## 13 Oct The fantastic use of permutations and combinations in Indian music

The field of mathematics has seen a ton of contributions from Indians. For example, it is a well-known fact that ‘0’’ came from India. While there was some debate about zero  The guardian recently ran a piece that revealed that a Bakhshali manuscript, dating from the 3rd or 4th century contains references to the concept of ‘zero.’

The dot symbol in the Bakhshali script, was originally a placeholder that ultimately evolved into the symbol we know today. Brahmagupta, an Indian mathematician, and astronomer is said to have first referenced zero as a number all the way back in 628 AD.

By no means did this highly advanced knowledge of mathematics among the Indians stop with the invention of zero. Several art forms from India integrate very advanced mathematical concepts, in a very intriguing, complex and stunningly beautiful manner.

Consider this: The South Indian style of music, known as the Carnatic music system is a  very intricate and advanced music form. It has several thousand ragas, a raga being based on a particular pattern of musical notes. The noted from which these Ragas form are basically just 7 notes- known as the Saptaswaras.

The seven base notes – S R G M P D N- expand into ‘16 swarasthanas’ – depending on the frequency of the swaras- R, G, M, D, N.  The swaras R, G, N, D have 3 variations each, while the swara has 2 variations. The swaras S and P have no variations and are known as sthira swaras( stable swaras.)

With only these 16 swara variations, there are several thousands of Ragas.

How?

It is done through the deployment of the concept of permutations and combinations in mathematics. These 16 swarasthanas are juxtaposed in various combinations to produce thousands of unique patterns of melodies. These ragas are further divided into Janaka ragas( parent ragas) and janya raga( child ragas.) The janaka ragas also known as Melakartha ragas are 72 in number. These ragas use all seven swaras( hence, also carry the name Sampoorna  or full). These ragas spawn several thousands of ragas that pick out only specific swarasthanas of these ragas, picking up and leaving out some of the swarasthanas.  Many of these ragas are lost to the present day, but at last count there are known to be approximately 36000 ragas.

Carnatic music’s counterpart, Hindustani music boasts of a similar repertoire.

Our ancestors not only knew advanced concepts of mathematics, but knew enough to deploy it to produce entire art forms.

(This is just one part of the beauty of Carnatic music- there are several other areas where advanced scientific concepts are seen in the art form.)

By Ms. Devishobha Chandramouli

udaylalpai1@gmail.com