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  • Urmi Battu


Updated: Jan 31, 2023

Merukhand is an age-old practice in Indian Classical music which involves the systematic permutation of swaras. In this practice, we take a set of swaras and sing all the possible combinations or arrangements of these swaras, in a particular order. In mathematical terms, Merukhand is a permutation of swaras.


Merukhand practice can be traced back to the 13th century, mentioned in the Sanskrit classic text "Sangeeta Ratnakara", written by Sarangdeva. The word “Merukhand” is composed of two words: "Meru" and "Khand", where "Meru" means an axis, and "khand" means parts. In Merukhand practice, the axis refers to a fixed set of notes, which are broken down in parts, in all possible combinations. Merukhand is also popularly known as Merkhand, Meerkhand, Sumerukhand and Khandmeru.


The basic concept of Merukhand practice, is to take a set of swaras, and sing all different combinations of these swaras, in a particular order. Each pattern is distinct, and

the swaras cannot be repeated. When we practice Merukhand, there is a particular sequence in which we sing the patterns, that’s why we say Merukhand is a Swara permutation.

Given a set of swaras, we can find the number of unique combinations that can be made with these swaras using the mathematical formula of factorials.

By definition, the factorial of a positive integer n, denoted by n!, is the product of all positive integers less than or equal to n.

Factorial of an integer n = n! = n x (n-1) x (n-2) x (n-3) x …. x 3 x 2 x 1

For example:

Factorial of 3 = 3! = 3 x 2 x 1

Factorial of 5 = 5! = 5 x 4 x 3 x 2 x 1

There are 7 swaras in the Indian music scale. The table below shows how many unique combinations can be made with a given number of swaras. Here “n” represents the number of swaras.


Let’s take some examples.

If there are 2 swaras, say S and R, the two possible combinations will be SR RS

If there are 3 swaras, say S, R and G, there will be 6 permutations:


If there are 4 swaras, say SRGM, we get 24 combinations, and they are arranged in such a way that 6 of the patterns end with M, 6 with G, 6 with R and 6 with S, shown below :

SRGM RSGM SGRM GSRM RGSM GRSM .... 6 patterns ending with M

SRMG RSMG SMRG MSRG RMSG MRSG .... 6 patterns ending with G

SGMR GSMR SMGR MSGR GMSR MGSR .... 6 patterns ending with R

RGMS GRMS RMGS MRGS GMRS MGRS .... 6 patterns ending with S

Commonly, upto 4 swara patterns are practiced. Only very advanced singers practice 5,6 and 7 swara patterns.


Merukhand patterns can also be elaborated in many ways:

  • Singing the patterns in the descending scale

  • Create pattern with notes that are not adjacent. For exmple: SRMP, or SGPD

  • Make patterns with the notes of a raga

  • Sing it in aakaar, and all the volwels

  • Practice in increasing tempo

  • Expand across octaves

  • Create paltas with partial patterns.

All this can lead to endless practice. Merukhand practice has many benefits. It improves our sense of pitching, helps in creativity, improvisation and elaborating patterns.


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