Concept korvai

Miscellaneous topics on Carnatic music
cmlover
Posts: 11498
Joined: 02 Feb 2010, 22:36

Re: Concept korvai

Post by cmlover »

Right!
The number of digits in decimal system for 2^63 = Log(2^63) = 63*Log(2) ~ 19

Ranganayaki
Posts: 1760
Joined: 02 Jan 2011, 06:23

Re: Concept korvai

Post by Ranganayaki »

Nick H wrote:
Merriam-Webster is not an English dictionary! :P ]:)
First of all, Nick, very cute, LOL - made me - to read this in the midst f all the back and forth!!! :)

Haven't we had this discussion before, in another context? :D

Ponbhairavi,
Ponbhairavi wrote: The first person who felt uncomfortable with the usage of chi is NOT me..Pl see post 31. I did not do any quibbling. I made only one short post and I did not find fault with any person,
Ponbhairavi, I don't remember this part of the discussion too well, I can't go to the previous page without losing this one.. I think I was just addressing you to clarify the Tamil/Sanskrit part.. I will have to look it up.

In talking about the fault finding attitude, I was not referring to you but just remembering how valid or not I felt the attitude of nit-picking on the words was, and it was really these relatives of mine I was thinking about. And I was just expressing my disagreement from the standpoint of an old memory. Some of them are in fact still my favorite relatives :). The Chi-Sow thing here sounded SO familiar! Please don't take it personally.

Oh, I've landed myself in so much trouble in this thread!

I did not mean that "sow" as abbreviation IS a homonym of "sow" meaning "female pig". It is not. I just talked about an attitude we can adopt because "sow" is a common abbreviation among Indian people. And it has been accepted into the Indian parlance. All that said, I must say that I think Sowbhagyavati and Chiranjeevi are much nicer and convey much more meaning than an abbreviation can. Mr. conveys all the meaning of Mister. But to me "Sow." conveys only the meaning of "Miss" and not the beauty and auspiciousness of Sowbhagyavati. For that reason, I would prefer not shortening it.
Last edited by Ranganayaki on 27 Jan 2012, 02:14, edited 1 time in total.

Ranganayaki
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Joined: 02 Jan 2011, 06:23

Re: Concept korvai

Post by Ranganayaki »

Ranganayaki wrote:
If you can explain in a simple way what we are talking about, it would be very helpful to have a meaningful discussion, at least one that has meaning to more than just a couple of us.
sureshvv wrote: From the rest of your post, it is readily apparent that you lack the necessary humility to understand this arcane topic :-) May be you can work on that aspect for a while and try again!
Suresh, I get what you mean, re-reading this line. "Meaningful" seems to be the word that jars here, I do agree. In that light, I do feel it can be interpreted as talking down to Sri Akella!! It now sounds to me as though I believe this is a meaningless discussion, and I apologize. I meant "have a discussion that had meaning to more than a couple", "make the discussion accessible to more people". I am so sorry. Was this my worst line, that you selected for the punch? But I don't want to look at the rest of my post and find more things to feel bad about, so just a blanket apology if I have annoyed anyone.

chitravina ravikiran
Posts: 216
Joined: 28 Apr 2011, 10:30

Re: Concept korvai

Post by chitravina ravikiran »

I apologise in advance for this long post!

I had taken time off to go over Akella garu's book, Indian Genius in Talaprastara and it is doubtless a monumental effort. I have only glanced at some parts of it so far but intend to puruse it in greater depth as and when time permits. Based on this, I will, from time to time share some observations/demystify some parts of it.

1. Tala-prastara (permutation) is a fascinating subject of empirical ramifications.

2. It is essentially not only a calculation tool but also a predictive one (what are the possible permutations using various parts of the tala such as anudhrta, dhrta, laghu, guru, plutam etc, which serial number can give what kind of part-permutation or viceversa).

3. A smaller parallel is the 72 melakarta scheme wherein we can detect the notes using serial number or viceversa.

4. A much larger parallel is seen in the number of possible ragas (parent as well as derivative) using 4, 5, 6 or 7 notes including vakra prayogas (zig-zag patterns). The book, Sangita Chandrika (pub in 1902 by Manicka Mudaliar) comes up with over 7.2 million ragas using permutation and combination. Almost any normal raga discovered by a musician can fit into one of these 7.2 million. And one can create a method to serialise them based on the number and type of notes, order, zig-zaggedness and various other complex factors.

5. The exercise can be of fascinating academic interest but when one deals with these numbers in reality, it's almost like naming stars as X 235897583 or X988734390. What personalises ragas or talas is aesthetic beauty churned out by explorations of great musicians or composers. That said, prastara is a subject that we surely need to acquaint ourselves with if only to take pride in the founding geniuses of this all encompassing concept.

6. While tala-prastara is a a huge subject, I noticed a significant point, which Akella ji can corraborate - the books including his make it clear that the focus is only on the external count of the talas (based on angas). It has nothing to do with internal units or their developments within - those do not alter the tala or beget a new tala. For instance, when we talk about possible permutations for 64 units and come up with
9223372036854775808,
we are only talking about a tala of 64 whole units wherein parts such as dhrta/laghu can be permuted in various ways. We are not referring to the 64 units embedded in say, Adi tala in 2 kalais here.

7. And this begs some question, which Akella garu would surely be able to shed some light upon...

(a) What ramifications does prastara have with respect to korvais that we come up with? For instance, the korvai that I mentioned in post #1 can as well fit into Adi tala, Tishra Mathyam, or Khanda Jhampa (all 8 units) or even Chaturashra Eka (which have different serial numbers, based on prastara - the order in which the parts are displayed).

(b) I also was struck by the numbers Akella garu himself has provided for some of the 35 talas in P 114 of his book.

(i) How can the serial number be 41 for Adi tala as well as Tishra Mathya?
(ii) How can it be the same for Mishra Eka, Khanda Rupaka (both given as 1), Sankeerna Eka and Mishra Rupaka (again 1)?

From what I gleaned, this would be impossible. But am I missing something here?

8. To get back to the initial topic, any korvai deals with internal divisions within a tala. It neither gets affected by nor affects anga-prastara (in talas of same units). The two are quite distinct paths.

9. Practical music is mostly based on aksharas within a tala and not its angas.

Ranganayaki
Posts: 1760
Joined: 02 Jan 2011, 06:23

Re: Concept korvai

Post by Ranganayaki »

And so I move on, ready to put my foot in my mouth one more time. I'm quite nervous now.

Sri Akella, I think I understand all that you have said here. I have been reading online.
http://www.berklee.edu/bt/211/lesson.html
https://canvas.instructure.com/courses/179456


I have a question, a doubt I would like clarified, I do not mean to challenge (as Vasanthakokilam nicely distinguished).

I understand that these are really permutations, positional changes. Then the number of permutations of a small number, say, 3 units should be 6 and not 4.. and by extending that thought, the number of permutations of 64 units should be a MUCH bigger number than 2 to the 63rd power. I asked you this question yesterday too (about the permutations of 3 units), but you answered in more general terms. Can anyone tell me if there is anything wrong with my reasoning? There must be because no one else has pointed it out ! :( My idea of the right number is 64!. [Sri Akella, I don't know if you are serious about your inabilities you mention, or if it is purely rhetorical, but in case you do not know what 64! is, it is understood as 64 X 63 X 62 X 61.......... 3 X 2 X 1 (all the way) ]

One of these two websites above lists permutation numbers for up to 12 units and the number it listed for 12 units is 479,001,600. I checked and it is equal to 12!. In your table, it reaches 2048. Please resolve this for me, you or anyone else.

All this said, if the purpose of this is to find the serial number of one particular permutation, what is the use of that? What is the use of saying (for example) that Ravikiran's work already appeared somewhere else? His work remains original. What is the aesthetic purpose of knowing these serial numbers? Still, if there is a quick, methodical way of arriving at this serial number and if it was truly codified centuries ago without the help of computing aids, it is an amazing feat.

msakella
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Joined: 30 Sep 2006, 21:16

Re: Concept korvai

Post by msakella »

Chi. Ravikiran dear, I am extremely happy of this development which forced you glance into this highly interested science of Talaprastara.

To tell the fact, in music, I did never find such an absorbing topic having more precision than Talaprastara in music. More over, most unfortunately, it has been proved beyond any doubt that this most interesting and invaluable topic has absolutely been vanished due to the sheer negligence and ignorance of the egocentric authors of our treatises since last 8 or 9 centuries and, very pitiably, each and every musician is very busily engaged in earning money, fame, honours and titles and none did care to retrieve this lost topic and give it to the posterity until I, only by the grace of the Almighty, could decipher it fully and bring it in three books which altogether consumed the lion’s share of forty years of my life. Nobody can even imagine how much hardship I had undergone, how much discouragement I had faced and how much I have sacrificed in my life to do this all unlike any other person on earth.

I shall give you answers to all your questions one after the other. At the first instance, if you don’t mind, please modify anudhrta, dhrta & Tishra Mathyam as anudrta, drta & Trisra Mathyam.

Yes, as you wrote, this element focuses only on the external count of units of the rhythmical form but not the internal units or fractional-units or their developments like nadai or gati or kalai or marga.

Prastara is the process of permuting a particular number of units into different kinds.For example 4-units could be permuted as - 4, 1-3, 2-2, 1-1-2, 3-1, 1-2-1, 2-1-1 & 1-1-1-1 – in all, into 8 different forms altogether but each carrying 4-units only. Thus, 64-units has ‘9223372036854775808’ varieties of rhythmical forms among which some can be used as Talas basing upon the established norms to use them as Talas and some cannot be.

Any where in the universe 8 x 8 = 64 and thus, being mathematics, any one who works out accordingly will certainly get the same serial-numbers of the 35 Talas. As you do not have the required acquaintance with this topic you felt struck on finding these serial-numbers.

As you do not have the required acquaintance with this topic you are able to see the common serial-number ‘41’ only but not the difference of the total units of 8 & 7 of Adi & Trisra-mathyam respectively.
In the same manner you are unable to see the required difference even in respect of others Talas you have mentioned obviously revealing that your are certainly missing the required in this respect.

You are writing ‘practical music is mostly based on Aksharas within a tala and not its angas’ but, in the absence of the required knowledge of Prastara you are unable to understand that this topic is also based on Aksharas or units within a Tala but not its Angas. That is the pity. Most unfortunately, no musician is aware that this topic is the only origin of all the rhythmical forms of the universe. amsharma

Chi. Sow. Ranganayaki dear - In the process of permutation of 12-units we get ‘2048’ only but not ‘479,001,600’ as mentioned in that website.

From 25-02-1995 to 02-03-1995 (6 days) one workshop on Talaprastara, sponsored by the South Central Zone Cultural Centre, Nagpur was held at Hyderabad under my Director-ship. For this 25 participants, Teachers, Lecturers and Professors from the Music Colleges and Departments of Andhra Pradesh, Tamilnadu, Karnataka, Kerala, Maharashtra and Madhya-pradesh are invited to participate including Prof. N.Ramanathan from Taminadu and Dr.Sachi Devi from Karnatanaka. In the end of it, in the valedictory function, all the participants spoke and unanimously expressed that all the Doctorates they already have must be conferred upon me for bringing out this amazing topic, Talaprastara. Such amazing topic this Talaprastara is. amsharma

VijayR
Posts: 198
Joined: 13 Jul 2011, 21:59

Re: Concept korvai

Post by VijayR »

Ranganayaki wrote: I understand that these are really permutations, positional changes. Then the number of permutations of a small number, say, 3 units should be 6 and not 4.. and by extending that thought, the number of permutations of 64 units should be a MUCH bigger number than 2 to the 63rd power. I asked you this question yesterday too (about the permutations of 3 units), but you answered in more general terms. Can anyone tell me if there is anything wrong with my reasoning? There must be because no one else has pointed it out ! :( My idea of the right number is 64!. [Sri Akella, I don't know if you are serious about your inabilities you mention, or if it is purely rhetorical, but in case you do not know what 64! is, it is understood as 64 X 63 X 62 X 61.......... 3 X 2 X 1 (all the way) ]
Ranganayaki, these are not really permutations (which have a different meaning in formal mathematics). What is really being done here is called "sampling with replacement". Think of this in the following way (sorry if this is a confusing explanation):

You are given a small box containing two pens, one of which is a red pen (R) and the other is a blue pen (B). You also have a piece of paper with 3 empty squares to color. You proceed with the coloring by first dipping into the box and selecting (sampling) one of the pens. Use it to color the first square on the paper and put (replace) the pen back in the box. Repeat for the second square, and then for the third square. At the end, you have a Red-Blue sequence on your piece of paper.

As you can see, because of the replacement, the process is completely independent for each square on the paper. For the first square, you can have 2 possibilities (R or B). For each of these, the second square can have 2 possibilities, resulting in a total of 4 possibilities so far (RR, RB, BR, and BB). For each of these four possibilities, the third square can have 2 more possibilities, resulting in a total of 8 (RRR, RRB, RBR, RBB, BRR, BRB, BBR, and BBB). That gives you the total of 8 possibilities (i.e., 2x2x2 = 2^3 = 8 ).

If R denotes a unit of silence, and B denotes a swaram, then any korvai that is 3 units long has to fall into one of the 8 possibilities below: (silence, silence, silence), (silence, silence, swaram), (silence, swaram, silence), (silence, swaram, swaram), (swaram, silence, silence)m (swaram, silence, swaram), (swaram, swaram, silence), and (swaram, swaram, swaram). You can extend the same up to 63.

If R is denoted as a 0 and B is denoted as a 1 (traditional Boolean notation), then this becomes fairly simple Boolean number theory. It is simply the number of Boolean/binary numbers that can be represented using 3 digits, which is 8 (the process is the same; each digit can be either a 0 or 1, independent of the other digits).

Nick H
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Joined: 03 Feb 2010, 02:03

Re: Concept korvai

Post by Nick H »

If R denotes a unit of silence, and B denotes a swaram, then any korvai that is 3 units long has to fall into one of the 8 possibilities below: (silence, silence, silence), (silence, silence, swaram), (silence, swaram, silence), (silence, swaram, swaram), (swaram, silence, silence)m (swaram, silence, swaram), (swaram, swaram, silence), and (swaram, swaram, swaram). You can extend the same up to 63.
So rhythmic (not tonal) combinations are binary: silent or sound, 0 or 1, thus we end up with powers of two for the possible combinations of any given number of units?

ShrutiLaya
Posts: 225
Joined: 14 Sep 2008, 01:15

Re: Concept korvai

Post by ShrutiLaya »

msakella wrote: Prastara is the process of permuting a particular number of units into different kinds.For example 4-units could be permuted as - 4, 1-3, 2-2, 1-1-2, 3-1, 1-2-1, 2-1-1 & 1-1-1-1 – in all, into 8 different forms altogether but each carrying 4-units only. Thus, 64-units has ‘9223372036854775808’ varieties of rhythmical forms among which some can be used as Talas basing upon the established norms to use them as Talas and some cannot be.
Part of the problem arises from the fact that Sarma garu is using a commonly accepted mathematical term "permuting" to mean something completely different. In Number theory, the technical term for what he is getting at is "composition" (see http://en.wikipedia.org/wiki/Compositio ... _theory%29) "a composition of an integer n is a way of writing n as the sum of a sequence of (strictly) positive integers. "

The proof that a composition of N units contains 2^(N-1) parts is quite interesting. Taking the number 4, for instance, write it as follows

1 ? 1 ? 1 ? 1

Now replacing each question mark by either a plus or a dash gives one composition - eg.

1 + 1 - 1+1 = (2-2)

So all the compositions can be obtained by systematically replacing the ? by + or - and clearly, there are 2^(n-1) ways of doing this (2 choices at each of n-1 positions)

- Sreenadh

VijayR
Posts: 198
Joined: 13 Jul 2011, 21:59

Re: Concept korvai

Post by VijayR »

As an addendum to my previous post, you can also look at it another way (might be more intuitive). [Edit: this is exactly the composition that Sreenadh refers to in his previous post as well]

This is related to the the number of ways of assigning "n" indistinguishable objects to "k" distinguishable boxes, with the constraint that no box should be empty. The answer to that is C(n-1, k-1) = (n-1)! / ((k-1)! * (n-k-2)!).

The exact problem that Akella garu refers to is the number of ways that "n" aksharas can be split into 1 box + the no. of ways it can be split into 2 boxes + the no. of ways it can be split into 3 boxes + ... + the no. of ways it can be split into n boxes.

This is given by: C(n-1, 0) + C(n-1, 1) + C(n-2, 2) + ... + C(n-1, n-1), which is well known to be 2^(n-1).

Therefore, for n = 4 (same example given by Akella garu in post #81, this comes out to:

C(3, 0) = 1 (this is the - 4 that he mentions)
C(3, 1) = 3 (these are the 1-1-2, 1-2-1, and 2-1-1 that he mentions)
C(3, 2) = 3 (these are the 2-2, 3-1, and 1-3 that he mentions)
C(3, 3) = 1 (this is the 1-1-1-1 that he mentions).

For n = 64, it comes out to 2^63 which is the long 19 digit number listed.
Last edited by VijayR on 27 Jan 2012, 19:45, edited 1 time in total.

VijayR
Posts: 198
Joined: 13 Jul 2011, 21:59

Re: Concept korvai

Post by VijayR »

Nick H wrote:
So rhythmic (not tonal) combinations are binary: silent or sound, 0 or 1, thus we end up with powers of two for the possible combinations of any given number of units?
Yes, you're right.

msakella
Posts: 2127
Joined: 30 Sep 2006, 21:16

Re: Concept korvai

Post by msakella »

Dear brother-member, VijayR, I have seen your last post also but somehow missed to reply. I am extremely sorry for this, dear.

I have toiled my self to the saturation point in digging out this element, Prastara when neither calculator nor computer are available. More over, I was so poor in mathematics that I could score only 11% in my SSLC examination in 1951 and successfully failed. Only by the grace of the Almighty, I could retrieve the lost topic, Prastara with great difficulty. In this process, in formulating flawless rules and regulations for writing figures for different tables and also for the short-cut-methods which have never been furnished by any author of any century, I have calculated mostly up to 5 or 6 digits maximum. Only very few times I have proceeded up to 19 digits. But, I am not sure of the correctness in furnishing such large figures due to my old age and other constraints for which I can’t help. amsharma

cmlover
Posts: 11498
Joined: 02 Feb 2010, 22:36

Re: Concept korvai

Post by cmlover »

Nice to have this interesting introduction to Math 101.
Let us move on to more interesting practical application of 'Talaprastara' and to issues adverted to by Chi. Ravikiran.
Technically the division of an integer into integer components falls under the 'Theory of Partitions'.
The partition number itself is interesting whose calculation is not so simple; an area to which our Ramanujan had made a monumental contribution which finds application in Quantum Theory.
The total number of permutations of the partitions however of a number 'n' is simply 2^(n-1).
These partitions can be used to construct interesting korvais and played/sung effectively.
Our ancestors, not being aware of the maths enumerated these (talaprastara?) at times erroneously.
Now we can cast them in a sound mathematical foundation thanking our all-time mathematical genius Ramanujan!
For an inkling on partion theory see
http://www.virtuescience.com/partitions.html

With the able assistance of our Sarmaji/Ravikiran/.. let us formalize the theory of 'Construction of Korvais' which will be a valuable scientific contribution to our CM Theory..

ShrutiLaya
Posts: 225
Joined: 14 Sep 2008, 01:15

Re: Concept korvai

Post by ShrutiLaya »

In the interests of clarity and to keep to accepted mathematical terminology - what is being discussed here is not a partition, it is a composition. In a Partition, the order is not important eg. 1-2-1 is considered the same as 2-1-1; However, these are different Compositions

- Sreenadh

chitravina ravikiran
Posts: 216
Joined: 28 Apr 2011, 10:30

Re: Concept korvai

Post by chitravina ravikiran »

In the interests of clarity
In the same vein, let us also note that prastara discussions in the treatises and in this discussion by Akella garu is about tala Compositions and not korvais, which have more to do with the internal elements. So, all discussions about serial numbers of talas etc that Akella garu and I have been having - while certainly of academic interest - are not connected with the korvais and principles thereof.

Prastara aims to give serial numbers of talas and not of korvais. Korvais is a wholly different subject and the principles of akshara-prastara have to be employed to study this.

Akella garu:

Thank you so much for your patient answers. However, both of us missed out a vital (unintended) incorrectness in my question, 7 (b) (i).
(i) How can the serial number be 41 for Adi tala as well as Tishra Mathya?
The fact is Adi and Tishra Mathya do not have the same number. Adi is 41 and Trisra Mathya is 21. It was Chatushra Mathya which had 41, which makes that question invalid. Given that, I am even more curious about your answer. Can you please clarify again about all my questions 7 (a) and 7 (b) (ii)?

vasanthakokilam
Posts: 10956
Joined: 03 Feb 2010, 00:01

Re: Concept korvai

Post by vasanthakokilam »

chitraveena Ravikiran wrote:Prastara aims to give serial numbers of talas and not of korvais. Korvais is a wholly different subject and the principles of akshara-prastara have to be employed to study this.
Yes, that was my understanding from before and hence I was surprised that Akella ji mentioned about serial numbers in the context of your Korvai.

But, coming to think of it, 'Akshara-prastara' can also be studied using the same 'composition' technique ( as discussed by Vijay and Sreenadh above as a mathematical term ) since the structural aspect of a korvail is about spliting N Aksharas into various groupings. So it should indeed be possible to talk of Korvai serial numbers along the same 'composition'al lines as Talaprasthara.

As an example, a 64 akshara Korvai (for, say, Adi ), will have the same set of serial numbers as a tala with an avarthana count of 64.

If talaprasthara has a defined Anga model ( i.e. the angas defining the groupings ) and has rules and restrictions on what combinations of angas are permitted, then we will have cases that serial numbers that are not valid in talaprasthara are valid in aksharaprasthara, since aksharaprasthara ( korvai ) may not have the same rules and restrictions.

Akellaji had written before about certain talas that are not allowed by talaprasthara because it violates some talaprasthara rules ( like the one example of the tala used by Sri. Shyama Sastri in a tala competition ). I am keying in on that recollection to theorize that not all serial numbers are valid talas, as per talaprasthara.

( I am using Aksharaprasthara in a generic form, I really do not know if our treatises talk about it with that name )

cmlover
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Joined: 02 Feb 2010, 22:36

Re: Concept korvai

Post by cmlover »

Interesting!
While serial numbering of talas (talaprastara) is just academic
construction of Korvais is eminently practical. If there is already info on 'aksharaprastara' (as VK terms it) do please share, if not let us collaborate and work on it....

vasanthakokilam
Posts: 10956
Joined: 03 Feb 2010, 00:01

Re: Concept korvai

Post by vasanthakokilam »

>'aksharaprastara' (as VK terms it)

Ravikrian called it that and I was piggybacking on it ;)

msakella
Posts: 2127
Joined: 30 Sep 2006, 21:16

Re: Concept korvai

Post by msakella »

Chi. Ravikiran dear, Clarifications:
7 (a): Unless you go deep into Prastara you can never understand that all these korvais are only of the mathematical base and, thus, each and every korvai certainly comes under Prastara only. We can fit any korvai in any Tala. VK’s Aksharaprastara also comes under this Prastara.

(b) (i) Unless you get the needed acquaintance with this topic you cannot understand this, dear. (ii) Unless you get the needed acquaintance with this topic you cannot understand this, dear.

In the absence of the required knowledge you are unable to follow me. I am not all talking about any Tala-compositions, dear. I may not be well educated like all you people. But, every one among you must mind that I, unlike any other human being on earth, have toiled myself for 40 long years of my precious life to bring out this rarest topic which has never been brought out fully by any author of our so called treatises and you all are becoming ready to define it within few minutes. In which way it is justifiable, dear? Unless you go deep into it none of you can understand this in your lifetime. I am talking about the rhythmical compositions only. This is not of academic interest only, dear. In the absence of the required knowledge you all are unable to recognise the relation between the rhythmical form and korvai. I can prove what I write at any time and place, dear. amsharma

cmlover
Posts: 11498
Joined: 02 Feb 2010, 22:36

Re: Concept korvai

Post by cmlover »

Sarmaji
I am totally lost since I certainly do not have 40 years to spare unless the Divine in his infinite mercy will spare me!
Good luck with you young guys!

chitravina ravikiran
Posts: 216
Joined: 28 Apr 2011, 10:30

Re: Concept korvai

Post by chitravina ravikiran »

CML,

1. Akshara prastara is a term that can be used to denote practical compositions of music (melody/rhythm) based on number of aksharas (units within a tala) that one is dealing with. The principles of prastara are same. The excellent Foreword by Dr R Sathyanarayana in Akealla garu's book talks about how all types of prastaras owe a lot to chandah-prastara (based on how short/long syllables could be arranged in various ways).

2. Even in theory, Akshara prastara can get far more sophisticated and involved than anga-prastara or chanda-prastara because:

(a) in chanda, we are only dealing with short/long syllables - in music parlance, this can translate into units of 1 or 2. In music, once you talk of sustained syllables/notes beyond 2 units, the number of ways of expressing each possibility can get exponentially higher.
(b) in anga-prastara: we deal with only permissible angas of the tala of various units and the rest are combinations and as it has well been established, certain rules have been laid out to make them valid prastaras.

3. If we were to also bring in melody into this equation, the possibilities become literally endless, even within one raga. Then imagine the ramifications of 100s of ragas.

4. That said in music, aesthetics come into play and at the end of the day, an exercise in akshara-prastaras could sound like computer-generated sequences unless one has the musical sense to hone in on arrangements that are aurally and emotionally satisfying.

5. An anology to 3 is: we can theoretically say X number of stars/planets are within a cluster and any particular star discovered by an observer could be 'already there'. But in practice, those stars/planets supporting life as we know it are of more interest to us.

On a personal note: very few artistes venture into even akshara prastara - in most concerts they focus on vistara. But I have been fascinated by this topic from my childhood thanks to my father's genius in making me do a lot of practical exercises in musically expressing something as simple as even a 7 or 15 in various ways when we used to do kalpana swaras. Certain tavil artistes have been excellent exponents of prastara. But more on this later!

Akella garu:

Words cannot express the admiration we all have for your dedicated efforts. I do intend to read your book in detail. Meantime, since you already have the expertise in the field, we may trouble you for certain clarifications now and then! I am not contradicting your statement at all:
that all these korvais are only of the mathematical base and, thus, each and every korvai certainly comes under Prastara only. We can fit any korvai in any Tala
It is almost self-evident. I was merely talking in terms of practical ramifications.

cmlover
Posts: 11498
Joined: 02 Feb 2010, 22:36

Re: Concept korvai

Post by cmlover »

Thx Ravikiran
I can follow your line beautifully. The math is accessible to all of us. However the indefinable 'aesthetics' is accessible to only a few blessed souls like you! Though I can drive my automobile well there is always the curiosity to know how it works. Same is true more in trying to understand the mechanics of CM as a Rasika since our system is totally scientific...

msakella
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Joined: 30 Sep 2006, 21:16

Re: Concept korvai

Post by msakella »

Chi. Ravikran dear, Thank you all for your affectionate admiration towards me and I am always ready to ably serve our community to the maximum without expecting anything in turn.

While there are fixed number of rhythmical ramifications for a particular number of units there are umpteen korvais for each rhythmical form of them. That is the nicety of music. amsharma

Ranganayaki
Posts: 1760
Joined: 02 Jan 2011, 06:23

Re: Concept korvai

Post by Ranganayaki »

VijayR wrote: Think of this in the following way (sorry if this is a confusing explanation):
.
VijayR, thank you for that lovely explanation, it wasn't confusing at all.

vasanthakokilam
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Joined: 03 Feb 2010, 00:01

Re: Concept korvai

Post by vasanthakokilam »

all types of prastaras owe a lot to chandah-prastara (based on how short/long syllables could be arranged in various ways).
This is quite significant. One thing that is not explicitly talked about is the relationship between musical emphasis/stress and tala 'beats'. I am now curious if there is a correspondence between Chandah-prasthara and where automatic emphasis occurs in phrases. One can observe that if a short is followed by a long, the emphasis/stress naturally falls on the beginning of the long.

If this is true and if there are more such things, then there is an intriguing possibility of relating tala prasthara as an intersection of akshara prasthara and chandah-prasthara, on the notion that the thala 'beats' are aligned with where emphasis/stress occurs ( for the most part ) in non-syncopated musical phrases.

Then it may be possible to say something like Serialnumber(s) in aksharaprasthara and serial number in chandah-prasthara(s) matche with a serial number in talaprasthara. This will then help us provide a formal answer to the oft asked question: 'why a certain song is in Adi as opposed to trisra matya or khanda jhampa'.

(The chandah-prasthara has correspondence to lyrical aspects as well, as we see in tamil veNpA grammar ( kuRil, neDil based ) and similar lyrical prastharas in Kannada poetry. This makes it the 4th dimension of a musical composition, thus integrating the rhythmical aspects with the lyrical aspects. The melodic aspects, the 5th dimension, rides on top of this rhythmic-lyrical structure)

msakella
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Joined: 30 Sep 2006, 21:16

Re: Concept korvai

Post by msakella »

Dear brother-member, vasanthakokilam, Chandas is nothing but rhythm in which shorter and longer units are dealt with. In poetry as it has to deal with letters and, in general, no letter is pronounced too long like our music notes srgmpdn only two varieties, short and long units which are called laghu and guru are used. But, as these syllables srgmpdn could conveniently be elongated and pronounced with a music sense, in our music, anudruta the shortest, druta longer than anudruta, laghu still longer than druta, guru still longer than laghu, pluta still longer than guru and lastly kakapada still longer than even pluta thus extending up to 16-units are used. To tell the truth Rhythm is a discipline to put the things in an order. Things without an order or discipline look awkward. In the same way even the words, even without music, spelt in a particular rhythm attract people and make them attentive. That is why this rhythm is induced into our music. Even in the attractive film music if the rhythmical element is removed there will not be any audience.

Even in this rhythm Chaturashra-gati has very high level evenness unlike other odd-gatis and even among the metered varieties of Talas Adi-tala has very highly balanced evenness unlike Trisra-jati-mathya or Khanda-jati-Jhampa or Mishra-sankeerna-jati-eka or Divya-sankeerna-jati-rupaka or Pakshini-jati-dhruva or Pakshini-jati-ata. Even to disturb this evenness in Adi, it is more than enough to make it bad, though not worse, if the Laghu is kept between the two Drutas. Even in the evenness a particular evenness only gives you the maximum soothing effect. In a properly scented room, even if the things are not in order, a person enjoys the pleasant smell and forgets the disorder of the things. That is why always discipline is given the highest place in the world. amsharma

srkris
Site Admin
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Re: Concept korvai

Post by srkris »

Chandas is a fascinating topic. If we take a famous mantra (from the Rigveda 3.62.10), the laghu syllables and the guru syllables are ordered as follows (the chandas is the classical tripada gAyatri, if we ignore the fact that the seventh and eighth syllables fused together in later times to make the count defective i.e nicRt gAyatri):

Underlined = Guru
Non-underlined = Laghu

Pada 1 - tát sa vi túrre Ni am
Pada 2 - bhár go de vás ya dhI ma hi
Pada 3 - dhí yo naH pra coyAt

GL LG LG LL
GG GG LG LL
LG GG LG LG

So talas take their birth from chandas which is 'poetic metre'.

msakella
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Joined: 30 Sep 2006, 21:16

Re: Concept korvai

Post by msakella »

Dear brother-member, srkris, All the rhythmical forms of the universe took birth only from the Chandah Shastra i.e., the science of metrics which is also called ‘Shatpratyaya’. Even among these rhythmical forms the forms which fit in the norms of our Talas has only be taken and being rendered as Talas and other forms like Sharabhanandanam come under the rhythmical forms which do not fit in the norms of our Talas and cannot be rendered. All these details are available in the topic, Talaprastara which is the origin of all the rhythmical forms of the universe. amsharma

cmlover
Posts: 11498
Joined: 02 Feb 2010, 22:36

Re: Concept korvai

Post by cmlover »

Sarmaji
Was there a taaLam in Sama veda chanting?
What was that?

srkris
I had always wondered about the truncation of gayatri to nicRt.
Some vaishnavas still do not truncate and chant it without the fusion.
The Sama chanting of gayatri (keeping the Gayatri chandas) is as
'tatsaviturvarENiyOM'
which is the fusion of praNava and would mean
"That Sun God's adorble praNava (OM)... on which may we meditate..."
Thus the incorporation of the praNava (Om ityEkAkSharam brahma) is logical in this supreme mantra..

I appreciate if you/others have any references towards this..
(sorry for the digression)

msakella
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Joined: 30 Sep 2006, 21:16

Re: Concept korvai

Post by msakella »

Dear Brother-member, cmlover, While the Laya is universal some ‘Chando-rupas or rhythmical forms’ of Laya have been metred to suit the needs of our music and in that process they have also been named after Talas having their own limbs according to Taladashapranas. Thus, any Tala must fit in the rules and regulations of Taladashapranas and in such case only they must be called as Talas. In respect of our music only we must call them Talas. For another purposes they should not be called as Talas like in respect of the Chando-rupas of Great Arunagirinathar which, in fact, should not be rendered at all as Talas. amsharma

srini_pichumani
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Joined: 24 May 2006, 11:29

Re: Concept korvai

Post by srini_pichumani »

Dear CMLover,

talk of taalam wrt sAman chanting can be misleading. But the concept of time is indeed significant, as is the accompanying mudras or chironomy -- great attention is paid to the mAtras covering a section of the chant or the whole.

Even here, the Nambudiri Jaiminiya chants are more characterized by and noted for their great attention to mAtras rather than the tonal compass. They take particular care in delimiting their understanding of the term "svara" as a tonal movement rather than a scale degree. Wayne Howard has captured this very well in his 1977 classic "Samavedic Chant".

If you hear the various ways in which the first chant corresponding to the rc "agna aayaahi vitaye..." is chanted -- first by Kauthuma reciters, Jaiminiya reciters of TN, and then Nambudiri Jaiminiya reciters, you will see this contrast very well.

-Srini.

cmlover
Posts: 11498
Joined: 02 Feb 2010, 22:36

Re: Concept korvai

Post by cmlover »

Thanks Srini
I know timing is important in Sama chants though there are variations in different regions. The namboodiri chants differ from those of our TN priests. Even there, there is difference between Tinnevely and Tanjore or even Andhras. There are no angas in the Sama chant except for the nodding of the heads among the Namboodris. By the by is there any prescribed timing in the regular Rudram/Camakam chants or is it just practised synchrony?

sureshvv
Posts: 5523
Joined: 05 Jul 2007, 18:17

Re: Concept korvai

Post by sureshvv »

SahanaVasud wrote:
Also, here is my attempt at the Kalyani korvai above (repeated 3 times): http://snd.sc/ySuoHV.
Can't find this anymore?

vanajan
Posts: 60
Joined: 01 Jan 2019, 21:13

Re: Concept korvai

Post by vanajan »

Don't know why it doesn't work. Shared again. Pl try this link:https://soundcloud.com/musicinmath/kaly ... ai/s-n7TmM

Vanaja

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