026-4