Talaprasthara (Combinatorics)

Tālam & Layam related topics
sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#101

Post by sbala »

listener,
Welcome. Are you based in Chennai?

Sharmaji,
I'm sure you would be happier if a musician understand this. I don't know about Ram and listener but I'm like a bowler holding a 2.8 pounds bat.
Last edited by sbala on 26 Mar 2007, 10:35, edited 1 time in total.

mridhangam
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#102

Post by mridhangam »

dear Members Bala and listener and Akellaji
I also understand being a musician. But not giving out my contribution here as i am a silent spectator infront of giants like you. Though the combinations come naturally to me i was awestruck with the scientific way in which the whole tala prastara has been thought out and brought out centuries ago and assimilated by Jambhavans like Akella Garu. Thanks for the efforts. With the help of sbala i have understood a few basic things. Due to heavy professional commitments I am not able to fully concentrate on each and every aspect of this.
J.Balaji

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
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#103

Post by msakella »

Dear brother-members, sbala & mridhangam, I have already taught to some of the musicians who are able to enjoy the greatness of this rarest topic, Talaprastara and, in turn, are also teaching others enthusiastically. In fact, long long ago I was compelled to take an oath that I shall not reveal some secrets of Kanakku to any musician or any Mridangist, in particular, at all by a professional Mridangist who very accidentally spilled out very few of his own beans before me but I could make 100% out of them. When I shall meet you all in near future I shall tell you these short-cut methods which will be helpful even to professional Mridangists. amsharma.

listener
Posts: 16
Joined: 06 Jul 2006, 21:09

#104

Post by listener »

Hello sbala,

I'm a student currently in the United States. I hope to visit Chennai in the near future.

mridhangam
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#105

Post by mridhangam »

Dear Akella sir
I have studied upto Uddishta and i cant tell you how i am addicted to the subject. Most of my note books are filled with exercises and the figures are so exciting and now i understand your lifetime achievement in this work. May your tribe spread sir. Thanks a ton for such a great rewardless work.

J.Balaji

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
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#106

Post by msakella »

Dear brother-member, mridhangam, Feel very happy to know that you have proceeded up to Uddishta. I shall explain the remaining details when we meet next. Even though physically I am well off with 5’ 11â€

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#107

Post by sbala »

Just thought of reviving this thread with the explanation for Mahapatala - the total number of figures of all the permutations for a given total number of units. As indicated in the posts, the Mahapatala of "n: unit permutations is the sum of Sankhya and Mahapatala of all the relevant proxies (S+M). The reasoning for that is similar to the reasoning for Sankhya

Total Number of figures of 'n' units = Sum over all angas of (Total number of figures in permutations that don't end with a particular anga + Total number of permutations of (n-unit value of the anga))

This is equal to Sum of S+M for all the relevant proxies. Relevant proxies are determined by the angas allowed in the prastara. For instance, in Pananga prastara, the angas allowed are Drutam (1 times Druta), Chaturasra Laghu (2 times Druta), Guru (4 times Druta), Pluta (3 times Laghu or 6 times Druta) and Kakapada (4 times Laghu or 8 times Druta).
Therefore, the proxies woud be 1,2,4,6 and 8.

msakella
Posts: 1939
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#108

Post by msakella »

Dear brother-member, sbala, You are right, my dear. In any mode of Prastara the respective values in terms of the least Angas of the constituent Talangas become the
respective Proxies as furnished at the end of the 43rd post of this thread. Please go through that once again and have a correct picture of the relevant proxies. amsharma.

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#109

Post by sbala »

Samyoga Meru

In this example below we list all the prastaras containing combinations of Durta and Plutam ie (OS' or S'O) in Pancanga Prastara. The numbers at the extreme right denote the number of units of permutation in terms of Drutas (ie i denotes 1DP, 2 denotes 2 DP etc).

The first column gives the details of Sankhya and Mahapatala for the respective units for an all druta permutation. The first sub row gives the Sankhya and the second sub-row gives the Mahapatala. Similarly, the second column gives the same details for all Pluta permutation.
The third column give the details for all prastaras containing the combination of DP or PD named as OS'.

O S' 0S'
1 1
1

1 2
2

1 3
3

1 4
4

1 5
5

1 1 6
6 1

1 0 2 (1+1) 7
7 4(1+1+1+1)

1 0 3 (2+1) 8
8 9 (2+4+1+2)

1 0 4 (3+1) 9
9 16(9+3+1+3)

1 0 5 (4+1) 10
10 25(4+16+1+4)

1 0 6 (5+1) 11
11 36 (5+25+1+5)

1 1 7(6+1) 12
12 2 49 (6+36+1+6)

msakella
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#110

Post by msakella »

Dear brother-member, sbala, Please refer page 107 to know the seriatim of the 31 combinations pertaining to Panchanga-prastara and 63 combinations of Shadanga-prastara pertaining to all the 5 Jaatis and page 108 for the 69 combinations of Samyuktanga-prastara of 12-units. Please also follow the matter furnished in pages from 24 to 30 pertaining to Samyoga-meru of my book ‘Indian Genius in Talaprastara’ and try to write all the details of it comparing it with the matter furnished in 6.10. in page 105 and page in page 110. Also refer pages from 35 to 43 of my book ‘ Talaprastara of Nisshanka Sharngadeva’s Sangita Ratnakara’. amsharma.

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#111

Post by sbala »

Dear Sharmaji,
As I have some time this week, I will try to absorb everything I can and post here. Please continue to correct any mistakes.

frpatte
Posts: 4
Joined: 31 Aug 2008, 18:47

#112

Post by frpatte »

Hello Dear Members,

I am working on "samgitaratnakara" by Sharngadeva. and I would like some information about nashta-uddishta rules in this works, am I allowed to post some sanskrit questions on this forum?

Thanks for attention.

F. Patte

vasanthakokilam
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#113

Post by vasanthakokilam »

Sure. If it is thala related, open up a new thread in the Tala/Laya section. Otherwise create a thread in the Technical Section or Languages ( if it is about Sanskrit in general ) or just in the General Section ( we will move it to another sub forum if needed ).

msakella
Posts: 1939
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#114

Post by msakella »

Dear b/s-member, frpatte, Welcome to ask any Sanskrit-questions in regard to Talaprastara. I shall try to clear off your doubts. I have already brought out the free-English-translation of the Shlokas from 312 to 408 of Taladhyaya of Sangita Ratnakara in my book, Indian Genius in Talaprastara (English) which is available from ‘Carnatic music book center, Chennai or with me. Some copies of it are also available in US with my friends I remember. If you are a resident of US I shall try to get and give their e-mail addresses to enable you get it. amsharma.

frpatte
Posts: 4
Joined: 31 Aug 2008, 18:47

#115

Post by frpatte »

Thanks for this welcome.

I have some doubts while reading shlokas 323-325 of samgitaratnakara (anandashrama edition --> shlokas 325-329 1/2 Adyar edition) more precisely this:

..... atha "se.sata.h|
paatayet puurvapuurvaa"nka.m tatra tv apatito druta.h|
puurva"s cet patito na syaal laghus tu patitaad bhavet||
uttare.naak.rtaarthena sahitaat tadasa.mbhave|
ak.rtaarthena puurve.na.........

It seems to be an utsarga:

atha "se.sata.h|
paatayet puurvapuurvaa"nka.m tatra tv apatito druta.h|

then an apavaada:

puurva"s cet patito..... etc.

(I am using the Velthuis scheme of translitteration, as I don't know if unicode char will be correctly transmitted)

Neither commentaries by Kallinatha or by Simhabhupala are clear about it.

I give a few examples: take the druta+pluta prastara and try to find out the 22nd bheda. The samkhyaa"sreni.h is:

1 2 3 6 10 19 33

So: 33-22 = 11

You cannot remove 19 in 11, so you get a druta (apatito druta.h)

Then, you can remove 10 in 11: 11-10 =1 and you get a laghu for number 10 (laghus tu patitaad bhavet...)

After that, you cannot remove 6, 3 or 2 from 1, and you get another laghu while removing 1 in 1.

So the 22nd bheda is laghu+laghu+druta (right)

But why the "apatito druta.h" rule does not apply for numbers 6, 3 and 2?

Now, take the laghu+pluta prastara and try to find out the 40th bheda. Here the "sre.ni is:

1 2 3 6 10 19 33 60

60 - 40 = 20

You cannot remove 33 in 20 and get a druta; then you can remove 19 in 20 and get a laghu, remainder being 1. Same phenomenon as above occurs: you get a new laghu with the first number of the "sre.ni (1) but, this time you must get 3 drutas between the two laghus.....

Where is this difference explained in Sharngadeva rule or in Kallinatha commentary?

Thanks for attention.

F. Patte

msakella
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#116

Post by msakella »

Dear (as I am unable to take you either as a brother or sister from you name) b/s-member, frpatte, I am very glad for your intricate findings of Nashta. In my previous post I also forgot to mention about my another book, Talaprastara of Nisshanka Sharngadeva’s Sangita Ratnakara – a critical interpretation in which I have furnished the inconsistencies of the topic.
In fact, I know very little of the language, Sanskrit. But, having some how been blessed by the Almighty I am able to get through the latent secrets of Nashta and Uddishta of this Talaprastara. Even after writing these books my research has not been concluded and in due course I could further delve into this topic to find still easier short-cut methods in regard to Nashta and Uddishta than the ones already furnished in my book. But, being physically unable to re-write this entire book again at this old age of 70 years, I have made some additions of notes in this regard in this book in page 35.
However, I shall hereunder give the updated details of Nashta
by which the Sanskrit version has to be modified suitably.
Updated rules for answering Nashta:
01.Write the ‘Sankhya’ line of figures up to the required units of permutation.
02.Subtract the question-number from the Sankhya and later from the remainder subtract the respective proxies consecutively.
03.In the process of subtraction of the relevant proxies if the 1st proxy is not subtracted from the remainder write the Anga of it and start again fresh the process of subtraction by subtracting the relevant proxies of the ‘un-subtracted-proxy’ from the beginning from the remainder. For the successful subtraction of the 1st proxy consider the ‘non-subtraction’ of the 2nd proxy only, for the successful consecutive subtraction of 1st & 2nd proxies consider the ‘non-subtraction’ of the 4th proxy only, for the successful consecutive subtraction of the 1st, 2nd & 4th proxies consider the ‘non-subtraction’ of the 6th proxy onloy and for the successful consecutive subtraction of the 1st, 2nd, 4th & 6th proxies consider the ‘non-subtraction’ of the 8th proxy only thus always considering only the ‘non-subtraction’ of the last proxy and leaving if off to write the Anga of it and start again fresh the process of subtraction by subtraction the relevant of the ‘un-subtracted-proxy’. In the absence of the remainder no figure is needed to be left off.
04.To fill in the deficit value of the permutation one or more least Angas should only be written in the left extreme irrespective of their number.
Accordingly, in the 1st example of 22nd permutation pertaining to 7-drutas, as per rule No.2, if the question-number is subtracted from the respective Sankhya (33-22) ‘11’ is the remainder.
From this remainder ‘11’, as per rule No.3, as the 1st proxy ‘19’ could not be subtracted write the Anga of the 1st proxy which is Druta.
Later, as per rule No.3, starting the subtraction afresh, from this remainder ‘11’, as the 1st proxy ‘10’ could be subtracted
(11-10=1), considering only the ‘non-subtraction of the 2nd proxy ‘6’ from the remainder, write the Anga, Laghu of the 2nd proxy and leave off the 2nd proxy ‘6’.
Later, as per rule No.3, starting the subtraction afresh, from the last remainder ‘1’, as the 1st proxy ‘3’ of the last un-deducted proxy ‘6’ and, again, as the 1st proxy ‘2’ of the last un-deducted proxy ‘3’ could not consecutively be subtracted twice, write two Drutas representing the 1st proxy.
Later, as per rule No.3, starting the subtraction afresh, from the last remainder ‘1’, as the 1st proxy ‘1’ of the last un-deducted proxy ‘2’ could successfully be subtracted, considering only the ‘non-subtraction’ of the 2nd proxy ‘1’ of the last un-deducted proxy ‘2’, write the Anga, Laghu of the 2nd proxy (Hope you know that, as per rules, figure ‘1’ should always be written even before the 1st house in the Sankhya-line of figures).
Thus, you get (Angas or figures of any permutation should always be cited from right to left only in respect of Talaprastara) ‘l 0 0 l 0’.

Accordingly, in the 2nd example, as per rule No.2, if the question-number is subtracted from the respective Sankhya
(60-40=) ‘20’ is the remainder.
From this remainder ‘20’, as per rule No.3, as the 1st proxy ‘33’ could not be subtracted, write the Anga, Druta of the 1st proxy.
Later, as per rule No.3, starting the subtraction afresh, as the 1st proxy of the last un-deducted proxy ‘20’ could successfully be subtracted (20-19=1) considering only the ‘non-subtraction’ of the 2nd proxy, write the Anga, Laghu of the 2nd proxy and leave of the figure ‘10’ of the 2nd proxy as you have to continue the process of subtraction again with the remainder ‘1’.
Later, as per rule No.3, starting the subtraction afresh, the 1st proxy ‘6’ of the last un-deducted proxy ‘10’, again the 1st proxy ‘3’ of the last un-deducted proxy ‘6’ and again the 1st proxy ‘2’ of the last un-deducted proxy ‘3’ could not consecutively be subtracted thrice from the remainder ‘1’, write three Angas, Drutas consecutively.
Later, as per rule No.3, starting the subtraction afresh, from the remainder ‘1’, the 1st proxy ‘1’ of the last un-deducted proxy ‘2’ could successfully be subtracted (1-1=0) considering only the ‘non-subtraction’ of the 2nd proxy, write the Anga, Laghu of the 2nd proxy.
Thus, you will get ‘l 0 0 0 l 0’.

Most unfortunately, in the annals of our music literature itself, neither of the author or commentators or editors of any treatise have nowhere explained this ‘Nashta’ clearly without any ambiguity to the reader.

As I am not well educated like you people there may be some lacuna in my explanations. Please feel free to ask any number of questions. amsharma.

frpatte
Posts: 4
Joined: 31 Aug 2008, 18:47

#117

Post by frpatte »

msakella wrote:Dear (as I am unable to take you either as a brother or sister from you name) b/s-member, frpatte,
brother
msakella wrote:Most unfortunately, in the annals of our music literature itself, neither of the author or commentators or editors of any treatise have nowhere explained this ‘Nashta’ clearly without any ambiguity to the reader.
I do not agree with you: I am a mathematician working on Sanskrit texts in mathematics and, as far as my experience is concerned in the field of mathematical texts, every time I was thinking that there was some ambiguity in the Sanskrit text, I was wrong and a better reading with a sharper attention, could solve the ambiguity.... I am sure that it is the same for theoretical texts on music, as Sharngadeva's.
msakella wrote:Please feel free to ask any number of questions.
So, I use this permission.... It is still not clear for me (from the Sanskrit text point of view) why there are some numbers with drutas and some others without: take the plutaprastara, samkhya is: 1 2 3 6 10 19

When the nashta question is about the second bheda, you get one laghu for 10, one laghu for 6 (as they are consecutive, you get a guru) and one laghu for 1 and nothing for 2 and 3.

When the nashta question is about the 8th bheda, you get a laghu for 10 (beause 11-10= 1) and, the next time you get a laghu is for 1. So, in that case you must find 2 drutas in between. How do you "calculate" this?


Moreover, could you show us what is a practical layout to answer the nashta question, I mean: do you know how they executed the nashta computation in Sharngadeva times, writing in the sand or something of the like?


I imagine something like this (but i maybe totally wrong, and that's why I do not understand some things):

1st example:

1 2 3 6 10 19
- 2
----
17

1 1 1 7 17
-1 -2 -3 -6 -10
0 1 7
I I I <--- Why there are no drutas under 2 and 3
I S


2nd example:

1 2 3 6 10 19
- 8
----
11

1 1 1 1 11
-1 -2 -3 -6 -10
0 1
I I <--- here where to put the 2 drutas ? I think under 2 and 3, but why?


Thanks a lot for any clarification.

F. Patte

msakella
Posts: 1939
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#118

Post by msakella »

Dear brother-member, frpatte, Elderly people tell that it not nice to find fault with the Sanskrit texts as they were written by great stalwarts. Up to some extent I was able to agree with this. But, the mathematical facts which have wasted some decades of the prime period of my life, did not permit me to do so. That’s why I, at any time, without moving at all from my stand and also having enough mathematical base, very well declare, though not we call them mistakes, that Sharngadeva had furnished some inconsistencies in his Sanskrit Shlokas. However, I shall be thankful to you if you later prove my stand is incorrect.

I repeatedly tell you to always feel free to ask any number of questions in regard to Talaprastara as the truth always comes out through rational discussions only.

In my previous post I have furnished four rules which belong to Akhanda-prastara (of course, the rules slightly differ with marginal understandings for Khanda-prastara).

1. Answering 2nd bheda of 6-drutas permutation:
As per rule No.1 write the Sankhya-line of figures up to 6-drutas permutation which is
1 1 2 3 6 10 19.
Later, as per rule No.2 the remainder is (19-2=) ‘17’.

Later, as per rule No.3, from the above remainder ‘17’, as the 1st & 2nd proxies could consecutively be subtracted (17-10=7-6=1) considering only the ‘non-subtraction’ of the 4th proxy ‘2’, write the Anga, Guru of the 4th proxy and leave off the same proxy ‘2’.

Later, again as per rule No.3, from the last remainder ‘1’, as the 1st proxy of the last left-off proxy ‘2’ could successfully be subtracted (1-1=0) considering only the ‘non-subtraction’ of the 2nd proxy ‘1’, write the Anga, Laghu of the 2nd proxy.

Thus we get ‘l S’ which is the answer.

2. Answering 8th bheda of 6-drutas permutation:
As per rule No.1 write the Sankhya-line of figures up to 6-drutas permutation which is
1 1 2 3 6 10 19.
Later, as per rule No.2, the remainder is (19-8=) ‘11’.

Later, as per rule No.3, as the 1st proxy ‘10’ could only be subtracted (11-10=1) considering only the ‘non-subtraction’ of the 2nd proxy ‘6’ write the Anga, Laghu of the 2nd proxy and leave off the same 2nd proxy ‘6’.

Later, again as per rule No.3, as the 1st proxy ‘3’ of the last left-off proxy ‘6’ could not be subtracted and again in the same manner the 1st proxy ‘2’ of the last un-deducted proxy ‘3’ also could not be subtracted consecutively, write two Angas, Drutas of the 1st proxy.

Later, again as per rule No.3, as the 1st proxy ‘1’ of the last un-deducted proxy could successfully be subtracted (1-1=0) considering only the ‘non-subtraction’ of the 2nd proxy write the Anga, Laghu of the 2nd proxy.

Thus we get ‘l 0 0 l’ which is the answer.

By God’s grace I am able to formulate the rules without any ambiguity at all. There may be some lacuna either in my narration of things or in your understanding but not in the formulated rules at all. amsharma.

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
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#119

Post by msakella »

Dear brother-member, frpatte, Even after 12 days of posting my response you did not respond in any manner.

You have written that you do not agree with my contention.
As you all are aware ‘mathematics’ is the only topic on earth having high precision than any other topic and there is no question of escaping away in one way or other like in the matter of ’22 Shrutis’ or any other topic of ambiguity in music which always leaves some scope or other to escape away.

In the annals of our music literature this topic, Talaprastara has ever been dealt with in only 13 books. Most unfortunately, the secrets of either Nashta or Uddishta or Kalita have never been brought out without any ambiguity and within the easy reach of the aspirant. More over none of them is an exception from incorrections and contradiction. As this is mathematics I am ready to prove these facts of Talaprastara at any time.

When I have brought out these incorrect versions of Sangitaratnakara to the notice of Dr.R.Sathyanarayana of Mysore, the internationally reputed great musicologist of our times and the personification of Sangitaratnakara he also agreed with me and mentioned in his fore-word ‘Shri Sharma has unraveled the mysteries of the taalapratyaya in such minute detail that he has been able even to correct some inaccuracies in exposition and fact of great authors of the past’. Thus, my contention was long ago approved even by a great musicologist of our times.

I shall not tell you to agree with me but, at the least, make me agree with you as an eye-opener to the posterity. Even to make this event historical you must come out and do the needful or, if not, you must agree with me. Without doing either of them keeping quiet only proves the inefficiency of your argument. amsharma.
Last edited by msakella on 14 Sep 2008, 12:45, edited 1 time in total.

frpatte
Posts: 4
Joined: 31 Aug 2008, 18:47

#120

Post by frpatte »

msakella wrote:Dear brother-member, frpatte, Even after 12 days of posting my response you did not respond in any manner.

You have written that you do not agree with my contention.
I did not write something like this, did I?

If you understood what I was writing like this, there is a misunderstanding! I am "fighting" with texts and I want to fully understand these texts.

From my point of view there is absolutely no problem about nashta and uddishta: This is fully "working", the problem is: "how Sharngadeva explains the algorithm?" Sharngadeva's shlokas are difficult, he is saying a lot of things in a sharp and concise language (as any Indian pandit). I am working on Sharngadeva's texts with the help of Kallinatha and Simhabhupala commentaries, but it is not so easy. Unfortunately, the editions of these texts (from Anandashrama an Adyar) are not well done: parts of text are missing, one says "yes" where the other says "no", and I am searching some manuscripts to have several readings, that's why I am not answering too fast....

Your way of explaining nashta is working without any ambiguity, but it is slightly different from the way of Sharngadeva and I want to understand Sharngadeva's text. That's why I asked you if you could show a practical disposition to perform nashta.

msakella wrote:As you all are aware ‘mathematics’ is the only topic on earth having high precision than any other topic and
This is, perhaps, the point where I can explain where is the misunderstanding: I agree with you about the "high precision of the topic", but if you read a mathetical text, you cannot avoid some ambiguity due to the person who has written the text, and it is sometime very difficult to fully understand a mathematical text without the help of other mathematical texts dealing with the same mathematical topic as the one you want to understand....

This is my problem with Sharngadeva's description of nashta and uddishta, I have no doubt about nashta and uddishta themselves: samkhya is perfect, there is no reason why "inverse" algorithms should not work: the only problem is: what was exactly Sharngadeva's method?

With best regards.

F. Patte.

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
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#121

Post by msakella »

Dear brother-member, frpatte, When I, at first, wrote that either of the author or commentators or editors of Sangita Ratnakara have never furnished the correct and clear definition of either Nashta or Uddishta or Kalita without any ambiguity to the reader you wrote that you do not agree with my contention.

Having seen your post I felt very happy that you are trying to delve into these texts to fully understand them. Very nice to hear it from you. I am always here to help you at any time in each and every manner I can as I have already struggled hard for years together to know the latent secrets, Nashta, Uddishta and Kalita. Only to avoid any hardship of anybody in future in understanding these texts I have brought out brief details of this topic dealt with in all the 13 works in my book, Indian genius in Talaprastara and I wrote another book itself, Talaprastara of Nisshanka Shargadeva’s Sangita Ratnakara-a critical interpretation, with full details of the lacunae. If you are interested to go through these books if you give me your address and phone numbers I shall try to send the copies of them to you.

In fact, our people tell that the people who wrote such treatises are far developed than many of the modern-men of the present days. But, I am compelled to doubt this statement when I have suffered a lot, that too for years, in finding
1. the direct and extremely convenient connection in between the Sankhya and Mahapatala which facilitated not only the absolute removal of the less-important Patala but also the extension of Mahapatala to all the tables of Talaprastara unlike any other author of any treatise dealt with Talaprastara in the annals of our music literature,
2. the nature of the complex-Druta-meru than the original-Druta-meru and
3. the nature of the wantonly changed version of the Samyoga-meru.

Without any exception, everybody agrees with me that it is the duty of the elders to make all the things easier to our kids. In such case, how can I appreciate these elders who wrote such great treatises making them more difficult to follow than making them easy to our aspirants? If you prove it with evidences that I am wrong I, at any time, am ready to apologise. amsharma

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
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#122

Post by msakella »

Like the recent rare exhibition of Simhanandana-tala by Chi. SR Vinay Sharva while one side of the coin is successfully exhibiting the Tala before the audience, which has previously been done by some such highly talented people the other side of the coin is giving out the specific-serial-number of the Tala to prove its authenticity about which people are not even aware at all of such specific-serial numbers of the rhythmical forms and which has never even been attempted by anybody in respect of these longest Talas in the annals of our music history.

As already told previously, there are only two kinds of rhythmical forms, 1.the rhythmical form which can be rendered like Simhanandana-tala and 2.the rhythmical form which should not be rendered like Sharabhanandana-tala. In particular, while Simhanandana-tala, which can be rendered, has three kinds of specific serial-numbers, 1.pertaining to Panchanga-prastara 2. pertaining to Shadanga-prastara and pertaining to 3.Samyuktanga-prastara, Sharabhanandana-tala has only one specific-serial-number pertaining to Samyuktanga-prastara.

After introducing this sticky thread ‘TALAPRASTHARA’ in this forum some people have learnt this topic either directly or indirectly and either partly or fully. I shall be very happy if any one of them comes out and gives out the specific-serial-number of Simhanandana-tala along with the work-sheet and stands as the 1st person to do so in the annals of our music history though not to get ‘Sangita Kalanidhi’. amsharma.

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
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#123

Post by msakella »

Dear brothers and sisters, A large bound book containing the digitized process of 32,768 permutations pertaining to 16-units of Samyuktanga-prastara which pave way for 73,740 rhythmical forms of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12 & 16-units has been handed over to Shri Shrivathsa when I have met him in Chennai few years back along with Prof..N.Ramanathan to preserve it in the Library of the Music academy. They have been digitized by one young enthusiast from Hyderabad. Interested persons can go through this book. amsharma

msakella
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#124

Post by msakella »

Hi all,
Recently on 27-09-2008 Chi. Vinay Sharva had very successfully demonstrated a Pallavi in the famous lengthy-tala, Simhanandana-tala consisting of 128 units for each cycle of Tala and this information has been posted in our forum. Having seen this congratulating him for such a fete of demonstration of this lengthy-tala as one side of the coin I have suggested him to possibly give away its specific serial number which is the other side of the same coin. By seeing this he and his brother contacted me and asked me to teach them the topic ‘Talaprastara’. Later, accidentally, when I had been to Bangalore in December his brother Chi.Vijaya Raghava was able to learn Talaprastara within a very short time of only three days and, recently, he was also able to successfully bring out the 3 kinds of specific serial-numbers of Simhanandana-tala. Thus, as far as my knowledge goes, he stands the first person in the history to find out the specific serial numbers of the Great Simhananda-tala. amsharma

bharadwajrs
Posts: 2
Joined: 03 Oct 2008, 22:56

#125

Post by bharadwajrs »

One of the brothers Chi Vinay Sharva started it and his elder brother Chi Vijay Raghava completed the circle... Brothers create History!!!
Hearty Congratulations!!!

B...

violinvicky
Posts: 18
Joined: 02 Apr 2009, 17:19

#126

Post by violinvicky »

Dear Sharma Sir:

I am going through this thread from the first page. What I find is that many of your responses are truncated halfway through; The posts stop abruptly.. Therefore I miss the complete picture and am not able to understand the basics that you have explained on the subject of 'Talaprastara'.

Are these responses copied from some other thread into here..? Is there another location where the discussions are available in full..?

Following are the examples of incomplete responses that I am referring to:

"to obtain the above two key-figures, Sankhya and Mahapatala and to obtain the" .........?
"sing order of value i.e., by permuting 1-unit we will get only" .......?
"I would like to tell you another easy method. While permuting the figure" ...........?

So what should I do see the complete text of each post ..? Please Help..

With Love
Vicky
Last edited by violinvicky on 07 Nov 2009, 02:04, edited 1 time in total.

vasanthakokilam
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#127

Post by vasanthakokilam »

Vicky: There is some past data corruption history.

Please post the references to the posts that are truncated to this thread: http://rasikas.org/forums/viewtopic.php? ... reads.html

The admin will see if it can be recovered.

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
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#128

Post by msakella »

Dear brother-member, violinvicky, Previously me too find many of my posts are truncated and reported to the administration. But I did not get any reply.. Later, I almost forgot that and did not review the position.

But, as I have always been used to save everything of all my posts and as I have already saved entire material in my computer, if you want and if you giv e me your email address I shall certainly send it to you by email. amsharma

rajeshnat
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#129

Post by rajeshnat »

msakella garu
If you have saved each and every post ,then you can edit and repost it too sir.

msakella
Posts: 1939
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#130

Post by msakella »

Dear brother-member, rajeshnat, At this age I do not have that much patience to edit the entire file. More over, every time it is truncated I cannot replay the same. Instead it is more easy to send it by email. That why I wrote accordingly. amsharma

violinvicky
Posts: 18
Joined: 02 Apr 2009, 17:19

#131

Post by violinvicky »

Dear VK:
I have alerted the moderator on the "report truncation" thread.

Dear Sharma sir:

My email id is: [email protected]
I would be grateful if you can send me the original text to this email address. Thanks once again.

With Love
Vicky

msakella
Posts: 1939
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#132

Post by msakella »

Dear brother-member, violinvicky, Just now I have sent two files on Talaprastara to your email address. Kindly acknowledge the same. amsharma

violinvicky
Posts: 18
Joined: 02 Apr 2009, 17:19

#133

Post by violinvicky »

Dear Sharma Sir:

Yes. I have received your email with the attachments in tact. I will now start to learn the concepts from the basics and will certainly ask my doubts.

Sir, I have no words to thank Your service for a generation of new Carnatic musical learners such as myself.

With Love
Vicky

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
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#134

Post by msakella »

Dear brother-member, violinvicky, This is our culture and every Indian must always work hard to keep it in tact. That’s what I am able to do by the grace of the Almighty. Nothing else great. I shall be extremely happy if you too learn it fully and pass it on to our kids. It is not that hard to learn this topic as many others think. Chi. Vinay Sharva, a Bangalore-kid based in Chicago had swallowed the entire topic within four days only which took four decades of my life. You can also do so. Never hesitate to ask me any detail of it. I am always ready to help you. With all best wishes, amsharma

vasanthakokilam
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#135

Post by vasanthakokilam »

>Chi. Vinay Sharva, a Bangalore-kid based in Chicago had swallowed the entire topic within four days only which took four decades of my life.

Sharmaji, you are in great company. When I read the above statement of yours, I was immediately reminded of what I once read about Ptolemy. He spent a few decades trying to understand what Hipparchus, Menelaus, etc. wrote about Trigonometry. He cleared up all the confusion, cleaned it up and wrote his own book. His Shishya spent 10 years learning it from him. These are now taught in one semester to 10th standard students. But that is all possible because of the giants like Ptolemy ( and early Indian mathematicians too who had worked on Trigonometry ) on whose shoulders we stand. That is the same case with your tireless life long work on Talaprasthara.

msakella
Posts: 1939
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#136

Post by msakella »

Dear brother-member, vasanthakokilam, I have passed Diploma in Music (Violin) from Andhra University in 1959. In 1961 I have appeared for an Interview for the post of Lecturer in Violin in the Govt. College of Music & Dance, Hyderabad. I may be playing well but even without any teacher-training-certificate (in those days nowhere music-teacher-training-course was available) they have appointed me in that post which helped only to successfully ruin many of the Violin aspirants for nearly 15 years. Later, I woke up a little, and then onwards my teaching abilities gradually increased by 1% yearly in a negative music environment. On the date of retirement in 1996, I can now assess, my teaching ability was not more than 20% while 35% is the minimum pass-mark. More over, adding fuel to the fire, as per our country-wide tradition, since last more than 50 years there was no academic supervision at all upon the teaching staff of the music departments or music colleges. At this juncture, just imagine the fate of my aspirants in the hands of such infficient teacher like me. However, I am successfully retired without any harm. By all this, I felt very bad of my past, and been struggling hard to rectify all my deffects and serve the kids of our music efficiencly to the maximum until my last breath. By the grace of the Almighty I am able to do so in so many ways. amsharma

kraig
Posts: 1
Joined: 09 Nov 2009, 16:57

#137

Post by kraig »

Thank you so much for enlightening myself on the subject of Talaprasthara. I first came to this sequence of post just days ago and was having much problem because the chart was missing. I am happy to see it there now. I did attempt to figure out as much as i could. In the process I created a few charts which while they do not coincide with the one put you have so kindly provided i thought i would share as it shows it in a slightly different way that might or might not be useful. I hope i do not show disrepect by doing so.
http://anaphoria.com/tala6.gif

msakella
Posts: 1939
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#138

Post by msakella »

The mode of writing this table is furnished somewhere in these posts. You can follow that if you need. If you are unable to locate that I shall guide you, if you need. amsharma

Chandrashekar
Posts: 34
Joined: 01 Dec 2009, 14:28

#139

Post by Chandrashekar »

Sorry to butt in with an off-topic comment. I was just skimming through this thread ("skimming" because of my extremely limited understanding of all these detailed discussions). But, seeing the dialogue between Sharmaji and sbala reminded me of Adi Shankaracharya's great work "Vakya Vritti" where the Guru responds to the Shishya's questions to help him progressively along the path to reaching his goal (in that case, ultimately realising "Aham Brahmasmi" by himself). This is really a great thread, in the highest traditions of our Guru-Shishya parampara, and I hope more people will gain from all the efforts that have clearly gone into it.

msakella
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#140

Post by msakella »

Dear brother-member, Chandrashekhar, Thank you for your supportive comments. Aspirants to break this hardnut are gradually increasing, amsharma

vasanthakokilam
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#141

Post by vasanthakokilam »

>But, seeing the dialogue between Sharmaji and sbala reminded me of Adi Shankaracharya's great work "Vakya Vritti" where the Guru responds to the Shishya's questions to help him progressively
>along the path to reaching his goal

Well said Chandrashekar. That is quite true. Sharmaji is a great teacher. sbala jumped in with great enthusiasm. We not only learn from Gurus but from "students" as well.

Member_First
Posts: 91
Joined: 14 Apr 2008, 16:56

#142

Post by Member_First »

We not only learn from Gurus but from "students" (piluthams..) as well.
Last edited by Member_First on 22 Dec 2009, 09:58, edited 1 time in total.

SrinathK
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#143 Re: TALAPRASTHARA ( Combinatorics)

Post by SrinathK »

Dear sir, where may I get the books of yours, namely, 'Indian Genius in tala prasthara,' ‘Permutative genius in Tala Prasthara in Indian music' and ‘Tala prasthara of Sarngadeva's Sangita Ratnakara.' as well ‘Sangeetha Swararaga Sudha'. (The last one is on sangeethapriya I know, but I need a hardcopy for myself). If it is currently available in Chennai, I may be able to get them when I go there next time. Otherwise I could order them online.

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
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#144 Re: TALAPRASTHARA ( Combinatorics)

Post by msakella »

Dear brother-member, SrinathK, The titles, Talaprastarasagaram (Telugu) and Permutative Genius in Talaprastara in Indian Music (English) are the first ever publications on this rare topic by Sangita Academy of Andhra Pradesh and Telugu University respectively to whom I have given the right of publication of these books. Later, in the NTR Government, unlike in any other State in our country, all the Academies have been merged in Telugu University. When, in my extensive research, 80% of the subject of Talaprastara has been increased I have requested the authorities of the Telugu University to re-print them at the earliest while I am alive. Unfortunately, due to the local dirty politics, as usual, they did not respond at all positively (being straight forward, I had many such bitter experiences all along my life). Then, as more than 80% of the matter of them has been increased, I re-wrote them and published them on my own changing the titles Talaprastara Ratnakaram (Telugu) and Indian genius in Talaprastara (English).

Thus, now, the new titles are only available. Among them Indian genius in Talaprastara (English) and later publications, Talaprastara of Nisshanka Sharngadeva’s Sangita Ratnakara-a critical interpretation (English) and Systematisation of Prastara details of Deshi Talas (English) are available with Karnatic music book centre, Chennai. Sangita Svararaga Sudha (English) is also available with them. You can book them even online.

If you are a resident of US I shall give you another US-address to get all these books. amsharma

SrinathK
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#145 Re: TALAPRASTHARA ( Combinatorics)

Post by SrinathK »

Happy to say that I got hold of the 1st book this music season at the book centre. :D

msakella
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#146 Re: TALAPRASTHARA ( Combinatorics)

Post by msakella »

Dear brother-member, SrinathK,

Hearty congratulations, dear. There are two more books to get (1.Indian Genius in Talaprastara, 2.Talaprastara of Nisshanka Sharngadeva’s Sangita Ratnakara and 3.Systematisation of Prastara Details of Deshi Talas). Don’t worry, if you tell me where you reside I may be able to find any easy way to get them.

Not only in getting them you can also learn it very easily. Our people are very great in making everything difficult but not in making easy even for our own kids. It took me 40 years to get it out fully but I was able to give it to a kid from Bangalore in 40 hours, working from 7 am to 11 pm daily for 4 days with a recess for meals, refreshments and others. It is not that easy to follow that book. Just to give everything out what I came to know I was compelled to write these books in a particular manner in those days and, now at this old age, I cannot rewrite them. But, believe it or not, in the meantime I have found many easy methods for many things to give them out. Very sadly, people are unable to believe me due to their own ego. Their ego is not allowing them even to sit together and discuss things even for the betterment of our own kids and art. That is the pity of our people. We can’t help. amsharma

SrinathK
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#147 Re: TALAPRASTHARA ( Combinatorics)

Post by SrinathK »

I was going through this thread last week after a long time. It reminded me of just why rasikas.org was so interesting once upon a time (I stumbled upon it in 2008) when we had so many people sharing and learning so much about music in one place. By that yardstick the overall level of the discussions has indeed declined - people are growing older, many others have passed on, some people no longer come here, many topics have been exhausted, the General Musical discussions page is often synonymous with the lounge, of late there is only a lot of talk if Sangeetha Kalanidhi or TMK comes up and the fraction of venomous air polluting species :mrgreen: seems to have increased a little, while there is a lot more music out there, there is a lot less sharing now...

The related disciplines section however is going on strong as ever. :D

Anyway I digress - all that can be fixed with some fresh energy. I came here to make a point on why certain combinations of rhythmic patterns can't be talas in the modern tala system, which while it has been explained before, I feel needs to be explained a little more clearly.

Take the 16 combinations adding up to 5

5
14
23
113
32
122
212
1112
41
131
221
1121
311
1211
2111
11111

Now, from numbers to actual talangas. If we take the value of Anudhrutam = 1 count, then Dhrutam = 2. If we go for chatushra jaathi, then Laghu = 4, Guru = 8, Plutam = 12 and Kakapadam = 16

It's plain obvious that only the 1st 3 of these 6 are possible here.

And owing to the length of each talanga, only the combinations containing the numbers 1,2 and 4 are permissible. Combinations containing 3 and 5 are not. That eliminates 6 of these 16 and they cannot be rendered as talas, because of this pesky filter called jaathi.

It is possible to throw out the rule book, but then these talas are not a part of the system. They can be called chandas (meters) instead.

It may be argued that 3+2 may be rendered with samyuktangas as Dhruta virAmam + dhrutam, but there is a problem with this.

First, originally the word viraama referred to an element that was half the length of whatever talanga it was attached to. That would work only with chatushra jaathi where Laghu (4), Guru(8), Plutam(12) and Kakapadam(16) had an even number of counts.

This viraamam later became identical to the anudhrutam, which is basically an extra beat before whichever talanga it is attached to. Redundant isn't it?

Now here's the interesting part -- there is a rule that a tAlanga starts with one audible beat. All other counts after that are supposed to be silent. The exception is the kAkapadam, which is totally silent. The tala system was designed this way to measure out the lengths of each talanga properly. Yes I know that no one in practice ever puts a tala like that, but practice = what is convenient.

This is actually the reason why the finger counts for laghu and the handwaving for dhrutam exist. This wasn't done on mere whim. There is a fair bit of thought and research that went into investigating all the movements possible with the hands and how to count in a structured manner with that. I have for a long time been trying to find out how to count on my feet and so I can get the idea.

When tAlangas are combined, the resulting pattern has more than 1 audibly struck beat. If you want to avoid this, the way in which the talangas are rendered on the hands has to be compromised.

Therefore a 3+2 pattern in chatushra jaathi (5th combination), if attempted, will end up as a 1+2+2 (6th combination in the list) or a 2+1+2 (7th), which fundamentally alters the original combination. The original 3+2 pattern is lost and cannot be rendered.

In other words, samyuktanga is fundamentally redundant. You end up rendering it as another pattern adding up to the same total anyway.

Therefore while Anudhrutam + Dhrutam + Dhrutam is possible (1+2+2) and allowed, a direct 3+2 simply does not exist in chatushra jaathi. So while it is possible to trace out which combination of 5 is 1+2+2 (or deduce the pattern from the serial number), the serial number of 3+2 cannot be found because it is not possible.

However, in tisra jaathi, it is possible to render a 3+2 as a Laghu+Dhrutam as L = 3 counts in tisra jaathi. But here, none of the combinations containing 5 or 4 are possible.

This method of trying to understand this topic through numbers first before using actual talangas is special - because it's only covered in this thread. It's not in the book I have. By covering it through numbers, automatically all the keys to mastery of tala and laya is right here in this one topic.
Last edited by SrinathK on 12 Jul 2018, 16:35, edited 1 time in total.

msakella
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#148 Re: TALAPRASTHARA ( Combinatorics)

Post by msakella »

Dear brother-member, SrinathK,

As this permutation is of ‘5’ units, if we write these permutations in terms of Talangas, we have to write Anudruta with figure ‘1’, Druta with figure ‘2’ and Laghu with figure ‘5’. Thus, the permutations carrying these three figures can only be treated as (7) Talas and all others carrying the figures ‘3 & 4” have to be written with ‘Samyuktangas’ and treated as (9) Chando-rupas. amsharma

SrinathK
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#149 Re: TALAPRASTHARA ( Combinatorics)

Post by SrinathK »

Small clarification - if it is of 5 units, does it mean I have to compulsorily take khaNDa jAti laghu of 5 counts? I was using chatushra jAti laghu of 4 counts.

On counting, I think there are 8 out of 16 patterns which are valid tALAs in khaNda jAti.
5
122
212
1112
221
1121
1211
2111

On a side note, do laghus of 6,8, 10 or 12 counts exist? Logically there is no reason why jAtis can be more than 5, although this itself is enough for several lifetimes.

EDIT : 11111 is the 9th pattern.
Last edited by SrinathK on 12 Jul 2018, 20:12, edited 1 time in total.

msakella
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Joined: 30 Sep 2006, 21:16
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#150 Re: TALAPRASTHARA ( Combinatorics)

Post by msakella »

Dear Brother-member, SrikanthK,

Many of our musicians think that there is only Chaturashra (4) and accordingly brought out Shodashangas (16) which is absolutely incorrect.

Here we must take Khanda-jati-Laghu only. But, who are not aware of the Tala-prastara will write Laghu-virama (4+1=5) which is not correct.

Why did you leave away the ‘11111’, the last one I do not understand. By that, in total, there are ‘9’.

Also there are additional Laghus, Divya-sankeera (6), Mishra-sankeerena (8), Deshya-sankeerna 10), Mishra-deshya-sankeerna (12) and Deshya-shuddha-sankeerna (16). amsharma

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