Kanjira G Harishankar

cmlover · Post by **cmlover** » 15 Aug 2006, 01:53

No pains No gains!
Doesn't the mridangam guy 'dictate' to kanjira and GhaDaM in the final phases!
We seldom appreciate upapakkavaadhyam skills in trying to accommodate to the pakkavaadhyam!
(that is why your writeups on Hari is so enchanting!)

thathwamasi · Post by **thathwamasi** » 15 Aug 2006, 01:59

vasanthakokilam wrote:
thathwamasi wrote:We can put Kanda jaathi Ata thalam chathusra nadai in one hand(the common ata tala varnam's thalam) and put Adi talam misra nadai in the other hand...

Ata talam will be 14 beats * 4 counts making it 56 and adi talam misra nadai will be 8 beats * 7 counts making it 56. So every time cycle will bring a samam to them...
This kind of dwi-thala pallavi is lot easier to mathematically explain ( not easy playing or keeping track ). We do not need nadai change. It is actually LCM calculation that will suffice. You can stick to chathusra nadai and the LCM of 8 and 14 is 56. The two thalas will converge at 7 avarthanams of Adi and 4 avarthanams of Ata.

(rhythm instrumentalists use the word 'thisram' and 'misram' in a different context as well. With the same chathusra nadai sub-beats you can group them to give the "illusion" of misram. I think that is what you would call "playing misram over chathusram" ( which does not involve nadai change ). So, if you take the LCM of 56 and multiply by 4 chathusram sub-beats, you get 224 chathusram sub-beats.. If you group it by 7, you will have 32 such groups. So you play it 32 times, you will be come back to samam. But that is just playing technique and not nadai change. )

I agree its not easy. But its not impossible. Its a very subtle technique that a music student needs to understand to keep time in two different nadai's in two hands. I don't deny that in the same nadai 7 avartanams of adi and 4 avartanams of Ata. But when you sing in that style and ask a mridangist to play tani avardhanam, they will have to struggle. Because they will exactly have to calculate their entire thani avardhanam in such a away that their mohra and korvai ends in a 7th avarthanam of adi and fourth avartanam of ata which is a bit silly. But in nadai change, its just the main artiste's confidence that matters, as the mridangist can play a regular tani avartanam like how he plays in ata. But the flip side in this nadai change is that mridangist has no option but to play chathusra nadai. If he plays thisram based on the ata, it won't sit in the misra nadai adi talam.

Overall, you observation is right, but the method that Rajamani mama told me(nadai change) is challenging. It gives you such confidence as a main artiste once you master it. He thought me how to approach two thalams of two different nadais and explained me the pros and cons.

thathwamasi · Post by **thathwamasi** » 15 Aug 2006, 02:06

cmlover wrote:No pains No gains!
Doesn't the mridangam guy 'dictate' to kanjira and GhaDaM in the final phases!
We seldom appreciate upapakkavaadhyam skills in trying to accommodate to the pakkavaadhyam!
(that is why your writeups on Hari is so enchanting!)

You are right!!!! The mridangists generally dominate the finishing of thani avarthanams. In order to break that domination, Hari started playing in gaps. Even during the last flurry, there are gaps that can be filled. Hari used to play "gumukki" on his Kanjira in a fascinating manner during the final flurry of tani avardhanam. And his reflexes are too good that he would split and analyse any korvai by the end of the second turn and during the final turn, he would improvise it so beautifully.

One tip for all rasikas - If you wanna listen to best of Hari, please listen using ear phones. Thats when intricacies of Hari would be heard. Even in the recording that coolkarni has posted of TRS, pls listen to it on a earphone and you could listen to Hari's conception of accompanying a keerthanai on kanjira. He has played 'gumukku' with such bhavam and he has not played mere sarva laghu.

There are two levels of excellence - One is playing for the keerthanai...which many people know how to...thats were most people concentrate as well.

The next level is playing the song itself on your percussion instrument...Hari belongs to the second category.

thathwamasi · Post by **thathwamasi** » 15 Aug 2006, 02:10

I came to the conclusion that Hari belongs to the second category, when I heard a recording of MSG solo where he plays thodi varnam. I don't remember who played the mridangam. The mridangist struggled as he was not familiar with the varnam, but Hari came along till the end. And when me and my friend analysed it, he has instinctively played the bass sounds(essentially dhom and gumukki) corresponding to Sa and Pa and treble sounds(tha, thi and others) for the other notes. Its amazing how he did it. Kanjira doesn't have a sruti, I agree, but I would say Hari did achieve a sruthi shudham on that instrument.

drshrikaanth · Post by **drshrikaanth** » 15 Aug 2006, 02:23

thathwamasi wrote:You are right..8172244080 is the right number...I am wrong in saying,..115 years...its 259 years...if we imagine one beat to be one second. You are also right in saying Sarma's guruji's technique cannot be the answer for this puzzle.

I arrived at a number that brings down the original number by a factor of 2.3 which adds to 112 years. Thats not too bad for a start. Certainly will only need about 4 generations of artistes

The number I arrived at was 355314960. And the group of tALas with 7 and 14 beats wrer the nasty ones that pulled this number up. Without them , the number will only be 50759280, which will only be 1.6 years!

Each of the tALas with 11, 13, 17, 18, 22, 23, 29 beats are played in khaNDa naDe. The nasty group(7s and 14s) can be played in any but the miSra naDe. The rest get played in caturaSra naDr. Can someone take it further. If I manage, I will come back.

cmlover · Post by **cmlover** » 15 Aug 2006, 02:27

DRS

You are again forgetting hari's statement that
the answer is simple
(like the famous Fermat's Theorem:)

arunk · Post by **arunk** » 15 Aug 2006, 02:34

drs,

I am wondering since a korvai typically involves mixture of nadais between avarthanas, and the question is posed by a master percussionist, whether that also figures in and if so that can help (i think) bring it down a lot further.

For example, between say 23 and 29 cycle talas, instead of trying to satify satisfy 23*n1*X = 29*n2*Y (where X and Y are # of avartahanas each in nadais n1 and n2 respectively), one could achieve it say in 4 avarthanas (i.e. X and Y are 4), wherethe 23 cycle tala is played in misra, misra, sankirna, tisra-mel-kalam nadais over 4 avarthanas, and 29 cycle one is played in khanda, misra, khanda, misra, tisra-mel-kalam nadais over 4 avarthanas. Essentially the equation is then:

23*7 + 23*7 + 23*9 + 23*6 = 29*5 + 29*5 + 29*7 + 29*6

23*(7+7+9+6) = 29*(5+5+7+6)
23*29 = 29*23

I am not sure how exactly to extend this to the problem but i think it applies somehow (;-)

Arun

arunk · Post by **arunk** » 15 Aug 2006, 02:36

cmlover - it is simple to a genius (:-).

Reminds me of the Einstein's book on relativity with the title itself including "with an explanation anyone can understand". I sure didnt understand it then (:-)(;-)

drshrikaanth · Post by **drshrikaanth** » 15 Aug 2006, 02:48

arunk wrote:I am wondering since a korvai typically involves mixture of nadais between avarthanas, and the question is posed by a master percussionist, whether that also figures in and if so that can help (i think) bring it down a lot further.--Arun

That would be cheating because you cannot change naDes wily-nily in a tALa. But hang on, you maybe onto something. Well yes, you could play different Avartas(not within one Avarta though) in different naDes and arrive at a smaller no.Good lateral thinking

But that is still not free from blame of cheating

arunk · Post by **arunk** » 15 Aug 2006, 03:01

guilty as charged (:-) - although i am a literal zero w.r.t percussion techniques. In fact i didnt know even this much about korvai (3 times typically with different nadais) until a few days back (:-).

I was indeed implying switch across avarthanas only - isnt that pretty common for mridangists?

Yes switch within an avarthana - that could make the problem even simpler!! Hmmm.. maybe thats what Harishankar meant - would be pretty devious (:-).

Arun

drshrikaanth · Post by **drshrikaanth** » 15 Aug 2006, 05:20

Another point. Whatever calculations we do, we can ignore sankIrNa naDe(No Not jATi of course) as what can be accommodated in sankIrNa naDe can essentially be done with triSra naDe itself. So that is one thing less to reckon with.

baz1908 · Post by **baz1908** » 15 Aug 2006, 05:46

Hi guys,

I haven't contributed to this forum before but found this question very interesting.

I think cmlover is on the right track. However the sentance at the end will contradict this solution: "if one thalam is 8 beats and the other is 3 beats...both will end at the same time after their LCM which is 24 beats. Similairly it should be done for 35 talams..."

If Harishankar sir actually said this, then we cannot use the 'same time to complete all 35 avarthanas' theory.

Barathan

arunk · Post by **arunk** » 15 Aug 2006, 05:58

actually coming to think of it, doesnt this (24 beats for 8-beat and 3-beat talams to coincide as pointed out as an example by Harishankar) rule out different gati/nadais for the different talas? I mean, it seems to imply that he may not have been thinking different gatis for the various talams either.

But that will put us back to square one (:-).

baz1908 · Post by **baz1908** » 15 Aug 2006, 06:16

Well it implies that all the 35 thalams should be in the same gathi.

Using the LCM method I get a number (3 X 4 X 5 X 7 X 9 X 11 X 13 X 17 X 23 X 29) = 6,129,183,060 beats ~ 194.22 years
I doubt very much that this is the simple way!

baz1908 · Post by **baz1908** » 15 Aug 2006, 06:45

sorry, I have to divide by 3 as 9 is alredy there and multiply by 4 to take account of 16 - your number is correct = 8,172,244,080 ~ 258.96 years

thathwamasi · Post by **thathwamasi** » 15 Aug 2006, 09:36

8,172,244,080 is the right number.

cmlover · Post by **cmlover** » 15 Aug 2006, 10:06

Is a kOrvai tALa dependant? Or is there a kOrvai (or can it be constructed) that will flow evenly in all the 35 tAlas in synchrony?

thathwamasi · Post by **thathwamasi** » 15 Aug 2006, 10:27

cmlover wrote:Is a kOrvai tALa dependant? Or is there a kOrvai (or can it be constructed) that will flow evenly in all the 35 tAlas in synchrony?

Thats the issue here. The Korvai need not be tala dependant. There can be a Korvai which flows in synchrony with 35 talas. Its just that it would be such a huge figure.

One more interesting anecdote about Harishankar. He plays cards. And while playing cards, he has a unique style of serving cards.

For example, if there are 4 players playing rummi, he has to serve 56 cards. Generally people count after laying each card for each man, 1,1,1,1 then 2,2,2,2, so on and so forth.

Hari used to do it in his own way. He would select a Korvai which is 56 aksharams totally. He will start serving and start saying the korvai. And be sure that when the korvai ends, he has served 13 cards to all of the four players and would finish the samam by serving the open card. I believe his blood had too much layam in it.

vasanthakokilam · Post by **vasanthakokilam** » 15 Aug 2006, 11:03

I have not had much time to spend on it, so some random observations.

The thala counts under consideration are: 3, 4,5,6,7,8,9,10,11,12,13,14,16,17,18,20,22,23,29

The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
So except 19, all the prime numbers are reflected in the thala counts.

The gathi/nadai counts are: 3,4,5,7,9 - some primes

Just a scary thought: For millenia, countless mathematicians have spent their life time on primes and still there are unsolved problems.... but then Hari had said it is simple. That is the confusing part and I am wondering if we are off into some complex path that is not going to lead anywhere. That is pretty common when dealing with prime numbers

Arun's idea is interesting in one aspect: For the 23 and 29, a simple LCM yields 667 beats but with Arun's way of calculating it is 667 gathi counts. That does lead to some compression of total time. ( but then we are not sure if playing around with gathi is what Hari had in mind ).

Reason for this summary is, if you are good at prime number theory, may be there is a prime number theorem or something that fits this situation nicely. May be. I can not think of any yet.

drshrikaanth · Post by **drshrikaanth** » 15 Aug 2006, 13:33

thathwamasi wrote:For example, if there are 4 players playing rummi, he has to serve 56 cards.

52 cards.

[quote=""vasanthakokilam""]The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
So except 19, all the prime numbers are reflected in the thala counts.[/quote]
2 is left out too.

drshrikaanth · Post by **drshrikaanth** » 15 Aug 2006, 14:40

Just for everyones info
The number of beats in the various tALas can be reduced to the following formulae

dhruva- 3X+2
maThya- 2X+2
rUpaka- X+2
jhampe- X+3
aTa- 2X+4
tripuTa- X+4
Eka- X Where X is the number of beats in each laghu (Depending on the jAti)

The number of akSharas in each tALa will be the number of beats(as calculated above) multiplied by the naDe/gati(again one of the 5). Reiterating, the sankIrNa naDe can be left out of calculations for all practical purposes as what can be chieved by sankIrNa can essentially be achieved by triSra.(I wonder if purandaradAsa overlooked this fact!).

So we have 140 tALas(4 variations of 35 tALas) to contend with. There are overlaps of numbers even among these- either in number of beats being equal and/or a multiple or in the number of akSharas overlapping.

baz1908 · Post by **baz1908** » 15 Aug 2006, 18:10

thathwamasi,

are these Harishankar sir's exact words? : ""if one thalam is 8 beats and the other is 3 beats...both will end at the same time after their LCM which is 24 beats. Similairly it should be done for 35 talams..."

If so, gathi should not be considered to solve the problem.

arunk · Post by **arunk** » 15 Aug 2006, 19:19

drs,

A silly question:
> sankIrNa can essentially be achieved by triSra
I thought with triSra you go 3, 6 and 12; 6 => double, 12 => quadruple i.e. double of double. So sankIrNa would not be a "normal/natural" super-set of triSra. To get it you could of course go in "triple speed" but is that done in cm? I mean is there a triple-speed say for catuSra i.e. as in 4*3 = 12? I thought it was generally 1, 2, 4, 8, 16 etc. for catusra, and 1, 3, 6, 12 for triSra, 1,5,10,20 for khaNDa, 1,7,14,28 for miSra and 1,9,18,36 for sankIrNa (although 16,12,20,28,36 and even some others may be more academic rather than used in real practice).

Thanks
Arun

drshrikaanth · Post by **drshrikaanth** » 15 Aug 2006, 19:27

arunk wrote:> sankIrNa can essentially be achieved by triSra
I thought with triSra you go 3, 6 and 12; 6 => double, 12 => quadruple i.e. double of double. So sankIrNa would not be a "normal/natural" super-set of triSra. To get it you could of course go in "triple speed" but is that done in cm?

No you dont have to treble the speed. But you can use 3 Avartas of the tALa in triSra naDe to cover 1 Avarta of sankIrNa naDe.

arunk · Post by **arunk** » 15 Aug 2006, 19:47

> But you can use 3 Avartas of the tALa in triSra naDe to cover 1 Avarta of sankIrNa naDe.
ah yes. For this problem sake then that does makes sense.

I think this problem definitely involves some twist which makes the solution easy or simple. Going brute-force, straightforward approach as has been tried by many of us leads only to an impractical solution. We have also tried some twists like different gatis across talams, and across avarthanas within a tala, and even that hasnt led us to the answe. Cmlover's different tempo is another one, but i am not convinced that is practical either.

I have no facts/reason to back this up, but my hunch is the "correct" twist will be a formula/approach that is easily and uniformly applicable to a mixture of any number of talas - 2 or 35. Since harishankar sir is no more, may be i can truly say "God only knows what that is"!

Arun

drshrikaanth · Post by **drshrikaanth** » 15 Aug 2006, 20:01

arunk wrote:We have also tried some twists like different gatis across talams, and across avarthanas within a tala, and even that hasnt led us to the answe.--Arun

I havent tried too hard on different combinations of naDes in different Avartas for each tALa. I think randomly doing it would be extremely time-sosuming. I agree we need to use a formula. But I think this will definitely lead to a fairly simple solution.

arunk · Post by **arunk** » 15 Aug 2006, 20:27

i am not sure but that mixture of nadais approach doesnt simply it that much as i had initially thought and hoped. Take the 23 and 29 cycle talas I mentioned. Now if both are in catusra gati, then the synchronization point is after 23*29*4 mathrais, but with mixture of nadais it is 23*29 mathrais (4 avarthanas of varying nadais as i mentioned before). That is a 75% reduction - very sizeable indeed. The eventual number in both cases of course must be divisible by 23 and 29 and the smallest such number is 23*29 since both are primes. We have figured out that with mixture of nadais you can indeed get to that number. This still does sounds promising but you throw in other talas with prime number of akasharas and the number will creep up again to impractical number since the smallest number is a product of those primes and there are a lot of primes in the 35 talas. So while it looked promising unless there is some other magic, it may does run out of gas quickly.

(While this may be obvious and I hope i am on the right track), I am basing this on just extending my example to 3 talas of 13, 23 and 29. You can repeat the 4 avarthanass 13 times for 23 and 29 cycle to arrive at a mathrai count of 23*29*13. So both 29, and 33 akshara tala would be done for 52 avarthanas. For the 13 akshara tala, you take e.g. again 4 avarthanas of nadais 5, 5, 7, 6 (23) and do it 29 times and thus 29*4 = 116 avarthanas to again arrive at 13*23*29. So while it is possible to arrive at the "smallest possible" number, that number still seems very high for a "simple solution". Unless there is another trick hidden here - may be me laying this out in detail will trigger a light bulb in some one else's brain!)

But then again a simple solution may be one that is "simple" in approach (one may think the above as not too complex?) and not necessarily lead to a "small" answer!

Arun

cmlover · Post by **cmlover** » 15 Aug 2006, 22:31

Here is another simple solution!
As thathwamasi points out nadai change will screw up the korvai and hence it is out. The problem demands that the 35 mridangist play simultaneously and that all the 35 taaLams must be played. It does not say that all taaLams be played concurrently; nor does it say that each mridangist should play only the same taaLam.

Accordingly let me use DRS's nice table for guidance
dhruva- 3X+2
maThya- 2X+2
rUpaka- X+2
jhampe- X+3
aTa- 2X+4
tripuTa- X+4
Eka- X Where X is the number of beats in each laghu (Depending on the jAti) where X = 3,4,5,7 or 9

The longest is the sankeerNa dhruva = 29 counts. That is the deciding length of the avartam.
Every body will play their taaLa at least once and then play other taaLa(s) to reach the total of 29. For example,
the Misra jAti Rupake will play two avartams (18) followed by a thisrajAti dhruva (11) to attain 29.
Since there is no nadai problem. Finally the Korvai(29 aksharas) will flow smoothly!

Note that 29 is the smallest length that will satisfy the requirements. There are otherwise infinite number of solutions!

There is no other simpler solution:)

baz1908 · Post by **baz1908** » 15 Aug 2006, 22:41

I read the original problem as being 1 percussionist and 35 people putting thalam. Ofcourse this is all theoretical?

Also the thalams should start at the same time and finish on samam independent of the number of avarthanams.

We cannot change a thala in the middle of a korvai.

thathwamasi · Post by **thathwamasi** » 16 Aug 2006, 00:16

baz1908 wrote:thathwamasi,

are these Harishankar sir's exact words? : ""if one thalam is 8 beats and the other is 3 beats...both will end at the same time after their LCM which is 24 beats. Similairly it should be done for 35 talams..."

If so, gathi should not be considered to solve the problem.

Nope...I dont think so. Exact words of Hari as told to me was "35 people keeps time for 35 thalams, starting at same point, can you make a korvai which will end when all the 35 thalams end in the same samam? I know how to do it."

vasanthakokilam · Post by **vasanthakokilam** » 16 Aug 2006, 00:56

May be what Harishankar meant by 'simple' is the simplicity of construction of the Korvai and not how long it takes to finish the korvai. May be there is a 'pattern' or 'master plan' or 'formula' which is 'simple' to layout which when played according to that plan will end after a couple of centuries.

baz1908 · Post by **baz1908** » 16 Aug 2006, 01:14

I think cmlover's original idea is the right one.

If we say a korvai, that say lasts 30 seconds, on tape and play it back we can fix any thalam for this by setting the time for each beat by dividing the total time for the korvai by the number of beats in the chosen thalam. Ofcourse putting the thalam for this will not be practically possible for most people. We would need to remove ourselves from listening to the korvai and put the thalam so that it completes a certain number of avarthanams in 30 seconds.

cmlover · Post by **cmlover** » 16 Aug 2006, 01:17

VK
That is a complex explanation of 'simple'

But I see you are driving at an algorithm than the complete solution itself
(since there may not be enough paper to write out the 2 century long solution!)
Incidentally what is the longest word in the english language?

drshrikaanth · Post by **drshrikaanth** » 16 Aug 2006, 01:19

CML
Your idea of starting different tALas at different times is innovative. But I dont think thats what Harishankar had in mind. Its too devious and plays with the fundamentals of both music, the idea under construction as well as integrity of the musician

Maybe VK is right about the method being simple and not the answer itself.

cmlover · Post by **cmlover** » 16 Aug 2006, 01:25

DRS

I think Hari is (if he was not pulling the leg) talking about a feasible solution. The straight mathematical one is the LCM which is humanly infeasible! Then we have to look for compromise in the questionitself to find an answer. Like the famous puzzle of making a line smaller by not erasing it:)

cmlover · Post by **cmlover** » 16 Aug 2006, 01:29

In a tani can the upapakkavadhyam (ghaDam, morsing, kanjira) maintain different talas from the mridangist?

baz1908 · Post by **baz1908** » 16 Aug 2006, 01:35

Does anyone have anything on the definition of a Korvai and the rules that need to be obeyed in setting a Korvai?

The upapakkavadhyam as with the mridangist would need to play to the thala of the main vocalist or instumentalist. They can however switch gathis.

drshrikaanth · Post by **drshrikaanth** » 16 Aug 2006, 01:59

arunk wrote:For example, between say 23 and 29 cycle talas, instead of trying to satify satisfy 23*n1*X = 29*n2*Y (where X and Y are # of avartahanas each in nadais n1 and n2 respectively), one could achieve it say in 4 avarthanas ----Arun

Arun, correct me if Iam wrong. First of all, if we are looking at naDai combinations within a variety of tALa, then the number of beats in each tALa is redundant for the final calculations. We are now working with akShara kAlas.

Secondly, I think 23*n1*X= 29*N2*Y is an incorrect representation of the equation. We are looking ate an equation of this type

23(A*3+B*4+C*5+D*7)= 29(A*3+B*4+C*5+D*7).

A, B, C & D being the number of Avartas in each naDe. Needless to say one or more of them can be zero and one may equal another.

This could significantly reduce the final answer right?

vasanthakokilam · Post by **vasanthakokilam** » 16 Aug 2006, 02:31

DRS, yes, that generalizes it.

23(A*3+B*4+C*5+D*7)= 29(A*3+B*4+C*5+D*7).

Generalizing it even further.

23(A*3+B*4+C*5+D*7)= 29(E*3+F*4+G*5+H*7).

arunk · Post by **arunk** » 16 Aug 2006, 02:44

drs,

> 23*n1*X = 29*n2*Y
Yes. That formula applied only if same naDai was used and i was actually referring to that because we were presuming so before i pointed out the possibility of mixture of nadais across avarthanas. That is why i started with "instead of trying to ...".

You are right that once you bring in a mixture, the formula changes to something what you mention. But no matter the formula, the simple eventual rule that must be satisfied is the total count of mathrais must must be divisible by # of aksharas (as that is a common factor as you say and will figure as a multiple). If # of aksharas happens to be a prime, then our possibilities are severely restricted when used in combination with other tala(s) whose akshara count are also primes. Product of the primes would be the smallest posssible number/multiple (and higher ones would obviously be multiple of that smallest multiple). There are just too many darn primes here (:-)!

If Harishankar was pulling "trick question", then we might as well consider mixture of nadais within an avarthanam like how mridangist usually tackle it (:-)? But the trouble is he was referring to 35 people putting talam and one mridangist, and not 35 mrindangists! The general expectation would be to stick to same nadai when putting talam (atleast within an avarthanam). I mean with this changing nadai's across avarthanams itself is a stretch.

Arun

drshrikaanth · Post by **drshrikaanth** » 16 Aug 2006, 02:45

Right VK. And we have 10 such equations to contedn with. Some of the tALas have twice or four times the beats of another SO we can use the equation for the tALa with the highest number of beats in that group as that automatically helps to find the number of Avartas need for the smaller tALas. I can put up the ten equations if that will help.

cmlover · Post by **cmlover** » 16 Aug 2006, 04:29

Are we talking about Hari or Diophantane:)

cmlover · Post by **cmlover** » 17 Aug 2006, 23:29

Let us designate this as an unsolved mathematical problem and name it Harishankar Problem in honour of our maestro. Somebody should cast it in mathematical terms spelling out the constraints and post it perhaps in the American Mathematical Monthly. Who knows even Grigory Perelman (the current outstanding mathematical genius) may have a crack at it!

vasanthakokilam · Post by **vasanthakokilam** » 18 Aug 2006, 00:01

I talked to a mathematician friend of mine. He is an amateur mathematician now since he has switched to software writing but he is a guy who finds solving complex math problems relaxing!! He said he will think about this further.. ( may be he will win the Harishankar prize ).

One humorous and one serious note ( both at extremes ).

- If Hari meant it with a wink, two centuries can be shrunk to a really short time if each beat is the smallest interval achievable..Currenty with a casium atomic clock at the resolution of 9,192,631,770th of a second.

- Now this mathematician friend sent me this today for my study ( who is he kidding? ). On first look, if it looks like a random assembly of words put together by a monkey, that is only a natural reaction

http://www.maths.ex.ac.uk/~mwatkins/zeta/bump-gue.htm

EDIT: His follow up:" It's deep math about the distribution of primes, related to the Riemann hypothesis. Their correlations (e.g. intervals) are conjectured to have frequencies according to some (theoretical or natural?) physical system. Frankly I don't understand it much myself. I think maybe Ramanujan could solve this. He was one of the geniuses in this area, and he was inspired by classical Indian music."

drshrikaanth · Post by **drshrikaanth** » 18 Aug 2006, 04:28

These are the equations. VK, you can give these to your mathematician friend:)
They all have the same value.

(3,6,12 set)----36*A1+ 48*B1+ 60*C1+ 84*D1
(13)-----------39*A2+ 52*B2+ 65*C2+ 91*D2
(7,14 set)-----42*A3+ 56*B3+ 70*C3+ 98*D3
(4,8,16 set)---48*A4+ 64*B4+ 80*C4+ 112*D4
(17)-----------51*A5+ 68*B5+ 85*C5+ 119*D5
(9,18 set)-----54*A6+ 72*B6+ 90*C6+ 126*D6
(5,10,20 set)--60*A7+ 80*B7+ 100*C7+ 140*D7
(11,22 set)--- 66*A8+ 88*B8+ 110*C8+ 154*D8
(23)-----------69*A9+ 92*B9+ 115*C9+ 161*D9
(29)-----------87*A10+ 116*B10+ 145*C10+ 203*D10

vasanthakokilam · Post by **vasanthakokilam** » 18 Aug 2006, 04:51

I have sent the equations to him. Let us see if he takes this up. I told him to find a set of values for those 40 variables first, though we are interested in optimizing it for the minimum sum.

baz1908 · Post by **baz1908** » 18 Aug 2006, 04:53

Sorry, I'm quite confused!

Can you explain where you're going with these equations?

Thanks

Barathan

cmlover · Post by **cmlover** » 18 Aug 2006, 09:19

8172244080 which is the LCM is the minimal aksharakaalam. Notice that all the ten equations are divisible by the contained prime numbers. Hence their multiples which is to be divisible by them has to be their LCM. The nadai does not come into the picture in the calculation of the aksharakaalam.

But nadai comes in the calculation of the avatams to be played. If the korvai is aslong as the above number then for example the sankeerna dhruam guy (29 aksharas) will have to play 29x281801520=29(3x93933840) or 93933840 avartams in thisra nadai,
or
= 29(4x70450380) or 70450380 avartams in chatusra nadai etc
He can do a mixture of other nadais if he wants to minimize the number of avatams. Similarly for the others.

Hence the minimal korvai has to be 8172244080 long! It can be constructed anyway you want using all kinds of patterns which will not affect the talas since everybody reach the samam ultimately. Perhaps that is the 'simplicity' implied in the construction that Hari hints at.

thathwamasi · Post by **thathwamasi** » 18 Aug 2006, 09:20

I have posted this earlier.

http://rapidshare.de/files/29321751/06_Track_6.wma.html

Just thought of writing a few words about this.

This is a masterpiece. A few words of commentary.

In the pallavi, the mridangam T.K.Murthy straight away starts rolling...Its a very common for a Murthy fan to listen to rolls in a song with such kalapramanam. But the surprise element arises for a normal listener by the third or fourth sangadhi, when u start hearing rolls on Kanjira..Hari has painstakingly played on Kanjira (Please listen to this on an earphone and you will distinctly hear base rolls and the Kanjira roaring.). And a very cute thing is that, instead of mridangam playing an arudhi to end the pallavi, Kanjira would have played.

In the anupallavi, during the first line, murthy again would have played his bit and hari would have responded amazingly well. And the rest of the anupallavi is like Diwali night. And apart from so many cracking stuff Hari would have also done a kanjira's duty of playing the 'gumukki' often.

And finally comes the charanam...When DKJ sings the first line and stops, you can hear Hari bring down the Sky..Then DKJ begins to improvise. At this point, the so far dominant percussion takes a back seat..thats something that amazed me...the Pakkavadhyam men(murthy and hari) are so matured that when the main artiste is trying to improvise and show his prowess, the percussion has not interfered...They have let DKJ improvise without improvising...And once DKJ stops improvising and gets back to normal singing...percussion takes over again...and finishes the song with such a grace..when the song was over, you almost feel that a pralaya is over..

baz1908 · Post by **baz1908** » 18 Aug 2006, 10:02

cmlover wrote:or 93933840 avartams in thisra nadai,

Not exactly, you are confusing aksharas and mathras