Origin of the special terms Kaikasi and Kakali for Nishadam

[arunk]

vk,

Both gramas are as old as whatever information in texts we have - i.e. they make their appearance as two (evolved) "equal" i.e. peer entities from the very early texts. In fact Bharata and Dattila talk of an even older Gandara Grama (which they claim is found only in heavens).

While the texts recognize getting from one grama to another (i.e. sadja <=> madyama) by sruthi-adjustment, both gramas are of equal status. ALL music entities then were classified by gramas. How/whence the gramas came about - as far as I know, there is no direct information in the text.

Regarding sruthi vs swara vs grama:
(Ref: Mukund Lath on Dattilam)
Bharata takes svara as a topic first, grama second topic and then sruthi and implies that sruthis are subservient to not only swara but also to grama. Another author Visakhila also places sruthi after grama and quotes similar reasons as Bharata.

But Dattila takes sruthi first. Then svara, then grama, He says svaras arise from sruthis. Matanga takes similar course and says "through the process of deduction (arthapatti), inference (anumana) and through direct perception sruthis are found to be the cause that manifests svaras.

So basically there is some difference of opinion. All this suggests, that these may have been different schools of thought on a subject which may already have been evolved for a while. So which came really first etc. - we may not find the answer in the texts themselves.

One possible hypothesis (on the fly as I type this , the basis of which is that theory almost *originates* from practice (after which they feed of each other). So perhaps practice i.e. music in practice in the form the tunes/melodies came first. Then came analysis. Perhaps this resulted in (pitch) "intervals" translating to svaras. Then classification into gramas - then someone did analysis on the difference between them to give raise to the sruthis.

But does this mean that sruthis are a by-product of earlier stuff? We found molecules first, then atoms, then sub-atomic particles. So would you call atoms a by-product of a molecule or the underlying cause?

Arun

[vasanthakokilam]

Arun: Excellent. What you wrote addresses exactly what I was wondering about. I was worried I may not be expressing my question clearly.

And what you hypothesized is what I was looking for as well. That makes reasonable sense to me. That is the chronological order of discovery but then it may turn out the reverse is how it actually is. That is fine and your example of the molecules is right on the money. That is how both experimental and theoretical science has progressed, along with predicting and validating a few things in either direction ( further lower levels of detail or at a higher level macro phenomenon. ).

Since we are at the same wavelength, let me push my luck further and ask this, in case you are prone to thinking about the underlying 'meaning' behind experimental proceudres and the mathematics. I have not yet fully absorbed the experiment and the mathematical derivation. Let us assume that the two gramas are independent and were 'revealed' to our forefathers, thus making them axioms in a true sense. Is there something inherent in those two gramas that enables the sruthis to be found by the two vina experiment? In other words, hypothetically, if another two pairs of gramas were 'revealed', are the sruthis 'detectable' through such experiments and secondly, would the ratios of those resulting sruthis be different? I am trying to see if the S and M gramas are accidental or their evolution ( survial in practical terms, they were the ones ended up in normal practise ) was in a way due to the underlying sruthis.

[uday_shankar]

One possible hypothesis (on the fly as I type this , the basis of which is that theory almost *originates* from practice (after which they feed of each other). So perhaps practice i.e. music in practice in the form the tunes/melodies came first. Then came analysis. Perhaps this resulted in (pitch) "intervals" translating to svaras. Then classification into gramas - then someone did analysis on the difference between them to give raise to the sruthis.
Arun

This hypothesis has merit and I would bet my money on it. In fact it should be writ in gold.

vk,

It angers me to speculate that these "shrutis" were a divine "revelation" to some wise forefathers.

There is nothing sacrosanct about the "22" shrutis or the particular set of "22" shrutis that would turn out to be the final set, or about the gramas. It's just a random, incidental evolution.

Far greater analysis, experimentation and evolution has been done by pioneers of western instruments, without without making tall claims of any divine "revelation".

In contrast to the splendid research in instrumentation in the west, the Carnatic world has evolved a rather sub-optimal resonator and ambiguous fretting for its flagship "divine" instrument, the vina. Even the vina that was "handed by the goddess saraswati" to Dikshitar in the Ganga suffers from this suboptimal resonator and ambiguous fretting from what I can make out from photos. Saraswati must have been a suboptimal "divine" scientist.

On the other hand, the infidel Amir Khusru and his associates were far better instrument experimenters and came up with the superb idea of movable frets and "soraikkai" resonators as well as the one-playing-string idea for the sitar.

It is foolish to ascribe any "divine" revelation to every secular subject known to man. Music is a secular subject.

[nigamaa]

Cntd shruti
Fact not fiction
11 th shruti Vajrika aka Dhumaketu (Vishnu Purana) akin to Bible St. John Revelation chapter on Armageddon
Actual Polaroid photo taken from blue sky here, photo No 4
http://www.rosesfromheaven.com/miraculous_photos.htm
quote
Photo taken on the Vigil grounds in the early '70's, which shows a full view of the the comet God is planning to send our way before the year 2000 unless we amend our lives.
end of quote
On scientific background see TV documentary online ZDF Armageddon
Impaktsimulation
http://www.zdf.de/ZDFmediathek/startseite
select Armageddon part 1 and 2

now anyone pls xplain how this is not “supernaturalâ€

[arunk]

Uday/vk

I am not sure but perhaps vk was attaching some importance to this sentence in my write-up:

Hence, it is my opinion that the magnitudes of the ratios for each division were perhaps not carefully designed to have specific values such that they yield singable intervals every step of the way. They seem to be just a consequence of the difference in pitches between the panchama of the shadja grama and madhyama grama.

Why 22? Can it be only 22?
My Take - A hypothetical scenario: Let us assume that we were at a point of time Bharata's world, before they/he knew of how many sruthis. He knew how to tune the vina/harp just based on how the individual tones sound given say a particular pitch for sa for sadja grama. That is he had two vinas one in sadja grama, and one in madyama grama and their "sa's" and "ma's" matched. He didnt know how many sruthis there are between adjacent swaras, just knew their individual tones by 'playing it by ear'.

Now note that AT every step of the experiment, each reduction is defined as one that reduces from one swara in chala vina whose "destination pitch" matches a swara on the dhruva vina. Here is a quote on the reductions from my writeup:

• The first reduction is such that panchama becomes consonant with "original" rishaba,
• The second reduction is that the new gandhara/nishada (following the first reduction) matches the original rishaba/dhaivata.
• The third reduction is such that new dhaivata/rishaba (following previous reductions) matches the original panchama/shadja.
• The final reduction is such that new madhyama/panchama (following previous reductions) matches the original gandhara/madhyama.

So the amount of reduction always makes that swara match another "swara-sthana" (warning: bad usage - but I hope you get my point).

If you do the math, I believe that you will see that this will inevitablly lead to 22 and only 22 decrements/sruthis - because of the spacing of the intervals in each gramas and their sole difference in the ma-pa spacing. Again, this was something I am not sure if it is highlighted. I do think the texts (Bharata? Sarngadeva? Dattila? not sure) say that there can be only 22 sruthis - although some later texts prescribe higher number (to infinity)

Now, one's personal inclination may lead them to then see this as proof that there can only be 22 sruthis and not because 22 is some universal, metaphysical constant!

Yes for this specific case of music, and specific prescription of sruthi-spacing (i.e. reduction principle), 22 it has to be. But can one go and say ancient Greek Music, or Jewish music would also be be only 22 if we looked close enough, because 22 is universal constant, or any other music which claims to have other "isnt divine" etc.? Well some may so, and some would dismiss it.

If you go by the basic definition of sruthi i.e. something discernible to ear, I do think you can have way more than 22 (or less depending on our hearing abilities) . So I do not think 22 is magical, it just is the correct answer for that particular system's parameters.

Innate in the structure of sadja-madyama grama that led to their development?
I am not sure. If you ask me a ri of 9/8 (i.e. pretty much how we use today) would have been even more perfect . But for some reason they avoided it (it just doesn't fit for several reasons).

But seriously, I have scratched my head as to WHY there were 2 gramas which given the same mUrchana (i.e. sa to Sa, or ri to Ri, ga to Ga) would be nearly identical in structure except for one interval being different by a mere 22 cents! What was the purpose of the 2 gramas? Now people do say - that our ancients were able to differentiate music at such a fine level would tell us how great they were, and what we have lost over a period of time. Perhaps, but I would like to see the practical side. I would like to think evolution of Indian music follows normal courses of human evolution. Our good people arent that more blessed than good people in the rest of the world that out Gods will give us something that they wont give others.

(Note: In the above 22 cents only if 10/9 is assumed for ri. You assume a lower value for ri, it will grow larger)

Sometimes I guess that there were perhaps two independent schools of music which had slightly different tunings. In those daysm communication was not like today and so it is quite possible that the two schools evolved well but within some common framework (established by religion?). Both became equally important - and when they merged both were considered peers etc. You consider this with the (older) Gandara Grama which one author (a certain Narada) gives utmost importance - perhaps yet another school which followed yet another tuning.

But it doesnt add up. If the differences were "slight" you would think when the merge happened (i.e. by Bharata, or atleast by Matanga) the classification to different gramas would sort of loose importance. It didnt - for a long time (until 14th century - a very long time).

Some have argued that this could be "just respecting tradition" at the expense of having books "not be that much touch with current practices" (i.e. more in tune with past, than present). There is definitely some truth to the basic premise of that but all it does it completely muddles the picture - how then can you say which is true and which is not in that text? It becomes completely subjective (not that this topic isnt to begin with )

PS: Sorry for the long post

Arun

[uday_shankar]

Arun

In fact noting the "22 cent" discrepancy (didn't know the calculation then) in a fretted vina a long time back is what led me to think about these things in the first place. So even lots of "contemporaries" can routinely distinguish 22 cents. The question of how important it is to a moving melody is a different matter.

I've trained myself to like 9/8 for R2 but I can tolerate 10/9. In most moving melodies I try to "hit" that, however right or wrong. Statistically, I think I should be quite close.

However, for D2 I am less tolerant. I would insist on 5/3 and I find 27/16 too high. A prominent violinist of yesteryears used to play D2 slightly higher, perhaps stemming from the notion that R2 and D2 are at the "same distance" on different strings.

The following is a general "rant" not directed at Arun :

There are many magical constants in nature (you must know about the famous fine structure constant 1/137) , but so what ? Independently the west and India have come up with 12 useful intervals for melodies. In between the two pardigms, there's Arabic music with really unusual intervals which have influenced (as far as I know) neither the west nor India.

In fact one may claim some magical significance of 22 cents and 22 shrutis not to mention that there are 7 "divine" swaras, the saptaswaras each one standing for the saptarishis, and miraculously 22/7 is an approximation for the "transdendental" number pi. Is anybody ready to swoon yet ?

Such "connections" are an unfortunate attempt to find mysticism in pedestrian mundane phenomena. The real and only mystery is that of life, death and self-identity. That was the basis of Nachiketas' inquiry and it is the only inquiry really worth undertaking.

[cmlover]

Uday
11 is a very important Vedic number, since there are ekAdasha (11) rudras. Of course the rudras have to be accompanied by their shaktis which leads to the number 22. Hence 22 is magical

if you are still not convinced note that 22 is the smallest number divisible by 2 and 11. Even Lord MahEsha cannot find another such number ( as venkatamahi would say

Now the coup de grace!
UDAYSHANKAR = 11
What is Uday without Radhika accompanying which leads to 11x2 =22

So don't put down the foresight of our ancient seers

[uday_shankar]

what a mischief maker .

[vasanthakokilam]

Uday_Shankar wrote: It angers me to speculate that these "shrutis" were a divine "revelation" to some wise forefathers.

It is foolish to ascribe any "divine" revelation to every secular subject known to man. Music is a secular subject.

Easy, easy, now.. no need to fly off the handle

Since what set you off is the word revelation, I owe you this explantion. I put that word in quotes to take care of a wide variety of possibilities on how that came into being. That is just another way of saying that it is an Axiom. That is all.

Also, that is so miniscule and incidental to the point of that post.

BTW, you are on the same wavelength as I on what is significant regarding spirituality and about ascribing divinity to normal things. But that is a separate topic.

[cienu]

CML ,

That was indeed a good one

[uday_shankar]

vk,
Sorry but even the mock "anger" is really directed elsewhere .

[vasanthakokilam]

I am not sure but perhaps vk was attaching some importance to this sentence in my write-up:

Arun, yes..I was indeed attracted to this topic by such content that you wrote.

If you do the math, I believe that you will see that this will inevitablly lead to 22 and only 22 decrements/sruthis - because of the spacing of the intervals in each gramas and their sole difference in the ma-pa spacing

So, what math is at work here? pair-wise Combinations and Permutations? Can you think of the formula to get at 22 from the two 7s and the algorithm.

[arunk]

So, what math is at work here? pair-wise Combinations and Permutations? Can you think of the formula to get at 22 from the two 7s and the algorithm.

I didnt mean a formula (maybe there is - i dont know). Just that if you work the reductions out step-wise (i.e. like I did), you will find that from ri to sa there are 3 reductions, ga to ri there are 2 reductions. ma to ga 4, pa to ma 4, da to pa 3, ni to da 2 and sa to ni 4 etc. leading to the spacing between the swaras expressed in shruthis. You add all to get 22 - i.e. 22 sruthis in an octave.

This is only significant if you presume at the start you did NOT know what spacing the swaras had and how many total # of shruthis there are. Perhaps significantly, this 22 is preordained by the precise prescription of the reduction i.e. reduce a particular swara in the chala vina such that it matches a certain swara in the dhruva vina (except the first step where it is reduction such that pa on the chala vina is samvadin with ri).

If you look at this from one angle, it can seem significant. If you look at it from another angle (i.e. assume there are 22 to begin with), then it is "no revelation". Just re-dressing - it is simply a different side of the same problem i.e. simply describing what is known in another way

Arun

[arunk]

Is anybody ready to swoon yet ? .

[vasanthakokilam]

Uday, understood.

If you look at this from one angle, it can seem significant. If you look at it from another angle (i.e. assume there are 22 to begin with), then it is "no revelation". Just re-dressing - it is simply a different side of the same problem i.e. simply describing what is known in another way

Exactly. That is what I am trying to understand at that one level of depth. I will have to read your write up again to see if the 22 sruthi assumption is somehow built-in in that experimental setup. I am going by your hypothesis that the two gramas were in practise indepdently and then proceed with the experiment.

This is also related to adding all those steps to get to the number 22. I need to understand clearly where the 2, 3 and 4 etc. originate in that step wise reduction process involving "ri to sa there are 3 reductions, ga to ri there are 2 reductions. ma to ga 4 reductions, etc." and make sure there are no circular assumptions.

[vasanthakokilam]

Arun, one question on this scheme of sruthi->Swara->Grama->jAti..

I understand that there are 7 suddha-jAtis and 4 of these come from the Shadjagrama and 3 from Madhyamagrama. Do they use the same notes as their parent grama or variations there of? How many of these are sampoorna, 6 notes and 5 note jathis? Are the sampoorna jAti then same as the grama itself?

Our hypothesis of 'practise led to the theory' actually need to start at the jAti since that was probably what was on the 'streets' so to speak. It will be a good intellectual exercise to speculate if the jAtis actually gave birth to the Gramas as a unifying principle. That may shed some light on why these two gramas.

I am fascinated by this for another reason as well. In Europe, the western classical music struggled with getting rid of those tritone (devil's notes) but could not and so started mucking with different tuning systems and approximations and getting nowhere. Our people seemed to have run into the same problem but solved it differently by creating two tuning systems based on these two gramas. The musicians probably picked a particular Grama tuning that matched their consonance requirements. That probably afforded them considerable flexibility

[uday_shankar]

and so started mucking with different tuning systems and approximations and getting nowhere.

1. Complete nonsense. They got to the signal achievement in tuning in the world - equal temperament.

2. The requirements of harmony and melody are entirely different. The audacious and completely successful achievement of equal temperament is amazing.

3. For Indian music, on the other hand, where you have ONLY a single running melody, ANY tuning is fine. There is really no "problem" to be solved. We can fix a note slightly higher or lower and be none the wiser. Hence Indian music works with several different, but close, tuning systems. Including equal temperament (harmonium, U srinivas, etc...). Potentially, for each raga, you can use a different tuning system, grama, etc.. and be none the worse.
(This is essentially the same as your point , just like to hear my own voice)

Having said all that, I don''t like to play Indian music using equally tempered scale.

[vasanthakokilam]

Uday, I know that. I was referring to the struggles that they went through in their early stages of evolution, possibly the same struggle Indian musicians went through a few centuries earlier. 'going nowhere' was meant to point out an inherent problem in an all integer ratio based tuning systems. Our people seemed to have taken a more practical approach of adopting two tuning systems depending on the melodic need.

I personally would not call the equal tempered scale an achivement of any earth-shattering significance ( significant indeed ). That approximation was necessary for their environment. People do realize that but it is a major convenience and Bach, by composing the heck out of that scheme, solidified its place in their system. Anyway, not a topic for this thread.

Since you brought up harmony, here is a thought from left field ( only tangentially related to the above point ). The use of the drone and fixed ground note ( aadhara shadja ) convention seem to be a later evolution in Indian music. This is just a speculation but without a drone and without a fixed aadhara note, I can imagine Ancient Indian theatre with multiple instruments playing polyphonically. Don't ask me to provide proof, it is just my gut feel reading through the history of evolution of the music. The only supporting evidence is, the Suddha Jati based melodic lines seem to allow for the starting note to be different. So if two instruments play two consonant jAtis simultanesouly that would indeed be polyphonic.

[uday_shankar]

Interesting.

Also worth examining the limiting effect of having panchama in the drone which I think is a very recent evolution ? If I'm not mistaken even in recent times, for example Tyagaraja type of unchavritti folks went about town with that small single stringed tampura and a chipla kattai ?

These days I try to practice (during the bluemoon, of course) with just shadja drone and it is a much better experience.

[arunk]

Ok. Here is an example to elucidate why 22 is a direct result of the following
1. The spacing of the two gramas (and thus) the difference(s) in the spacing of the gramas.
2. The way the reduction is defined/stipulated and how that is equated to sruthis (i.e. if it took 3 reductions to get from swara A to swara B, then it is implied there are 3 sruthis in between.

Consider this hypothetical world had 2 gramas X and Y.
1. X is identical in "spacing" to sadja grama.
2. Y is sort of like madyama grama but its pa was even "flatter" say mid-way between the ma-pa
of sadja grama, specifically such that M-P of Y-Grama is same distance as R-G and D-N.

We dont know the # of sruthis in the spacing, but we know that we the following "sizes" of intervals
1. R-G (both gramas), D-N (both gramas), P-M (Y-grama), Px-Py (difference between the two gramas)
2. S-R (both gramas), P-D (X-grama)
3. G-M (both gramas), M-P (X-grama), N-S (both gramas),
4. P-D (y-grama)

In other words, e.g. we can discern that spacing of #4 > spacing of #3 > spacing of #2 > spacing of #1.

The spacing of the two gramas is as follows:

Code: Select all

             S   R  G     M     P   D  N    S              (X-grama)
             S   R  G     M  P      D  N    S              (Y-grama)

In the above the amount of spacing between two swaras is proportional to the pitch spacing.

I will show that if the gramas were like this, we would be talking about 15 sruthis and not 22
(although I will not vouch for 100% accuracy in my approach)

Initial configuration:
There are 2 vinas X1 and X2 tuned to "X grama". I will throw in a third one
tuned to Y-grama just for reference (initially)

Code: Select all

             S   R  G     M     P   D  N    S              (X1)
             S   R  G     M     P   D  N    S              (X2)
             S   R  G     M  P      D  N    S              (Y)

REDUCTION #1:
We drop P of X2 vina down to match P of Y-grama vina. As a result the vinas look like:

Code: Select all

             S   R  G     M     P   D  N    S              (X1)
          S   R  G     M     P   D  N    S                 (X2)
             S   R  G     M  P      D  N    S              (Y)

X-Grama Inference: Note that ga of X2 matches ri of X1. So in one reduction we got ga down to ri. So ga-ri interval is 1 "sruthi". Also ni of x2 matches da of x1. So da-ni interval is 1 "sruthi".

So we have ri-ga = 1, da-ni = 1.

Y-Grama Inference:. Since ri-ga and da-ni interval is same as X-grama, we get ri-ga = 1, and da-ni = 1 here too. Since this is spacing #1, we know that M-P of Y-grama belongs to that category and so it must be 1 too.


REDUCTION #2:
We drop ri of X2, down to match sa of X1. As a result, the vinas look like:

Code: Select all

             S   R  G     M     P   D  N    S              (X1)
         S   R  G     M     P   D  N    S                  (X2)
             S   R  G     M  P      D  N    S              (Y)

X-Grama Inference: We see that ri matches sa - obvious as that was what we were attempting. It took us 2 steps to get the ri to sa. So sa-ri interval is "2" sruthis".

Also note that da of x2 now matches pa of x1. Again 2 reductions to get da down to pa. So pa-da interval is "2" sruthis".

So we have sa-ri = 2, ri-ga = 1, pa-da = 2 and da-ni = 1

Y-Grama Inference: The da-ni interval of Y grama matches that of X-grama and so in Y-grama we have: sa-ri = 2, ri-ga = 1, ma-pa = 1, and da-ni = 1.

Note: The pa-da interval of Y grama is NOT the same as X-grama.

REDUCTION #3:
We drop pa of X2 down to match ma of X1. As a result, the vinas look like:

Code: Select all

             S   R  G     M     P   D  N    S              (X1)
       S   R  G     M     P   D  N    S                    (X2)
             S   R  G     M  P      D  N    S              (Y)

X-Grama Inference: We see that pa of x2 now matches ma of X1. So we took 3 steps to get pa down to ma's level. So pa-ma interval is 3 sruthis.

We also note that ma of X2 matches ga of X1, and that sa of X2 matches ni of X1. So We also note that sa of x2 now matches ni of x1 and so sa-ni interval is 3 sruthis. So ga-ma and sa-ni are also 3 sruthis.

So we have sa-ri = 2, ri-ga = 1, ga-ma = 3, ma-pa = 3, pa-da 2, da-ni = 1, and ni-sa = 3. We have all that is needed for X-grama. The total is 2 + 1 + 3 + 3 + 2 + 1 + 3 = 15

Y-Grama Inference: The sa-ri interval, ga-ma and ni-sa intervals of Y grama are the same
as X-grama. So we can use above.

So for the Y-grama we have: sa-ri = 2, ri-ga = 1, ga-ma = 3, ma-pa = 1, da-ni = 1 and ni-sa = 3.

We still dont know pa-da. But way back in the initial configuration D for X2 matched D of Y. We have done 3 reductions and it is at not yet at Pa but close to it (see above). Hence we carry one more reduction.

REDUCTION #4:
We drop da of X2 such that it matches P of Y. As result the vinas look like

Code: Select all

             S   R  G     M     P   D  N    S              (X1)
      S   R  G     M     P   D  N    S                     (X2)
             S   R  G     M  P      D  N    S              (Y)

Y-Grama Inference: The da of X2 matches P of Y. It took 4 reductions from the initial configuration and so pa-da interval in Y-grama is 4.

So we have for the Y-grama: sa-ri = 2, ri-ga = 1, ga-ma = 3, ma-pa = 1, pa-da = 4, da-ni = 1 and ni-sa = 3. The total is 2 + 1 + 3 + 1 + 4 + 1 + 3 = 15

So 15 it is in these two pairing of gramas.

[arunk]

Our hypothesis of 'practise led to the theory' actually need to start at the jAti since that was probably what was on the 'streets' so to speak.

Cant say. Melodies were there, which got classified into jatis that belong to gramas. This classification itself implies theoretical analysis.

Arun

[vasanthakokilam]

Arun,

Thanks for your effort in presenting this to us. I like the graphical approach you took, so all this 'sliding' and alignment bring out the nature of the experiment and subsequent inferences very clear.

first a possible typo:

>2. S-R (both gramas), P-D (Y-grama)

Did you mean to write "2. S-R (both gramas), P-D (X-grama)"

Second, in this hypothetical 15 sruthi scheme, the sruthis are wider than the 22 sruthi scheme, right? I guess that is obvious but your initial setup itself demands that the resulting sruthis are less than 22 since you are picking a larger difference between Px-Py. But I have a significant question on this.

>1. R-G (both gramas), D-N (both gramas), P-M (Y-grama), Px-Py (difference between the two gramas)

I can see how one can satisfy your stipulation that P-M ( Y grama ) is same as R-G. That can potentially be done by ear. But how did Px-Py become equal to R-G. That is critical to your first inference. May be I am missing something.

( Also, your stipulation that "pa of Y is mid-way between the ma-pa of sadja grama, is it just a mention in passing since you also prescribe that it is located at the same distance from M as R-G or is that significant as well?).

If I get over ( gloss over ) this block, the rest of the procedure makes sense.

BTW, are we taking it in good faith that all these reductions amount to 'equally spaced' sruthis? That does not seem to be an automatic conclusion based on your experiment. ( May be you already addressed this in your original write up ).

Outside of all this, one fundamental question on the experiment. What is the vina player's responsibility in this experiment? Just to execute the step as prescribed "drop P of X2 vina down to match P of Y-grama vina" or in adition also check other matches by experiment, like ' ga of X2 matches ri of X1 ( instead of looking up the table for 4 groups of known equal interval positions ).
The reason I am asking is I do not know where your 4 groups of "known" categories of equal intervals come from. But if the vina player can figure out the second match 'G of X2 matching R of X1', then we do not need that a priori group of 'knowns'. If that is done, then it is truly an experimental discovery process. But the way you presented helped me understand what is going on much more clearly. May be that was your intention. If so, thank you!

[vijay]

What a wonderful thread! "Endaro Mahanubhavu"...keep it going. Meanwhile I am still struggling with the basics of Arun's original article and the follow-ups...think I got the basic hang of it...will give it a few more readings befoe responding with queries

[vijay]

What I have understood so far:

1) The objective is to understand the values for the srutis as per Bharata based on his definitions of Madhyama and Shadja Grama
2) Based on this we get exactly and no more/less than 22 shrutis - this depends on 1) the existence of 2 gramas and 2) assumption made for Rishabham
3) An interesting result is that some values are different from those in use today - like R2

Obiter Dicta:

1) The 22 shrutis assume the existence of 2 gramas which as Arun rightly points out may have been the result of 2 diff schools and this would naturally be in an Indian context. Hence the 22 shrutis arise from a reconcilitation of 2 schools of tuning and are not relevant outside India.

2) Since the Madhyama Grama is no longer in use (not sure), the relevance of these shrutis is limited even in Indian music today.

3) These 2 different schools - might it have been "Aryan/Vedic" music and "Tamil/Dravida/Pann" music...

But my flights of fancy have already reached extremely uncomfortable limits!

[vasanthakokilam]

Vijay: On the two gramas, they were part of a single musical system ( however and wherever they originated ) by the time of Bharatha. Also, Bharatha was not really trying to reconcile to the two gramas, but uses them judiciously to tease out the underlying quarks ( using a Physics analogy ).

A few centuries later, the kudimiyan malai inscriptions do refer to grama-ragas but I do not think one of the gramas is of Pann origin. As you said, I am at the limits of my knowledge on this. I will defer to Guru Arun!!

[arunk]

first a possible typo:

>2. S-R (both gramas), P-D (Y-grama)

Did you mean to write "2. S-R (both gramas), P-D (X-grama)"

Yes that was a typo. I fixed it

Second, in this hypothetical 15 sruthi scheme, the sruthis are wider than the 22 sruthi scheme, right? I guess that is obvious but your initial setup itself demands that the resulting sruthis are less than 22 since you are picking a larger difference between Px-Py.

Cannot say they are always wider. The first reduction is wider, the P-D interval of Y-grama than any swara spacing Sadja, Madyamagrama. But the X-grama is identical to Sadja grama. The Y-grama is same to Madyamagrama except for M-P-D part.

But yes the spacing will change # of sruthis - that was the point I was trying to make . That 22 is a result of the specific spacing of the Sadja and Madyama gramas. If those gramas had different spacing (like X,Y here), we may have arrived at 15. Some other spacing may result in something else.

Consider it another way. Sruthis are a sub-division of the spacing between swaras. Now again forget the sub-division. We still have spacing. In the combination of Sadja-Madyama grama there are 4 different spacings (ascending order):
1. Spacing I will label as S1. This is the spacing between the pas of the two grama (and is the only one that is a "inter-grama" spacing)
2. Spacing I will label as S2: R-G (both gramas), D-N (both gramas)
3. Spacing I will label as S3: S-R (both gramas), P-D (Sadja grama), M-P (madyama grama)
4. Spacing I will label as S4: G-M (both gramas), M-P (Sadja grama), P-D (madyama grama), N-S (both gramas)

Now Sadja grama has 2 S2s (R-G, D-N), 2 S3s (S-R, P-D) and 3 S4s (G-M,M-P,N-S)
Madyama grama as 2 S2s (R-G,D-N), 2 S3s (S-R,M-P), and 3 S4s (G-M,P-D,N-S). Basically same only difference being which pairs are S3 and which are S4

If these spacings are expressed in internal units i.e. sruthis, then we get 22.

How?

Simply make S1 = 1, S2 = 2, S3 = 3, S4 = 4.

So Sadja Grama = 2*2 + 2*3 + 3*4 = 22. Same for Madyama Grama.

It is extremely important to note that this assignment is NOT mathematical in the sense that the S-R interval (S3) is not precisely 3/2*S2 in terms of pitch distance. The 22 sruthis are NOT equal pitch distance. So the assignment can said "empirical" (? right choice?). Each decrement/reduction that was "discernible" *because* it was done such that the ending pitch of the swara which was prescribed as the starting point of the reduction - matched some pitch. IMO *that is how they defined* discernible (as opposed to minimally discerible change in pitch - which would have resulted in a larger number, but would also not be as easily accomplished as this one perhaps requiring technology?). That is how the ancients knew how much to reduce. But each such reduction was taken as an atomic unit (sruthi). But consecutive reductions need not be same - they were of amounts of "whatever was needed to get to that discernible point i.e. a destination pitch matching some swara" and that whole reduction amount was taken as an atomic unit.

Note the S1 spacing does not occur WITHIN a grama - but it plays an importtant role. Without it (say no madyama grama) perhaps you would have just 3 spacings. Perhaps got labelled 1, 2 and 3 and you would end up with 2*1 + 2*2 + 3*3 = 15

(interesting usnt' it? I got 15 for X-Y, using a different but similar approach in the sense I eliminated S1 from the picture in a different way)

But I have a significant question on this.

>1. R-G (both gramas), D-N (both gramas), P-M (Y-grama), Px-Py (difference between the two gramas)

I can see how one can satisfy your stipulation that P-M ( Y grama ) is same as R-G. That can potentially be done by ear. But how did Px-Py become equal to R-G. That is critical to your first inference. May be I am missing something.

The assumption/presumption is you knew it by ear based on the melodic nature of the scales, and . we knew the "approx" spacing of swaras "by ear" - we just dont know if there are any sub-units in between and how many.

Consider this: Does one have to show by experiment in order for the ancients to know the G-M spacing < S-R spacing < N-S spacing? I think not. I think they had an reasonable idea of what the spacingswere and their order.

So that was why I laid those down. If I didnt lay those down, and I said when I dropped Pa of X2 to Pa of Y, the Ga of X2 also matched Ri of X2 - one could ask "uh? Come again?"

(PS: no matter how "fair" those pictures looked, it is either not possible or extremely hard to represent the spacings through the experiment with ASCII text - atleast I had to struggle a lot)

( Also, your stipulation that "pa of Y is mid-way between the ma-pa of sadja grama, is it just a mention in passing since you also prescribe that it is located at the same distance from M as R-G or is that significant as well?).

Again it is not a stipulation per-say. In my hypothetical X-Y grama pair that was the "observation" which again I presumed can be "judged" by ear (i.e. based on the melodic nature of these hypothetical scales). One needs to that to tune the vina by ear.

For example, how do we know that S-R2 is about the same distance as P-D2? Only because pitch analysis says both are about 200 cents? Or does our ear+brain already think they are close enough and pitch analysis simply validates that.

BTW, are we taking it in good faith that all these reductions amount to 'equally spaced' sruthis?

No. They are never "equally spaced sruthis" even in the 22 sruthis (viDiya viDiya rAmAyaNam ... )

The only "consistency" is the reduction at each step is the same for the entire vina.

Arun

[arunk]

2) Based on this we get exactly and no more/less than 22 shrutis - this depends on 1) the existence of 2 gramas and 2) assumption made for Rishabham

Assumption for rishabam has some bearing (e.g. if it was 9/8 then S-R would have been 4, or if it was 16/15 then S-R would have been just 2) but not as much. But it need not be precisely 10/9 for this. Theoretically a range of values would fit - but among then 10/9 would be a "most probable" one (unless evidence changes).

2) Since the Madhyama Grama is no longer in use (not sure), the relevance of these shrutis is limited even in Indian music today.

Madyama Grama was gone by Vidyaranya and Ramamatya's time i.e. 14th-16th centuries. The theory is that the appearance of Sadja as the ONLY tonic resulted in a Vina like today i.e. one instrument that can represent ALL intervals eliminating the need for Madyama-Grama. But I dont know if all the dots are filled in.

3) These 2 different schools - might it have been "Aryan/Vedic" music and "Tamil/Dravida/Pann" music...

No evidence for that. The original equivalent of grama/scale/tuning in the paNN system was "semPalai". It also has 22 sruthis (called narambus). The spacing is 4, 4, 3, 2, 4, 3, 2. (i.e. Sa to Sa - but of coure they used different terminology). This does not match the madyama grama. I had some other thread said incorrectly that it doesnt match any grama or its murchana. But I am wrong. This spacing matches the madyama murchana of the Sadja Grama (corrected from last time)


Sadja Grama: 3 2 4 4 3 2 4
semPalai: 4 3 2 4 3 2 4 (corrected from last time)

But it is interesting to note the following:
This semPalai (if interpreted the same way) is similar to harikAmbhOji. So is the madyama grama (only if taken from ma to ma, and that is exactly how it is prescribed i.e. in Madyama Grama tuning, ma is the initial note). Also semPalai's spacing if interpreted the same way, would result in a "Ri" of 9/8 (but Da of 3/2*9/8 = 27/16) perhaps more like today's harikAmbhOji particularly in purvanga.

Arun

[arunk]

I will defer to Guru Arun!!

Oh no! The trouble with this is then people may assume/presume (and eventually expect, demand) what I say would be correct, or should be correct. I want to forever retain the right to screw up and spew/blabber nonsense and be able to say "sorry, I was wrong because I am not an expert. Pl Disregard that". That right is very liberating to have

Arun

[nigamaa]

Arun,

What I don’t understand with u is that,
u quoted somewhere above some text, stating it was written the ga-grama, gandharva grama came from heaven, or became obsolete played only in heaven, right?

Now, ppl into the matter know that this gandarva country is not heaven but what is considered west of indus valley society, modern Afghanistan. There is still a town called Kandahar. Now, isn t this an evidence that some of the music originated outside India, perhaps needs older sources to understand? You never mentioned much about that there is a lot mention of older scriptures than BNS, where were they located then?

rgds

[vasanthakokilam]

Arun:

I will read and reflect on your answers to my questions and get back to you if needed.

BTW, are we taking it in good faith that all these reductions amount to 'equally spaced' sruthis?

No. They are never "equally spaced sruthis" even in the 22 sruthis (viDiya viDiya rAmAyaNam ... )

Definitely, I missed that in the original Bharatha experiment. I always thought Bharatha's formulation resulted in equal width sruthis. I never gave it a second thought. I did see in your X-Y grama setup, there is no such assumption, that is actually what prompted me to ask that question.

Now I need to reset and think about this: When we talk about N sruthi intervals, say in the poorvanga of the grama vs the uttaranga of the grama ( so to speak ), isn't there either a '=' relationship or a 'integer ratio' relationship'? Is it really that wide open that each of the sruthis is considered to be of possibly different width.. Back to the drawing board for me.

[arunk]

nigamaa,

That was gandhara grama and not gandarva grama. The spacing for it is given in some book (i forgot) and it is one that takes ga as starting swara (just like sadja-grama takes sa, and madyama grama takes ma).

If there is earlier evidence that can point to earlier status of the music, I am all for analyzing it. I dont think it *originated* with Bharata. I am sure it was evolved then. But when we correlate say earlier works which perhaps belong to other cultures - we have to be careful and judicious in our correlations. For example, a sumero-tamil connection to me at this point would not carry weight. A perhaps avestan connection would carry more weight (??) But even so, to be honest, I have not concentrated much on HOW the gramas came about etc.

So I dont want to comment on them much more than what I find in texts (i.e. BNS, Dattilam etc.) etc. I did speculate on the origins (i.e. theory came after practice etc.) - but that is just my speculations as I clearly said so! In fact the whole topic has geared towards "what arun's ideas are on this subject". hence I would strongly advise to take it all with a pinch of salt given I am no musicologist! If any, I would however still advise to contemplate things logically, and look for evidence etc. etc - you know just follow proper logical procedures with due-diligence.

My interests actually like in why there were 2 gramas i.e. what exactly were there roles (particularly when they seem almost similar in certain respects), how from gramas we got to melas (or how to further corroborate the spacings of melas). There are holes at crucial periods of time there.

Arun

[arunk]

When we talk about N sruthi intervals, say in the poorvanga of the grama vs the uttaranga of the grama ( so to speak ), isn't there either a '=' relationship or a 'integer ratio' relationship'? Is it really that wide open that each of the sruthis is considered to be of possibly different width.. Back to the drawing board for me.

There is a "=" relationship. Two intervals assigned the same "n" sruthis are equal in length. I would advise perhaps just to re-read 2 things from the article.
1. the (import of) the Mapping between sruthi intervals and specific ratios part. Here I say why say R-G and D-N are equal. Because in the experiment when ni merges with da, ga also merges with ri - both underwent the same reduction.
2. Conclusions part of the article. This talks about the "amount" for each reduction (and also how to see consistency in them)

Arun

[nigamaa]

Arun,
I still think gandhara and gandharva do mean the same, so that the gandharvas are meant to have played in the gandhara grama.
the article below has some mention of gandhara.
http://www.hinduwisdom.info/Hindu_Music.htm
The Hindus divide the octave into twenty two intervals, which are called Sruti, by allocating four Sruti to represent the interval. The sruti or microtonal interval is a division of the semitone, but not necessarily an equal division. This division of the semitone is found also in ancient Greek music. It is an interesting fact that we find in Greek music the counterpart of many things in Indian music. Ancient India divided the octave into twenty two and the Greek into twenty-four. The two earliest Greek scales, the Mixolydic and the Doric show affinity with early Indian scales. The Indian scale divides the octave into twenty-two srutis.
Gramas
Indian music is traditionally based on the three gramas. First reference to Grammas or ancient scales is found in the Mahabharata and the Harivamsa. The former speaks of the 'sweet note Gandhara', probably referring to the scale of that name. The Harivamsa speaks enthusiastically of music 'in the gramaraga which goes down to Gandhara', and of 'the women of Bhima's race who performed, in the Gandhara gramaraga, the descent of the Ganges, so as to delight mind and ear.'

As to the question, why there should be three gramas, there could be an easy explanation. Experiments have proven that music eventually follows the human organ of hearing. Western music which evolved from various scales of oriental origin, finally settled at three scale forms, that is major, minor harmonic and minor melodic. This is found to be sufficient since centuries now, it is in fact like three gramas.

rgds

[vijay]

Thanks Arun, point 3 is particularly interesting. Perhaps you are on to something there!

[uday_shankar]

Hey Arun
Just finished reading through the write up. Excellent. Will send you some feedback soon. BTW, did you append your original write-up after listening my saveri "demo" a few years ago ? The phrase "aurally discernible" is something I use quite often, not that it may not be found elsewhere . BTW, I lost that "demo" in some previous hard disk, if you have a copy by chance could you email it to me ?

[uday_shankar]

Arun,

Some thoughts on the write up...

http://arunk.freepgs.com/blog/bharatas_22_sruthis.html

Instead the shadja and rishaba are consonant.

Typo - should read "Instead, rishaba and panchama are consonant".

I am actually puzzled at how Bharata or his contemporaries chose the pitch for rishaba and dhaivata as they do not have consonant relationship (i.e 4/3 or 3/2) with other svaras in shadja grama

My speculation: it may stem from the choice of 5/3 for dhaivata. While the ratio 5/3 may not be termed a strict "consonance", it is weakly consonant and after some practice very clearly so. From my experience, if I were to create a hierarchy of consonances, from the easiest to the most difficult, it would be 3/2 (P), 4/3 (M1), 5/4 (G3), 5/3 (D2) and 9/8 (R2). With training, very accurate ear tuning can be done for all of these consonances. It may come as a surpise to some that Sa-Pa is slightly easier to tune than Sa-ma. For example, vina players interesting in tuning well would be well advised to tune their second string Pa after first tuning their third string (lower Sa) and then tuning the pa with respect to that lower sa.

I will try to dig up the psychoacoustics of non-culture based consonance perception. I suspect some of it is simply the odd harmonics inherent in a vibrating string... for example, pa (3/2, third harmonic) and G3 (5/4, fifth harmonic) and R2 (9/8 ninth harmonic).

Coming back to your "puzzle", therefore Bharata may have established 5/3 for dhaivata based on weak consonance with shadja and then fixed 10/9 as a strong consonant of that for rishaba...As an aside, I am convinced that our current fixation with 9/8 stems from using panchama in the aadhara shruti. Just using a Sa-only tampura somewhat removes the 9/8 fixation since the ninth harmonic is not readily discernible (in a tampura with Pa, the 9/8 stands out prominently as the third harmonic of the Pa string). I'm trying out tampura with sa-only as well as 10/9 for khpriya and it is really pleasant. Will post a clip soon.

For my part, I was wondering why Bharata (or whoever, BTW, my only reference to Bharata is your write up!) would declare consonance between R and D as an axiomatic "rule" for the shadja graama. For this I have a speculation from my own tuning practice, based on pleasantness, for harikamboji scale. What I use ends up being a madhyama mUrchana of the shadja grama. The shadja grama is 1, 10/9, 32/27, 4/3, 3/2, 5/3, 16/9,2 and its madhyama murchana would be the beautiful harikamboji scale 1, 9/8, 5/4, 4/3, 3/2, 5/3, 16/9 and 2. What's interesting is that 9/8 seems appropriate for all the "major" scales (hari, shank, kalyani) and 10/9 for all the "minor" scales (khpriya, natabh). Also, when playing a raga like kamboji (derivative of harikamboji) one can explore the vadi-samvadi relationship of the phrases ND and MG very beautifully. As I understand Harikamboji was a prominent scale at some early time ??

I think that When thinking about gramas and tuning practices one must think concurrently about murchanas and graha bhedas and then find out the best combination of consonances that would work out for a variety of graha bhedas. In this shadja grama, some other murchanas are:

Ri - 1, 16/15, 6/5, 27/20, 3/2, 8/5, 9/5, 2 (todi with slightly different "ratios" than we might try to use today)
ga - 1, 9/8, 81/64, 45/32, 3/2, 27/16, 15/8,2 (kalyani with slightly different "ratios" than we might try to use today)
ma - 1, 9/8, 5/4, 4/3, 3/2, 5/3, 16/9, 2 (harikamboji, perfect fit)
pa - 1, 10/9, 32/27, 4/3, 40/27, 128/81, 16/9 (natabhairavi with a lowered panchama)
da - nothing useful because there's no panchama
ni - 1, 9/8, 5/4, 4/3, 3/2, 27/16, 15/8, 2 (almost perfect shankarabharanam, higher dhaivata than we might use today)

Note that with the exception of "natabhairavi" the panchamas of all the murchanas fit perfectly. I know I am using current raga names when discussing a very early phase in the development of music. The names are only a place-holder since I don't know much history .

Now obviously all the above ratios are quite intimidating and might seem nonsensical

Did you examine the possibility that ALL the strings of the chala vina need not be decremented by the SAME amount every step. After all the process is not purely about strict mathematical ratios. It is about practical stuff. Also Bharata does not seem to have been aware of the different "shades" of his "pramana" shruti - 81/80, 25/24, 256/243. Therefore, one can postulate the following (implicit in Bharata):

"At each step, every svara of the chala vina is decremented by one pramana shruti which can take values of 81/80, 25/24 or 256/243 on a svara by svara basis"

Did you examine if this would make some of the ratios less daunting, although I agree that they are quite irrelevant. I am too lazy to work out the math and combinations . The only problem here may be that while we have implicitly assumed that the shadja grama can be tuned by some prior art (which is not a bad assumption, as even I can do it myself based on a variety of consonance sequences), based on fixing ANY one note, we don't know if these alternating scenarios can be tuned at all ! After all, it is complete idiocy to presume that somebody can reduce a string reliably by one pramana shruti. Without a consonance, one cannot even be sure of Sa-pa-sa leave alone a pramana shruti lower. So there goes that theory .

but there does not seem a strong enough rationale then to claim that an intervening sruthi with a ratio like 256/243 yielded via such a division is singable and is indeed sung today. One could argue that it is based on an inaccurate interpretation of Bharata's division to express a pitch that is perhaps perceived as lower than typical mayamalavagowla rishaba (the gowla rishaba is sung as a pitch inflexion from shadja)

Folks like Arvindh have analyzed current Carnatic practice very well but might also have thrown a small baby with the bathwater . What is "singable" really depends on the level of training and commitment. For example, nobody would dispute that the ratios Sa (2) and pa (3/2) are "singable". And yet, I can cite umpteen practitioners of Carnatic music, right up to the present day, who sometimes find those notes not so "singable" . Does this mean they cannot do it ? Maybe they aim for one thing, and end up elsewhere due to physiological and other limitations. Therefore, with sufficient training it is possible to "aim" at different sounds (i.e., ratios) and achieve success depending on the factors cited. The bigger question, whether it has any impact on the listener, is also not easily answerable. For example, when MMI or KVN or MSS sing, some people find the "purity" exhilarating. At the bottom of this "purity" lies one predominant fact - they knew what ratios to "aim" for and consistently achieved a very high statistical hit rate. So even if an ordinarly listener cannot empathize with the aims and success rate, they might discern some special "purity". Now is this "purity" the only thing in CM ? Absolutely not. Semmangudi and GNB sometimes aimed poorly and yet continued to thrill audiences.

[uday_shankar]

Here's another original and illuminating article on the subject by my friend Vidyasankar:
http://www.carnaticcorner.com/articles/22_srutis.htm

[cmlover]

Thanks uday! That ref was quite illuminating...
Ultimately it appears there is no magic in that number 22...

[nigamaa]

Thx US,
One can notice that Vidyasankar:
http://www.carnaticcorner.com/articles/22_srutis.htm
wrote similar to what I wrote about the value of Vajrika shruti above.


The 11th Sruti
can rigorously satisfy the relationship 11 + 11 = 22, only if the 11th
sruti is given a value 2^(1/2). Thus

22 = 10 + 12 (<=> 27/20 x 40/27 = 2)
= 11 + 11 (<=> 2^(1/2) x 2^(1/2) = 2).

If we now go back to the ratio values obtained between 4/3 and 3/2
in the table, we find the numbers 27/20 and 40/27. However, 2^(1/2) is
impossible to find there, simply because 2^(1/2) is not a ratio. It is an
irrational number. 2^(1/2) is the value for Ma in the tempered scale of Western classical music.

[arunk]

Uday,

Thanks for the comments.

Typo - should read "Instead, rishaba and panchama are consonant".

Thanks I will fix that.

Yes it is possible dhaivata was fixed first at 5/3 etc. Although I have not explored how consonant 5/3 etc. is - it is certainly plausible. But if we go strictly by text, only 2 intervals are highlighted as consonant (i.e. samvadin) - 9 and 13, the first for sa-ma (4/3) and second sa-pa (9/8). So there is no evidence per say - but then there is not much direct evidence as to how they arrived at the swaras. So to repeat, it is plausible.

Also quite possible that my considering 9/8 as being "more apt" is related to attaching higher importance to pa (actually 3/2 interval) - a "current conditioning". But again, the two samvadin intervals highlighted were 9 and 13 - so some of my "unconscious preferences" were colored by that too.

The shadja grama is 1, 10/9, 32/27, 4/3, 3/2, 5/3, 16/9,2 and its madhyama murchana would be the beautiful harikamboji scale 1, 9/8, 5/4, 4/3, 3/2, 5/3, 16/9 and 2.

Which is why I scratch why there is a madyama-grama (starting i.e. ma-murchana) which is almost identical to this (except second degree would be 10/9)

What's interesting is that 9/8 seems appropriate for all the "major" scales (hari, shank, kalyani) and 10/9 for all the "minor" scales (khpriya, natabh)

That is indeed interesting. Need to mull over what it means

Did you examine the possibility that ALL the strings of the chala vina need not be decremented by the SAME amount every step. After all the process is not purely about strict mathematical ratios. It is about practical stuff.

No I didnt - but only if all swaras are decremented the same way, the vina would maintain the tuning of sadja-grama. There is no explicit mention of this, but it seems to make more sense and remain practical. Also, if different swaras undergo different change BUT still ga merges to ri, excatly when ni merges to da (again ri to sa when da to pa etc.) - the "equality relationship" (i.e. two swara-pairs with same number of sruthis have same interval) gets more complicated and throw more assumptions out of whack. For example, how would you claim that while sa-ma is 4/3, how do we know ma-ni is 4/3 (ok - consonance can be used, but even this would become a "bigger assumption" than what I did in the write up).

So I think same reduction for all swaras in each step seems to make the most practical sense based on the info I know and can deduce.

Arun

[arunk]

Regarding your last point, we have been through this a lot before - and I am not sure I can remember all the points

In short I am with Arvindh - I think many of those ratios don't mean anything in practice, and there is no evidence to indicate that for many of these ratios, they represent the ideal, and deviations are "imperfections in practice". So I think they do not mean much in theory either.

Also, I don't think the musicians aim for a ratio, they aim for a "pitch colour" which in the case of e.g. the eka-sruthi rishaba is a pitch curve. Saying that pitch curve's "ideal" (i.e the perfect eka-sruthi rishaba) is for one end to be at a non-negotiable 256/243 - I just don't see enough rationale (and evidence) for that. Research seems to indicate that the pitch perception is a multi-dynamic thing - if the sound varies in pitch, the rate of variance, the volume dymamic etc. all play a role in determining color - as much as (if not more) as the end-point. So we observe localized variations for that swara - minute ones but significant enough once you start getting as fine as 256/243.

So why is 256/243 more perfect particularly in use in tandem with the tonic? People proposed ratios like but no experimental analysis was done when this was possible (unlike with old grama music where all we can do is theorize ). It was all theory and hypothesis - which is fine. But had they followed up with experiments etc. it may been better.

This 256/243 ratio was probably arrived as follows.
1. They recognized that today's suddha-rishabham was around 16/15 and lower thabn the suddha-rishabam of old and assigned it 2 sruthis compared to 3 (Note that Ramamatya got it wrong here)
2. They recognized that while the gowLa/sAveri rishabha's were oscillatory, its "overal feel" was that it 'seemed/felt' lower than this suddha-rishabham.
3. Given that the standard (current) suddha rishaba was 2 sruthis, this must be 1.
Now let us calculate mathematically which ratio LOWER than 16/15 makes sense i.e. arrivable via cycle of fifths/fourths
4. Voila! 256/243. So let us make that the rule. Eka-sruthi rishaba's ratio is 256/243.

Where is the scientific analysis here following step 4.

Besides, consider the basic tenet here. Could we dare propose that the need to express 16/15 as 2 sruthis, and thus a lower one is 256/243 as 1 sruthi, itself is a baggage from olden times that may be is not as applicable in later music. I can see how Bharata arrived at 22 - he had 2 gramas to work with and they directly leads to 22. In fact, I think this is one reason why he delegated sruthis to later - he felt they were a manifestation of the gramas - but I will check this info later.

In any case, later on, it was clear that 22 are interpreted as a magical (universal within out music) constant - and hence must accomodate all "the nice ratios". So in came 10/9, 9/8, 6/5,5/4, 16/9, 15/8 etc etc. Of course "what is nice" can be subjective - so we had differences of opinion.

In short the way these ratios were arrived itself makes me skeptical. That skepticism would have been tempered if
1. Evidence was looked for in later texts (i.e. mela period)
2. Experimental analysis was done

Also, I am not 100% sure but among the many many many ragas Sarngadeva discussed, I am not sure if in any of them he says "the rishaba/nishada/gandara here uses such a such shruthi" - They had names for all 22 (completely different ones, and different ancient texts had different names).

Arun

[arunk]

Hey Arun
Just finished reading through the write up. Excellent. Will send you some feedback soon. BTW, did you append your original write-up after listening my saveri "demo" a few years ago ? The phrase "aurally discernible" is something I use quite often, not that it may not be found elsewhere . BTW, I lost that "demo" in some previous hard disk, if you have a copy by chance could you email it to me ?

Not sure but possible (i do remember "throwing the baby out of the bath water" ). I had been thinking of "understanding the 22 sruthis" much before that.

I will see if I have your demo - I dont think I have but I will check.

[arunk]

Thanks Arun, point 3 is particularly interesting. Perhaps you are on to something there!

Vijay I had quoted the spacing for semPalai incorrectly. It doesnt change things much except it would "sadja grama in madyama sruthi" - so gets more interesting.

But truthfully, unless I think of some Aryan/Dravidian conspiracy of "borrow and then act as my own", I don't find much evidence (yet) for tamil system to influence this system. So without evidence, it would be another theory.

I have commented earlier, that evidence for this (seeminly fairly well accepted theory i.e pANNs being precursor) is sparse. When enough evidence arrives later, it seems to clearly indicate that the paNN system had merged with the grama system, and the pANN system had borrowed stuff (many many pANN names are of non-tamil, and particularly Sanskrit origin).

Arun

[uday_shankar]

Also, I don't think the musicians aim for a ratio, they aim for a "pitch colour" which in the case of e.g. the eka-sruthi rishaba is a pitch curve

I agree 256/243 may be an irrelevant ratio but what a musician "aims" for is strictly his business. I think for a musical aspirant with the keenness of ear, some useful tuning exercises can be had from examining ratios. That's all I have to say. I have discussed/demonstrated this to some sensitive musicians and they agree. Shruti shuddam does not come from a "contour" but an idea of what the pitch of a note must be ! Also, the idea that a kampita gamakam can be defined by "color", "volume" and "contour" is nonsense. These are vague words that mean nothing. Pitch is a simple thing, and ONLY the end points remain in the head of an unprejudiced listener with a keen ear. Any other perception is purely Carnatic prejudice. We've been through this in some other thread, it's Uday's law.

Anyways, I'm out of this discussion. It's meaningless. I know what's useful to me. So who cares .

[arunk]

yes . What is meaningful to one can be nonsense to someone else and vice versa.

The point anyway was not that 256/243 is meaningless in every possible aspect - that it is not meaningful when used to define eka-sruthi rishabha, particularly when you look at the methodology and rationale people have used to arrive at that. If you find it useful (as you have said before), to provide great sounding gowLai/sAveri (like I know you do ) - then that is useful to you. No one can taketh that away.

(If your main objection was to me somehow implying it isnt useful to anyone, then I will clarify that I did not imply it.)

But in case, you claim it is mandatory for anyone to get perfect ekashruthi rishaba, and any deviation would be less than perfect, and its perfection is because of it being in the path of nth iteration of fourths/fifiths etc. etc. well you may find disagreement from some. But if then can still find satisfaction in "I know what's useful for me. So who cares", then I would say you are bullet-proof. You got all angles covered and in your mind, you just cannot lose !

Arun

PS: I know you know, but just to be sure - lot of that purely in jest

[arunk]

Pitch is a simple thing, and ONLY the end points remain in the head of an unprejudiced listener with a keen ear. Any other perception is purely Carnatic prejudice. We've been through this in some other thread, it's Uday's law.

The point was there are various pitch curves that will satisfy a certain gamakamized swara (e.g. sAveri ri) to even keen listeners. And not all such pitch curves end at the same point, they can vary in rate of variance between start and end etc. (But I will add the caveat that this is my interpretation based on some pitch analysis on my own, and some info in Arvindh's paper which was also based on pitch analysis. In other words, I hope I am remembering right and some corroboration/confirmation wouldn't hurt)

But to claim that such a swara has a precise end-point for "perfection" (or correctness) - cant that can be argued as prejudicial/opinionated? Only way to say no, would be to prove why and how it is the only correct answer. I was simply questioning that.

Aruin

[uday_shankar]

But to claim that such a swara has a precise end-point for "perfection" (or correctness) - cant that can be argued as prejudicial/opinionated? Only way to say no, would be to prove why and how it is the only correct answer. I was simply questioning that.

Arun

It's a free world and people are free to do exactly as they please! I personally enjoy all kinds of music includiing Carnatic music with equally tempered instruments (I am the staunchest online "defender" of keyboard sathya!) as well as Carnatic music with apasrutis. Therefore, all "rules" are only personal rules, and they are subject to change. I don't believe in cultural fascism of any kind (it was disturbing to read sbala and others propose "vetting" systems for composers. bizzare!).

Anyways, I can't relate to intellectual arguments that have no practical analogue. Therefore, for the last time...for those who are interested, there's some useful pitch exercises to be had from examining ratios with the ear by playing with strings. In moderate doses, without getting caught up in the trees and missing the woods.

BTW, here's why I think 5/3 sounds consonant with keen hearing. I think because it's consoant with the dominant 5th harmonic 5/4 (BTW 1, 5/4 and 5/3 it becomes the natural minor chord). Sometime in the future you'll add a paragraph about this 5/3 in your Bharata article and not acknowledge the source .

[sbala]

I have not gone through this thread, so I will refrain from commenting on the other posts. Anyway, I don't understand how testing composers equates to fascism. I've never been convinced by 100% free market theory and my opinions on this are the same across all fields and not just limited to music. That doesn't imply that I'm supporting authoritarian bodies that suppress all forms of expressions. Such organisations rarely survive beyond the dictator. I will remain an ardent supporter of innovations at a personal level. If I like it, I accept it. However, a system should accept and reject contributions in a fair manner and the only method that I know is through testing and competition. They might not be perfect solutions. I'm only looking at weeding out mediocrity. If there are other methods that will work at the systemic level, I'm more than willing to listen. If composers need not be rated, it begs the question on why artistes go for AIR rating. I don't believe we can have separate rules for performers and composers.

[cienu]

1)Anyway, I don't understand how testing composers equates to fascism.

2)If composers need not be rated, it begs the question on why artistes go for AIR rating. I don't believe we can have separate rules for performers and composers.

Bala ,

I have slotted the points I wanted to reply as 1) and 2). (Forgive me for tampering with your flow )

Well , the composer is a free bird . His/Her mind overflows with creativity & spontaneous feelings / emotions and should never be bound by such tests. You are free to test & the composer is free to compose. I doubt very much if the general public would use the composer rating as a sort of reference guide while listening to an artist sing. Why does a song become popular is something very difficult to gauge.
Rajaji's only Tamizh composition "Kurai Onrum Illai" became one of the most popular songs ever sung (many years after he had passed away) and there could be more than one reason for this. If a " Rating bench" had rated this song before MS took it up , it is possible that on many parameters it would have found itself behind a Sivan Masterpiece.

But it became an immortal song possibly because of the simplicity , the ability to touch the heart and ofcourse the Singer behind it

With regard to the second point , if I am not mistaken, artists do get additional benefits if they get a higher Grade from AIR. In earlier days , when CM was not supported by Business Houses / NRI's etc to the extent it is today , AIR was a sort of monopolist of Govt. Largesse towards Fine Arts.

The relevance of AIR rating vis a vis public opinion would not hold much water in today's context. For example , I would not be particularly bothered about say Abhishek Raghuram's AIR rating if I want to attend his concert

[vasanthakokilam]

bala, is it possible you posted your last message in the wrong thread? If so, let me know I will move the posts.