Talaprasthara (Combinatorics)

Tālam & Layam related topics
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SrinathK
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#151 Re: TALAPRASTHARA ( Combinatorics)

Post by SrinathK » 12 Jul 2018, 20:12

That was a mistake. 11111 is the 9th pattern
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Christian Kenit Ram
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#152 Re: TALAPRASTHARA ( Combinatorics)

Post by Christian Kenit Ram » 21 Jul 2018, 03:55

In one book of Mister Akella the serial numbers of some carnatic talas are given , for ex :

~~~~ The serial number of Rupaka Tala ( angas : 2 4 ) is 3 .

So according to the tables , I think this corresponds to

1) __ 6
2) _1 5
3) _ 2 4

2-4 is the third combination for 6 units , according to the process of Akhanda-Prastara , Sankhya mode ( if I understood correctly ) .



~~~~~ The serial number of Tishra Rupaka Tala ( angas : 2 3 ) is 3 .

1) 5
2) 1 4
3) 2 3

2-3 is the third combination for 5 units .

Not sure if i am right .

(Whichever way I write , I can not get to align the rows nicely ....)
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msakella
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#153 Re: TALAPRASTHARA ( Combinatorics)

Post by msakella » 23 Jul 2018, 15:46

You are absolutely right, dear. The digits you have to follow from the right to left only. amsharma
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Christian Kenit Ram
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#154 Re: TALAPRASTHARA ( Combinatorics)

Post by Christian Kenit Ram » 25 Jul 2018, 03:02

Thanks for confirming , Sir !
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SrinathK
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#155 Re: TALAPRASTHARA ( Combinatorics)

Post by SrinathK » 04 Sep 2018, 17:55

I am glad to make a momentous discovery. I cracked the serial number of Simhanandana's rhythmic pattern.

The Serial Number of Simhanandana Tala's underlying numerical pattern (note, I meant NUMERICAL PATTERN, which is
8 8 4 12 4 8 2 2 8 8 4 12 4 12 8 4 4 16 = 128 counts is

The 2,768,588,535,255,736,445,300,122,568,917,121 st permutation

out of a possible 2^127 or 170,141,183,460,469,231,731,687,303,715,884,105,728 permutations total that add up to 128 counts. (For the computer geeks out there, this is equal to half the number of IPv6 addresses on the planet.)

This is not however it's actual serial number in terms of tAlAngas because this is done using numbers starting with
128
1 127
2 126
1 1 126 etc... and not tAlAngas.

If it were tAlAngas, the permutations would start from

K K K K K K K K
L P K K K K K K K
D D P K K K K K K K
A A D P K K K K K K K and so on.... that calculation is for another day...but I assure you the number will be of a much smaller size ... phew!

Therefore, do I become the 2nd person to calculate the serial number of this tALA?
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msakella
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#156 Re: TALAPRASTHARA ( Combinatorics)

Post by msakella » 05 Sep 2018, 09:22

Dear brother-member, SrinathK,

The serial number of Simhanandana-tala in Samyuktanga-prastara, you got and furnished here, is correct and you are the 3rd person (2nd one being Chi. Vijaya Raghava from Bangalore) to do so. Do remember that I got all these umpteen calculations when no calculator or computer was within my reach.

There are three modes of permutations, Panchanga-prastara in which Anudrutas are absent, Shadanga-prastara consisting of Anudrutas also and Samyuktanga-prastara consisting of all Talangas including combinative-angas. While all the other two modes of permutations are also covered, Samyuktanga-prastara is the ultimate.

But, while the serial number of Sharabhanandana-tala must be obtained from Samyuktanga-prastara only as it consists of combinative (Samyuktangas) angas also, the serial number of Simhanandana-tala, which must be rendered with all the five Talangas except Anudruta, could be obtained both from Panchanga and Samyuktanga-prastaras. You have already furnished its serial number in Samyuktanga-prastara. But, try to furnish the Panchanga-prastara also. amsharma
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SrinathK
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#157 Re: TALAPRASTHARA ( Combinatorics)

Post by SrinathK » 05 Sep 2018, 09:41

msakella : The serial number of Simhanandana-tala in Samyuktanga-prastara, you got and furnished here, is correct and you are the 3rd person (2nd one being Chi. Vijaya Raghava from Bangalore) to do so. Do remember that I got all these umpteen calculations when no calculator or computer was within my reach.
:D :D Ok. And one other thing, the serial number in reverse permutation (samyuktAnga) will be :

Permutation number : 170,138,414,871,933,975,995,242,003,593,315,188,608

I totally agree on the sheer difficulty of this. Even on a computer, there are only some websites on the internet which allow you to add very big numbers. https://www.calculator.net/big-number-calculator.html

The exact value of the powers of 2 are available here : http://www.tsm-resources.com/alists/pow2.html

Without a calculator it would have taken at least 1-2 months or more of hard labor to do this exercise (and many more years of research before that because the descriptions in the old texts are very hard to understand while the same thing could be shown in a much simpler manner using mathematics). All the powers of 2 up to 128 need to be calculated, then the relevant proxies need to be identified and added up. But now that you have brought it out it has become easier to understand with some effort.

Now I understand slowly how the logic works for tAlAngas. Maybe in future I will be able to (With the help of the computer of course) do it for both 6 angas and 5 angas in both forward and reverse permutations and see how it works.

I have read on this forum that there are tAlAs longer than the Simhanandana. By any chance, are their tAlAngas available? This is for my curiosity.
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msakella
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#158 Re: TALAPRASTHARA ( Combinatorics)

Post by msakella » 05 Sep 2018, 16:20

Dear brother-member, SrinathK,

Had there been a restriction that each and every Tala must be provided with the authentic serial-number of Prastara nobody would not have dared to bring out any new Tala. But, in the absence of the knowledge of this Prastara everybody took the liberty of bringing out as many Talas as any one could.

In the same manner even the Great Sharngadeva brought out a new list of 120 Talas in which, along with all other old Talas and some of his other new Talas together, he had included one Tala in his own name and another Tala in his title, Shargadeva-tala and Nisshanka-tala (in fact while Sharngadeva had already made a mess of this topic, adding fuel to the fire, Vasudeva Shastry included his mess and later even his daughter still included her mess too. But, as nobody is bothered either to disscuss all these things or to give the authentic version to the society this mess will never come into light). In the same manner even the author of Sangeeta Suryodaya, Bhandaru Lakshmeenaarayana, apart from these 120 Talas of Sangeeta Ratnakara, brought out another list of 120 new Talas in which the last two Talas in his name and title like of Sharngadeva.

Even though I may have 5 or 6 lists of Talas all I wrote them long long ago in Telugu and, at this old age, I am not in a position either to search them all or to type them in English. Very vaguely I remember (not names) one or two Talas carrying around 500 units as against 128 units of Simhanandana. amsharma.
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