Kanjira G Harishankar

cmlover · Post by **cmlover** » 18 Aug 2006, 10:19

8172244080=29x3x93933840
The number on LHS is the total minimal matras.
For the sankeerna dhruva taalm the toal akSharam =29
For thisra nadai the matras =3
Hence 93933840 is the required avartams to reach the toal matra count which is at samam!

cmlover · Post by **cmlover** » 18 Aug 2006, 10:36

thathwamasi

Is this chatusra Ekam in thisra nadai? Pl help with the parameters!

thathwamasi · Post by **thathwamasi** » 18 Aug 2006, 11:09

cmlover wrote:8172244080=29x3x93933840
The number on LHS is the total minimal matras.
For the sankeerna dhruva taalm the toal akSharam =29
For thisra nadai the matras =3
Hence 93933840 is the required avartams to reach the toal matra count which is at samam!

8172244080 is the number of aksharas that the korvai should be...so it has to be 8172244080 beats...So not to be confused with nadai...If we have decided to make a korvai for 8172244080 aksharams long, we might as well do it for chathusram instead of complication..

drshrikaanth · Post by **drshrikaanth** » 18 Aug 2006, 13:35

cmlover wrote:Hence the minimal korvai has to be 8172244080 long! .

CML
I have already made short shrift of this number by showing a smaller number. SO this numer is NOT the mimimum. See previous pages. As for them all being divisible by the prime numbers in them, yes, thats a point. But it also happens to be divisible by several other numbers which could be the crucial difference.

arunk · Post by **arunk** » 18 Aug 2006, 19:33

drs,

i havent done the calculations thoroughly myself but your smalrer number 355314960 is not visible by 23 (??). Doesnt it have to be?

Arun

cmlover · Post by **cmlover** » 18 Aug 2006, 21:32

Precisely
355314960x23=8172244080 is the answer and that is the number of matras for the korvai! Every taalam will reach samam in that korvai and that is minimal.
For example if you consider only Triputa taaalas (there ar 5 of them) the minimal korvai is 72072 long. Everybody will reach samam at the end. Note this is the LCM.

cmlover · Post by **cmlover** » 18 Aug 2006, 21:55

The general formula is
every Korvai (matras)= aksharam x (Sum of (nadai x avartam))
Hence the commonkorvai must be divisible by all the prime number akshara counts. This number is the LCM for the 35 taalas which is 8172244080.
At this point nadai is immaterial. This is the minimal size of the korvai.
nadai becomes important in the implementation only. Just as if a Triputa and rupaka (catusra laghu) playing together then the minimal korvai is 24 (LCM of 8 and 6). When they play the Triputa must use thisra nadai and Rupaka ust use catusra nadai. They are forced to for the minimal solution. Similar logic prevails!

drshrikaanth · Post by **drshrikaanth** » 18 Aug 2006, 23:39

arunk wrote:i havent done the calculations thoroughly myself but your smalrer number 355314960 is not visible by 23 (??). Doesnt it have to be?

Thanks for pointing out. Strange. Tell me what I did wrong. The smaller number 50759280 is th LCM for all the other groups except 14 (the naDes being as I explained in my earlier post on this calculation). And then I calculated the LCM of this number and 14 LOL Is that incorrect? As for

355314960x23=8172244080 is the answer

, that is only a coincidence as far as I can see.

One end, it makes sense to think that whatever the choice of naDe, the beat count is waht that counts as the rest are simply multiples of this number. BUT at the other end, when you do the actual calculations, the LCM you get is different depending on what naDe you choose. For example the LCM of (14, 23), (14,69) and (14, 115) yield different result although the second numbers in each pair are from the same original 23 subset.

Thinking about it, is this inference of mine correct:- regardless of which naDe we choose, the smallest LCM results from using the beat count(using naDe variants can either give the same or more, but never less).

Appreciate your thoughts.

cmlover · Post by **cmlover** » 19 Aug 2006, 00:01

The problem is to find the smallest korvai which all 35 guys can keep thaalam at samam. This cannot be smaller than the LCM that we have found. They can play it in many different ways using nadai changes. That will also change their number of avartas. We can also try to find a solution that will minimize the total cumulatve number of avartas (but that is a different question).

The smallest Korvai is of length 9 which only the thisra Ekam will be able to play.
No body can ever play a korvai of length 10 or 11 at samam!
For the korvai of lenth 12 there are two guys who can play; thisra laghu Ekam at chatusra gati ass well as chatustra laghu ekam with thisra gati.
Nobody can play korvais of length 13 or 14.
Nobody can play a korvai of length 17 at samam!
For korvais of length 18 and over at least one of them (and many other with nadai changes) will be able to play a samam.

The math is simple and straight forward and we do not need parabolic equations and elliptic numbers

cmlover · Post by **cmlover** » 19 Aug 2006, 00:04

The above discussion does not take into consideration 'kaLai'!

vasanthakokilam · Post by **vasanthakokilam** » 19 Aug 2006, 00:05

is this inference of mine correct:- regardless of which naDe we choose, the smallest LCM results from using the beat count(using naDe variants can either give the same or more, but never less).

True. I think CML's equation and inference also leads to the same result.

drshrikaanth · Post by **drshrikaanth** » 19 Aug 2006, 00:06

cmlover wrote:This cannot be smaller than the LCM that we have found.

Who is we here?

No body can ever play a korvai of length 10 or 11 at samam!
Nobody can play korvais of length 13 or 14.
Nobody can play a korvai of length 17 at samam!

Can you explain why?

The math is simple and straight forward and we do not need parabolic equations and elliptic numbers

When we cannot get a "simple" answer by using "simple" maths, we have to try and use complex approaches. Even if we dont understand it, there is no har in trying is there!

drshrikaanth · Post by **drshrikaanth** » 19 Aug 2006, 00:06

cmlover wrote:The above discussion does not take into consideration 'kaLai'!

It wont make a difference.

vasanthakokilam · Post by **vasanthakokilam** » 19 Aug 2006, 00:07

cmlover wrote:The above discussion does not take into consideration 'kaLai'!

If nadai count does not matter for the minimal number, kaLai should not matter either, as you yourself have shown since that just is also a multiplier like the nadai count.

drshrikaanth · Post by **drshrikaanth** » 19 Aug 2006, 00:08

vasanthakokilam wrote:True. I think CML's equation and inference also leads to the same result.

So to my next question. If it is true that the LCM is different for differnet combination of naDes, is it not possible to get a smaller LCM by using a varying combination of naDes? If not, why not.

drshrikaanth · Post by **drshrikaanth** » 19 Aug 2006, 00:14

vasanthakokilam wrote:If nadai count does not matter for the minimal number, kaLai should not matter either, as you yourself have shown since that just is also a multiplier like the nadai count.

They are not the same. doubling and quadrupling is very different from trebling or multiplying by 5. Which is why I ahve grouped (4,8,16) together and not 12 with them. (6,12) go together.

cmlover · Post by **cmlover** » 19 Aug 2006, 00:15

The samllest number for aksharas is 3 (occurring for thisra jAti laghu ekam).
The smallest nadai is 3 for the regular thisra nadai.
(note you can have a count of one in the chavukka kaalam!0
You cannot play 10 maatras in madhyama kaalam in any taaLam.
(of course you can play 3 matras in thisra Ekam in chavukka kaalam!)
Does that count?

vasanthakokilam · Post by **vasanthakokilam** » 19 Aug 2006, 00:16

I can not quite wrap my head around it yet, but are we open to considering two possibilities:

1) Expand out the mathrai count of all the 175 thalas. Pick 35 out of this and see if the LCM is smaller for any such 35 combination. Once chosen, you can not change the period. Only thing this allows is, upto 5 people can use the same basic thala.

2) The equations of DRS where a thala can be used only by one performer but for each avarthanam you can change the nadai. Those equations are very hard to solve since it involves 40 variables. My Math friend has not gotten back to me yet.

arunk · Post by **arunk** » 19 Aug 2006, 00:17

drs,

i have to look back at your calculations but i do think cmlover has got it right. The minimum korvai length (in mathras) in this problem is indeed equal to the LCM if there is NO restriction on mixture of nadais, and the nadais involved is really "implementation" as he puts it.

As long as you can arrive at the akshara count of ANY tala using a mixture naDais, you dont have to worry about naDais in figuring out korvai length as it will always be equal to the LCM. Now is this always true for *any* mixture of talas? It would be long as you build ANY akshara count (>2) using additions of 3,4,5,7 and 9 and I think that is indeed the case.

Now may be you knew all this and were only disagreeing on the LCM value. If so apologies! I will look at your calculation a bit later. But at first glance it seems that 355314960x23=8172244080 is not a coincidence.

Arun

drshrikaanth · Post by **drshrikaanth** » 19 Aug 2006, 00:18

CML
I dont know where you are getting at. When you say 10 mAtrAs, are you meaning that as an equivalent of 10 hrasva swaras sung in madhyamakAla. akShara and mAtre are not the same.

drshrikaanth · Post by **drshrikaanth** » 19 Aug 2006, 00:21

vasanthakokilam wrote:1) Expand out the mathrai count of all the 175 thalas. Pick 35 out of this and see if the LCM is smaller for any such 35 combination. Once chosen, you can not change the period. Only thing this allows is, upto 5 people can use the same basic thala..

I already expanded out the 175 tALas which is how I arrived at the 10 equations.

baz1908 · Post by **baz1908** » 19 Aug 2006, 00:28

As i understood it, the original LCM calculated was for the number of beats (aksharas (independent of nadai)) in the korvai not the number of mathras (sub-beats(dependent on nadai)).

cmlover · Post by **cmlover** » 19 Aug 2006, 00:29

My equation is
akshara x nadai = total matras
(I am assuming nadai change inside a taaLam is inadmissible!)

vasanthakokilam · Post by **vasanthakokilam** » 19 Aug 2006, 00:31

drshrikaanth wrote:
vasanthakokilam wrote:1) Expand out the mathrai count of all the 175 thalas. Pick 35 out of this and see if the LCM is smaller for any such 35 combination. Once chosen, you can not change the period. Only thing this allows is, upto 5 people can use the same basic thala..
I already expanded out the 175 tALas which is how I arrived at the 10 equations.

Do your equations then allow for picking any 35 out of the 175? As an example, can one mridangamist choose thisra nadai chathusra jati ekam and another one choose chathusra nadai chathusra jati ekam? ( If that is not even allowed by Hari, then it is a moot point ).

baz1908 · Post by **baz1908** » 19 Aug 2006, 00:34

Remeber, Hari sir did say 35 thalams and not 35 of the 175.

The 2 thalams you have mentioned would be the same in the 35 thalams, only chage of nadai.

drshrikaanth · Post by **drshrikaanth** » 19 Aug 2006, 00:37

vasanthakokilam wrote:Do your equations then allow for picking any 35 out of the 175? As an example, can one mridangamist choose thisra nadai chathusra jati ekam and another one choose chathusra nadai chathusra jati ekam? ( If that is not even allowed by Hari, then it is a moot point ).

Thats not what I said VK. It is obvious from the equations I provided. I have not wily nily chosen different nades from different tALas and grouped them together.

vasanthakokilam · Post by **vasanthakokilam** » 19 Aug 2006, 00:37

Alright then.. Since that is not allowed, I will drop that line of thinking.

DRS, I did not mean to say you said that.

cmlover · Post by **cmlover** » 19 Aug 2006, 00:38

vk

the 175 taalas (35x5 nadai) from which you select 35 (making sure all the basic 35 types are represented) will have the minimum LCM 8172244080. So that is not not going to reduce the value!
nadai is irrelevant and redundant

arunk · Post by **arunk** » 19 Aug 2006, 00:39

Wow! Lot of posts before i could complete mine (:-).

As I stated earlier, no mater what mixture of naDais you use for *each tala*, the eventual mathrai count you arrive for that tala MUST be divisible by the akshara count. So this implies that the smallest possible korvai length in mathars will indeed be *least*-common-multiple of all the akshara counts. This is of course probably stating obvious, but in itself implies that mixture of nadais dont matter for LCM calculation. They cannot bring the value down, in fact they can only help approach the minimum possible value (minimum here being redundant as we are finding LCM - but i thinking it is important to emphasize this).

For example, between tisra-triputa (7) and say tisra-eka (3), if you cannot mix gatis, and you must stick to catusra gati, then you are finding LCM between 28 and 12 and that is 84. If you are in tisra, you are finding LCM between 21 and 9 and that is 63. But if you can mix gatis, your LCM is simply 21, which is 7*3 (you do one avarthana, with tisra-triputa in tisra gati, but tisra-eka in misra gati), which is the LCM of the akshara count. So if you cannot mix gatis, you will always arrive at an answer that is a multiple of the LCM of the akshara count, hence no need to bring gatis into the mix here (pun intended!). You bring that to figure how each tala would be put to arrive at the korvai mathrai count

To get at LCM, you separate the 35 talas into 2 sets: One set P with akshara count of primes. Another set NP with those whose akshara count are non-primes. The set P, you leave alone as you cant do much. But in NP, you eliminate any member whose multipe (any mutiple) is also in NP (e.g. eliminate 3, if 6 or 9 is present; eliminate 6 if 12 is present, eliminate 11 if 22 is present). Once done, simply multiply all the members in the union of N and NP, that is the answer. At this point, I tend to believe (only because i am lazy to do this now) the answer is 8172244080.

Arun

cmlover · Post by **cmlover** » 19 Aug 2006, 00:45

tathAstu!

vasanthakokilam · Post by **vasanthakokilam** » 19 Aug 2006, 00:45

Arun, we are all convinced beyond doubt that if you strictly go by akshara count , the LCM is 8172244080. Having said that, to make your method of calculation whole, in your reasoning, since P is a set of primes, how can it contain a multiple of numbers from NP?

arunk · Post by **arunk** » 19 Aug 2006, 00:46

that was a typo. I edited that post 3 times (:-)

arunk · Post by **arunk** » 19 Aug 2006, 00:47

only 3 mistakes in a post of mine, could be my LCM least committed mistakes (:-)

vasanthakokilam · Post by **vasanthakokilam** » 19 Aug 2006, 00:49

oops, sorry.

drshrikaanth · Post by **drshrikaanth** » 19 Aug 2006, 00:51

arunk wrote:To get at LCM, you separate the 35 talas into 2 sets: One set P with akshara count of primes. Another set NP with those whose akshara count are non-primes. The set P, you leave alone as you cant do much. But in NP, you eliminate any member whose multipe (any mutiple) is also in NP (e.g. eliminate 3, if 6 or 9 is present; eliminate 6 if 12 is present, eliminate 11 if 22 is present). Once done, simply multiply all the members in the union of N and NP, that is the answer. At this point, I tend to believe (only because i am lazy to do this now) the answer is 8172244080.

Yes I did exactly that. First the LCM for primes and then do it with Nonprimes. I used different nades but they are giving the ssme result. I rechecked my calculations and yes, one data entry was wrong which is why I got the smaller number. SO, 23 was actually left out and so it was no coincidence indeed that the number I obtained multiplied by 23 is the LCM. So, I can only conclude that Harishankar may have been joking as there is no way to reduce this number, (unless you break all rules)

arunk · Post by **arunk** » 19 Aug 2006, 00:53

actually my approach has a mistake: I had mentioned that you multiply all remaining numbers and that is incorrect for LCM if some are non-primes as those remaining in NP. You instead first find LCM of "NP" and then multiple it with the product of each number in P.

Sorry.

Arun

drshrikaanth · Post by **drshrikaanth** » 19 Aug 2006, 00:55

Arun
I took it that thats what you meant, as is evident from my previous post.

vasanthakokilam · Post by **vasanthakokilam** » 19 Aug 2006, 00:56

cmlover wrote:tathAstu!

I think we are now moving our head up and down in agreement ( we need a emoticon for that

)

drshrikaanth · Post by **drshrikaanth** » 19 Aug 2006, 01:00

vasanthakokilam wrote:I think we are now moving our head up and down in agreement ( we need a emoticon for that )

A moving emoticon :rolleyes: Just pray that Meena does not see this post of yours

vasanthakokilam · Post by **vasanthakokilam** » 19 Aug 2006, 01:03

Sorry Meena.... This will do for now..

meena · Post by **meena** » 19 Aug 2006, 01:04

OH NO, i protest, not those thingys.

arunk · Post by **arunk** » 19 Aug 2006, 01:17

vk - that is pretty cool!

(sorry meena - unlike some of the others, this one seems quite appropriate!)

Arun

cmlover · Post by **cmlover** » 19 Aug 2006, 01:37

So just as Venkatamahi concluded that even
SrikaNTha cannot change the number 72 for the total meLakartas, we have, even
SrikAnta cannot change the number 8172244080 for attaining equanimity for tALas!
OM SAnti SAnti SAntiH|

drshrikaanth · Post by **drshrikaanth** » 19 Aug 2006, 01:43

haha! Thanks for comparing me with the great vEnkaTamakhi

inconsequential · Post by **inconsequential** » 21 Aug 2006, 07:45

Thathwamasi sir,

Thanks very much for some nice anecdotes on srI harishankar. Amidst all the number crunching, a couple of nice reads on this laya maestro:

http://www.sruti.com/mar02/marmain.html
http://carnatica.net/tribute/tributekhanjiras.htm

regards

thathwamasi · Post by **thathwamasi** » 21 Aug 2006, 09:41

Inconsequential..Thanks so much....

I was just thinking of uploading some videos tracing some important aspects of Hari's playing. I have uploaded the earliest of Hari videos I have. He is accompanying MLV along with Kanyakumari, Bhaktha and EMS. Its so refreshing to see such a young Hari and Bhaktha. After looking at Hari in this video, I have named him as the Devil of Rishiveli...lol...

He is so young and vibrant, with such golden fingers. He has played a luvly bit of thani avardhanam. There would be no fun if I just upload Hari's bit due to some reasons. Hence I have putup the entire thani.

Points to be noted..

Hari's way of holding the Kanjira..just perfect. And his fingering is amazing.

Bhaktha might have changed his style of playing now, but you can see his affinity towards Karaikudi Mani's playing in this Thani.

The unique thing in this thani is that, the mridangist has played in Thavil bhani and the Ghatam artist has played in Mridangam bhani..(as in, he hasn't played much of ghatam sollu). Hari has played perfect Kanjira stuff. And the way Hari improvised in the final Korvai is a pleasure to watch/listen.

Hope you guys like it.

http://rapidshare.de/files/30172626/Hari011.wmv.html

Try this. Please let me know your comments.

vasanthakokilam · Post by **vasanthakokilam** » 21 Aug 2006, 11:28

Fantastic. Hope no one took a bathroom or cafeteria break during this thani

sshankar_1970 · Post by **sshankar_1970** » 30 Jan 2008, 12:55

thathwamasi wrote:While we are all trying to find the answer for the puzzle, let me write about something else.

The combo's that I could imagine would be Harishankar of 1990's with Mani iyer, Pazhani and murugabhoopathy of 1940's. I always felt, Hari was born 30 years late...Instead of '58 he should have been born by 1928. I can't help but to imagine how enthralling it would have been, if Flute Mali tries to play a kuraippu with Mani iyer and Harishankar....

Well .. Those who had a chance to listen to Mali's last concert will appreciate the last point .The mridangam vidwan (will not name him ) slipped , but Harishankar matched Mali beautifully..

Another person who brought out the best in Harishankar is TNS . TNS- KRM-HS is probably the best after the hypothetical Mali- PMI-HS combo

Nick H · Post by **Nick H** » 30 Jan 2008, 13:50

The mridangam vidwan (will not name him ) slipped

Such things are allowed, and even heighten the interest in a concert. I'm sure your vidwan met the vast majority of his rhythmic challenges, and there is no shame in knowing his name in the context of having missed one.

At Harishankar's level of genius the instrument becomes almost irrelevant. Yes, he chose a very difficult instrument and his fingers more than mastered it, but his true skill was in his head, in his ability not only to answer, but to calculate, re-calculate and juggle again, seemingly effortlessly.

Not just a kanjira master, but a total master percussionist.

cienu · Post by **cienu** » 30 Jan 2008, 14:16

nick H wrote:
The mridangam vidwan (will not name him ) slipped
Such things are allowed, and even heighten the interest in a concert. I'm sure your vidwan met the vast majority of his rhythmic challenges, and there is no shame in knowing his name in the context of having missed one.

At Harishankar's level of genius the instrument becomes almost irrelevant. Yes, he chose a very difficult instrument and his fingers more than mastered it, but his true skill was in his head, in his ability not only to answer, but to calculate, re-calculate and juggle again, seemingly effortlessly.

Not just a kanjira master, but a total master percussionist.

In a different thread I had called Harishankar the " Mount Everest of Kanjira" .

It would not be inappropriate to call him "Mount Everest of Percussion"