Lesser Known Gruhabhedams: 2X4: A Typology of Gruhabhedams| Rasikapriya, Dharmavati, and more

Here's the last video in the Lesser Known Gruhabhedam series:

Lesser Known Gruhabhedams: 2X3: Hindolam vs. Hamsanandi

Lesser Known Gruhabhedams: 2X2: Charukesi vs. Gowrimanohari

Lesser Known Gruhabhedams: Season 2

Decided to make a second round on Lesser Known Gruhabhedam. Here's the first one in this second set:

Lesser Known Gruhabhedams: Lalitha and more

Here's the fourth and the last one in the Lesser known Gruhabhedam series.

Lesser Known Gruhabhedams: Lalitha

Here's the third in the Lesser known Gruhabhedam series.

Lesser known Gruhabhedams: Nattakurinji

Here's the second in the Lesser known Gruhabhedam series.

Lesser known Gruhabhedams: Rageshri

First of a series of videos on relatively lesser known gruhabhedams in classical/ film music.

Rethinking Ragas in Film Music

Or, How I learned to stop worrying about ragas and just love film music.

Some 16 years ago when I was just starting life on the internet, one of my entry points was this lovely page called 'Raga of Songs' on tfmpage.com. It was a discussion forum where day in and day out, enthusiastic folks (some, over-enthusiastic like myself) would pore over the use of ragas in film songs. We would get down to the minutest of details, unearthing (now in my view some of the most insignificant) 'anya' swaras in the chords of a particular interlude that made the song deviate from its 'main' raga. The whole exercise was a mad obsession for me. It remained a mad obsession for quite a while. And this was of course not just me or the few people on tfmpage.com. 'Ragas in film songs' has forever been a pet topic for several rasikas as well as musicians. My own interest in this in fact comes from several people in my immediate and extended family. I still fondly remember a G.S.Mani tape on the topic my dad used to play decades ago. Many practicing Carnatic musicians have also often discussed this with great interest. For instance, here is the legend T.N. Seshagopalan praising Ilaiyaraja's use of Hamsanandi, here is Sikkil Gurucharan talking about Ilaiyaraja deftly alternating between Kalyani and Kosalam in Sundari Kannal, and then of course there are the many lec-dem videos by Charulatha Mani on the topic.

Over the last few years though, I've begun to question this whole idea of associating film songs with ragas for many reasons. Not all of these reasons are objective (in the sense of being removed from personal judgment). I'll admit that these are a combination of (what I think are) some principled reasons based on certain fundamental aspects of the Carnatic tradition, and some purely personal and idiosyncratic factors that have to do with my general propensities moving in a different direction over the years. Let me say at the outset that I don't claim to break any ground here. Probably by the end of it some of you will have found all of this entirely obvious but still find intellectual and entertainment value in figuring out ragas of film songs. I have no qualms with that :)

So why am I less enthusiastic about ragas in film songs today?

1. (Mis)appropriation of the idea of 'Raga' in Carnatic music: It might probably help by starting with what a raga is not. A raga is not a set of notes or swaras. Scholars and musicians have time and again reminded us that a raga has a form and life that goes beyond its constituent notes. And therefore - and more to the point here - a raga is not a scale, i.e. a raga cannot be reduced to its arohana and avarohana. A raga comprises phraseologies, pidis, gamakas, and prayogas that go well beyond its basic notes. This is a classic instance of the whole being more than the sum of its parts. Sure, some ragas are closer to the scales formed by their notes than others, and have fewer of typical prayogas etc., but no raga is just a scale. My biggest beef with associating film songs with ragas, saying "Song X is in a Raga Y" is that more often than not the song is not in that raga, but just has the swaras of that raga in their most basic form. In essence then, when claiming that a film song is in a particular raga, what we are doing (often if not always) is appropriating a classical term into a non-classical context: and that is problem # 1. When we claim that Sundari kannal is in the raga Kalyani, we are appropriating the term 'raga', as well as the idea of 'Kalyani' itself from a classical into a non-classical context, and I think to avoid misunderstanding, we need to be very clear about this if we want to make this claim. In my view, Sundari kannal is not Kalyani, and the charanams don't go into Kosalam. Why? Because the song has none of the characteristic phraseologies or prayogas of Kalyani. What it does have, are the basic notes of Kalyani. So I think the song is really in the Kalyani scale, stripped of all the lakshanas of Kalyani. (Thanks to my awesome student, I learned that this is called the Lydian Mode in Western classical, so that's probably what this song is closer to, than Kalyani.) To my ears, there isn't an iota of similarity between Sundari kannal and say, Nidhi chala sukhama. And for similar but slightly different reasons I don't think there's Kosalam in it (in the charanams and interludes) either. Sure, the Kalyani scale, with the Ri2 replaced by Ri3 yields the Kosalam scale, but some 45 odd seconds of some subsets of Kosalam notes - and rendered pretty plain without any gamakas - don't maketh a Kosalam. Kosalam is definitely a much more "scalar" raga than Kalyani, so I would be relatively more sympathetic to the Kosalam claim about this song than the Kalyani claim, but I'd still have reservations in saying that the charanams are in full-blown Kosalam. (Of course, I'm sure Gurucharan knows exactly what he's talking about and that he would be able to pull off a fabulous RTP in Kosalam - as he in fact briefly does in the video - that will sound almost nothing like Sundari kannal - but I still think it's important to remind ourselves of this difference between raga and scale.)

For similar reasons, Ennavaley is not Kedaram - not even just the first lines of the pallavi (and no, one occurrence of Ri3 doesn't make it Kedaram + Nattai), Sundari neeyum is not Kedaram, and Pon maalai pozhudhu isn't Kedaram. (For starters, none of these songs has the typical S-M-G-M phrase of Kedaram, let alone the pidis, gamakas etc..) Puducheri kacheri is SO NOT Shankarabharanam and sadly, even Omkara nadanu is not really Shankarabharanam. You get the idea. As I said, the problem is less acute when it comes to the more scalar ragas - ragas without many typical prayogas or phraseologies - but I still think it's a long stretch to say Kaali perungaya dabba is in Rishabhapriya or Ooru vittu ooru vandhu is in Shanmugapriya - even though these are both relatively scalar ragas. These songs are so un-Carnatic in nature that we simply cannot associate them with ragas. We might say they use the scales of these ragas.

Needless to say by the way, none of this is about making any value judgments about the compositions. I think many of these are fantastic songs.

"But of course!", you might say: "A "filmi" Kalyani is not going to sound the same as a Carnatic Kalyani, and don't we know that very well? We just use the name 'Kalyani' more loosely/ broadly in the film context and we're very aware of that." Well, if there is always this understanding of the distinction, the problem - at least at the level of comprehension of the 'Carnatic Kalyani' - is probably not as big. But there's a problem nevertheless - at the level of categorization and nomenclature. I think it's not just an approximation to say that Sundari kannal is in Kalyani. I think it's plain false - for reasons explained above. And such raga associations with film songs could cause a misunderstanding for people not familiar with the Carnatic paradigm.

"Ilaiyaraja does not know Carnatic music." thunders T.M. Krishna, here: https://youtu.be/9zVVy62EtHg?t=33m33s

(I wonder how this hasn't made headlines and gone viral on social media yet - clearly, not many people (particularly Ilaiyaraja fans) have watched this yet which is probably good ;) )

As much as I didn't quite appreciate the confrontational tone he takes (here and at various points throughout the lecture series) - despite making the purportedly humble claim that he doesn't know any film music (and I trust that was earnest) - I really recommend these lectures to anyone looking to learn anything about Carnatic music. It's quite an educative series, and the man makes several important and interesting points, particularly about the history and evolution of Raga in Carnatic music. I personally learned quite a bit from them and many points he makes here reinforced my understanding of the idea of Raga in Carnatic music and influenced much of what I'm saying here. (I'm not completely on board with him on the "scales vs. ragas" issue though - and this musical fiction I wrote sometime ago talks about why: http://srutimag.blogspot.com/2016/01/ragaland-romance-of-many-anubhavas.html) Coming back to the Ilaiyaraja comment: Raja claiming that Maand is a Carnatic raga - even if that's wrong - doesn't necessarily mean he doesn't know Carnatic music. (By the way a Hindustani musician once told me - contrary to what T.M.Krishna says - that Maand is not even of Hindustani origin, but comes from the Rajasthani folk tradition. Now I don't know which one of these is true.) The most charitable way I can think of to interpret that remark about Ilaiyaraja is to situate it in the current context of ragas in film songs. All we can probably say is that the bulk of Ilaiyaraja's songs are not in Carnatic ragas. (There are definitely quite a few exceptions like Poo maalai vaangi vandhaan.) This still doesn't mean that Ilaiyaraja "does not know Carnatic music" - all it means is that he doesn't operate in the Carnatic paradigm. But moving on...

2. Songs that are not really in any raga OR scale getting put in a box: I don't think "What raga or scale is this song in?" is a valid question for any and every song. A song might even sound very classical and still not be in any raga or scale - for instance Ennavaley or Manam Virumbuthey or Sippi irukkudhu... These are some of my favorite songs, but I often see songs such as these getting boxed into some raga. I think these (and several thousand others) don't fall into any raga or even a (existing) scale. Each of these is just a (really well-done) melange of different scales and ragas (as the case may be).

3. A personal decline of appetite for figuring out ragas in film songs: Gradually over the years, I've become much less interested in finding out ragas of songs - except of course cases where the raga of the song is so obvious it leaps out at you. Involuntarily, my focus has shifted to the overall aesthetic and emotional appeal of the song irrespective of what raga it is (or is not) in. This is in (large) part due to the above reasons, but it also just has to do with an idiosyncratic move away from the obsessive need to break down a song to bits and analyze it. This in fact also happens when I listen to Carnatic songs in a new raga, but to a lesser extent.

[While I find myself moving away from putting raga names to film songs and generally (over) analyzing songs, one phenomenon I still can't resist is gruhabhedam: both in the Carnatic and film contexts. I'm still a sucker for really intriguing theoretical ideas being aesthetically executed. If you think about it though, recognizing/ appreciating gruhabhedam has nothing to do with ragas. As long as we have in place our fundamental concepts of shruthi, tonic, shadja, swara, and swarasthana, we can talk about gruhabhedam without reference to raga. I've written on this topic many times on this blog, the most recent one is here.]

Having said all that though, I think there are many situations where it does make sense to talk about the raga of a film song:
1. When the song is actually classical in nature and is true to the raga (even if only in parts) and doesn't just make use of the notes of the scale: several old classics come to mind: Paarthen siritthen (Sahana), Mounathil Vilayadum (Sama), Poo maalai vaangi vandhan ((Darbaari) Kaanada) to name a few.
2. When the song is not really classical in nature, but in a scale that is not too far from the raga: As I mentioned earlier, some ragas are much closer to the scale formed by their notes than others. In such cases, since the difference between scale and raga is not too huge, it might be more acceptable to say that a song is in a certain raga. Lots of ragas fall under this category: Hamsanandi, Panthuvarali, Hamsadhwani, Mohanam to a good extent, Simhendramadhyamam, Dharmavati to name a few. Even in these cases, we're still misappropriating the term 'raga' into a non-classical context, but the misappropriation may not be as grave. This is the reason I think why a Sundari kannal sounds nothing like a Nidhi chala sukhama, whereas a Vellarikka pinju vellarikka sounds quite related to a Mohana Rama or Evarura. An interesting case in point is the assoication of Hindustani ragas to (mostly older) Hindi film songs. To the best of my knowledge Hindustani music is not as "hung up" or hardcore about prayogas and phraseologies as Carnatic is, and so lots of the ragas there are quite similar to the scales. So I think it's easier and less problematic to make this association of raga with song in the Hindustani-Hindi film music context. (Of course, even here I'm sure there are exceptions.)
3. For pure intellectual gratification derived from figuring out a scale and putting a name to it: This is great, but to be exercised with caution :)

In a nutshell then, "ragafication" of film songs doesn't work a lot of the time, and if we still want to do it, we should be very careful about it.

Okay, that was a LOT of rambling, and I'll stop at that. Thanks for reading!

Gruhabhedam and Ilaiyaraja - again

Gruhabhedam as a musical phenomenon can never cease to amaze. Gayathri's (of Ranjani-Gayathri duo) brilliant, awe-inspiring Music Academy lec-dem on the topic has recently generated a lot of interesting discussion in the Carnatic music circles, and prompted me to write this long-pending post.

But this post is not about Gruhabhedam in Carnatic music. It is about Ilaiyaraja. Again. (Here and here are articles I've written on Raja and Gruhabhedam in the past.) In my view, just like in Carnatic music, there are good and bad ways of doing Gruhabhedam in film music. I'll get to the bad at the end, but here's the good - or rather, the really, really good. The song I have in mind is aasai adhigam vechu from the film Marupadiyum: http://mio.to/album/Marupadiyum+%281993%29

Gruhabhedam in Sindhubhairavi has been handled exquisitely by stalwarts in Carnatic music - check out this piece by Tanjore S. Kalyanaraman for instance, and then there's of course Lalgudi's legendary swarajathi. But this song - aasai adhigam - is a brilliant case of gruhabhedam from Sindhubhairavi in the film music context. It seems like an innocuous song at first glance but on closer listening you see the beast unleashed in the first interlude and go on to wreak havoc till the end. What a masterpiece! Let me say at the outset that this is not a traditional gruhabhedam involving two "ragas" per se. The song is predominantly in Sindhubhairavi but what it morphs into via gruhabhedam is not really a raga: it's more a scale, or rather parts of a scale - the major scale, roughly speaking.

UPDATE: See this video where I discuss this song.

It starts out in straightforward Sindhubhairavi and continues to be so until half of the first interlude. Then at 1:35 you see it happening. There's a departure from Sindhubhairavi and you hear a more fun and upbeat few seconds there from 1:35 to about 1:42. For a long time I didn't think it was anything special - it just seemed to be a normal change of notes/ modes/ moods. But on closer inspection I found that those notes should really still just sound like Sindhubharivai - 1:35 - 1:43 the notes should be nnnn rr rsss... Why do they sound different? Because there are background chords there that have changed the shruthi! If you listen closely you'll hear a pa-sa bass in the background that makes the nnnn rr rsss sound like rrrr mm mggg. And that's where it starts - taking the Sa of Sindhubhairavi as Ga. And then there's a superbly seamless transition back to Sindhubhairavi around 1:43. And then back to major scale (ish) again in the charanam from 1:53 - 2:09. And then back to Sindhubhairavi at 2:09. What's this man made of?

The charanam beginning ("chinna poNNu naa...") sounds like gpgss... ns rr npp... Why? Again, because he's made us subconsciously move the shadjam. The corresponding Sindhubhairavi notes for that line would be sgsdd... pd nn pgg. But we don't hear it as Sindhubhairavi because of the way Janaki sings it - long, plain notes, and a landing on the da of Sindhubhairavi on the word "naa" making it feel like sa. Here's a short demo I did, singing these lines as in the original, and in a slightly different way if we want to retain Sindhubhairavi. With some very slight modification to the rendering, the feel can be changed back to Sindhubhairavi: with some small gamakas and highlighting the pa. (The singing isn't great - Janaki's shruthi is insanely high for me and the corresponding lower pitch too low.)





So it looks like by simply highlighting the pa and not fixating on da, you get a Sindhubhairavi feel rather than the "fun-n-frolicky" major scale feel. But why remain in plain old Sindhubhairavi when you can come up with genius stuff like this? The second interlude again goes back and forth between major scale (ish) in the instruments and Sindhubhairavi in Janaki's humming. I think for me this song will go down as one of the most incredible gruhabhedams done in film music.

There's of course a lot more the song has to boast about: the tune, the singing, and the instruments all brilliantly capture the state of mind of the woman singing it in the movie and the context couldn't have asked for a better song.

That was about the brilliant stuff. And as promised, here's the bad stuff:
Ilaiyaraja fans, please forgive me but I think nanna neenu gellalare - the 80s Kannada song - is a particularly mundane way of doing Gruhabhedam: 2nd song here. It could serve well to initiate someone into the very basics of Gruhabhedam but beyond that I find it quite shallow and in-your-face. It is too overt and the mood doesn't change along with change of ragas and I find the song to have little musical value. In fact I think the ragas don't change really - all that's happening is that the singers are mouthing different swaras.

Edit: While I think the song is musically flippant objectively speaking, friends have made me realize that it is unfair to evaluate it in a vacuum, stripping it of its context - I acknowledge that the song is set in a particular milieu and reflects the image of the iconic "Dr. Raj" of the 80s. And the context/ film in which this song occurs was probably flippant to begin with. Hat tip to Chaya Rao and Madhusudhan Rao.

Anyway - this was just an e.g. to illustrate a specific point. Needless to say there's simply way too much awesomeness to take from Raja's music - and that's that.

Reverse engineering a gruhabhedam: the genius of Raja

If there's one piece of music that leaves me transfixed every time I listen to it, it's Composer's Breath from Ilaiyaraja's album Nothing But Wind featuring the flute maestro Pt. Hariprasad Chaurasia.

-Art by my amazingly talented sister Sumi.
-----

Where do I begin...I bought Raja's two non-film albums (read "cassettes") - How To Name It and Nothing But Wind back during my undergrad days and for almost a year I would pretty much listen to nothing else. Raja taught me several lessons and each one of those would vie with the others to make me feel it was the sole purpose of my life :) But one lesson stands out till today as the most revealing, the most intriguing, and the most awe inspiring. Unfortunately, it came to me much later - I hadn't quite seen the genius through for until numerous times of involved listening. But come, it did, and to this day it gives me goosebumps.

Amidst trying to get a grip on the treacherous equations and derivations of Electrodynamics and Statistical Mechanics - not to mention, in the dingy IIT hostel room - solving Raja's puzzles in Nothing But Wind was a much more satisfying experience, needless to say. The epiphany under discussion hit me on one such occasion of listening to Composer's Breath. Let me try and explain to my understanding, one of the underlying theoretical ideas behind this piece that the man has so ingeniously woven in - the reason for this post.

Disclaimer: my apologies in case this is all too familiar to you and sounds platitudinous.

First, here's the track: https://www.youtube.com/watch?v=I4g6Zl4nB_g

It starts off with a lovely Hindolam/ Malkauns. Hariprasad Chaurasia's bhava-rich and masterly playing
make it a most pleasurable experience. The main melody (starting at 3:54) is beautiful. It goes, Sa,, ni da ma ga ni da ma gm da# ni# sa,,,,. I'm certainly not an expert on analyzing chords and harmonies but parts like 4:26 that recur throughout just sound heavenly. The drama starts at 6:12 (and there is a lot of build up to it in the chords that just precede) when you start hearing Hamsanandi/ Sohini. What's happening here? Just an ordinary raga change? Absolutely not. A random change in shruti as well as raga? No again. Let's do this piecemeal. First, notice that the shruti is reduced by half a step - or half a note. The new sa is at ni3 of the original shruti. Next, observe that the absolute positions of all the other swaras remain the same. So basically, what starts at 6:12 is Hindolam relative to a new sa; but what's most crucial here is that unlike in a standard gruhabhedam, the new sa is *not* one of the swaras of Hindolam itself: it is a newly introduced swara. So what was a pentatonic raga becomes a hexatonic one due to the additional swara and that turns out to be Hamsanandi. And when you do this, lo and behold, a thrilling coincidence (pun intended) occurs: every swara of Hindolam remains the same, albeit of another variety. ni2 becomes ni3, da1 becomes da2, ma1 becomes ma2, ga2 becomes ga3 (and of course, sa becomes ri1). It is obvious and stunning at the same time. The main melody in Hindolam that I mentioned above now changes to Hamsanandi as follows: Sa,, ni3 da2 ma2 ga3 n3 da2 m2 ga3 r1 sa d2# ni3# sa,,,.

Okay, so far so good. But this made me rack my brains: I had never come across such an unusual way of doing gruhabhedam - such a gruhabhedam would probably not be permitted on a Carnatic stage. I was wondering if there was any way of reconciling it with the standard process. And then, I started thinking about how we might bring about the opposite gruhabhedam: Hamsanandi to Hindolam. Hamsanandi's ri would have to be taken as sa... and... if you do a sa varjya (omit sa), you get Hindolam. And immediately it dawned on me that THIS one was indeed a standard Carnatic gruhabhedam! It is not unusual in Carnatic to do a gruhabhedam transpose from hexa (or heptatonic) ragas to pentatonic ones by omission of sa (and pa)! (And that's because gruhabhedam or no gruhabhedam, one often renders phrases in a raga without sa - and sometimes pa- just to add beauty) In fact, here is a reference that talks about the Carnatic master of all times, T.N. Seshagopalan doing exactly this: http://ramsabode.wordpress.com/2007/04/10/tns-musiri-chennai09042007/
(There is also a youtube video of a breathtaking Hamsanandi alapanai by TNS where he shifts base to Madhyamavati using the same concept)

So WOW - the brilliance of Raja in Composer's Breath lies in that he has actually reverse engineered a (standard) gruhabhedam! Who would've thought of it! If only I could enter his head and see the workings.

The rest of the track goes in and out of many, many ragas - malayamarutham, bhageshri, sindhubhairavi etc which all sit smiling and pretty in Chaurasia's safe custody (and bring poignant flashes of 80s Tamil cinema along with them - probably because they remind me of many of Raja's 80s songs). But the highlight for me is that even after the Hamsanandi episode is over, Raja teases you with some brilliant sparks alternating between the two sa's (thus alternating between the two ragas) within a matter of seconds, like between 6:44 and 7:33 - pure magic! Also at the very end of the track starting at 15:32.

Sometimes I wonder if I'm overly pedantic. Sometimes people say that too much analysis especially in art is not healthy and robs it of its beauty and charm. But the more I think about it; no...I beg to entirely disagree. This situation always reminds me of something a celebrated Astrophysics prof G. Srinivasan told us in a class - a physicist apparently once said that understanding that stars are nothing more than huge blobs of gas and studying the equations governing their behavior doesn't make them seem any less pretty and poetic! :) Unfortunately I don't remember which physicist this was.

As I complete another year of existence on this planet today, I cannot thank Raja the God enough for giving infinitely more meaning to my appreciation of human creativity, godliness in art, and life.

My article on raga recognition in Sruti Magazine

I'm happy to share that my article on the neurophilosophy of raga recognition appeared in the September 2011 issue of Sruti. What started as a term paper for a class I took long ago (more than a year now) with Prof Paul Churchland has resulted in this. Thanks to Swaroop who first spotted it on my blog when I'd posted it for a very brief period last year; and of course, to the editor Ramnarayan.

As Octaves completes five years this month (that's right, five! hard to believe for me); it's a nice feeling to be writing musicology/ music theory related posts back to back. After all, I've always primarily been a theorist at heart.

Here's the article.
(Disclaimer: the model I discuss as I conceived of it in this context is just that: a model; a kind of an artificial neural network for heuristic purposes only)

PS: Please do subscribe to Sruti if you're interested in the Indian classical arts. It's an immensely valuable resource!

Raga recognition

Gruhabhedam... again

Here is an AWESOME gruhabhedam demonstrated by Prince Rama Varma:

http://www.youtube.com/watch?v=Nnq5tdukBeg

Once the concept of gruhabhedam is clear, doing it with linear (monotonic) ragas is fairly straightforward- say between Mohanam and Hindolam. But here, its two vakra ragas (i.e. with scales where swaras don't exactly monotonically increase or decrease) which is what makes it so special! The "pa ma2 pa ga3 ma1 ga3" phrase of Behag mapped to "ga2 ri2 ga2 sa ri1 sa" of Sindhubhairavi was so revealing!
What's more, the inflections (or "brighas"/ "gamakams") of the swaras match too!

Music is beautiful. Math is beautiful. And the two put together- ah, bliss!

For those interested, here's an earlier post of mine where I'd explained the concept of Gruhabhedam (albeit overly simplified)- http://octaves.blogspot.com/2007/06/carnatic-chills.html

(Note: It was only later that I learnt from Shri.Kumaresh (of Ganesh-Kumaresh) that the word "Shruthibhedam" for such transposes is a misnomer, for it only means what it literally means: change of shruthi, and nothing more)

'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!