October 2008

In this post, I will attempt to tackle the role of dissonance in Carnatic Music in a detailed manner.

(Note: While most of this topic is a diarrhea of words, there is some audio to liven up the proceedings. Audio from two extremes – (a) A rank amateur’s vivadi related experiment (b) Sample from a consummate yester-year legend!  Perhaps they are meant to reinforce dissonance vs. consonance 🙂 !! )

One of the unique aspects of Carnatic Music is the status enjoyed by the concept of dissonance in carnatic melodies. The word for dissonance in carnatic music lingo is vivadi (vivādi), which in turn leads us to vivadi swaras i.e. notes tagged as inherently dissonant, vivadi melas and ragas e.g. parent scales/ragas and offspring ragas tagged as inherently dissonant. As you may know, Carnatic Music has 72 melas and out of those 40 are vivadi melas, which incorporate one or more of those so-called vivadi swaras.

Some pertinent questions now are

  1. What are these vivadi i.e. dissonant swaras?
  2. And why are they considered (inherently) dissonant that they make a raga that employs them vivadi i.e. dissonant?

The first one is easy to answer while the second one is not so.

Which are the vivadi swaras?
The swaras Suddha gandharam (G1), SaTSruti rishabham (R3), Suddha nishAdam (N1) and SatSruti dhaivatam (D3) are the vivadi swaras. Any mela that includes one or more of these swaras is a vivadi mela.

These vivadi swaras actually do not occupy a unique position in the octave. Their position (swarastanam) is the same as that of other (non-vivadi) swaras:

  • Suddha gandharam (G1) occupies the same position as catuSruthi rishabam (R2), i.e. the ri we find in Sankarabharanam. This is the position of the 2nd degree in the western major scale. The raga varALi is a prominent raga to employ G1.
  • SaTSruthi rishabham (R3) occupies the same position as sAdhAraNa gAndhAram (G2) i.e. the ga we find in kharaharapriya. This position is the same as that of the second degree of the natural minor scale. The raga nATA is a prominent raga to employ R3.
  • Suddha nishAdam (N1) occupies the same position as catuSruthi dhaivatam (D2), i.e. the dha we find in SankarAbharaNam. This is the position of the sixth degree of the major scale. The raga kanakAngi (very first mela) employs this vivadi swara N1.
  • SaTSruthi dhaivatam (D3) occupies the same position as kaiSiki nishAdam (N2) i.e. the ni we find in kaharaharapriya/harikAmbhOji. This is the position of the seventh degree of the minor scale. The raga nATa employs this vivadi swara D3.

Here is a graphical representation of the vivadi swaras (third column):

C C#/Db D D#/Eb E F F# G G#/Ab A A#/Bb B C
S R1 R2 G2 G3 M1 M2 P D1 D2 N2 N3 S
G1 R3 N1 D3

Why are they dissonant?
We can see that the vivadi swaras actually occupy what one may consider as “normal” positions. So why then are they called dissonant?

This is because each vivadi swara mandates the presence of a nearby swara and the (melodic) combination of the two is what is termed as dissonant.

  • For  Suddha gandhara (G1), the Suddha rishaba (R1, i.e. flat second) is required. Without R1, G1 becomes more like the “normal” R2.
  • For SaTSruthi rishaba (R3), the antara gAndhara (G3 – i.e.  third) is required. Without it, R3 becomes more like the “normal” G2
  • Similarly Suddha nishAdam (N1) requires Suddha dhaivatam (D1 – i.e. flat sixth)
  • SaTSruthi dhaivatam (D3) requires kAkali nishAdam (N3 – seventh).

In other words, any raga that uses e.g. G1 must not only also use R1, it should use R1 and G1 together (e.g. S R1 G1 or M1 G1 R1 S) most, if not all the time (? must be all the time? ).

Thus, it is incorrect to assume that these swaras are inherently vivadi. One could argue that to use them in phrases without that neighbouring swara altogether would not achieve the intended objective and hence is not good practice.

In spite of all this, people subconsciously always associate R3, G1, D3 and N1 with vivadi and not pay enough attention on the requirement of the neighboring swara. A phrase like S D2 P usually cannot become S N1 P (use of N1 without D1). Now, in a raga that uses D1 and N1 (and hence no D2), during an energetic kalpanaswara one may run into S N1 S – but in general here, the N1 does not give out dissonance and hence this would usually be avoided. Now if this was done as S N1 D1 P, then it will “ooze vivadi” 🙂

However, it is possible that a Carnatic music rasika with his/her carnatic conditioning etc,  may temporarily always associate  the pitch position of N1 with vivadi while listening to a D1 N1 raga.  Thus even S N1 P may be perceived as “more vivadi” compared to the equivalent “S D2 P” (if rendered flat) in a non-vivadi raga. Of course there is also the case that the gamakas D2 can take won’t usually apply to N1, which can provide N1 a different identity from D2 in practice.

A related Experiment:
Let us take the vivadi raga vanaspati and “compare” it to the nice non-vivadi raga dEvamanOhari. The  arohana/avarohana for both is as follows:

Update: Following feedback in form of comments, please note that the avarohana of devamanohari is s n d n p and not s n p d as originally indicated.

vanaspati: S R1 G1 M1 P D2 N2 S / S N2 D2 P S N2 D2 N2 P M1 G1 R1 S
devamanohari: S R2 M1 P D2 N2 S / S N2 D2 P M1 R2 S

So basically if we ignore R1, and also not consider the gamakas of swaras, vanaspati is sort of equivalent to devamanohari except it uses G1 vs. R2 of devamanohari.  So what would we get if e.g. we take a vanaspati kalpanaswara sample that concentrates only on G1 M1 P D2 N2 S  region and compare it with devamanohari sample that concentrates only on R2 M1 P D2 N2 S region? Would the G1 in vanaspati loose its vivadiness?

I will leave you to draw your own conclusions and inferences:

Warning: This is a highly contrived example from a rank amateur who hopes it would serve merely as a catalyst to more food for thought.

[Update: Second Warning –  Following feedback in form of comments, please be forewarned that the demo is flawed in two respects: (a)  As mentioned above, the avarohana of devamanohari is s n d n p and not s n p d. What this means is patterns like a straight descent from d (as d to p, and d to m etc.) are disallowed unlike what is sung. b) the ni for vanaspati do not take the gamakas like in devamanohari and is usually flat.
So at best what is presented is a corrupt and loose form of devamanohari and a corrupt form vanaspati. However, IMO, in spite of these two (fairly large) flaws, the objective of the experiment which is to look into the nature of G1 itself without the presence of R1 still holds.]


(In case you were even half-way impressed, don’t be. It is easy to sing kalpanaswaram as kalpitaswaram i.e. reading from a sheet, and more importantly not have to give a hoot about tala, and ending at the correct take-off point for a refrain 🙂 )

Now as you can see for the long R2 and long G1, a different intonation/gamaka was used as per the raga (at least that is what the rank amateur thought was appropriate for the respective ragas). But in other places, they are more similar – yet subtly different with R2 involving a tiny stress, and G1 mostly flat.  The amateur is not sure if the gamakas for ni in devamanohari also apply as-is to vanaspati as done here. Heck – he is not even sure what he did applies to devamanohari 🙂

Here are some questions you may want to ask yourselves:

  • Did the presentation of the arohana/avarohana initially influence the interpretation of the flat ga (i.e. perceived it as vivadi in your mind)?
  • Did the slide from ma to ga, influence it more?
  • Or did you find it to be “normal” in most places except for that slide from ma to ga (and thus needed R1)?

Okay – but still … why are they dissonant?
So G1 supposedly becomes quite vivadi/dissonant only when used in tandem with R1 (e.g. G1 R1 S), R3 in tandem with G3 (e.g. S R3 G3 or R3 G3 M), D1 with N1 (S N1 D1), and D3 with N3 (P D3 N3 S). But why? I myself do not have the fully answer yet …

Three consecutive notes/swaras semitone apart?
One possibility is in all these cases you end with 3 notes right next to each other (i.e. one semitone apart):

  • S R1 G1
  • R3 G3 M1
  • P D1 N1
  • D3 N3 S

So may be that is it? Three consecutive notes that are one semi-tone apart is how Carnatic Music defines dissonance? Not quite. In very prominent (and non-vivadi) ragas like mAyamALavagowLa you have N3 S R1 – three consecutive swaras one semitone apart. In ragas like pantuvarALi, you have M2 P D1 again three consecutive swaras that are one semitone apart. So this can’t be it.

Three consecutive semitones and jump of three semitones?
Perhaps three semitones followed/preceded by a relatively huge jump of three semitones) like in S R1 G1 M1 or S R3 G1 M1 etc.? Well once again we have mAyAmALavagowLa with N3 S R1 G3 🙂 ! So that can’t be it.

Two of a kind?
Let us consider the octave without the vivadi swaras as follows in ascending order of pitch:

  • Sa
  • Two ri’s – i.e. R1 and R2
  • Two ga’s – i.e. G2 and G3
  • Two ma’s – i.e. M1 and M2
  • Pa
  • Two dha’s i.e. D1 and D2
  • Two ni’s i.e. N2 and N3

Now if we go back and apply what it takes for a mela to be vivadi, we find it will involve one or more of the following: two ris, two gas, two dhas and two nis! So simply put vivadi is when you imply both flavors of a rishabham, gandharam, dhaivatam and nishadam. In such a case, in carnatic music one of the flavor gets labeled by a different swara.

This does have a concise, attractive feel to it. However, we still don’t have answer as why e.g. two rishabhams (together) cause dissonance. Proximity? Maybe – but then why does not S-R1 or M2-P or P-D1 or N3-S cause as much dissonance?

Vivadi and a prominent swara?
One other possibility is a vivadi three consecutive swara combination i.e. S R1 G1,  R3 G3 M1,  P D1 N1, and D3 N3 S all share the common characteristic of the swara labelled vivadi at one end, and a prominent swara (sa, pa, ma) on the other end. Maybe that has got something to do with it? Whatever it is, I do not know.

And how about the two mas?
So what about M1 M2 combination? Is that vivadi? We don’t know. It certainly was taboo to consider them together in a straightforward way per tradition. But there are ragas like behAg, Saranga, hamIr kalyANi etc. which employ both ma’s.   These two ma’s do not occur consecutively in a phrase. The only exception is some artists’ interpretations of behAg do employ p m2 m1. More recently Tanjore Kalyanaraman specialized in many ragas that employ both M1 and M2 but with no pa. Here is rendition of Madurai Mani Iyer’s behAg where he brings in s n3 n2 d2 p m2 m1 AND g3 (!!!!!) and still makes it sound so nice, so melodic 🙂 !

The concept of vivadi over history
If we consult the early music texts starting from Bharata‘s NatyaSastra (early first millenium), we find that vivadi is always applied as a relationship between two swaras (as we saw above). So in a sense to tag one particular swara as vivadi swara (as done today) was never prescribed. During those early period, the swaras with the closest spacing between them were tagged to be vivadi. In those early periods, there was only one ri and one ga etc. and the ri-ga and da-ni spacing (which was smallest) was labelled as vivadi.

The status that dissonance enjoys today in carnatic music is largely attributed to the system allowing for 72 combinations of diatonic/sampoorna ragas as that mandates allowing certain combinations that are tagged vivadi. The “father” of this 72 mela model is venkatamakhin who outlines this in his caturDanDi prakASika (17th century). It is interesting to note that while it is normal practice nowadays to explain the position/swarasthanam of a vivadi swara like G1 in terms of a non-vivadi swara (R2), venkatamakhin does the exact opposite.  He gives both Suddha gandhara and Suddha dhaivata more importance both when talking about pitch positions of frets in vina, as well as reasoning for 72 scales. To paraphrase one of his thoughts “when  Suddha gandhara  is taken as a rishabha, it becomes the rishaba of SrIraga”.  The main reason why he elevates these (now) vivadi swaras above (now) non-vivadi swara is that he was keeping in line with tradition, which accorded the “Suddha” swaras the highest status since their legacy goes all the way back to Bharata. Of course later research suggests that the actual pitch positions of the Suddha swaras today are not the same as the ones during Bharata’s times – but that is a heady topic for another day.

Dissonance is cultivated
Research has also shown that the concept of dissonance itself is cultural and hence is acquired or cultivated. I can certainly relate to that. Music in the middle east with their quarter tones etc. generally comes of to folks in India as somewhat dissonant (until they get used to it). For Carnatic music aficionados, certain popular vivadi ragas like nATa etc. don’t sound dissonant but to a person from another culture, it may sound quite odd. They may even feel that way about ragas which we may not consider vivadi/dissonant!

Ok, a controversial post and one that also reveals my political inclinations although that was made somewhat obvious in my rant long ago (at least Babu saw through that 🙂 ).  This post may not be to your liking depending on your political inclinations, but I just found the connection mentioned below too enticing! But in case this gets your blood boiling, be assured that the connection below could potentially be adapted to a different version that can make you smile too 😉 !

There is a song by Pink Floyd in their Animals album called Pigs (Three Different Ones). It is an awesome song which really should have been mentioned as one of my favorites in my earlier post on the Floyd.

The Animals album’s main concept is to portray different sections of society as animals:

  • Pigs, who are the (scheming, sleazy)  people who influence/control society/system – i.e. typically politicians
  • Dogs, who are the enforces of the schemes of the Pigs
  • Sheep, who are the common folk at the low end at the order and thus helplessly manipulated by the other two.

The song Pigs (Three Different Ones) is an angry, menacing outburst at Pigs. It is in three stanzas, each talking about a (different) pig, a certain politically/socially influential person. A couple of stanzas actually refers to specific people in England (see here).

But I think with a little modification, this song fits three people who have been prominent in the US political spectrum in the last decade or so:

Karl Rove
(Initially thought of Donald Rumsfeld but the lyrics maybe fit Rove better? Or may be I could have picked Rush Limbaugh?)

Big man, pig man, ha ha, charade you are
You well heeled big wheel, ha ha, charade you are
And when your hand is on your heart
You’re nearly a good laugh
Almost a joker
With your head down in the pig bin
Saying “keep on digging”
Pig stain on your fat chin
What do you hope to find?
When you’re down in the pig mine
You’re nearly a laugh
You’re nearly a laugh
But you’re really a cry.

Dick Cheney
(fits him like a glove – except for the hat pin part)

Bus stop rat bag, ha ha, charade you are
You f****d up old hag bag, ha ha, charade you are
You radiate cold shafts of broken glass
You’re nearly a good laugh
Almost worth a quick grin
You like the feel of steel
You’re hot stuff with a hat pin
And good fun with a handshot gun
You’re nearly a laugh
You’re nearly a laugh
But you’re really a cry.

George Bush
Hey you Whitehouse, ha ha, charade you are
You house proud town mouse, ha ha, charade you are
You’re trying to keep our feelings off the street
You’re nearly a real treat
All tight lips and cold feet
And do you feel abused?
You gotta stem the evil tide
And keep it all on the inside
MaryDubya you’re nearly a treat
MaryDubya you’re nearly a treat
But you’re really a cry.

Although very raw and menacing (certainly dicey in the current political climate), the correlation is still interesting isn’t it 🙂 ? I though the second stanza with “Radiates cold shafts of broken glass”, and “Hot stuff with a handgun” was just too good as-is in the orignal. Same with Whitehouse and “house-proud town mouse” – to be funny.

Now, if you are on the other end of the spectrum,  am sure, if you think hard enough, you could come up with three liberals/democrats to fit you needs too 🙂 !

Oh btw, you can catch the (original) song itself here. Even if you don’t enjoy the correlation, enjoy the song!

The two terms Arohana (ārōhaṇa) and Avarohana (avarōhaṇa) are used in Carnatic Music as a terse formula/description of the order of swaras (notes) in a carnatic raga i.e. a decription of the raga’s structure. The Hindustani system calls the same terms Arohi (ārōhi) and Avarohi (avarōhi) respectively. The arohana defines the ascending order of swaras in the raga, and avarohana defines the descending order. The arohana and avarohana are orthogonal in that the ascending order and descending order can be different for a raga. In Western Music, this is rare (e.g. some versions of the melodic minor scale). In Indian classical music this is very common. I believe it is rare in Western Music perhaps owing the dominance of harmony, whereas it is common in Indian classical music owing to the dominance of melody.

The asymmetry in arohana and avarohana comes in many forms

  • Different number of swaras between arohana and avarohana (e.g. sAvEri, vasanta, maNirangu etc.) – this is very common
  • Same number of swaras in arohana and avarohana but different flavors (e.g. brindAvana sAranga and some interpretations of bhairavi)

Linear vs. Non-Linear arohana/avarohana: On top of this, the arohana and/or the avohana can be linear or non-linear.

  • A linear arohana has the set of swaras laid out in increasing order of pitch (e.g. S R1 M1 P D1 S for sAvEri). Similarly a linear avarohana has the set of swaras laid out in decreasing order of pitch (e.g. S N3 D1 P M1 G3 R1 S for sAvEri).
  • A non-linear arohana/avarohana may have zig-zag (vakra) patterns, and/or special phrases included in it.  For example,  SrIraga is a case that has both. Its arohana is a simple linear S R2 M1 P N2 S. The avarohana however is S N2 P D2 N2 P M1 R2 G2 R2 S. Here P D2 N2 P M1 is a special (but rare and non-mandatory) phrase, and the only one that can include dha. The M1 R2 G2 R1 is the vakra/zig-zag where while descending from ma, you cannot go to ga directly but must go to ri, then ascend to ga, and then back to ri. This is mandatory in SrIraga.

This indicates that the arohana and avarohana come in various flavors with potentially a lot of complexities implied. In fact, in complex phrase oriented ragas (e.g. nATakurinji, Anandabhairavi, rItigowLa etc.), the arohana and avarohana fall short of being fully representative of the raga structure, and thus become less useful, and also potentially misleading. There is also subjectivity and inconsistency which comes into play in these cases (e.g. are all special phrases included?).

In the simplest case of linear and symmetrical arohana/avarohana (e.g. all melakarata ragas, and ragas like mohanam etc.), as well as the simplest form of asymmetrical arohana/avarohana where both of them are linear, the terms do serve quite well.

Confusion regarding interpreting simple asymmetrical arohana/avarohana:
One of the interesting confusions some rasikas of carnatic music have is regarding the interpretation of the asymmetrical arohana and avarohana – even for the simplest case where both are linear.  Let us take one such raga – sAvEri. Its arohana and avarohana is as follows:

arohana: s r1 m1 p d1 s

avarohana: s n3 d1 p m1 g3 r1 s

As you can see there is no ga and ni in arohana but both are in avarohana.  Now what does this mean?

  1. Is s r g r allowed?
  2. Is the phrase d n d m allowed?
  3. How about the phrase n d n s?

Many rasikas look at the arohana s r m p d s and conclude that all three must be disallowed.  But in truth,  only #3 is disallowed.  When rasikas encounter #1 and #2  in concerts (e.g. kalpanaswaras), they may conclude that “Well – sAvEri must really be a special raga whose usage defies easy representation”.  Now there are indeed ragas whose arohanas/avarohanas are not fully representative, but in this case, there is actually a logical explanation that follows directly from the arohana and avarohana as to why #1 and #2 are allowed, and why #3 is not.

To get there, let me state the rules of interpreting linear (i.e. on-vakra, non-phrase-oriented) arohanas/avarohanas:

  1. You can ascend from a swara, if it appears in the arohana. In other words, if a swara appears in the arohana, you can ascend from it.
  2. You can descend from a swara if it apppears in the avarohana. In other words, if a swara appears in the avarohana, you can descend from it.

Simple isnt it? But what is the big deal? It perhaps seems obvious!

I think one of the main reason why folks (I was one some time ago) may conclude that the first phrase (s r g r) as disallowed is that they see the s r m as arohana of sAvEri, match it against s r g r – and immediately conclude that s r  g combination is disallowed. For some odd reason, many of us initially seem to easily fall for this. However, this considers the half of the picture as in just arohana. The arohana does indeed says s r m – but the avarohana has m g r s and that is being left out in reaching such a conclusion! In fact, if we apply the rule above, we will find that s r g is certainly allowed as long as we descend from g after 🙂

Now let us look at these phrases and methodically apply our rule:

  • #1: s r g r:
    • Take the first transition i.e. s r. We are ascending from sa. This is allowed because sa is in arohana.
    • Take the next transition i.e. r g. We are ascending ga here. This is also allowed because ri is in arohana.
    • Take the next transition i.e. g r. We are descending from ga here. This is allowed because ga is in avarohana.
    • Since all transitions are allowed, the phrase is allowed. If you are still not convinced, you may want to note that this is pretty much how the sAvEri varnam starts (as s r g r g ri <=> sa ra su . . Da)
  • #2: d n d m:
    • First transition d n is allowed as we are ascending from dha, and dha is in arohana
    • Next is n d, which is allowed as we are descending from ni, and ni is avarohana
    • Next is d m, which is also allowed as we are descending from dha, and dha is also in avarohana
    • Since all transitions are allowed, the phrase is allowed. This phrase also occurs (more than once) in the sAvEri varnam.
  • #3: n d n s:
    • First is n d, which is allowed as we are descending from ni and ni is avarohana
    • Next is d n, which is allowed as we are ascending from dha and dha is arohana
    • n s is disallowed as we are ascending from ni, and ni is not in the arohana
    • Since the last transition is disallowed, this phrase is disallowed – not because of n d n, but only because of n s.  The n d n as such is allowed but only as long as we descend from ni after that which we did not do here.

As an exercise for the reader, see if following are allowed or not:

  1. For sAveri,
    • s g r  for sAveri  (can you find a rendition which includes this phrase?)
    • d G R S (capital implies tara stayi or higher octave)
  2. kAmbhOji , whose arohana is S R2 G3 M1 P D2 S, and avarohana is S N2 D2 P M1 G3 R2 S (ignoring S N3 P which a rare, special phrase):
    • d n d m p d n da
  3. nATa/nATTai whose arohana is S R3 G3 M1 P D3 N3 S. And avarohana is S N3 P M1 R3 S.
    • p m g r s
    • p m g m p
    • p m r g m p
    • p d p

Limitations of applicability of above rule:
The above rules should work for all ragas whose arohana and avarohana is linear (symmetrical or not). The non-linear world is sort of fraught with inconsistencies – but I believe for some cases (e.g. mandatory vakra as the only additional feature) logical rules can apply. I will try to post on that later.