Origin of the special terms Kaikasi and Kakali for Nishadam

[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.

[cmlover]

Yes VK!
Looks like an error! If discussions continue we will be in a real mess!

[sbala]

VK,
My post was in response to Uday's comment.
"I don't believe in cultural fascism of any kind (it was disturbing to read sbala and others propose "vetting" systems for composers. bizzare!).".

Feel free to move this to another thread.

Cienu - As regards composers being creative and going with the flow, so does everyone. Creativity is not the exclusive domain of composers or artistes. I did say that every song be rated but that was a suggestion taking a parallel with films being rated and not a demand. Someone suggested in the other thread that artistes know what is a good composition and what is not. That is exactly what I wanted to break. Composers should become equals to performers and these steps would also aid in giving them visibility. It would be interesting to see how the CM scene changed from composer dominated during the Trinity era to performer dominance as we witness now. Anyone who has listened to CM for a year can reel off the names of Sudha, Sanjay, TMK etc. How many of us even know modern composers? To be honest, the good ones will not fear being tested. As far as earning money, a good rating can definitely get more recording companies interested in a composer and give an incentive for them to take it up as more than a serious hobby.

[vasanthakokilam]

OK, that is fine then. It would have been better if you quoted his words, so it will be clear what your post is in reference to. Thanks.

[cienu]

sbala,

Your point is well taken and appreciated Now the Moderators may kindly move this discussion to an appropriate forum.

[vijay]

Uday I think sBala's views on accreditation was in the context of secular music. As he says, he did not recommend a "license" which is a different thing.

Anyway, let us keep this wonderful thread on track here. This proving to be a veritable treasure-trove of information and the quality of discussion/knowledge of participants is astounding! Specifically I would like to know from Uday how one should go about improving sruti sense...I can barely tell R1 from R2 and so on! Is this only possible if one plays an instrument? Are there any electronic devices that can reproduce, say, any given ratio between 1 and 2 (with the reference points displayed for instance)? Maybe it is time for another Jam session!

[vgvindan]

arun,
I came across the following pdf document -
http://www.newtalavana.org/ebooks/saptasvarah.pdf

[cmlover]

Thanks VGV! Interesting doc and the reference to Quantum Theory is fascinating! Will read it carefully....

[arunk]

Thanks VGV (and welcome back). On a cursory glance, I found the Figure 7 quite interesting - it adds fodder to "22 being special" in a very unique way

Arun

[uday_shankar]

Specifically I would like to know from Uday how one should go about improving sruti sense...I can barely tell R1 from R2 and so on! Is this only possible if one plays an instrument? Are there any electronic devices that can reproduce, say, any given ratio between 1 and 2 (with the reference points displayed for instance)? Maybe it is time for another Jam session!

Vijay,
I'm going to answer with a cliches as well as unorthodox suggestions!

1) First cliche - learn many Tyagaraja kritis in different ragas from a good guru. Nothing better for raga, swara and laya gnyanam to develop. vgvindan might add to the list of attributes .

2) Second cliche - get a tampura, get trained to tune it (I'll be glad to help when you're in Chennai) and practice everyday.

3) Unorthodox suggestion...initially, there's no better way to get your ear accustomed to the ballpark swarasthanas than playing with a chromatic (i.e., equally tempered) instrument like the keyboard. Later, if you feel the compulsion to explore shrutis in a deeper way, you can experiment with ratios. I've found in the chitravina sympathetic strings a convenient dhruva as well as chala vina . A surmandal (?) like the one Pt. Jasraj uses may do the same. Keep in mind that most practising musicians, even ones with good shruti gnyanam, don't know about ratios but just sing intuitively. Again, many folks explore ratios and write about them as a theoretical hobby quite disjointed from their music practice which is all intuitive. Nothing wrong with that either. Bottom line, at this stage don't expect to improve shruti gnyanam with numerical ratios. There may come a time for that. Instead follow the 3 T's - Tyagaraja, Tampura and Tempered (equall tempered!).

[cmlover]

So then the 3 D's will be Dikshatar, Damaaram and Diatonic scale which will help develop Laya as well as extended CM consciousness

[vijay]

Thanks Uday...would certainly be great to learn how to tune the tamboora once I am in town...will call you sometime after I get back and figure it out....about keyboard, I actually had one once (before I donated it away!) and it was certainly very useful in helping things along...but one would not be able to make out different "shruthis" as opposed to swaras...

There is also one fundamental Q about sruthis emerging from the above...how is it possible to play a different sruthi for 2 ragas say having the same note but different sruthis in a fretted instrument like the Veena? Is it retuned before the song?

[vainika]

how is it possible to play a different sruthi for 2 ragas say having the same note but different sruthis in a fretted instrument like the Veena? Is it retuned before the song?

You can pull strings to get where you want to be

[vijay]

Hmmm...after all, art is a mirror of society...

[vasanthakokilam]

Vainika, Vijay: Good one...

[PUNARVASU]

Vainika, I really liked it;good sense of humour!
As a student of veena, I agree with you.

[uday_shankar]

Indeed, clever all round, so I'll let that "slide" .

[arunk]

Somebody out of band suggested that maybe I should use my "gamaka modeling with MIDI" online software to demonstrate that experiment. Not sure about that but here is a silly attempt at something else

I have *tried* to use the "popular" ratios derived for sadja grama and madyama grama with my software. Some huge caveats:
1. (My opinion) I dont take these ratios as the highest laws of land. I would like to consider them as as close to what the gramas probably were. So two caveats built in here "close to" and "probably" . You may feel differently (i.e elevate them or demote them) about these ratios - that is fine.
2. The software doesn't allow enough resolution to precisely nail ratios - it was not the original intent. So I dont think I got them spot on. I used http://www.music.sc.edu/fs/bain/atmi02/ ... fault.html to get the cents value from S and then used that to come at a "close enough" spot for that value. So again "close enough" caveat.

You can run this by clicking: http://arunk.freepgs.com/gcreate/load.p ... gramas.cdb

When you click on that link, the application should load. It is a java applet and so may take some time on some computers.
The application's window has two parts - the left part should have some ratios (under Default), and also finally two entries "sadjagrama", madhyamagrama_samurchana etc. Click on any of these and cllck "synth" button to play them.

(note: on Safari, the right window takes up all the room, and so you have to click at the dot on the left edge of the window to expose the right part).

This may be a good way to find out more about your perception skills (at the least it may something to fool around for a few minutes). Some things to check:

0. Can you spot where the ratios arent quite right i.e. due to big caveat #2 above? If so, skip all of the following steps - Your hearing is amazing (and that means you Uday )
1. Can you spot a difference between sadjagrama and madhyamagrama-samurchana?
2. What about pa_vs_pa?
3. What about 10/9_vs_9/8?

(NOTE: This is NOT a quiz. Its not like i have the correct answer - but it may prove fodder for some interesting thoughts. I myself found out that 40/27 isnt as bad as I thought it would be

Arun

[Sundar Krishnan]

Sub-Topic of this msg under this main thread :
22 Shrutis and Pramana, Purna and Nyuna Shrutis’ Calcs – Arun’s article

Hello Mr Arun, 4th Oct, 2008

This is wrt yr article : http://arunk.freepgs.com/blog/bharatas_22_sruthis.html.
My appreciations for writing a nice article.

1) This is just my guess. I presume that one of the main trigger keys for this article most probably came after “discoveringâ€

[Sundar Krishnan]

For those who may wonder what "ln" is (in Pt 7) PS of my previous msg just sent) :

ln => log to the base "e"

[arunk]

Sundar Krishnan,

Thanks for those (silly) typos - I will correct them when I get a chance. I may not be able to answer all your questions now -as there are just too many of them.

The objective of the article was NOT to show complex ratios but to show that what 22 sruthi ratios seem most plausible if one simply stuck to what is said in Natya Sastra (particularly the 2 vina experiment), and Dattilam (as other sort of from same time period) and followed it to the tee, with as little outside assumptions. As a corollary, it shows how some of those ratios differed from those other "popular ratios".

I was indeed trying to find out what the 22 ratios would be if one followed the experiment - that was the objective from the beginning. When I ran into complex ratios, I was initially doubtful as to whether all this made any sense. But I then realized they not only made sense but were an unavoidable outcome, because the experiment demanded two vinas to be "slightly out of tune" with each other after step-1 if that 80/81 as the first reduction is valid.

[quote]2-c-i) Pl check if the comment “as observed hereâ€

[Sundar Krishnan]

Arun, 5th Oct, 2008

Thanks for yr replies.

You have stated my guess in different words ! :

When I ran into complex ratios, I was initially doubtful as to whether all this made any sense.

This sort of indirectly confirms my guess - ie, intermediate ratios such 2560/2187 may have acted like triggers from deep within the subconscious. Let us not discuss further on this guess.

I never thought otherwise - I definitely agree that the article does not aim to be one on complex ratios, but to finally arrive at popular, simpler ratios - but, via some of those intermediate seemingly complex ratios.

Credit to you for bringing out these ratios by the simple act of shifting the shrutis one step backwards - 4 times. Similar experiments may have been referred to in the Granthas, but credit is to you for explaining it with some Maths.

****************

Yes, I was referring to ma's "current ratio" = 5/4 in Fig 4 - After Step 2.

BTW, you could consider adding this suffix in the legend to each Fig n : " - After Step n"

****************

I have not been able to grasp the reference to different gramas made so often by many who discuss in this forum - specially, if as you say, it is still an enigma, or if they (all the 3 gramas ?) have all merged now.

You state :

"Why 2/3 gramas" - no sure answer. It is still an enigma. The texts do not say - they just always start with the existence of the gramas as a given.

One could ask :
If as you say, all this "grama" talk is somewhat of an enigma, why base the experiments' foundation on 2 of the 3 gramas ?
But, yes, I know that atleast one benefit is to arrive at simple popular ratios, and to reconcile with the intermediate complex ratios.

Even the other article by Vidyasankar talks of shadja and madhyama grama ; also many forum discs take refuge to these 2 gramas. If it is an enigma, why resort to these gramas for support ?

****************

From a person who is the author of the article, I expected a better, more concrete answer on : "Why one more ri ratio = 256/243 was left out ?" ! - instead of simply saying : "not sure" !

256/243 is NOT complex ; why ? - because, it is derived directly using the cycle of fifths and fourths - it is (4/3)^5 (application of 4/3 rule 5 times).

I was hoping that you would either confirm or reject my assumption that of the 24 ratios in Table V of Vidyasankar's (VS) article, those 7 ratios that I listed, may not be initially so straight-forward - even though they themselves are realtively fairly simple ratios, not complex.

****************

I wanted to understand atleast "pAlaiyAzh" in VS's article.
Why ? - because, it has referred to 2 scales, one with Ri = 9/8 (which ratio, one may say, is a more straight-forward ratio), compared to 10/9 (which is a ratio arrived at by back-calculating for eg, from Ga = 5/4), yet, the 2 scales have same ratios except for Ri and ga - for it states :

shaDja grAma - same scale as that of kharaharapriya (kAfi thAT) :
sa Ri ga ma pa Dha ni
1 10/9 32/27 4/3 3/2 5/3 16/9

pAlaiyAzh, the same scale as of harikambhoji (khamaj thAT) :
sa Ri ga ma pa Dha ni
1 9/8 5/4 4/3 3/2 5/3 16/9

I wonder if there is a typo in the above 2 ratios' rows.

Since I have not understood pAlaiyAzh, and also because I have no Musical thoroughness wrt singing either KaraHarapriya (22) or HarikAmbhOji (28), I am hazarding a guess :

Purely, thinking from symmetries, and not from any musical background, I wonder if they should instead read as :
shaDja grAma :
sa Ri ga ma pa Dha ni
1 10/9 32/27 4/3 3/2 5/3 9/5 ??

pAlaiyAzh :
sa Ri ga ma pa Dha ni
1 9/8 5/4 4/3 3/2 27/16 16/9 ??

[Perhaps, the ga ratios also may change from symmetry point of view - not sure.]

If there is indeed a typo error in the ratios' rows, then this may have a direct bearing on / from the 7 ratios that I listed earlier, all my inferences being purely from guess, Maths and Symmetry point of view, and not from any Musical background.

On the other hand, if there is no typo error, I would like to understand mathematically, the real diff betn shaDja grAma (- KaraHarapriya (22) scale) and pAlaiyAzh (- HarikAmbhOji (28) scale).

Can we infer this diff from the A-A :
22 | KaraHarapriya | S R2 G2 M1 P D2 N2 S | S N2 D2 P M1 G2 R2 S

28 | HarikAmbhOji | S R2 G3 M1 P D2 N2 S | S N2 D2 P M1 G3 R2 S

Just as an aside : Looking purely at A-A of the 2 Ragams, it may appear that the only diff is G2 vs G3. But since these two ragams can be heard so distinctly different by the human ear, perhaps, there are differences in the other ratios too ?
If true, what are the exact base ratios of all the swarams in these 2 Ragams ? ie, forgetting for the moment, gamakas etc.

****************

I know you have said that you are not racking yr brain on this subject (of mathematical ratios' calculations ?), but may be, these questions give you an incentive trigger to re-think !
For Music lovers like me who can distinguish Ragams, and different singing / playing styles purely by listening alone, and not by any knowledge of singing ourselves or by playing any instrument ourselves, Maths and Symmetry are the only tools to find any underlying reasons for the differences.


Rgds

[arunk]

Sundar Krishnan,

You seemed to have ignored the main thrust of my response as to what the article was abou. Again, It was precisely about what is mentioned in natyasastra and dattilam - the earliest available sources on 22 sruthis, swaras and gramas. Those sources do not get into why different gramas, what they mean etc. etc. But ALL melodic entities are categorized by gramas and hence gramas were very important although WHY SO is not explained. That is what I mean by an enigma particularly w.r.t the question why did they have 2 gramas in the first place. Just because we cannot answer that question does not mean we cannot make any use of gramas. And as far as I can tell, nor do those sources (i.e. natyasastra, dattilam and even sangitaratnakara although that came almost 1000 years later) anywhere infer about cycle of fifths and fourths etc.

256/243 - yes I could have taken - but again you seemed to have simply ignored the point that this ratio will not work for the experiment anyway (although I comes later). Besides, we were selecting a ri for the grama - one of 3 sruthiis. This is closer to kharaharapriya. The 256/243 is quoted for saveri and gowla and lower than even the standard mayamalavagowa (i think it is around 90 cents and not 111 cents?). Now, why would I even consider such a ratio for the one ri for sadjga grama ? Simply stated there is simply no way 256/243 could have been the ratio for the ri of the sadja and madhyama gramas.

I am not going to to back into delving into these ratios. I now find the subject not as interesting, but more importantly, I think ultimately it is not very useful because
1. I find many of discussions seeming to run orthogonal to what is mentioned in the texts. While it is certainly good to try to "fill in the blanks" of what is not said in text, one cannot also ignore the points made in the texts as well.
2. The cycle of fourths and fifths is not a closed model leading to a "cantor dust" and so eventually one need to stop - and different people stop at different points, and develop their own affinities. So this gets more subjective
3. There are more other interesting subjects that involve me now from time to time.

But these are my opinions only, and so I dont expect all others to see it this way. So allow me to excuse myself. This will be the last post here (atleast on this subject). You can contact me by email if you wish (you can do it via the forum itself).

Arun

[Sundar Krishnan]

Yes, 90.22499... Cents is correct, not 110 Cents.
ie, ln (256/243) * 1731.234049 = 90.22499 Cents

Thanks Arun, for this correction, and yr nice article.

*****************

OK, let us forget the disc on gramas for now.

*****************

Arun has stated the R ratio as :

... 256/243 is quoted for saveri and gowla and lower than even the standard mayamalavagowa

Similarly, I hope, that someone can let us know the exact ratios of all the diff swarams for these 2 Ragams ie, the exact defined ratios for R2, D2, N2, G2 / G3 and M1 ratios in each of these 2 Ragams (and perhaps, even P if 40/27 is used in one or both Ragams instead of 3/2 ?) :

22 | KaraHarapriya | S R2 G2 M1 P D2 N2 S | S N2 D2 P M1 G2 R2 S

28 | HarikAmbhOji | S R2 G3 M1 P D2 N2 S | S N2 D2 P M1 G3 R2 S


********************

Similarly, could someone give some explanation for the various ratios in the pAlaiyAzh scale - specially, Dha and ni.

Thanks

[vk]

SaRi"Ve"Ri

[Sundar Krishnan]

vk,

I don't understand - if this is any answer to my previous query.

Could you pl explain.