About Raga Math

The rAga math operations help in:

• Understanding the arithmetic behind rAgams. This is especically true with shifting: simply starting at a different point of the scale of a rAgam results in a scale of a another rAgam.
• Noting that, at the same time, two rAgams that have the same scale may sound very different. We understand that there is more to a rAgam than just its scale.

• Creating themed sequences in different ways. Examples: a set of shifts all on the same rAgam; a cascade of successive operations - (e.g., shift rAgam 1 to yield rAgam 2; swap notes in rAgam 2 to yield rAgam 3, and so on.)

  The melody of the music will no doubt attract all listeners. In addition, technical listeners will also appreciate the mathematical intricacies.

A Note about Shifting

There are two schools of thought when thinking about rAgam scales. The conventional way is to view a rAgam scale as a set of svarasthAnams (S, R2, G3, M1, etc.), then layer gamakams on top, resulting in the rAgam with unique undulations that are characteristic of that rAgam. Shifting, in this context, is straight forward: while shifting we ignore the gamakams of the original rAgam and focus only on the svarathAnams. In effect, what we mentally do is:

• Ignore the gamakam of the svarasthAnams of the source rAgam.
• Do the shifting.
• Apply the gamakams of the target rAgam on the correct svarasthAnams.

Another school of thought considers gamakam to be an integral part of a svarasthAnam. Here's how it works.

Suppose there are ten kinds of gamakams in Carnatic music. Let's name them from 'a'...'j'. Then, if we take the svarasthAnam of, say, R1, we'll get 11 variations. (Let's call them R1, R1a ... R1j; R1 being the note without any gamakam.) Ditto for every other svarasthAnam.

In this notation, every svarasthAnam indicates its gamakam also. And, instead of just 12 svarasthAnams in an octave, we'll have 132 "gamakam-induced" svarasthAnams (assuming ten types of gamakam).

Thus, if some ragam X has the following notes:

  S R1d G3 M1c Pj ... etc.

If we shifted this rAgam at R1 we'll get something like:

  Sd R3 G3c M2j ... etc.
  (R1d -> Sd; G3 -> R3, and so on)

We run into at least two issues: first, the chances of finding a rAgam with this particular set of gamakam'ed notes is rarer than if we had ignored the gamakams and shifted the "plain" svarasthAnams. Secondly, in this example shift, R1d yields Sd (since R1's gamakam variation 'd' should carry over to the new S). By convention, S and P do not have gamakams in a rAgam, and thus the new rAgam we arrived at is unacceptable. A similar problem will result if shifting a note yields a Pa...Pj. Therefore, any shifted rAgam that contains a S or P with a gamakam will be invalid.

Raga Math Trivia

Ragams that shift back to themselves!

Here are a few:

• Gopriya. Every note of this ragam is exactly two svarasthAnams apart from its neighbouring notes.
• Mandari and JAlasugandhi, when shifted at M2.
• Kuvalayabharanam, when shifted at D1.

A Unique rAgam

Conventionally, all rAgams required either Ma or Pa. Note that saying/singing Ma or Pa requires the lips to touch each other. Harikeshanallur Muthiah Bhagavathar invented a rAgam without Ma or Pa. He called it niroSThA (sanskrit: niH + oSTha -> without lips). In addition, he also composed a song (rAja-rAja-rAditE) in this rAgam, whose lyrics also have no sounds that cause the lips to touch each other. (See here for more information on this rAgam.)