'Carnatic Chills'

Does the title seem familiar? Yeah, its a new fusion music album released by the violin maestroes Ganesh and Kumaresh. But no, this post doesnt have anything to do with that...

Nevertheless, Shruthibhedam I think is really one of those 'Carnatic Chills'...Its a concept that has intrigued me for so long now that I was tempted to try out a small aalaap incorporating the idea.

My undertanding of the concept:
(Much has been discussed about Shruthibhedam, among both Classical and Film Music lovers alike; Ilaiyaraja's music mostly being the subject matter for the latter :) Here is another such attempt by me to take up and deal with this in some detail. Given my limited knowledge,I'd be glad to have any inputs/corrections/clarifications.)

To avoid any confusion, I will refrain from using any terms from Western Classical Music and adhere to Carnatic terminologies.

Pre-requisites to understand Shruthibhedam:

1.Shruthi: A shruthi is defined uniquely by two distinct frequencies x and y (y>x)and their integral multiples, with a condition that the ratio y:x::3:2.
I.e., the frequency y is 3/2 times the frequency x. We give these frequencies x and y names, which are 'Shadjam' and 'Pachamam' respectively. (So since it is the shadjam that actually fixes a shruthi, it is called the "Adhaara Shadjam".) So, whether its 5 Hz and 7.5 Hz or 10 Hz and 15 Hz, it doesn't matter. Within any given pair x and (3/2)x, x will be Shadjam, and (3/2)x (or y), Panchamam.
What is to be carefully noted here, are the words 'within any given pair'. I.e., a frequency by itself cannot be called a Shadjam or Panchamam. It is only with respect to the other frequency in the pair that one can say that the particular frequency is Shadjam or Panchamam.
These are denoted in short by sa and pa respectively.
Now, given such a pair x and (3/2)x, all integral multiples of x will also be called Sa and all integral multiples of (3/2)x will also be called Pa.
Thus, a shruthi is uniquely defined by a series of frequencies x,(3/2)x, 2x,3x,4x,6x,8x..... where x, I emphasise, is a variable.
A shruthi is named by a number which corresponds to any sa (x,2x,4x and so on) convenient for performance by the human voice or any instrument. Let's call this convenient sa as the middle sa.
A middle Sa of 261.6 Hz is denoted by the number 1. The number notations for other frequences for the middle sa will be discussed eventually.

2.Sthaayi: A Sthaayi is defined by 3 frequencies x,(3/2)x and 2x.
So, x,(3/2)x and 2x form one sthaayi; 2x,3x and 4x form another sthaayi and so on.
If x is the middle Sa, then the set x,(3/2)x,2x form the 'Madhyama Sthaayi' ; the set
(1/2)x, (2/3)x,x form the 'Mandra Sthaayi'; and the set 2x,3x,4x form the 'Taara Sthaayi'.

3. Swara:Given a particular sa, we have so far only discussed about its corresponding sa and the other Sa's and Pa's; while (obviously) there can be a multitude of other frequencies.
It is largely agreed that the minimum ratio of two discernable frequencies should be 1.059.
So if we construct a geometric progression (GP) with x as the first term and 1.059 as the common ratio and compute upto the 13th term, we find that the 13th term is nothing but 2x.
So given an x which is the first term of the GP; like Sa and Pa, all the intermediate frequencies have particular names and these are called 'Swaras'. The nomenclature of the 12 frequencies as swaras are as below:
1st : Shadjam (sa)
2nd : Shuddha Rishabham (ri1)
3rd : Chaturshruthi Rishabham (ri2)or Shuddha Gandharam (ga1) in different cases.
4th : Shatshruthi Rishabham (ri3) or Sadharana Gandharam (ga2) in different cases.
5th : Anthara Gandharam (ga3)
6th : Shuddha Madhyamam (ma1)
7th : Prati Madhyamam (ma2)
8th : Panchamam
9th : Shuddha Daivatam (da1)
10th : Chaturshruthi Daivatam (da2) or Shuddha Nishadam (ni1) in different cases.
11th : Shatshruthi Daivatam (da3) or Kaishiki Nishadam (ni2) in different cases.
12th : Kaakali Nishadam (ni3)
13th : Shadjam (Sa)
Now going back to the number notations of Shrutis, a middle Sa corresponding to 1.059 times 261.6 Hz is denoted by 1.5; a middle Sa corresponding to 1.059^2 times 261.6 Hz is denoted by 2 and so on.
In other words, given a shruthi, if you want to go to the immediately next higher shruthi, you have to transpose the ri1 of this shruthi to sa and proceed to construct the geometric progression as usual. Taking the ri2 of the original shruthi as sa would give the 'next-to-next' shruthi and so on.
(Conventionally we denote swaras in mandra sthaayi with a "#" symbol and those in taara sthaayi with capital letters.)

4. Raga: A raga is a unique combination of a certain set of swaras in a certain pattern. The pattern of the swaras has to be defined for both ascent and descent of the swaras.
(Here I shall not dwell on the criteria for forming a raga.)
(Note: A raga is Sthaayi-independent.)
For example, the combination
sa ri2 ga3 ma1 pa da2 ni3 Sa; Sa ni3 da2 pa ma ga3 ri2 sa
forms the raga 'Shankarabharanam'.

Shruthibhedam :

It is to be borne in mind that cognizance/ interpretation of the shruthi of a piece is pivotal in determining its raga.
Hence, if we now retain the absolute frequencies of the above swaras, but decide to shift the sa to the present ri, i.e. make a 'bhedam' in the shruti, all the swaras change correspondingly.
So the above combination would now read:
ni#2 sa ri2 ga2 ma1 pa da2 ni2; ni da2 pa ma1 ga2 ri2 sa ni#2
(Obviously but importantly, this is possible only because the relative frequencies of successive swaras remain the same since they are in geometric progression)
Now this new combination forms the raga "Kharaharapriya".
Thus, a Shruthibhedam is said to happen when the shruthi is changed in a raga, resulting in a new raga.
The idea of Shrutibhedam has other interesting consequences too:
An entire song in a single raga can be percieved to be in one raga by one person and some other raga by another person, since it all depends on where the listener places her/his sa.
A classic example is Ilaiyaraja's andhi mazhai pozhugiradhu, which would be in raga Vasantha if one placed the starting swara of the song as ma, and Ramani if one placed the starting swara of the song as sa.
Now why is it that some people percieve it as Vasantha and some others as Ramani, and yet some others are able to pick both ragas with equal ease is a question I have not been able to answer. We would have to go into musical cognition processes for that, I'd imagine.
In other words, what is the criterion for deciding the shruthi (and equivalently the raga) of a song if it is not known to you beforehand?
And why/how is it that for a majority of songs (if the shruthi is not given), majority of people seem to find out the shruthi by some apriori ability, and also largely remain mutually consistent?
I wish to answer these questions some day!

Here is a small Alaap I did, in raga Sriranjani, with a transpose to Hamsanadam, and back to Sriranjani.
Sriranjani is defined by:
sa ri2 ga2 ma1 da2 ni2 Sa, same way back.
If the ga in the above is taken to be sa, and the Sa of the above omitted, we get,
ga2 ma1 da2 ni2 Ri2 Ga2, same way back.
This combination also corresponds to:
sa ri2 ma2 pa ni3 Sa, same way back, which is the raga Hamsanadam.
So when the {ga2 ma1 da2 ni2 Ri2 Ga2} phrase is repeatedly sung, with a stress on the ga so as to make it sound like the shadjam, what results is our perception of it as Hamsanadam.
Here it is:

--Ok, I really need to add here now that today, I'm really embarrassed by this piece :P I have to, have to, have to redo it. And really soon. Its perfectly ok if you've read the article and don't listen to this :P 02/09/2010 --


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UPDATE as of Nov 2011: Since the player I'd embedded here doesn't work anymore (thankfully!) and also since I did this very transpose (Sriranjani to Hamsanadham) live at a recent concert, I'd like to redirect you to that: http://www.youtube.com/watch?v=PeO9kjk7aPg
Feedback as always would be much appreciated, thanks!