06 Sep 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:
- The set must include the invariant swaras Sa and Pa.
- 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 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.]
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.