Talaprasthara (Combinatorics)

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

Post by SrinathK »

That was a mistake. 11111 is the 9th pattern

Christian Kenit Ram
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#152 Re: TALAPRASTHARA ( Combinatorics)

Post by Christian Kenit Ram »

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 ....)

msakella
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#153 Re: TALAPRASTHARA ( Combinatorics)

Post by msakella »

You are absolutely right, dear. The digits you have to follow from the right to left only. amsharma

Christian Kenit Ram
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#154 Re: TALAPRASTHARA ( Combinatorics)

Post by Christian Kenit Ram »

Thanks for confirming , Sir !

SrinathK
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#155 Re: TALAPRASTHARA ( Combinatorics)

Post by SrinathK »

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?

msakella
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#156 Re: TALAPRASTHARA ( Combinatorics)

Post by msakella »

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

SrinathK
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#157 Re: TALAPRASTHARA ( Combinatorics)

Post by SrinathK »

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.

msakella
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#158 Re: TALAPRASTHARA ( Combinatorics)

Post by msakella »

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.

msakella
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#159 Re: Talaprasthara (Combinatorics)

Post by msakella »

Interesting information of Talaprastara:
01.Since many centuries no author of any language had ever furnished the correct definition of Nashta or Uddishta or even Kalitha in his work which are very crucial to answer the form of the Talangas of any permutation carrying a particular serial number in question or the serial number of the permutation carrying a particular form of Talangas in question or the full details of all the different Talangas utilised in the process of permutation upto the Tala carrying a particular serial number in question respectively as none of them was aware of them. But, very sadly, even in the absence of this crucial knowledge many of the authors became bold enough to create and furnish quite a number of Talas of their own choice along with their new names and respective Talangas in their respective works.

02. In this above manner, prior to Sangita Ratnakara written by Nihshanka Sharngadeva in 12th century, while there was the list of 108 Deshi-talas only, this author had another idea to aggrandise his work by including 12 more new Talas of his choice along with their new names and Talangas in which two Talas are named after his title (Nihshanka-tala) and his name (Shargadeva-tala).

03. Moreover, adding fuel to the fire, Nihshanka Sharngadeva, the Great had also altered two tables, Druta-meru and Samyoga-meru by which I had to waste many years of my invaluable time in getting the correct version of them. Ultimately, I have found the correct version of Druta-meru in Gayakalochanam written in 20th century by Tacchur Singaracharya Bros., and basing upon a logical plan I could myself find the original version of the Samyoga-meru on my own. These versions of Druta-meru and Samyoga-meru are furnished in pages 106 and 110 of my book, Indian Genius in Talaprastara.

However, my friend and retired Professor of Madras University, and Dr.N.Ramanathan held a Conference on Sangita Ratnakara at Madras (without inviting me or even informing me) in which his teacher Dr.Premlatha Sharma and Prof.Herald Powers have participated and Prof.Powers in his final report said "One thing which struck me particularly, I must confess, is that I found the Tala-chapter singularly uninteresting. It is full of a long list of things we don't do anymore, probably it is just as well that we don't....". But, even the copy of the book released in this connection wasn't sent to me.

Late Pandit Subrahmanya Shastry already made a mess of the Adyar's earlier version of the Tala-chapter of Sangita Ratnakara and later his daughter, Smt. S.Sharada, while revising it made a more mess of it. In 1969, even before her revision when I addressed to the respective librarian of the Adyar Library, Mrs.Seetha Neelakanthan and requested to send me the revised MSS she replied "Smt.Sharada is highly versed in the science of music, theory and practice, and we feel there is no need to send the MSS to you for further scrutiny". Thus, while nobody bothers about the correctness of our great cultural heritage the later edition was also released with many more corrections than her father's edition.

04. Among the 17 works in which this Talaprastara was eloborated while the Sangita Ratnakara (Sanskrit-12th century) only furnished more information than all others, the Taladashapranapradeepika (16th century) furnished with Telugu-poems but without any figures at all and the Gayakalochanam furnished with many tables and figures but without any definitions at all. But, by the list of 158 new Talas furnished in Gayakalochanam (which are also reproduced by Dr.B.M.Sundaram in his list of 1000 Talas of Talasangraha but without these serial-numbers as he was not aware of them as serial-numbers) along with new-names, Talangas and for the first time in the history of our Indian Music with authentic serial-numbers it has obviously been proved that these authors, Tacchur Singaracharya Bros., are well-versed with the latent secrets of this Talaprastara. But, most unfortunately, they did never reveal them in any of their works.

05. In page 238 of his 'Sangita Ratnakara - A Study' of R.Rangaramanuja Iyyengar published in 1978 he wrote 'The numbers in the columns convey no clear idea of their significance. The two commentaries, Kallinatha and Simhabhupala, contradict each other in explaining the chart. The practical application of Patala to rhythm as a whole has to be determined by competent research' and in page 106 of his another book 'History of South Indian (Carnatic) Music' he wrote 'The forms are obsolete. The text is obscure. The two commentaries are vague and contradictory. Research gets stuck up in a tantalising bottle neck'. In spite of all this I have very successfully demonstrated this Talaprastara in the Music Academy, Chennai in December, 1984 for the first time in the history and I have also donated a copy of this to their library. But, in spite of all this, till now, no proper action has ever been taken to suitably modify the definition of this topic, at the least, in all the syllabi of their Music Examinations.

06. In Sangita Suryodaya (Sanskrit-16th century) written by Bhandaru Lakshminarayana, even though he had reproduced the 120 Talas of Sangita Ratnakara surprisingly omitted the last two Talas named after the title (Nihshanka-tala) and the name (Shargadeva-tala) of Sharngadeva but didn't forget either to furnish another list of 121 Talas along with new names and Talangas of his own or to includetwo Talas named after his own title (Bharatakuleshwara-tala) and his own name (Lakshmanaahvaya-tala) in his list.

07. The author Bhandaru Lakshminarayana of Sangita Suryodaya was the court- musician of Shri Krishnadevaraya of Vijayanagar empire (1509 - 1529) and he was honoured with Kanakabhisheka and Simhatalaata by the King. But, along with many other minor mistakes there are umpteen major blunders also to be rectified.

In fact many of these mistakes and blunders were brought to the notice of the editor, Shreev Kaamathaprasaad Thripaatheeji of Indirakala Sangita Vishwavidyalaya, Khairagarh. But, in the absence of any response from him I have again brought them to the notice of the then Vice Chancellor, Dr. Premlatha Sharma of the same University and she responded and agreed to pass them on to him. But, even later what happened God alone knows.

08. While some figures relating to Talaprastara furnished in Sangita Sampradaya Pradarshini of Subbarama Dikshitar are mis-printed in the original Telugu version of it I have furnished the correct figures of them to Dr.N.Ramanathan and they were modified accordingly in the next print but this was not acknowledged by them at the time of re-printing.

Interested parties can try to rectify the above in keeping our cultural heritage in tact. amsharma
9908822992

rajeshnat
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#160 Re: Talaprasthara (Combinatorics)

Post by rajeshnat »

Akella gaaru
I have no knowledge and understanding but looks you were sincere to present your viewpoints. You must put all these posts either in a blog or your sishyas can start a website for you and put all your thesis.

msakella
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#161 Re: Talaprasthara (Combinatorics)

Post by msakella »

Dear brother,
Thanks a lot for your kind suggestion.
Most of our people are interested only in getting the information. But they are not that interested to act accordingly and sincerely. Very rarely there may be a person who does something actively and sincerely. Only for this person I would like to give all this information. I have my own experiences in this respect. amsharma

msakella
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#162 Re: Talaprasthara (Combinatorics)

Post by msakella »

Now, presently i am trying to make this rarest topic in
this thread easily readable, followable, understandable and implementable in the interest of our poor aspirants as this Samyuktanga-prastara, which has never been defined fully in any treatises of any language on the globe. Moreover this has been brought out by me when either the calculator or the computer are not available at all. msakella

msakella
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#163 Re: Talaprasthara (Combinatorics)

Post by msakella »

20210408:
Even though my old age may not allow me to do, i wanted to try to make this thread readable, understandable, followable and implementable in the interest of our poor aspirants. But, very sadly, as usual, none had shown any interest and responded positively. Hence, as there is no meaning in taking this trouble at this juncture, i have dropped my idea to remain in peace. msakella

msakella
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#164 Re: Talaprasthara (Combinatorics)

Post by msakella »

20210512:
However, having recently received some positive response through a close friend of mine i have fulfilled my responsibility of possibly modifying it and sent it leaving the decision to the Admins themselves. msakella

msakella
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#165 Re: Talaprasthara (Combinatorics)

Post by msakella »

20210512:
Just now i have received a message that the Admins
kindly agreed to carry out the changes in this thread in the interest of the poor aspirants and also the subject.

I also hereby thank my friend Chi Chandramouli (Vasanthakokilam) and also the Admins for doing the needful in the interests of both our aspirants and the subject. msakella

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