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.

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

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.

Hello sbala,

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

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

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€

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.

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.

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)

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.

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.

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

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 ).

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.

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

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.

brother


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.


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

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.

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.

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.



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.

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

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.

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

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

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...