Structuring a Korvai in the thani

[shankarank]

@mridhangam

https://youtu.be/mzanBWsf6ko?t=1081

That kORvai in its current form: 24 + 25 + 15 = 64.

The 25 has two sections of khaNDam with kaRvais - 5*3 + 5*2 = 25.

I made another one for a total of 128.

where the first 24 remains.

The next one : 5*6 + 5*4 + 5*3 + 5*2 = 30+20+15+10 = 75. which leave 29. - i.e 24 + 75 + 29

29 can be handled 2 ways as is : 27+2 -> 9(1)9(1)9 OR 21+8 -> 7(4)7(4)7 .

But just by the feel of it , I could add 1 to 29 to do a 30. Where would that 1 come from?

Well the last 5*2 , borrow 1 from it - ta,di,gi,na,tom, - the last comma goes -> ta,di,gi,na,tom ( the kArvai removed) and immediately begin ta-ki-Ta-thom, ta-di-gi-na-tom (10) -> 3 times to get 3*10 = 30.

The much loved ta-di-gi-na-tom wins!

Well that is not the only deviation. A visiting vidvan with whom I happened to discuss it pointed out, that in the middle piece I left out a 5*5 - that will make it a 100 and I have to do something with one extra Avarta added for a remaining 4+64 = 68.

Or I will have to not do the 5*3 - just to make the reduction perfectly arithmetic 6->4->2 - so it is 60. I need to fill the remaining 44.

Now I will make a case for justifying this - you may still call it lakshya or altogether invalid.

5 *6, 5*4 an arithmetic reduction. 5*3, 5*2 is the geometric reduction of the first pair ( i.e. (6,4) -> (3,2) ). So it is a hybrid (arithmeto-geometric) reduction .

[Christian Kenit Ram]

@Christian Kenit Ram If you are not fixated on maintaining the same kAlam and mixup some higher kAla syllables:

|| ta dim - - | - ta ka dim | - - - ta | ki ta dim - |
| - - tAkiTA(2) | thom - tatA | kiTA(1) thom - ta| thi tAkiTA(2) thom ||

3(1) 4(1)5 = 14


|| ta dim - - | ta ka dim - | - ta ki ta | dim - - ta |
|tAkiTA(2) thom - | ta thi tAkiTA(2) | thom - ta di | - tAkiTA(2) thom||

4(1)5(1)6 = 17

|| ta dim - ta | ka dim - ta | ki ta dim - | ta di tAkiTA(2) |
| thom - ta di | - tAkiTA(2) thom |- ta - di | - tAkiTA(2) thom||

5(1)6(1)7 = 20

Will have a punch as well!

Thanks a lot for the ideas , Shankarank !

The frame is very clear , however I have a doubt about whether you are staying in Chatushra Gati the whole time or also get into Tishra Gati for some phrases .
Ex : | - - tAkiTA(2) | --- could be played with kiTa in double-matra speed ( 32nd notes ) or Takita as a triplet ( in Tishra Gati - 3 syllables of equal duration ) - 3 matras instead of 2 .

I assume " ta| thi tAkiTA(2) thom || " is the normal variation for Tadiginatom , where kiTA stays in Chatushra Gati , while being played as 32nd notes .

[shankarank]

I used captilization in tA - meaning an elongated syllable which occupies 1 unit and kiTA occupies the other 1 unit where the 2 units is in your caturASra gati only.

[Christian Kenit Ram]

^

Ok thanks !
I understand your nomenclature now .

[Christian Kenit Ram]

Balaji Sir , while listening again to Part 3 of your lecture demonstration I heard this Korvai ( 28m22 ) :

https://www.youtube.com/watch?v=lLGWJBGgiPk

ta - dim - tadim -
takadim - tadim -
ta - dim - tadim -

ta - dim - tadinginatom
ta --- di ---
ta - dim - tadinginatom
ta --- di ---
ta - dim - tadinginatom

Purvanga : 21 ( 7 x 3 )
Uttaranga : 43 ( 9 + 8 , 9 + 8 , 9 )

Coincidentally , I have been looking for some days to do the inverse : A Korvai with the uttaranga having 21 matras , but I could not manage it as easy as with other numbers . Maybe it has to do with the fact that 43 ( for the purvanga ) being a prime number , makes it difficult to split this number in the usual 3 palas with the kArvais in between .
So your technique of splitting 43 in 3x9 + 2x8 for the uttaranga in your Korvai gave me the idea for using it in my own " Korvai " ( ? or Composition or Abhiprayam ...) for the purvanga :

ta - tum - takitadim -
dintakadin takadina
ta - tum - takitadim -
dintakadin takadina
ta - tum - takitadim -

ta - din - ginatom
ta - din - ginatom
ta - din - ginatom

Uttaranga : 43 ( 9 + 8 , 9 + 8 , 9 )
Purvanga : 21 ( 7 x 3 )

I don´t know if it passes as a correct Korvai due to the fact that the uttaranga has the structure ABABA .

[Christian Kenit Ram]

...

ta - din - ginatom
ta - din - ginatom
ta - din - ginatom

Uttaranga : 43 ( 9 + 8 , 9 + 8 , 9 )
Purvanga : 21 ( 7 x 3 )

I don´t know if it passes as a correct Korvai due to the fact that the uttaranga has the structure ABABA .

Sorry , can not edit anymore .

Correction :

Purvanga : 43 ( 9 + 8 , 9 + 8 , 9 )
Uttaranga : 21 ( 7 x 3 )

I don´t know if it passes as a correct Korvai due to the fact that the purvanga has the structure ABABA .

[shankarank]

The next one : 5*6 + 5*4 + 5*3 + 5*2 = 30+20+15+10 = 75. which leave 29. - i.e 24 + 75 + 29
...................
Well the last 5*2 , borrow 1 from it - ta,di,gi,na,tom, - the last comma goes -> ta,di,gi,na,tom ( the kArvai removed) ....

I figured , the last 10 of 75, if I am to make it a 9 instead of 10, to get a 30 remainder, I might as well combine the 10 with 29 and do something continuous from there on:

ta,di,gi,na,tom-thangu-thangu ta,di,gi,na,tom-thangu-thangu ta,di,gi,na,tom |

9(6)9(6)9 = 39 = 10+29

Alternately :

ta,di,gi,na,tom-[ta,di,gi,na,tom] ta,di,gi,na,tom-[ta,di,gi,na,tom]ta,di,gi,na,tom |

where [ta,di,gi,na,tom] in square brackets is executed in mEl (higher) kAla triSram 6*(3/2) = 9

That is deceptively aesthetic and grammatically correct, instead of aesthetically deceptive and grammatically incorrect!

allowed?

[shankarank]

https://youtu.be/uU9YAALt828?t=6537

Above is a nice one in miSra cApu by SrI Arun Prakash. Wait until the naDai and mohra finish.

ta-dhi-gi-na-tom is handled with ta-dhi being given 7 each , 6 each ... down to 2-each

7+6+5+4+3+2 = 27 * 2 = 54.

A kurraippu that results in that is multiple of 3 would be this.

To get a common multiple of 14 and 3 - samam to samam for even Avartas would be 6*14 = 84 beyond 54 and that gives a remainder of 30.

30 has to be divided into 6 integral additive parts each divisible 3 to be given to gi-na-tom equally.

That is achieved as : 9+6+6+3+3+3

So it is: 7,7,9 - 6,6,6 - 5,5,6 - 4,4,3 - 3,3,3 - 2,2,3 to complete 84 aksharas.

As the time allocated to ta-dhi comes down from 7, gi-na-tom also gets less and less to give a feel of proportionality.

[tvr]

https://youtu.be/nbDkV3vH_14

This is a korvai of Tanjore Sri Upendran sir, which was originally played in chatusram. But here, it is rendered in tisram which looks challenging.

[mridhangam]

...

ta - din - ginatom
ta - din - ginatom
ta - din - ginatom

Uttaranga : 43 ( 9 + 8 , 9 + 8 , 9 )
Purvanga : 21 ( 7 x 3 )

I don´t know if it passes as a correct Korvai due to the fact that the uttaranga has the structure ABABA .

Sorry , can not edit anymore .

Correction :

Purvanga : 43 ( 9 + 8 , 9 + 8 , 9 )
Uttaranga : 21 ( 7 x 3 )

I don´t know if it passes as a correct Korvai due to the fact that the purvanga has the structure ABABA .

Generally these types of korvais dont pass. Normally purvanga is split equally.

But these days i hear korvais having a following structure too accepted and follwed/played by many.

D.tnkt tktr kttk tm . T. Tm .
Kttk d. Tnkt tktr kttk tm. T. Tm .
Trtrkttk d. Tnkt tktr kttk tm. T. Tm ..

Tdgntm-tdgntm- tdgntm//

If you observe the korvai split it goes thus:

8-4-2
2-8-4-2
4-8-4 (3)

555//

According to me this doesnt follow logical purvanga.

Many play this korvai and also justify that the ending kaarvai is a standalone which somehow i am not able to accept.

Mannarkoil J Balaji.

[Christian Kenit Ram]

^

Thanks a lot for your reply , Sir !

[shankarank]

Here is a single Avarta kOrvai , I made up based on caturaSra triSram type syllable formation, but it doesn't quite get into that naDai. Just the first phrase( pUrvAnga) is made using that.

Warning: It has negative adjustments of kArvai at the end of the first phrase.

2 - kaLai - one Avarta:

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|| ta,,din ,,din,   ,tata, ,din,,   din,,ta kata,,   din,,di tam,,,  |  ,,,ta digiNatom   tam,,, ,,,ta   digiNatom tam,,,    ,,,ta digiNatom || ta,,din ,,....

The adjustment is that I robbed the two mAtra kArvai to just make it "di" for the second din in the last repetition of the pUrvangA phrases.

Now I made a slight variation to the above to hide the adjustment, but still that now it looks instead it has a positive adjustment, but the pUrvanga ending now merges with uttarAnga. So hard to tell.

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|| ta,,din ,,ditam   ,tata, ,din,,   ditam,ta kata,,   din,,di tam,,,  |  ,,,ta digiNatom   tam,,, ,,,ta   digiNatom tam,,,    ,,,ta digiNatom || ta,,din ,,....

Now is the second considered regular or still adjustment?

It is somewhat like this : https://en.wikipedia.org/wiki/Waterfall_(M._C._Escher)

pUrvangam looks like it has been completed, but uttarAngam already began at the last tAm of pUrvAnagam and looks right!

[shankarank]

Above seems to be nothing unusual when I heard some kORvais where damaruka yati type formation is used. A phrase reduces to lowest pattern and the second part takes off from the last reduced pattern to build up again. The middle part bridges both.

[shankarank]

As a tribute to SrI Murthy Mama on his kanakabhishekam year:

https://youtu.be/-KmhTeKWXdg?t=5082

In the above concert he takes the kOrvai explained by Sri Balaji (https://youtu.be/mzanBWsf6ko?t=1081) , starts with using 5 as the factor as explained, executes it , then in next round advances by 2 beats ( or one 2 kALAI beat) starts from vIccu (wave) , makes it 6 based. 3 extra with 6*3, 2 extra for 6*2 and 3 extra for last 6*3 fast flourishing finish. Continues to do 7 , 9 and also 10 I suppose.

Just a patterned lesson ( as mentioned by one of his disciples) becomes full wholesome performance.

[shankarank]

Correction: In the above there is no 10. The last one is from half samam - 8 + 16 - 24 aksharas. So after the pURvAnga which goes for 6 aksharas ( 24 mAtras) , the remaining is 18 - which is executed with 9 as the factor.

18 * 4 = 72 mAtras = (9*3) + (9*2) + (3*9)

[shankarank]

Now more on this pUrvAngam and what can be done without any adjustments:

| ta,,din ,,din, ,tata, ,din,, din,,ta kata,, din,,din ,,, |

Above in 2-kaLai is 27+3 = 30 , leaving a reminder of 34.

34 is of course easy to handle in many ways 5, 5(2) 5, 5 (2) 5,5 using takitathom, tadiginathom tam, formation. Next in the same line one can do 8,5,8,5,8 tadi,taditAkitathom dintAngu and so on.

But I was thinking of ways to see , just like the pUrvangam which has prefixes that progress arithmetically , if anything like that is possible here to add to go beyond this formulaic approach of finding nearest multiples of 3 with even reminders.

Even reminders allow you to add intervals , which is only possible twice as they are in between the thrice repeating same pattern. And hence sum of the intervals spaces have to be an even total.

On possibility arose with 27 + 7 - with 7 reminder, an odd number. If I did prefixes starting with 1 , then can I do 1, 2, 4 as prefixes in the uttarAngam? 1, 2, 4 form a geometric progression for which you cannot start with 0. pUrvangam starts with nothing and adds a 'ta', and 'taka' as prefixes to the same repeating pattern. As prefixes they do sound out as separate entities and hence can be considered separately from the thrice repeating pattern itself. Otherwise people can project that the total ( prefix + pattern ) progresses arithmetically.

The latter question is important , since if we treat prefixes as their own separate entities, can they then have their own progression which could be geometric?

Common progression in prefixes heard are nothing (0) , ta, taka OR nothing (0) , taka, takathiku - things like that.

Now if geometric progression is allowed on prefix alone , like ta, taka, takathiku then we have many nice possibilities , especially when combined with intervals who sum is even.

So you can have just a 7 reminder handled. Or 7+4 where 4 is handled as 2 & 2 as intervals. 7 + 6 and so on. So multiples of 3 that leave many odd valued reminders have a new leash of life!

Is this something new or already in practice? Would like to know.

So in this case for the reminder of 34 mAtras , we can have 27 + 7 where it is 1,9, 2, 9 , 4 9 with 1, 2, 4 as prefixes.

If we also add interval into the mix we will have :

1 , 7 , 3 , 2, 7, 3 , 4, 7 where 7 is thrice repeating pattern , 3 is the two interval spaces and 1, 2, 4 form the prefixes, executed with their own emphatic sollus.

For 3 rounds we can add using a 6 and a 5 pattern:

For 6 : 1, 6, 3, 2 , 6, 3-3 , 4, 6 - where now the interval itself has it's own arithmetic progression 3, and then 3,3. Possible? Aesthetic?

For 5 : 1, 5, 3-3 , 2, 5, 3-3, 4, 5

So the patterns with 5, 6, 7 can be done in each of the 3 rounds of the kOrvai.

Welcome comments from experts!

[shankarank]

This sollukaTTu from Sri T.K Murthy staple, https://youtu.be/_ORCuoow6vY?t=2732

in 8 syllables per beat reckoning - dRta kalam.

tha,,, thakuthari kiTataka jikuthari kiTataka tha,tha, kiTataka takataki TathI,ngu dhin,ta, dhIm,,, ,,,,

The beauty and punch is in the split of the 8 as takataki TathI,ngu -> 5 + 3.

He starts with a 20 syllable pattern, tha,,, thakuthari kiTataka jikuthari kiTataka, adds a 8 tha,tha, kiTataka and finishes with 5 +3 and 4 (dhin,ta, )

I tried to find a progressively decreasing pattern with this type of phrases and arrived at another 1 Avarta kORvai.

I used a kanjira phrase kitataka dhom,kiTa dhon,ta, tarikiTa as the 16 base pattern to construct the kOrvai.

I made a start phrase of 20 using the tha,,, and the above 16.

tha,,, kitataka dhom,kiTa dhon,ta, tarikiTa dhom,kiTa dhon,ta, tarikiTa dhon,ta, tarikiTa dhon,ta, kiTAdhon,

takiTAdhon ,kiTAdhon ,gudhom, dhin,ta, | dhim,,, ,,dhin, ta,dhim, ,,,, dhin,ta, dhim,,, ,,ta, dhim,,, |

,,ta, dhim,,, ,,ta, dhim,,, ,,ta, dhim,,, ta,dhim, ,,ta, || dhim


So in a total of 128 syllables ( 1/2 matras) the math splits like this

20, 12, 8 , 6, 5, 4, 3,2 (60) - then 10, 10, 10 (30), 8, 8, 8 (24) , 6, 6, 2 (14) - the second part arudhi total 68.

20, 12, 8 , 6 is to be viewed as the decrement amount reduces geometrically - reduce by 8, then by 4, then by 2 and remain constant as 1 for the next 4 steps (this latter one within human limits ).

[shankarank]

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That is like a tornadic whirl wind (cuzhal kATRu) , I am going to have it named - pracaNDa mAruta yati or cakravAta yati.

See: https://www.learnsanskrit.cc/translate? ... ado&dir=es

[shankarank]

Now to make it the normal arithmetic reduction, if we add a 16 in between 20 & 12

20, 16, 12, 8 , 6, 5, 4, 3,2 (60) - then 8, 8, 8 (24), 6, 6, 6 (18) , 4, 4, 2 (10) - the second part arudhi total 52.


tha,,, kitataka dhom,kiTa dhon,ta, tarikiTa kitataka dhom,kiTa dhon,ta, tarikiTa dhom,kiTa dhon,ta, tarikiTa dhon,ta, tarikiTa dhon,ta, kiTAdhon, |

takiTAdhon ,kiTAdhon ,gudhom, ta,dhim, ,,,, ta,dhim, ,,,, ta,dhim, | ,,,, ta,dhim, ,,ta, dhim,,, ta,dhim, ,,ta, dhim,ta, dhim,ta, || dhim

It turns out 68 (from before) which is equivalently 34 full matras in normal syllables is 3 short of 36 = 3*12 - where 12 can be resolved as 5+4+3 . With a remainder of 2 ( 36 - 2) if the phrase formation for the last part is made ending with a dhim,,, (dhim, =2 in normal resolution) then it can be executed as 5*3 , 4*3 and 3*3 - 2 or (3, 3, 1) full matras.

Same way for 52 - which 26 in normal resolution is 1 away from 27 = 3*9. 9 can be resolved as 4+3+2. So we need a phrase formation that ends with a dhim, ( or simply dhim = 1 in normal resolution) for the last part.. It can then be executed as 4*3, 3*3 , 2*3 - 1 or (2, 2, 1).

Now technically if you want this arudhis to be played in any order like (3, 4, 5) or in the case of 26 as (2, 3, 4) it can be done.

For 34 - we need to ensure that all 3 patterns have a dhim, (2) ending in normal resolution of full matras.

For e.g for 3, 4, 5 order it will be 3*3, 4*3 , then 5*3 -2 as ( 3+2, 3+2, 3). Remainder 2's dhim, falls on samam and belongs to next cycle of the taLam.

You have to chose something like dhin,,, tha,,, thom or tarikiTa tarikiTa thom (4, 4, 2 = 10 this in half mAtras dRta kalam as notated in kOrvai).

For 26 - all 3 need to have a dhim (1) ending.

For e.g 2, 3, 4 order : 2*3, 3*3, 4*3-1 the last one as (3+1, 3+1, 3). The last dhim finishes on samam and belongs to next cycle of the tALam.

[shankarank]

!!!Correction!!!: The total on paranthesis above needs to be 76 when 16 is added : 20, 16, 12, 8 , 6, 5, 4, 3,2 (76)

Also this regular actually reduces by 4 each step and as numbers dwindle to switch to reduce by a lesser amount 2 ( and then 1 in above case) , is followed in many kOrvais, especially the famous kOrvai of SrI Harishankar recently discussed in this video by SrI Nerkunam Sankar: https://youtu.be/9QKu38ZZgLc?t=1394

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This more closer to a funnel with a linear edge that then slants more vertically. Can be named puTaka yati!

These are special cases of gOpuCCa yati.

[shankarank]

The next one : 5*6 + 5*4 + 5*3 + 5*2 = 30+20+15+10 = 75. ...............
.....................
5 *6, 5*4 an arithmetic reduction. 5*3, 5*2 is the geometric reduction of the first pair ( i.e. (6,4) -> (3,2) ). So it is a hybrid (arithmeto-geometric) reduction

https://youtu.be/oHt_COwOgIk?list=RDoHt_COwOgIk&t=5029

SrI Vellore is using this in the kOrvai that follows the mohra to end the tani.

75, 15, 4, 15, 4, 15 = 128 - 4 Avartanams in 1-kALai. The tALam for Gayati vanamali rendered in madyama Sruti Hamsadvani is 1-Kalai going by the hearing of taps , as well as the length of the sAhitya lines. The video description has it as 2-kaLai.

[shankarank]

This sollukaTTu from Sri T.K Murthy staple, https://youtu.be/_ORCuoow6vY?t=2732
in 8 syllables per beat reckoning - dRta kalam.
tha,,, thakuthari kiTataka jikuthari kiTataka tha,tha, kiTataka takataki TathI,ngu dhin,ta, dhIm,,, ,,,,

Based on the konnakkOl rendering, in dRtha kAla ( 128 solfas per avarta of 2 - kaLai Adi)

tha,,, thakadhina kiTathaka thakuthari kiTathaka (20) tha,tha, kiTataka (8) thaguthagu dhin,,gu (8) dhin,tha, dhin,,, ,,,,(48) repeated thrice.

It has 3 sections followed by a arudhi phrase dhin,tha, dhin,,, ,,,,. The way it said , I thought the second 8 thaguthagu dhin,,gu (8) is 5 + 3, but they seem to say it as 4 and 4 only. I have heard another kOrvai with a different measure for this ( there is a additional tharikitataka in between the two 8(s) in the latter), where the second 8 is split as 5+3.

So 48 + 48 + 48, then one section of 20 removed , 28+ 28, then another section of 8 removed , 20 + 20, the second 8 removed 12 + 4. The last bit removes the kArvai and ends on samam as it is the arudhi phrase as 4. i.e dhin,tha, dhin,,, ,,,, is 4 + 8, where dhin,,, ,,,, is gone with the samam.

48 + 48 + 48 + 28 + 28 + 20 + 20 + 12 + 4 = 256 ( two avarthAs of 2-kaLai Adhi tAlam in dRta kAla sollus).

So while the first pattern is repeated thrice , the subsequent smaller patterns after removing sections are repeated only twice , where the last remaining arudhi phrase goes once fully and the second time with karvai merged with the samam (4).

So how do we understand the structure of this kOrvai?

This can be understood as a structure similar to an arudhi or tIrmaanam. Where a pattern with sections strung together is reduced and the reduced patterns are repeated twice.

Actually from a sound experience all patterns are repeated thrice!!!

The twice repetition is considered a continuation of the previous to make it thrice, where there is a presence of this smaller pattern in the prior bigger pattern. Many simple trivial tIRmAnams are executed in this style. I will provide examples in a separate post.

Reminds one of fractal patterns, or Upanishadic statement ( aNOraNIyAn , mahatO mahIyAn), incorporated by SrI Purandara dAsa in his JagadhodhAraNa kiRtanam or Thirumandiram that has the same verses in tamizh.

Here the only remarkable thing is , the rounds of reduction continue for three cycles, -20, -8, -8 and is made to appear like a giant kOrvai.

Now about the pattern itself , how the sections are made:

tha,,, thakadhina kiTathaka thakuthari kiTathaka (20) tha,tha, kiTataka (8) thaguthagu dhin,,gu (8) dhin,tha, dhin,,, ,,,,(48)

One 20, 2 8(s) = 16, and you could say for the last section 3 4(s) = 12.

And the contrasting starts in each pattern:

20 - starts with a dhIRga viSranti (silence) tha,,,

Next 8 starts with two shorter syllables - tha, tha, providing a contrasting stress progression

Next 8 - has the maximum short syllables thaguthagu.

Final arudhi phrase brings in mellinam (softer consonant solfa).

So that sums up the marque kOrvai of SrI T.K. Murthy Mama.

[Nick H]

Amazing analysis and understanding.

This week, I was baffled by this simple thing. Medicine timing, working from first dose at waking to last at bedtime. find the times of other doses.

I kept either coming to one-too-many doses, or not arriving at samum (bedtime). I was staring at my errors, thinking, this is so simple, why can't I do? No wonder I was thrown out of maths class as a hopeless case!

After two days of rough estimation, a brain cell went ping: divide by the intervals, not the number of doses. Count the karvais, not the beats.

So, who knows... I might live long enough to understand something more than the simplest of korvais! (but probably not if it has mixed nadais!)

Still... at least I can enjoy the music of a korvai even if I will never get the maths.

And the ability of musicians and rasikas will always impress and inspire me.