why 7, not 12

[sung]

What are the reasons for our having only 7 distinct swaras instead of 12 distinct swaras?

In other words, why do we have two ri's, two ga's, two ma's, two da's and two ni's? Why didn't they assign two different letters for the two ri's, two different letters for the two ga's and so on? The latter would avoid us having to consider small ri and big ri, etc. I think the number of melakartas in the latter case would be far more than the current ones. Is this just the reason or are there much more fundamental reasons?

Thanks in advance for enlightening me on this.

[sung]

I think the number of melakartas in the latter case would be far more than the current ones.?

Oops! Doesn't appear to be a correct statement.

[Rsachi]

Sung,
before experts jump in, nursery answer:
frequency ratios of pure notes:
Sa to Pa is 1:1.5
Sa to Ma is 1:33
Sa to Ga is 1:25
Sa to Ri is 1: 125
the ratios Pa to Dha and Pa to Ni is similar to Ri Ga

The frequency ratios mean that these note positions all resonate with each other through harmonics.
this means there are seven "natural" resonance musical positions.
The other Ri/Ga/Ma/Dha/Ni values lie inbetween and are not natural harmonic/resonant values.

You will get more details in 22shruti.com

Melakartas use all 12 swaras.

[SrinathK]

It took some harmonic theory to get from 7 to 12 and then to go from 12 to 24. Maybe it could have also been this - The 2nd harmonic is the octave, the easiest one, giving you 2 intervals. The 3rd harmonic, 3/2, splits the octave into a fifth + a fourth, giving you two intervals, which naturally leads to the discovery of the fourth harmonic (4/3) as an inverse of a perfect fifth.

Now if you go through the cycle of natural fifths -- you get unison + 6 major notes and if you go through the cycle of fourths, you get unison + 6 minor notes. Therefore a 7 note system might have felt natural -- like Bodhayana, it is not necessary that Pythogoras was the only one who first realized the mathematical connections. Not to forget there was definitely cross cultural exchanges going on between the Greeks and Indians at the time. Though the credit could also go to the Sumerians...

Then someone discovered the perfect major third relationship (fifth harmonic 5/4 which is more perfect than the Pythogorean third) and worked out that including this increased the possible intervals from 12 to 24 (later trimmed to 22 for alignment with the fundamental). We stopped with 5 as the 7th harmonic is not mutually compatible with the others and including it would have taken the intervals from 22 to an absurdly large number beyond hearing sensitivity.

Lightly touching a string at the nodes will produce the harmonics. It's very possible someone playing with a string could have found out and invented the theory.

Which then makes you wonder why the notes are labelled as what they are. You would wonder why an U-kara note or O-kara was never a swara.

[vasanthakokilam]

sung,

Let me rephrase the question ( assuming I got the intent of your question right ).

What are the reasons for our having only 7 distinct swara symbols (solfa symbols S R G M P D N) even though there are 12 distinct swarasthanas?

(Let us leave out of vivadi ragas and dvi madhyama ragas for now to keep things simpler for pedagogical reasons)

There are variations for each R, G, M, D and N thus yielding the 12 swarasthanas. Having a common solfa name for each pair allows one to formulate a simple rule.

A scale/raga should not have both the variations of the same solfa symbol.

So it is more a theoretical device. If you had come up with 12 different solfa symbols, imagine how unwieldy and long the above rule will be to state.

Second is from the practice side. In kalapanaswara singing, the symbol cognition load on the audience is less with 7 than 12. I think it is more of a burden for the artist to sing the same symbol for different swarasthanas and I think it helps more the audience.

(on top of this basic rule, we can overlay vivadi and the HM imported dwi madhyama ragas like Behag etc. as exception cases in CM )

In western music, where they also have only Seven Solfa syllables or letters ( C D E F G A B ) they bring out the variations with 'flats' and 'sharps' to come up with the 12 swarasthanas. There is a theoretical difference between, for example D - sharp and E flat, though they both represent the same swarasthana but in the theoretical framework surrounding harmony it matters. Again, had there been 12 different symbols such rules would be much harder to specify )

[Ranganayaki]

There is a musical logic to it as Rsachi and Srinath have described, but if I simplify your question further it is this:

Why do we have 12 distinct swarasthanas, or pitches in an octave from our Sa to higher sa, but only 7 swara names, like sa, ri, ga, etc.

I don't know the history of swaras, and which came first, swaras or the melakarta system. I do know that the melakarta classification is fairly recent.

But the logic of the melakarta system is very very simple.

Of the 12, let us consider just the space between sa and ma.. the logic is similar throughout the octave.

1. Between Sa and Ma (not inclusive), there are four swarasthanas. Let us call them 1,2,3,4.

2. Between Sa and Ma, there are only two swaras, Ri and Ga, there has to be at least 1 R and 1 G AND no more than 1 Ri and 1 Ga.

3. Since at any time only two of the four can be used between sa and ma, you only need two swara names. You never need more than two names. Each name has multiple values, but you don't need multiple names. You must have two names though, to distinguish the two swaras that have to be there. In applying the same logic you only have 7 notes as follow:

Sa, pa are invariant (2)
3 ri partially overlapping with 3 ga (4)
2 Ma (distinct, not overlapping with other notes) (2)
3 dha partially overlapping with 3 Ni (like R and G) (4), together these are 12, with only 7 distinct names as you don't need more than 7 distinct names (sa, pa + ri, ga, ma, dha, ni - invariant + varying)

Having a common name for 3 different pitches and two different names for identical pitches (2,3 can be called either ri or ga in different ragas) allows you to classify in chakras of 6 otherwise you will have 72 melakartas with 72 individual swara combination, which doesn't allow you to think fast in identifying ragas by swarasthanas.


Note: It is incorrect to say there are only 2 R and 2 G.. There are 3 R and 3G. Of spaces 1,2,3,4 available between Sa and Ma, there are three available spaces that can be called Ri, not 2: These would be spaces 1,2,3. For G, the avilable distinct pitches are 2,3,4.

Ga has to be of a higher shruti than Ri. If sthana 2 is Ri, then sthana 2 cannot be Ga and the number of options for Ga are reduced from 3 to 2. If Sthana 3 is fixed as Ri, then there is only one option left for Ga, ie., Sthana 4. The reverse is true. If a Ga is known, the Ri has to be one of the pitches lower than the chosen Ga.

[Ranganayaki]

VK, I can't believe we both rephrased the question in an almost identical manner!! I suppose the logic is the same too!, will read the rest of your response.. Your first line made me think that I had clicked twice on submit!!

[cacm]

DR.S.Ramanathan in many LEC/DEMS USING THE Veena (& what is called SONOMETER - I have collaborated with him on this) has CLEARLY DEMONSTRATED that there are 22 Notes between a note & its octave. Palghat Mani Iyer could play ALL the 22 notes in his Mridangam also. In an area of Physics called SONICS (Used in the DESIGN of Auditoria like SYDNEY OPERA, NY PHILHARMONIC HALL ,amplifiers, loud speakers, microphones etc ) this has historically been known & used in their design . Other notes can also be produced but the Ear-Brain combination in experiments have rejected them as NON-Musical. Even the 12 tone scale (while popular in Western Music etc) in Carnatic Music Researchers have shown that the notes are produced & used by Different musicians like Mali & LGJ are SLIGHTLY different. MS& MMI in Carnatic Music are probably the BEST EXAMPLES of getting close to perfection in producing the notes. Rest take "Refuge" in Tradition, Folk Origins, etc tho' using Transducer Theory & other PHYSICS CONSIDERATIONS (which I have UNSUCCESSFULLY tried to discuss in this forum some years back) & the general lack of criticality on the part of listeners as well as Discipline in all the above aspects (if you exclude artists like KVN) the subject has fallen by the wayside.......VKV

[Ranganayaki]

I chose not to leave out vivadi combinations in my explanation (without actually referring to it), because the melakarta system of classification is very neutral and systematic and does not distinguish between vivadi and non-vivadi ragas. But it is an essential part of raga understanding. It does not distinguish between extensive ragas like todi and ragas that are little more than scales. It is the most logical answer to why 7 and not 12, because other explanations resort to a cultural response to the sounds, a certain stand on what constitutes beauty in sound and what constitutes the lack of beauty. I feel those are almost irrelevant to the answer of why 7. It is an arbitrary premise (4 sthanas, but only two swaras between s and m for example), and pure logic flowing from the premise.

Also, the 12 spaces are arrived at by dividing the space (pitch difference) between sa and higher sa into 12 equal (or approximately equal) parts or pitch intervals. (pl do correct me if wrong)

[Ranganayaki]

Cacm (Sri VKV), or others,

Please correct me if I am wrong.. the 22 intervals are assimilated into the 12 as varying levels of each swarasthana, such as a low n3 vs a high n3.. and our system recognizes these implicitly in its practice, especially among high-level singers and rasikas, but not explicitly as different notes, whereas n3 is different from n2.

(Edited to say correctly "intervals" instead of Shrutis, of which there would be 24 and not 22, including the lower and upper sa, the starting and ending notes)

But this is not really pertinent to the OP's question, is it? It is too deep for someone who is grappling with 12 over 7.

[SrinathK]

Only some months ago we had an extensive discussion on this here. http://www.rasikas.org/forums/viewtopic. ... is#p281979

There is a natural mathematical harmonic basis for 24 tones which is reduced to 22 intervals that I summarized briefly in my earlier post up there. The beauty of it is that it naturally gives a mathematical basis for graha bhedam.

Though I would advise going through the 22 shruti website first and understanding different musical tuning systems.

[Ranganayaki]

Would you say, Srinath, that that would be a fairly advanced answer for the purposes of the OP?

[SrinathK]

Let me sum it up, the more the harmonic relationships permitted, the more the number of available tones increase

1) Octave (up to 2 harmonics) = 2 tones
2) Up to 3rd harmonic (up to 3/2) = 7 tones through cycle of fifths
3) Up to 4th harmonic (up to 4/3) = 12 tones through both cycle of fifths and fourths (The end of the cycle is on the prati madhyamam M2. Strictly speaking, you get a slightly different value for the prati madhyamam between the cycle of fourths and cycle of fifths. The difference is called a Pythogorean comma
5) Up to 5th harmonic (up to 5/4) = 24 tones reducing to 22 shrutis by eliminating 2 dissonances and keeping S and P fixed. 5 limit tuning.
6) Up to 6th harmonic - 6 is not a prime number
7) Up to 7th harmonic (intervals like 10/7 or 7/6) = 7 limit tuning. Some intervals like 10/7, 7/4 are well known. As for how many tones are possible, no one's tried yet.

[cacm]

Would you say, Srinath, that that would be a fairly advanced answer for the purposes of the OP?

I am assuming that we can learn MORE by not restricting discussions to a simple discussion of 7 vs 12 etc when the problem has existed from time immemorial. Yet the question is well researched & for those interested in UNDERSTANDING it properly let me just summarize what the famous scientist (Sir James Jeans in his classic "Science&Music"-available at Amazon) has shown: The problem relates to what is called "Pythagoros Comma" & there exist various scales apart from 5,7 & 12 like 53, 306 notes between octaves & have been shown to be better. I do not wish to belabour the point except to point out SIR C.V.Raman himself was intrigued by this problem & those interested in this area should study the great research he did in this area.....Of course if one's comfort zone is all one is looking for they can ignore these posts of mine. It will automatically die!.....VKV

[vasanthakokilam]

VKV sir, the few of us who indulge in these matters are typically the ones taking it to an extent verging on excess So do not worry about it. What we all want is clarity and cohesive discussion however complicated it is. So go for it. And a lot of these have been discussed in various threads and I do not think there is one answer to all this. That is, there is no one answer to what exactly the 22 sruthi intervals are, whether what we use today have anything to do with the 22 sruthis that our ancient texts talk about etc. That does not mean all the research in this matter and all the discussions surrounding it are a waste of time. The problem comes only when people claim that whatever they have discovered is the only right thing and exactly what is stated in ancient texts.

BUT as Ranganayaki wrote, the OP may have asked a much simpler question. I already feel we have made it a couple of orders of magnitudes more complicated than what was intended. But I will let the OP comment on it.

[SrinathK]

All those tuning scales are however Equal temperament, which is however fundamentally different from natural harmonic tunings. The 24 tone scale (from which the 22 shrutis come) is the only scale I know that actually manages to incorporate and overcome this Pythogorean comma. Also the 22 shruti scale offers a much more elegant framework for graha bhedam and change of key than does the scale of 12 - Equal temperament and it can be shown to have mathematically the smallest possible error.

We've discussed it all on that thread over there sir. If you wish to, you can see my spreadsheet. That number 22 is by no means adhoc. Whatever little that has been written in the old books like the Natyashastra are just hints dropped here and there (in a couple of cases I was pleased to see that when you tune two veenas to different pitches on the 22 shruti scale, notes on one veena will match with a different set of notes on the other veena (essentially this is a kind of graha bhedam between 2 veenas) and one example I was actually able to verify in my sheet, but beyond that it is not so clear and the translations I could get my hands on only make me wonder just what the authors were trying to convey, or whether they had managed to fully research the topic with the near zero technology at the time. We do not know if the scale we have today was even the same as the one our ancestors had experimented with. I have even wondered looking at shadja and madhyama gramas as to whether the Indians tried for some time to establish a standard of absolute pitch.

So the 22 shruti scale we have today is definitely a "modern one".

But we are vindicated by the mathematics (it requires nothing more than an ability to multiply and divide fractions). Rather than taking it as an incomprehensible lost art I just took it as though it was a hint to an experiment and stumbled upon the full range of graha bhedam results in a spreadsheet. It has now made me wonder as to the kind of criticism that GNB must have faced when he took up shruti bhedam, when we did not have the tools to prove it.

Fine intervals come in many forms. At the cost of jargon spamming : http://www.huygens-fokker.org/docs/intervals.html
The "modern" 22 shruti scale is either 100% accurate even in graha bhedam or the only error that appears on certain intervals is an interval of 32805/32768 (1 schisma), which is much smaller than the (glaringly dissonant) Pythogorean comma of 81/80. The math literally proves itself.

Descending back down to earth, it seems obvious to me why there would have been only 7 labelled swaras -- when more and more tones were discovered, it simply became convenient to retain the existing labelling and use different variations of one note rather than invent a new system of notes -- this may have only been reinforced by the discovery that the number of tones would only keep increasing with more harmonics. There is a clear sign of research into harmonics back in those days slowly expanding the range of available musical tones until it would have become too large to deal with -- it is likely that the labelling would have become too complicated for practical music and the differences no longer discernable to the human ear -- which is when that research ended.

Of course, this is before the advent of gamakas, which have promptly turned the concept of a note upside down. Now a days a swara is like a label for a phrase in a raga more than anything else.

[SrinathK]

Ranganayaki :
Would you say, Srinath, that that would be a fairly advanced answer for the purposes of the OP?

@Ranganayaki, The OP can be satisfied with post #13 IMHO.

You may safely ignore my post #16 -- I summarize it by saying that 22 shrutis and graha bhedam are just so amazing.

PS : Rasikas score : 400* Only 13182 to go before I reach @arasi's level (God, what kind of numbers ARE those?).

[vasanthakokilam]

Ranganayaki, yeah quite a resemblance in how you and I chose to rephrased the question. Nice!

Would you say, Srinath, that that would be a fairly advanced answer for the purposes of the OP?

I think so but then I may be misinterpreting the depth of the original question.

But, let me try to poke some holes in what you wrote in an effort to test my own knowledge on this.

I chose not to leave out vivadi combinations in my explanation (without actually referring to it), because the melakarta system of classification is very neutral and systematic and does not distinguish between vivadi and non-vivadi ragas. But it is an essential part of raga understanding. It does not distinguish between extensive ragas like todi and ragas that are little more than scales. It is the most logical answer to why 7 and not 12, because other explanations resort to a cultural response to the sounds, a certain stand on what constitutes beauty in sound and what constitutes the lack of beauty. I feel those are almost irrelevant to the answer of why 7. It is an arbitrary premise (4 sthanas, but only two swaras between s and m for example), and pure logic flowing from the premise.

I am with you when you say that other explanations resort to cultural response to sounds etc. I also see what you are saying about Vivadhi intervals. But to keep it the least complicated. I do not think the vivadhi intervals are needed for a logical answer of why 7 and not 12.

The simplest explanation is that you have 7 solfa syllables, 5 of which have two swarasthanas a H(igher) one and a L(ower) one. A scale should only have either the H or the L variety. That is it. If you had 12 solfa syllabes or ( 16 ) the equivalent rule will be quite complicated to state.

(The rule applies when you bring in Vivadi. In fact, the reason why they had to give a new name like R3 instead of using G2 is to satisfy the above rule. There are ragas where you want to use both G2 and G3 but that will violate this rule, so give G2 an alias R3, now you can have S R3 G3 which respects the rule)

[Rsachi]

Part 2 of nursery answer.
Musicality is the key. In order to make musically naturally melodious notes, you need fo choose notes with pitch values having a degree of separation. That's why the melodic canvas is presented by tambura playing Pa-Sa'-Sa'-Sa.. Fifths and thirds mentioned by Srinath.

In fact as Dr Oke in 22shruti illustrates, there are no-go zones inbetween note positions.

The seven notes chosen either with full notes or half notes having these separations - these are the scales listed in the melakarta system.

In a raga like Sindhu bhairavi you will have all 12 notes. But the music and melody comes in judicious phrases that combine musically beautiful sequences. Thats what makes music!

Imagine your masala box in the kitchen. You will have 12 spices, but at any time you cook, you will use seven at most using prudence and taste (=musicality!)

[SrinathK]

@Rsachi, I have tried to approach the question from a different angle (the Pythogorean one in fact). But your explanation is in fact the simpler one (a.k.a The just intonation system). Nevertheless, allow me to treat it a little more rigourously.

On any open string, it can generate harmonics in additional to the fundamental tone -- the higher harmonics are too weak to be heard, there's usually not that much energy. So you have Sa as the open string,

You can derive 6 harmonics naturally :
1st : 100 - S (Fundamental)
2nd : 200 - S upper (octave)
3rd : 300/2 = 150 - P
4th : 400/3 = 133.33 - M1
5th : 500/4 = 125 - G3 (The pythogorean tuning using only the numbers 3 and 2 for it's intervals can never generate a perfect G3 for which we must use the next prime number, 5)
6th : 600/4 = 120 - G2

7th is an incompatible harmonic w.r.t all the other intervals for the same reason that 7 is the next prime number. Beyond 6 harmonics, the higher harmonics have virtually no energy at all. (Actually, no one has to derive all the possible intervals using 7 since it balloons to a HUGE number)

But if you could use the 7th harmonic, you would have obtained 7/4 for M2, a perfect 7th, which is the most naturally consonant value and completed the natural scale for all 12 swaras. Yes, our prati madhyamas are all imperfect actually just like the Pythogorean major third isn't perfect But it is VERY flat. Romba keezha.

Then you could try :

8th harmonic = 800 / 7 = Nope, this will again go into the realm of the 7th harmonic (and we don't use this anywhere). (See 16th harmonic below)

9th Harmonic : 900/8 = 112.5 - R2
10th Harmonic : 1000/9 = 111.11 - R2 (lower shruti)

The eleventh is again incompatible as 11 is the next prime number, no one goes to this point. No string ever manages to generate it.

In fact the next possible ratio that is valid, is only on the 16th harmonic : 8x2/15 = 106.667 = R1 (Note : octaves don't apply. 8/15 is simply 16/15 but in the lower octave) -- so in another way it may also be considered a function of the 8th harmonic.

You can't go further. You can repeat the exercise on the P string and you will get D1, both the values of D2, N2, and N3 in addition. (I am using the modern popular terminology).

In this process you have obtained all 12 notes from natural harmonics only.

[Ranganayaki]

All those tuning scales are however Equal temperament, which is however fundamentally different from natural harmonic tunings. The 24 tone scale (from which the 22 shrutis come) is the only scale I know that actually manages to incorporate and overcome this Pythogorean comma. Also the 22 shruti scale offers a much more elegant framework for graha bhedam and change of key than does the scale of 12 - Equal temperament and it can be shown to have mathematically the smallest possible error.

We've discussed it all on that thread over there sir. If you wish to, you can see my spreadsheet. That number 22 is by no means adhoc. Whatever little that has been written in the old books like the Natyashastra are just hints dropped here and there (in a couple of cases I was pleased to see that when you tune two veenas to different pitches on the 22 shruti scale, notes on one veena will match with a different set of notes on the other veena (essentially this is a kind of graha bhedam between 2 veenas) and one example I was actually able to verify in my sheet, but beyond that it is not so clear and the translations I could get my hands on only make me wonder just what the authors were trying to convey, or whether they had managed to fully research the topic with the near zero technology at the time. We do not know if the scale we have today was even the same as the one our ancestors had experimented with. I have even wondered looking at shadja and madhyama gramas as to whether the Indians tried for some time to establish a standard of absolute pitch.

So the 22 shruti scale we have today is definitely a "modern one".

But we are vindicated by the mathematics (it requires nothing more than an ability to multiply and divide fractions). Rather than taking it as an incomprehensible lost art I just took it as though it was a hint to an experiment and stumbled upon the full range of graha bhedam results in a spreadsheet. It has now made me wonder as to the kind of criticism that GNB must have faced when he took up shruti bhedam, when we did not have the tools to prove it.

Fine intervals come in many forms. At the cost of jargon spamming : http://www.huygens-fokker.org/docs/intervals.html
The "modern" 22 shruti scale is either 100% accurate even in graha bhedam or the only error that appears on certain intervals is an interval of 32805/32768 (1 schisma), which is much smaller than the (glaringly dissonant) Pythogorean comma of 81/80. The math literally proves itself.

Descending back down to earth, it seems obvious to me why there would have been only 7 labelled swaras -- when more and more tones were discovered, it simply became convenient to retain the existing labelling and use different variations of one note rather than invent a new system of notes -- this may have only been reinforced by the discovery that the number of tones would only keep increasing with more harmonics. There is a clear sign of research into harmonics back in those days slowly expanding the range of available musical tones until it would have become too large to deal with -- it is likely that the labelling would have become too complicated for practical music and the differences no longer discernable to the human ear -- which is when that research ended.

Of course, this is before the advent of gamakas, which have promptly turned the concept of a note upside down. Now a days a swara is like a label for a phrase in a raga more than anything else.

[Ranganayaki]

Srinath, it's very interesting. I have come across the Pythagorean comma, and though it is easy to understand mentally as a concept, I was unable to observe it in reality as I can only use a tuned piano (equal temperament). If what I say sound as though I have misunderstood it, please do inform me (and explain, if you don't mind).

I never considered graha bheda through the notion of 22 shrutis.. Is it because each Shruti has a specific frequency and you can just transpose the scale by multiplying / dividing fractions? Do you find it more elegant because you can just do it mathematically? Instead of thinking of notes and intervals? Please explain.

[Ranganayaki]

VK, what you wrote sounds fine, just the same logic, with a slightly different premise, and therefore a different work-around. I accept that, but I just prefer my view. In my earlier response, I wanted to adjust my thoughts to "In my opinion, it is incorrect to say there are 2 Ri and 2 Ga..." I forgot to add those words.

But I don't think I misinterpreted the scope of the op's question. That's my feeling, unless you know a lot more about his background than I do.

[Rsachi]

What makes me think Sung is a woman?

[vasanthakokilam]

Ranganayaki, I do not know any better about the intent but I think our scopes are roughly in the same ballpark.

It is fascinating that this can all be approached at so many levels, all are absolutely valid.

My take on this is more of the vanilla variety which can be roughly summarized as how one forms a diatonic scale ( the 7 note part ) out of the 12 note chromatic scale. People of course have experimented with composing music in the chromatic scale itself but for the most part world music is all about picking 7 or less from the 12. I know calling all 7 note scales as diatonic is not quite accurate but the fundamental aesthetics of picking the 7 notes is all about how far away are the semi tone intervals from each other and in between those do you want two or three whole tones etc. . Stripped of all complications, it all boils down to that choice. Details vary of course. That is why both east and west have settled on 7 solfa symbols though the chromatic scale has 12 swarasthanas. ( that is my interpretation of the question Why 7 instead of 12 ). Now of course one can argue why not a scale like S R1 R2 G2 G3 M1 M2 S
That is where the separation of semi tones by whole tones come into picture as an aesthetic device. A very efficient and compact way to achieve that is through the solfa system and the rule to not have more than one variety of a symbol in a scale. This forces one to mix semi tones and full tones in picking the 7 intervals. Given only 12, one of course can't go to the other extreme of picking all whole tone intervals. 7 is indeed a great magic number for this purpose.

Indian Melakartha system takes full advantage of that power and takes it to its logical and full derivation (lack of dwi Madhya Melakartha notwithstanding - SKR came to the rescue of that )

[vasanthakokilam]

One aesthetic aspect that falls out of the CM Melakartha portrayal is the absolutely wonderful ragas that HM has produced that use both Madhyamas. SKR's conception of dvi Madhyamas melas is not meant to bring such ragas into the expanded Melakartha fold since in his scheme M2 replaces P. So it does not naturally accommodate the sweet sounding Behag with its 'P M2 G3 M1 G3' jeeva prayoga.
I wonder if Prof. Sambamurthy's proposed expansion of the Melakartha system (in which Aro and Ava scales can be independently picked from the 72 variations) can accommodate these kinds of wonderful imports from HM.

( as we discussed elsewhere Bhairavi kind of bashanga melas can be readily fit into the Sambamurthy scheme )

[Rsachi]

VKM, altho many women think it was accomplished by SRK, I think you mean of course the late TSKR!

[vasanthakokilam]

fixed

Just to make it clear, SKR - Late Sri. Thanjavur S. Kalyanaraman.

[SrinathK]

You can get the dwi madhyama melakarthas by graha bhedam on the existing 72.

I would like to share my personal opinion --- which is that CM has on the whole been very rigid to explore what it can REALLY do if the last 200 years of known history are evidence and it persists even now till date (like the above). But making that song list has given me an idea as to why -- it is hugely vast as it is and it requires our brains to push beyond their comfort zones.

@Ranganayaki, Hmm...I suggest visiting the 22 shruti site and that thread I linked up there. It was a LOT of work. Yes basically I start off with the 24 tone scale, isolate 22 from them and then what I do is --- if I make G3 at 125% as the new Sa, then I divide all the other intervals by 125% also. The notes below G3 have to be multiplied by 2x to fit in the new octave as the whole scale is shifting upward. All the other conclusions are inferred by doing this exercise on all 22 positions. With this in mind you can go visit that thread. Earlier also, this was again discussed in the technical section.

It shows that the system sacrifices some of the 22 intervals in other graha positions to ensure that you can play at least 12 tones from any position -- you need only 12 positions where you can perform graha bhedam AND still be able to sing minimum 12 tones, but the system allows you to do it on 21 positions (on one position it sacrifices the panchamam, making panchama-less scales possible). The 24 tone scale is not symmetric in ascent and descent but it will allow you to do graha bhedam on all 24 positions. And this is the most interesting point about the 22 shrutis -- in that the number of swaras used at any time are only 12 -- a powerful solution to address the problems of Just Intonation and multiple keys.

[Ranganayaki]

VKM, altho many women think it was accomplished by SRK, I think you mean of course the late TSKR!

.. Nice posts, #s 25, 26, VK!

Ho, ho! Rsachi, yeah, right.. What would womankind do without you to point us away from the dashing Bollywood heartthrob that SRK is!! I hadn't noticed that the initials didn't correspond, but I heard only recently about this work by tSKR.

Srinath, yes, just checked and the list of topics is long! I am curious, so I am likely to read up one of these days. Oh no, I read Topic 8: of course it does not work on a piano... I had already understood the logic of the Pythagorean comma, but I suppose I have to actually do some arithmetic, and some writing down to make progress. Will tear myself away now..

[shankar vaidyanathan]

Which then makes you wonder why the notes are labelled as what they are. You would wonder why an U-kara note or O-kara was never a swara.

While I am unsure that I have understood the OP sung's question correctly, Srinath's above text triggered another line of thought: Why the Swaras may have been named as they are?

This is a question I have struggled with for many years for which I don't yet have an intellectually convincing answer. I have read the evolution theory of naming the solfege in various music systems. As a Chemical Engineer, I have a rudimentary understanding of the basic physics of the frequency separation as described by Dr. VKV, RSachi, Srinath, Ranganayaki, and VK.

The convincing answer that I have come across is that "Sa" being the "Shadja" ("Shat" + "Aja" = Six + Unborn One (or the Creator = Creator of the Six)) is of course the tonic from which the other six Swaras descend. Other Swars don't exist in a vacuum without "Sa."

"Pa" being the "Pancham" (means five) denoting the perfect fifth (or 1.5) spaced Swar from "Sa." Having these two especially the tonic and a guiding baseline fixed leads us to the other solfege.

Which is where I struggle. I am not sure how the labels "Ri" "Ga" "Ma" "Dha" "Ni" evolved. I am not entirely satisfied with the explanations based on chakras, gods, animal or bird sounds. I agree however that having first labelled these Swars, the komal or tivra notes (flat and sharp) denote the relative positions and so may not need their own solfege. These seems to be a good logic for this.

When we "hear" the Sur that underlies the Swar, is that sound a short tone? Meaning "not" a long sound? The "Akara" method of singing brings it out perfectly. I am not saying that the "Ikara" "Ukara" "Ekara" "Okara" methods don't work but the "Akaram" seems to capture the spirit of the Swar and is pleasant to the ear.

[sureshvv]

Mainly bcos it is not some abstract stuff designed on paper and has to sound pleasant to the listener

[Nick H]

I was thinking... In western music, there is no wondering about the origins of the "note labels," because they follow a simple alphabetical sequence of letters. Then I remembered Do, Re, Mi....

And, of course, why did they start at C, not A?

(That is something Google might know, I guess...)

[cacm]

Which then makes you wonder why the notes are labelled as what they are. You would wonder why an U-kara note or O-kara was never a swara.

While I am unsure that I have understood the OP sung's question correctly, Srinath's above text triggered another line of thought: Why the Swaras may have been named as they are?

This is a question I have struggled with for many years for which I don't yet have an intellectually convincing answer. I have read the evolution theory of naming the solfege in various music systems. As a Chemical Engineer, I have a rudimentary understanding of the basic physics of the frequency separation as described by Dr. VKV, RSachi, Srinath, Ranganayaki, and VK.

The convincing answer that I have come across is that "Sa" being the "Shadja" ("Shat" + "Aja" = Six + Unborn One (or the Creator = Creator of the Six)) is of course the tonic from which the other six Swaras descend. Other Swars don't exist in a vacuum without "Sa."

"Pa" being the "Pancham" (means five) denoting the perfect fifth (or 1.5) spaced Swar from "Sa." Having these two especially the tonic and a guiding baseline fixed leads us to the other solfege.

Which is where I struggle. I am not sure how the labels "Ri" "Ga" "Ma" "Dha" "Ni" evolved. I am not entirely satisfied with the explanations based on chakras, gods, animal or bird sounds. I agree however that having first labelled these Swars, the komal or tivra notes (flat and sharp) denote the relative positions and so may not need their own solfege. These seems to be a good logic for this.

When we "hear" the Sur that underlies the Swar, is that sound a short tone? Meaning "not" a long sound? The "Akara" method of singing brings it out perfectly. I am not saying that the "Ikara" "Ukara" "Ekara" "Okara" methods don't work but the "Akaram" seems to capture the spirit of the Swar and is pleasant to the ear.

I have paintings by S.RAJAM ON THE SAPTHA SWARAS BRILLIANTLY EXECUTED BY HIM ( at my wife's request) with his notes.. EVERYDAY I study it for at least 15 minutes as he has incorporated EVERYTHING there is to know about their origin & covers WHATEVER HAS BEEN WRITTEN ABOUT THEM: Mythology, COLOR, ORIGIN, MUSICAL ASPECTS, from VEDAS & PRACTICALLY ALL OTHER ASPECTS. The subject is very deep& profound & has to be STUDIED in great detail....VKV

[Ranganayaki]

The convincing answer that I have come across is that "Sa" being the "Shadja" ("Shat" + "Aja" = Six + Unborn One (or the Creator = Creator of the Six)) is of course the tonic from which the other six Swaras descend. Other Swars don't exist in a vacuum without "Sa."

I never thought of such a sandhi (or perhaps rather a samaas), but this is interesting. However I want to disagree with you. Shat and aja together would not be shadja, but Shataja or Shadaja. So it cannot be Aja or creator. On the other hand it can be the created.. Like Neeraja for the lotus born in the water, or Bhoomija for Sita, daughter of the earth where she was found..

This agrees with the idea of a tonic, the notion where all the notes seem to pull you towards the shadja, or they come to rest at the tonic, and the tonic is born of the six, Shat + Ja the note which is created of the other six, created from the other six, or to which all the other six tend to settle at.

I like this idea.. seems quite pretty. Would love some feedback, and thank you, Shankar Vaidyanathan.

[Ranganayaki]

I have paintings by S.RAJAM ON THE SAPTHA SWARAS BRILLIANTLY EXECUTED BY HIM ( at my wife's request) with his notes.. EVERYDAY I study it for at least 15 minutes as he has incorporated EVERYTHING there is to know about their origin & covers WHATEVER HAS BEEN WRITTEN ABOUT THEM: Mythology, COLOR, ORIGIN, MUSICAL ASPECTS, from VEDAS & PRACTICALLY ALL OTHER ASPECTS. The subject is very deep& profound & has to be STUDIED in great detail....VKV

That is very interesting, Sri VKV. Would you please share these? I am sure everyone will appreciate it. Thanks so much!

[shankar vaidyanathan]

Ranganayaki,

In fact, "Shadaj" is how "Sa" is referred to in HM.

Dr.VKV,

I have seen a painting similar to what you describe. Kindly post a photo at your convenience.

[Ranganayaki]

The word is of Sanskrit origin. What happens to it in Hindi is a distortion of the Sanskrit, but valid in Hindi. I wanted to give a different example of such a distortion but decided against it as it is truly an incorrect form that Hindi speakers tend to resort to. In any case, we are discussing etymology here and not later development or a contemporary usage in a parallel culture.

[kvchellappa]

'shat asmat jayante iti shatja' is perhaps etymologically correct. What is the rule for saying shat rest in this?

[kvchellappa]

I asked TMK whether the sthana of the letters (like head, palate, etc.) and that of the swarasthanas coincide and he said, 'I do not think so.'

[Ranganayaki]

I asked TMK whether the sthana of the letters (like head, palate, etc.) and that of the swarasthanas coincide and he said, 'I do not think so.'

You mean like the way the names of the swaras are pronounced, such as pa ma being bilabials of two kinds? I don't see how that can relate to the name.. Obviously ri is a short form of Rishabha and Ga is a short form of Gandhaara, and that's where you need to look for meaning. The swara name is not really ri or ga, so it would not work.

I am trying to figure your sentence out, it does not seem to fit grammar-wise to our context. Could you or anyone else please explain?

[Rsachi]

Ranganayaki, Chellappa, Shankar and co.!
Here is aomething I read a few weeks back thinking exactly on the same lines as you folks, and which I have scanned for you- page 1598 of the original Apte Sanskrit Dictionary (printed in 1890 and hence the scanned image has lost some details and Sha character's slanting inner line has not been captured) :



Shadja as defined here is the fourth note of the sequence Pa Dha Ni Sa Ri Ga Ma (as per one particular convention)
It is called Shadja because the sound Sa musically rendered, comes from engagement of SIX anatomic parts:
Nose- nAsa
Throat-kaNTha
Chest-uras
Hard palate-tAlu
Tongue-jivha
Teeth-danta

Literally the Sanskrit statement above means:
From six organs born/derived - as it is so, therefore is it so remembered/named.
Wonderful definition, is it not! I am amazed.

Here is another resource

[Ranganayaki]

Shadja as defined here is the fourth note of the sequence Pa Dha Ni Sa Ri Ga Ma (as per one particular convention)
It is called Shadja because the sound Sa musically rendered, comes from engagement of SIX anatomic parts:
Nose- nAsa
Throat-kaNTha
Chest-uras
Hard palate-tAlu
Tongue-jivha
Teeth-danta

Literally the Sanskrit statement above means:
From six organs born/derived - as it is so, therefore is it so remembered/named.
Wonderful definition, is it not! I am amazed.

Yes this and the online sanskrit dictionary that I checked do seem to resolve the question of shadja being "born of six". It's amazing that you have found a reference to this.. But according to this, Shadja alone is born of the six senses.. Rishabha and Gandhara, etc. are not. If the note called Rishabha is fixed as Sa, now suddenly that note is produced by the engagement of six senses while previously it was not?

What am I missing?

Also, I try to say Sa.. my Nose is quite disengaged. Ma and Ni alone engage the nose in pronouncing the note-name.

I don't mean to be argumentative... I still prefer the more dynamic idea of one being born of six others, it is just a conceptual birth.. The tendency to resolve to a tonic, that point of equilibrium.

[vasanthakokilam]

Actually, 'that out of which 6 others are born' would make more sense, wouldn't it?

[kvchellappa]

Not born of six senses, but born in six sthanas physically.
My doubt was whether the sound of say, ri in the scale and the aakaara emanate from the same sthana.
For example, Rsachi has come with how sa is from six sthanas. I am not capable of making out whether it is in practice so. Similarly whether there is any correlation like that for all the swaras, but TMK clarified it is not so.

[kvchellappa]

Etymologically, what VK says must be right, but what that six would be is for a musically knowledgeable to define.

[kvchellappa]

NSG also defined it as the source of six other swaras and prima facie it appealed to me.

[Rsachi]

Sandhi
ShaT+ja = six+born of.
Not parent of, but child of six.

Also Shadja, being the fundamental, got a lot more attention and definition I think in nomenclature. They surely wanted the muscian to sing Sa right!

Panchama would simply mean fifth from Shadja.
Ri or ऋषभ comes from bull, Ga from Gandhara (Kandhahar, centre od Buddhist culture etc), Ma from being the middle note. Ni comes from nishada or Hunter. I could not find any etymology for Dha.

[vasanthakokilam]

Thanks Sachi.

Yep, M and P makes perfect sense. In Tamil, we would call that ' kAraNappeyar'.

When it comes to meaning of names like this, I usually go through a 'may be note, may be, may be not' cycle.

One side of me thinks that we should not take these names too seriously. We typically err on the side of considering our ancestors to be all super brilliant and perfectly logical people. In reality, that is not true, they easily could have messed things up.

But on the other hand, Sanskrit because of its very nature forces people to name things along the lines of 'kAraNappeyar'. I remember reading about a Pre-Panini Sanskrit grammarian declaring that all we have are verb roots and all nouns without exception come out of those verb roots. That is a pretty strong statement indeed. That is why there are 100 different names for the same thing since it participates in so many different actions in the real world. That is why a 'chair' is nothing if not for its function of 'being sat on'. Given all that, an important name like Shadja has to denote something that informs of its purpose, what it is and what 'verb/action' it is associated with.

The one big problem with taking this route is, people seem to spin up derivations that may make sense in general but may not be true in reality. We hear about such derivations for words like tala, laya etc.. We Indians as a group are gullible on that front. If it refers to something spiritual, cultural or ancient, we tend to imbibe it without critical examination and most often some how go out of our way to accommodate them. Sanskrit especially has that hold on us, you quote something in Sanskrit, it acquires some amount of sheen and believability instantly. ( I recall now the practical joke Cho played in Thuglak long time back capitalizing on this gullibility )

So where does this leave us with the meaning of Shadjam. I do not know. All the ones we have thrown around seem to have major issues. One thing to examine is to take the meaning on its face value (what Sachi quoted) and see if things were once like that. That is, in this case, Shadjam is indeed a culminating result of 6 swaras thus it is the 7th swara, rather than the first swara. Just thinking out aloud, I am not sure if that will lead us anything but this is based on the belief that Shadjam was named that way because at one time in the past it made sense to name it that way even if it does not make sense any more since its meaning may have totally flipped.

[cacm]

quote="Ranganayaki"
I have paintings by S.RAJAM ON THE SAPTHA SWARAS BRILLIANTLY EXECUTED BY HIM ( at my wife's request) with his notes.. EVERYDAY I study it for at least 15 minutes as he has incorporated EVERYTHING there is to know about their origin & covers WHATEVER HAS BEEN WRITTEN ABOUT THEM: Mythology, COLOR, ORIGIN, MUSICAL ASPECTS, from VEDAS & PRACTICALLY ALL OTHER ASPECTS. The subject is very deep& profound & has to be STUDIED in great detail....VKV
That is very interesting, Sri VKV. Would you please share these? I am sure everyone will appreciate it. Thanks so much!

DEAR RANGANAYAKI,
DO YOU HAVE THE BOOK "MUSINGS ON MUSIC" BY S.RAJAM? In that book he has Sapthaswaras painrtings based on details available from Sri. Harikesanallur Muthiah Bhagavathar's "Sangeetha Kapla Drumam". The paintings he specially painted for my wife & me are QUITE DIFFERENT & uses avaivalabe datafrom many other sources.
It will take quite a bit of time to photograph them & mail them. Where do you live? Pl write your email. I live in Los Alamos, N.M. Regs, VKV