Merukhand Technique :: Theory

Introduction

Usually, practitioners of Classical Music have heard of Merukhand. But most probably they lack in-depth knowledge of it. For some reason Merukhand has been shrouded in mystery for a long long time. At times there are misunderstandings abound - such as that artists that use Merukhand are very mathematical in their approach and lack artistic credibility.

Actually the the converse it true. Merukhand technique can be immensely beneficial for riyaaz and performances as well. This post will try to demystify Merukhand and demonstrate that it can be used for carefully calibrated riyaaz and to discover new artistic expressions.

History

Merukhand is a compound word, consisting of "Meru" and "Khand". Khand means division or part. 
Meru has a lot of meanings:
1. A wooden support to which a swing is attached.
2. In Chhanda Shastra - deals with the various possibilities of laghu-guru (light-heavy) combinations.  
3. Confluence or coming together.
4. The kings of mountains as per the Sumeru Puran. It was said that it was impossible for any person to scale it in one go.

Musically, we can use all the above four meanings of Meru.
1. A strong support for the musical swings.
2. Mathematical possibilities by examining a combination of swars. 
3. A confluence of adjacent swars. 
4. Various pathways to scale the mountain of a Raag.

Merukhand is also known by it's alternative names viz. Merkhand, Mirkhand, Khandameru, Sumerukhand, etc.

Concept

Fundamentally, it involves the use of permutations of any given group of swars. In his treatise Sangeet Ratnakar, Sharangadev mentions the fact that 5040 permutations can derived from a group of 7 swars.

Let us look at the various permutations that can be derived. 
1. If we select only 1 swar - Sa - we get only 1 permutation. ie. Sa.
2. If 2 are selected - Sa, Re. We get 2 permutations: Sa-Re, Re-Sa. 
3. For a selection of 3 swars - Sa, Re, Ga - we get 6 permutations. Sa-Re-Ga, Re-Sa-Ga, Sa-Ga-Re, Ga-Sa-Re, Re-Ga-Sa, Ga-Re-Sa.

The Math

The math behind this is as follows:

ⁿP_r = n! / (n-r)!  (n! is pronounced as n-factorial)

where, n = total number of elements; r = selected elements from within n.

Now, if the total and selected are same, ie. n = r, then the above equation changes to:

ⁿP_n = n! / (n-n)! = n! / 0! = n! (since 0! = 1)

Using the above, for a 4 swar selection: 

⁴P₄ = 4! = 4 x 3 x 2 x 1 = 24 permutations

Similarly, for 5, 6 and 7...

⁵P₅ = 5! = 5 x 4 x 3 x 2 x 1 = 120

⁶P₆ = 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

⁷P₇ = 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040 permutations

Application

Now lets apply the above in terms of laying out the swars. 

1. If 1 swar is selected  - 1 permutation.
`

2. If 2 swars are selected - 2 permutations

3. If 3 swars are selected - 6 permutations

4. If 4 swars are selected - 24 permutations in the following way
a. The 6 permutations of Sa-Re-Ga with Ma at the end of each permutation.
b. The 6 permutations of Sa-Re-Ma with Ga at the end of each permutation.
c. The 6 permutations of Sa-Ga-Ma with Re at the end of each permutation.
d. The 6 permutations of Re-Ga-Ma with Sa at the end of each permutation. 

The SwarDhanu app will help you with this. If you select any 4 swars the app displays it's permutations instantly. 

SwarDhanu app for Google Android devices available on Google PlayStore.

The app will help save time in deriving and writing down these permutations. This time can fruitfully used in your riyaaz.

Finally...

Pt. Omkarnath Thakur has elaborated on 5040 permutations of 1 to 7 swars in his work Sangeetanjali - Vol.5.

The SwarDhanu app allows for upto 4 swars to be selected. The natural question then is why not 5 or 6? While it is technically possible, the main question is how relevant is it for performing raag's? 

The master of Merukhand gayaki, the great Ustad Amir Khan had the following observation to make -

" To remember these 5040 permutations, while not impossible, is certainly difficult. I have been doing this since my childhood and have found that if you can master the 4 swar permutations, it helps greatly in elaboration of any raag."

Hence, SwarDhanu app is limited to 4 swar selection. Additionally it provides 12 tanpura's.

We sincerely hope that this post and the app itself will help augment your creative pursuits in Indian Classical Music.