Rules relating to asymmetric rAgas


Date: 9 Jul 1997 00:31:44 GMT
Message-ID: <5pum5g$f9n@spool.cs.wisc.edu>
Subject: Re: Rules relating to asymmetric ragas

In article <5ptfgl$ro4@news01.aud.alcatel.com> vssridha@aud.alcatel.com (V. S. Sridharan) writes:

I would like some clarification on rules relating to asymmetric ragas. Asymmetric ragas are janya ragas which have some differences between arohanam and avarohanam. I would like to discuss only non-vakra ragas with no anya swaras to keep our life simple.

These can be of several combinations: sampoorna-shadava, shadava-sampoorna, sampoorna-audava, audava-sampoorna, shadava- audava, and audava-shadava.

Let's take a simple example, Bilahari, which is an audava-sampoorna raga originating from Sankarabharanam with the following progressions:

Arohanam - Sa Ri Ga Pa Da Sa
Avarohanam - Sa Ni Da Pa Ma Ga Ri Sa

The rules are that Ga Ma Pa and Da Ni Sa are not allowed. The following are the questions:

  1. Is Ga Ma Ga ok?
  2. Is Da Ni Da ok?
  3. Is Ni Sa ok?
  4. Is Ga Ma ok?
  5. If we introduce a pause in the middle of a disallowed string such as Da Ni Sa, does it become ok?
  6. Are the rules different with Hindustani music?

I would like some opinions from net-gurus on these, please. I haven't seen these defined adequately in any of the books I have. If you have any, please let me know. One answer that is not allowed is that, "as long as the bhava is maintained, anything is ok."

Before we go any further, let us forget about how many musicians, if any, adhere to the following set of rules. If asymmetry is to make any sense at all, then it must be true, at the very minimum, that:

Every svara transition in every sa~cAra must be legal, subject to the constraints of the scale and the rules of vakra and varja.

My claim is that this is the only rule we need to use (although I would have to define, fairly precisely, what the terms `transition' and `legal' mean---I will do this shortly). Of course, it goes almost without saying that the rule is only a minimum, since the use of the principles of vakra and varja means that any sampUrNa-sampUrNa mAELa rAga can be "legally" sung like any one of its upA~ga janyas. [This leads to an interesting question about "backward causality" that I shall come back to at the very end of this essay].

And clearly, as Sridharan asks (very reasonably), appeals to `BAva', `lakShya' (practice), and `tradition' are all ruled out here. We are talking only about `lakShaNa': what is allowed and what is disallowed in the formal structure of a rAga.

It may make sense to occasionally (or frequently) violate the rules (for the purpose of `beauty' or `BAva' or whatever)---but this obviously implies that there is some rule being violated, and thus that there exists a rule (and a first-order rule at that).

Even if no one at all followed these rules, their explication and analyses are what are considered here.

Before we consider the above transition rule, let us make some simplifying assumptions.

  1. Each svara in the ArOhaNa and the avarOhaNa of the rAga being analyzed is treated as independent and `unclustered'.
    I will reintroduce clustering at the end of this discussion and indicate how it might be folded into the rule. Clustering in the janya rAga is often important in limiting the scope of the application of vakra in the janaka rAga, but it will simplify the discussion to leave out any notion of a svara-cluster for now.
  2. Each AlApana, kRthe, naeraval, kalpana-svara being analyzed is treated as a sequence of sa~cAras.
    Where one sa~cAra ends and the next one begins is determined by a `pause' or `silence' between the two sa~cAras. The precise duration of the pause is less relevant than the existence and perception of the pause---clearly, 10 seconds of silence is more than adequate in even the slowest passages, while 0.5 seconds of silence may or may not provide enough of a pause, depending on the duration of the svaras in the surrounding context.
    Two or more people debating the legality of a composition must first agree on the sa~cAra sequences. Otherwise, they are likely to argue over axiomatic differences.
    Of course, it is possible to say that the process of identifying sa~cAras is the all-important process in analyzing svara transitions. I do not think so at a couple of levels i.e. I do not think that sa~cAra demarcation is difficult, nor do I think that it is of any formal significance in analyzing svara transitions. So, I will take for granted that the demarcation can be, and is, always done.
  3. Each sa~cAra is a sequence of svaras.
  4. All ornamentation (gamakas, bRgas, etc.) is eliminated. For example, a gamaka which oscillates between two svara-sthanas is either reduced to one or the other of the svaras, or else is expanded into a sequence of explicit svara alternations. Therefore, a kampetha "ga~" in the passage "s r ga~ ma" is resolved as one of "s r >g< m" or as "s r >gmgmgmg< m" or as "s r >grgrgrg< m" or whatever.

At the end of the ornamentation-removal process, the musical passage has been analyzed into a sequence of sa~cAras, each of which is analyzed into a sequence of svaras.

Let a typical svara sequence be S[1] .. S[N]. A subsequence S[i] .. S[i+1] is considered a `transition'.

The rule states that "every transition between svaras S[i] and S[i+1], for 1 <= i < N, must be legal".

In order to determine (define) `legality', one must make a decision as to whether the transition belongs to the ArOhaNa or the avarOhaNa. This may not be straightforward in the case of vakra rAgas, but is simple enough for avakra scales (if the frequency increases, then the transition is in the ArOhaNa; if the frequency decreases, in the avarOhaNa; else it is a repetition of the svara, perhaps with octave variation).

The transition S[i] to S[i+1] might be varja, i.e. it may be a transition (in the ArOhaNa or avarOhaNa) which skips past one or more svaras---this is perfectly legal for sampUrNa scales and should be legal for any other scale as well.

If it is not possible to find a (possibly varja) sequence in either the ArOhaNa or the avarOhaNa that can match a specific transition S[i] .. S[i+1], then the transition is illegal.

It is usually easier to work out the `forbidden' transitions in the scale and make sure that none of them occurs in the sa~cAras of the composition, rather than to verify for each transition that it is legal.

Let us see how these rules work in the example of belaharE.

ArOhaNa: s r2 g3 p d2 s+
avarOhaNa: s+ n3 d2 p m1 g3 r2 s

Every avarOhaNa transition is allowed since that scale is sampUrNa. Not all ArOhaNa transitions are allowed. In particular, the following transitions are forbidden:

g-m, m-p, d-n, n-s

These 4 transitions are truly forbidden since there is no vakra prayOga in the scale that contains any of these transitions.

For example, in a hypothetical scale where the avarOhaNa was not

s n d p m g r s

but

s n d p m g m g r s

(i.e. the inclusion of "g m") it would be legal to sing "g-m", but it would not be legal in the belaharE scale.

In some sense, the performer is required to identify svaras that are common to both the ArOhaNa and the avarOhaNa. These are the "direction switch" points. The performer, at these svaras, can choose to change from ArOhaNa prayOgas to avarOhaNa prayOgas (or vice versa) or choose to continue in the same direction as before. The rest of the notes of the scale are not direction switching points and cannot be used in that manner.

Therefore, instead of analyzing each rAga to identify forbidden transitions, one can instead identify each svara as a direction switcher or not.

It is possible to express the two approaches algorithmically as follows:


Algorithm "Forbidden":

    curr = /* some starting svara */;
    while (/* not done */) {
        sing(curr);
        do {
            next = /* a random "next" svara */;
        } until (! is_forbidden_transition(curr, next));
        curr = next;
    }



Algorithm "Direction-Switch":

    curr = /* some starting svara */;
    dir  = /* some random direction: UP or DOWN */
    while (/* not done */) {
        sing(curr);
        if (is_switch_svara(curr)) {
            dir = /* random new direction: UP or DOWN */
        }
        else {
            dir = /* remains unchanged */
        }
        curr = /* new svara in direction `dir' */
    }

The question of "direction switch svaras" means that those rAgas where there are no notes in common between the ArOhaNa and the avarOhaNa (except for the Shadja) will have every direction-changing transition forbidden. For example, consider:

ArOhaNa: s g p n s+
avarOhaNa: s d m r s

After singing "ga", one can, according to the rule, sing only "pa", "nE", or "sa+". Similar arguments hold for every other non-shadja svara in the scale. Changing between the ArOhaNa and the avarOhaNa can be done only at the Shadja.

Clustering

Consider a rAga like rEthegAULa.

ArOhaNa: s g r g m n n s+
avarOhaNa: s+ n d m g m p m g r s

The rules of varja presumably allow one to sing:

s g m n s+
s r m n s+
s r g m n s+

and so on. Most people, when listening to such prayOgas, would say that the `BAva' of the rAga is absent. What they presumably mean by that is that they expect to hear certain svaras as clusters, not as individual notes.

In some sense, the scale of rEthegAULa is better written as:

ArOhaNa: s grg m nn s+
avarOhaNa: s+ nd m gmpm g r s

or some such (some may prefer to link "gr" in the avarOhaNa, but I hope the point is clear). This clustering means that, for example, the ArOhaNa of the rAga does not consist of 7 individual svaras, but 4 svara clusters---and in all sa~cAras, svara clusters must be sung in full (i.e. the rules of varja do not operate within clusters but only between clusters).

Therefore, we can have the following kinds of transitions:

s grg m s+
s grg nn s+
s m nn s+

all of which, while not "100% pure-refined" rEthegAULa, at least are identifiable as being part of the rAga. The earlier prayOgas which split up a cluster are all disallowed. Likewise, the two algorithms specified earlier need to be modified to change "next svara" to "next cluster" and will continue to work.

Clustering reduces the scope of variation possible in a rAga. While it is possible in a purely formal sense to apply clustering to sampUrNa-sampUrNa mAELa rAgas, the principle makes sense for vakra janya rAgas.

Backward causality

For lack of a better term, I call the process of limiting the scope of a janaka rAga, due to the existence of a janya rAga, as backward causality.

Let us take the example of rEthegAULa and its janaka rAga naTaBIravE (for the sake of argument, ignoring the question of whether KaraharapreyA is a more appropriate janaka rAga).

Let us also assume that at some time in the past, rEthegAULa was not known and naTaBIravE was (this is probably the reverse of what was historically true, but bear with me).

Let us assume that some of the apUrva and ra~jaka prayOgas of naTaBIravE consisted of singing "sgrgm", "mnns+", "gmpmgrs" and the like. None of these prayOgas are `illegal' or forbidden---the rules of vakra and varja allow the performer to construct all of these patterns.

The problem is that after the "creation" of rEthegAULa (where these kinds of prayOgas, far from being apUrva, are jEva), a performer who sang naTaBIravE with "sgrgm", or "mnns+", or "gmpmgrs" would be guilty of "straying into rEthegAULa territory".

In some sense, the creation of a new rAga (rEthegAULa) has limited the earlier legal scope of an existing rAga (naTaBIravE). This is what I call backward causality.

Backward causality is a troublesome concept since it probably can be specified only in negative terms, and with reference to a potentially unlimited set. This means that in order to determine which transitions are legal in a rAga (janaka or janya, vakra or avakra), one needs to also know something about what other rAga or rAgas have so deeply incorporated these transitions and transition clusters into their grammar that singing them would involve a boundary violation.

This has implication for the earlier mentioned algorithms.

It is not only likely, but actually quite widespread, that musicians do not follow transition rules in practice (even when there is no backward causality involved).

Obviously, if one breaks the rule often enough, it becomes sensible to ask if one is performing rAga-A or rAga-B or "mixing the two" (whatever that means). If one breaks the rule occasionally, the violation may either go unnoticed or else be a totally novel and welcome prayOga that enhances the charm of the performance (and may even be a way in which a rAga evolves in its scope).

These kinds of questions cut deep. Are rAgas essences? How much overlap is allowed between the domains of two or more rAgas? (Is there really any difference between dharbAr and nAyakE :-)? Is L.Subramaniam justified in playing Sevara~janE for an hour, including a minor reference to the maDhyama at the very end, and then treating the entire composition as being in a new rAga SevapreyA---is this SevapreyA or apasvarapreyA?

I don't think there are any good answers to these questions because they cannot be answered empirically (i.e. by pointing to existing compositions or performances). What is at stake here are questions of philosophy. And philosophy, as we all know (or should know), has little relevance to the real-world.

[ Indian Classical Music | Krishna Kunchithapadam ]

Last updated: Sun Jun 27 17:00:19 PDT 2004
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