A Modern Introduction to Music – 16

By Anjum Altaf

If you read the last installment you would have picked up a clue to what a raga is about. Keep five swaras (S g M d n) in the air and you are beginning to work with the raga Malkauns. Ergo, it seems reasonable to infer that if you picked a different set of swaras, you would be working with a different raga. Of course, sculpting a fine raga out of these building blocks requires a few more details that we will discuss later but this is a good enough point to start.

However, if we proceed in this ad hoc way, we would be able to list lot of ragas but we would miss out on the schema that organizes the large number of ragas into more manageable sets. In particular, we would miss out entirely on identifying ragas that are related closely to each other.

At this stage, we can move immediately to the organizational framework developed by Pandit Bhatkande (1860-1936) but I prefer a slightly longer route. The rationale for this detour is the fact that while Pandit Bhatkande’s framework is useful its logic is not obvious to the newcomer. The downside is that eliciting the logic requires a little bit of mathematics.

I can hear some groans here. No sooner have you escaped the pain of physics that I am plunging you into the morass of mathematics. But the physics did add something to the understanding of music and so would the mathematics. Besides, the mathematics is a lot easier. So, bear with me as I work through the logic.

Recall that the alphabet of Indian music contains the seven pure/natural or shudh swaras S R G M P D N. Of these, in the Hindustani tradition, S and P have no variants while the other five natural swaras have a variant each, i.e., r g m d n. Thus there are a total of 12 swaras in the alphabet.

The organizational schema involves specifying parent families of related ragas comprising seven of these 12 swaras. The reason for this is that a raga, by and large, is comprised of a maximum of seven (and a minimum of five) swaras (i.e., the number of balls in the air has to be between five and seven for the performance to be classified as a raga equivalent). Thus we have to specify sets of seven swaras out of the available choices such that the following conditions are fulfilled:

  1. The set must include the invariant swaras Sa and Pa.
  2. The set must include either the natural or the auxiliary version of each of the variable swaras Re, Ga, Ma, Dha and Ni, i.e., one swara from each of the following subsets: [R r], [G g], [M m], [D d], [N n].

This is not difficult for those who know the mathematics of combinations but we can derive the total number of possible parent families from first principles as well.

There are two ways to pick the swara corresponding to Re (R or r). There are also two ways to pick the swara corresponding to Ga (G or g). Now you can convince yourself that there are 2 x 2 = 4 ways to choose the swaras corresponding to the combinations of Re and Ga, i.e., RG, Rg, rG, rg. By extending this logic we would find that because there are 5 swaras with two choices each, the total number of combinations we can derive is 2 x 2 x 2 x 2 x 2 = 32 and you can actually write them out if you want to. (Computer folks would find this trivial if they remember their Boolean algebra.)

What Pandit Bhatkande did was to reduce this exhaustive set of 32 to a more limited set of 10 parent families that in his judgment included the majority of the popular ragas in the Hindustani tradition. These are the famous 10 thaats of Hindustani classical music and while there is a continuing discussion of the limitations of this scheme, no satisfactory replacement has yet been proposed. Each thaat represents a parent family in which the included ragas share a family resemblance.

Let us illustrate this schema with a couple of examples:

The set of swaras [S R G m P D N] is given the name Kalyan Thaat. One of the popular ragas in Kalyan Thaat is raga Bhupali which is comprised of the swara subset [S R G P D].

At the other end of the spectrum is the set of swaras [S r g M P d n] which is given the name Bhairavi Thaat. A popular raga in Bhairavi Thaat is raga Malkauns which is comprised of the swara subset [S g M d n].

A complete list of thaats and the ragas in each family are listed on the Sangeet Research Academy website and also well presented by Khwaja Khurshid Anwar at the sarangi.info website.

A few things need to be kept in mind to avoid confusion. First, most thaats are named after the principal ragas in that family but thaats and ragas are not the same entity. A thaat simply signifies the parent scale from which the ragas in that family are derived. The derived subsets have to conform to additional requirements before they meet the criteria specified for specific ragas.  Second, the ascending and descending scales of a raga need not comprise the same number of swaras. For example, it is possible to have fve swaras in the ascent (aroh) and six in the descent (avroh). The complete set of possible combinations along with their names is listed here.

[Note: The alphabet of Hindustani classical music includes natural and auxiliary notes and the auxiliary notes are further divided into flats and sharps. For some purposes it is possible to reduce the number of variables from three types of notes (natural, flat, sharp) to two (flat and sharp). Leaving aside S and P which are invariant, one can think just in terms of the flat or sharp version of the rest of the five notes: [R G m D N] are the sharp versions while [r g M d n] are the flat versions. This follows because of the nomenclature adopted in the Hindustani tradition where four of the auxiliary notes [r g d n] are flatter versions of the corresponding natural notes [R G D N] and one of the auxiliary notes [m] is the sharper version of the natural note [M].

With this simplification, and ignoring the invariant notes, one can think of Kalyan Thaat as being comprised of all sharps and Bhairavi Thaat as being comprised of all flats.]

Now listen to a clip of raga Bhupali from Kalyan Thaat and a clip of raga Malkauns from Bhairavi Thaat and see if you can sense any kind of difference.

More soon.

Those of you interested in the mathematics of permutations and combinations should visit the Khan Academy for an easy introduction. This is a brilliant website that is well worth exploring. My risk in mentioning it is that you can get hooked on the maths and forget the music.


  • Vinod
    Posted at 12:19h, 06 September Reply

    Where there is mathematics and physics, there is a happy and gleeful Vinod.

    At the other end of the spectrum is the set of swaras [S r g M d n]. Where’s the P in this thaat?

    I was listening to those links. What is pakad?

    Did I notice a difference? It was too complex for my simple auditory intuitions. When I went to one raaga, I forgot what the other sounded like. There was no way I could make a comparison even though I went to and fro a few times.

    Wait. I did notice a difference. One of them starts at a higher point and has a faster and steeper ascent. While the other starts at a lower point and has a more gentle climb. I think the latter was Bhupali. Did I get that right?

    I was wondering if anybody knew what the term ‘melakarta ragas’ meant? Is it from Carnatic terminology?

    • Anjum Altaf
      Posted at 16:02h, 06 September

      Vinod: I am reassured that someone is reading these posts with care. I missed the P in the set. Thanks for catching the slip.

      I explained pakad (better written as pakaR with a hard R – the Hindi word for ‘to catch’) in the last installment as the DNA of a raga, a characteristic combination of notes that serves as the signature of a raga. Knowledgeable listeners ‘catch’ the raga when they hear the ‘pakaR’.

      Yes, you are on the right track. I wanted to find Bhupali and Malkauns rendered with the same instrument on YouTube as that would have made the comparison easier but I was unable to do so. If you can find sitar, violin or flute CDs with these two ragas you would be able to do better.

      The Melakarta scheme is the Carnatic equivalent of the Hindustani thaat framework. It is more comprehensive with 72 parent scales. Beware that the Carnatic nomenclature is more complex as Sakuntala has already pointed out. The naming of the scales is also quite unique and if you are interested in mathematics you should definitely look it up. This is a link that can start you off.

    • Vinod
      Posted at 01:01h, 07 September

      Anjum, Thanks. I’m going back to listen to those ragas again, this time paying attention to the pakaR.

      I read up on the Carnatic melakarta categories. Thanks for that.

  • Kabir
    Posted at 21:45h, 06 September Reply

    Why is Bhupali in Kalyan Thaat when it does not include either Shudh or Tivar Ma? I thought that the ragas in Kalyan Thaat were supposed to have the Tivar Ma in them?

    • Anjum Altaf
      Posted at 23:32h, 06 September

      Kabir: The omission of Ma is not the issue – you can have a raga without Ma, either shudh or tivra. Rather it is one of identifying the parent family. Technically Bhupali could be part of Kalyan Thaat (SRGmPDN) or Bilawal Thaat (SRGMPDN). Omitting Ma and Ni from either would give the swara set of Bhupali (S R G P D). So which Thaat should it belong to? As I mentioned the Hindustani thaat framework is nowhere as meticulous as the Caranatic Melakarta one so these kinds of ambiguities persist. If you listen to Khwaja Khurshid Anwar, he mentions that some people place Bhupali in Bilawal thaat although he has it listed under Kalyan thaat.

      For added complication I should mention that Deshkar has the same swara set as Bhupali but is classified as belonging to Bilawal thaat. The determination of the parent family rests also on the tonal patterns and characteristic movements (angas) of the ragas. See how categorically Rajan Parrikar states this aspect:

      Bhoopali (also known as “Bhoop”) and Deshkar are both auDav-jAti (pentatonic) Ragas with an identical swara-set: S R G P D. The corresponding Carnatic Raga is known as Mohanam…. Bhoopali is a Kalyan-anga Raga whereas Deshkar is a Bilawal-anga Raga; their respective characteristics can be inferred from this proposition. It must be underscored that this is a statement not of historical chronology but of the relevance of specific melodic groupings (“Ragangas,” in our terminology) attending the orthogenesis of Ragas and of their continual presence in the Indian musical imagination.

      For the advanced listener, Parrikar adds this interview with Pandit Jha:

      Our preamble is reinforced with a magnificent melologue of Pandit Ramashreya Jha “Ramrang.” This telephone recording splendidly demonstrates his didactic virtuosity as we find him engaged in a musical topiary of sorts, fashioning Bhoopali and Deshkar by pruning the respective parent Ragangas, Kalyan and Bilawal –


    • Kabir
      Posted at 23:38h, 07 September

      I suppose this illustrates the limitations of the thaath system. I always thought that Bhupali was in Bilawal thaat because it uses only the shudh swaras. Also, Hamsadwani is in Bilawal and it is only one note different from Bhupali (SRGPNS). The additional element of anga makes things more complicated.

    • Anjum Altaf
      Posted at 23:48h, 07 September

      Kabir: Yes, the thaat framework is just a rough guide and there are ambiguities about quite a few ragas. But it is appropriate that the characteristic chalan of a raga takes precedence over an ex-post classification. You have mentioned Hamsadhwani but even Deshkar is in Bilawal thaat and it has exactly the same swara-set as Bhupali. But this is what gives the music its challenge – you have to get the sense of the flow and the movement, not just rely on a guidebook.

  • Vinod
    Posted at 03:54h, 07 September Reply

    I’ve been trying for a while now. I listen to the definition of a raag in terms of the swaras. That seems all straightforward. Then I try discerning that in the singing demo – whether it be a popular song or a classical concert. And I just can’t hear it there. There’s too much going on for me to catch the raag in an actual performance. I need help with raag-catching.

    • Anjum Altaf
      Posted at 15:58h, 07 September

      Vinod: You will benefit from the advice given in the TED-X video on Hindustani music that I had linked earlier. Listen to film songs composed in the two ragas and you will begin to recognize their characteristic movements much more easily. A good place to find samples is Rajan Parrikar’s site. Ignore all the text because it is for advanced students. But he has samples of compositions in each raga and he always starts with light compositions. You will find Bhupali here and Malkauns here. Let me know if this helps.

      Another site you might find more convenient is here.

      Kabir: Do you have any tips for Vinod?

    • Kabir
      Posted at 23:35h, 07 September

      I agree that the best way to improve at identifying ragas is just to continue listening to music. If you listen to many film songs in the same raga, then eventually you can get an instinctive feel for the sound of a particular raga.

    • Anjum Altaf
      Posted at 23:40h, 07 September

      Kabir: Thanks. Most people enjoy film songs so just an additional step is needed: to find out the raga on which the song is based. And to write it down in a notebook as the Ted-X video recommended. Also, to work in the reverse direction: to listen to a lot of popular songs in any given raga. This list is useful – one can then find the song on YouTube.

    • Anjum Altaf
      Posted at 06:52h, 08 September

      Kabir: Perhaps starting with Bhupali and Malkauns was not a good choice from the listening point of view. Could you recommend two ragas that are so dissimilar that the ability to distinguish them would come more easily? It would help if they have pronounced chalans. I can think of Darbari and Anandi but would like to get your input.

    • Vinod
      Posted at 01:02h, 08 September

      thank you both. Will give those links a click and a close read

  • Arun Pillai
    Posted at 01:49h, 08 September Reply

    Regarding the classification of ragas into thaats, if one thinks of every raga as a language, then it has a syntax and a semantics. The semantics may be divided further into meaning and effect. This allows one to classify ragas either by their syntax or by their meaning/content or by their effects or a combination of these criteria. Trying to do the classification solely on the basis of the notes is purely syntactic; things like anga and chalan – which I do not fully understand – may be more semantic although there is something syntactic about them too (e.g. which note can follow which note, typical phrases etc.). It would be interesting for someone to do a more systematic analysis of this classification problem.

    • Anjum Altaf
      Posted at 04:09h, 08 September

      Arun: My sense (which could be mistaken) is that Pandit Bhatkande grouped ragas first by their semantics and then attempted to fit the groupings into a synytactic shcema. Given that there was no systematic structure derived from first principles underlying the attempt, there were a considerable number of ambiguities in the outcome. Personally, I don’t rely on the thaat framework for much except as a guide to the identification of closely related ragas according to their semantics.

      It would be natural to expect that there would be several PhD dissertations on this topic although I haven’t come across a reference. This is probably a reflection of the gap in archiving and disseminating scholarship on Indian music.

  • Anil Kala
    Posted at 05:33h, 08 September Reply

    Why the primary swars given nomenclature ‘Sa, Re Ga Ma Pa Dha Ni’. Does natural enunciation of these evoke desired frequencies?

    • Anjum Altaf
      Posted at 05:56h, 08 September

      Anil: The nomenclature was described in installment # 10. Sa, Re, Ga, Ma, Pa, Dha, Ni are the abbreviations of the full names of the swaras: Shadja, Rishab, Gandhar, Madhyam, Pancham, Dhaivat, Nishad. These abbreviations are helpful in teaching and learning and they are also a part of classical vocal music in the Hindustani tradition. I would doubt that their enunciation evokes desired frequency because one can just as easily enunciate all of them at the same frequency.

      If I recall right, Dr. Prabha Atre had written a PhD dissertation on the use of the sargam in Hindustani music.

  • Mohsin Siddique
    Posted at 18:17h, 22 October Reply

    Anjum –

    Do you know if Pandit Bhatkhnde’s books are still in print? Have these been translated in other South Asian languages and/or in English? Is it worthwile to revive those books if they are not available, or are there better compilation of the information/analyses he gathered now available?

    Good work you are doing! Keep it up.

    • Anjum Altaf
      Posted at 13:51h, 23 October

      Mohsin: Thanks. I have obtained the following information courtesy of two individuals who are very knowledgeable about Indian music – Dr. Sakuntala Narasimhan and Arpita Chatterjee.

      Pandit Bhatkhande’s treatise (Kramik Pustak Malika, books 1 – 6) is in print and can be ordered from Sangeet Karyalaya, Hathras, U.P. – 204 101 (India) Tel: 91-05722- 231111, 230123, 270270. Mobile 9927063111. They original is in Marathi but there are translations in Hindi and Bengali and at least Book 1 is available in English. Sangeet Karyalaya also sells a lot of other books on music (English and Hindi) and publishes a monthly magazine called Sangeet in Hindi (now in its 76th year). (By the way, Hindi is really easy to learn for Urdu speakers and worth it for those interested in music because virtually nothing current like Sangeet is available in Urdu.)

      Pandit Bhatkhande’s work and contribution is discussed in Janaki Bakhle’s book Two Men and Music: Nationalism in the Making of an Indian Tradition (2005). There are also numerous PhD dissertations on Pandit Bhatkhande’s work written at Indian universities with music faculties. Fortunately, this is a very alive area of research that continues to inform the development of the theory and practice of Indian music.

  • Anil Kala
    Posted at 00:50h, 23 October Reply

    From your write up it appears that ‘Ragas’ have merely swar restriction but no templates. A performer can do anything with the allowed ‘swars’ in any order. But when I see English movies, I come across actors playing piano reading from books of notations. Do western symphonies have proper templates?

    • Anjum Altaf
      Posted at 01:35h, 23 October

      Anil: I am not clear what you mean by template. We did not get far enough in the series for me to elaborate the structure of ragas. No, one can not do anything with the allowed swaras in any order. Sometimes the restrictions on order are very stringent. For example, the descent of raga Darbari cannot be the straight [S] n d P; it has to descend in a ziz-zag (‘vikr’) pattern, i.e., [S] d n P. If a performer goes to n from [S], it will not be Darbari raga anymore.

      Western classical music is written by composers and performers cannot deviate from the written score. Indian classical music does not have this kind of constraint. The performer has more freedom and can improvise within the template of the raga, i.e., the allowed swaras and the restrictions on order, if any. There are also other kinds of restrictions. For example, there are some swaras on which the performer can rest (‘nyasa’); others on which rest is not allowed. Some swaras are emphasized (‘vadi’ and ‘samvadi’); others that are allowed but not to be emphasized – they are weak or ‘durbal.’ You can say that all these are part of the template of the raga.

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