Seamless Korvais - The Elegance of Numbers

Learn about some intricate ways to form korvais or rhythmic patterns from this recorded session at The Music Academy presented by Sangita Kalanidhi Chitravina N Ravikiran

SeamLess Korvais Part 1

SeamLess Korvais Part 2

Transcript

Prelude

Korvais

All these can be termed as man-made korvais

Natural Korvais - Seamless Elegance

Seamless korvai – DEFINITION: Patterns (of usually two or more parts) from samam to samam/landing point of song that do not have remainder indivisible by 3 in talas or landings indivisible by 3.

Typically, they are in one gati though there are exceptions (but overuse of multiple gati will make it a different concept.)

 

Seamless korvais – amazing options

ADI 2 kalais = 64 units


Challenges: To get 3 khandams (3x5) in Part B, Part A has to be 49. Similarly, for 3x6, 3x7 or 3x9 in B, we need A to be 46, 43 or 37, none of which is divisible by 3. So, simple approaches will not work.

1. Simple progressive: These are most obvious types.
Ex 1: 7+3 (karvais), 6+3….. 1+3 as first part (A) and 5x3 as the second part (B).
(srgmpdn s,, rgmpdn s,, gmpdn s,, mpdn s,, pdn s,, dn s,, ns,,) as A and
(grsnd rsndp dpmgr) as B

Ex 2: 7+2…0+2 as A and B is 5x3 in tishra gati. (A can also be in srotovaha yati)
(srgmpdn s, rgmpdn s, gmpdn s, mpdn s, pdn s, dn s, ns, s,) as A and (grsnd rsndp dpmgr) as B in tishra gati.

2.Progressive with addition in multiple parts:
A= (2,3,4)+(2,3,4,5)+(2,3,4,5,6); B=7x3.
(s, ns, dns,) + (s, ns, dns, pdns,) + (s, ns, dns, pdns, mpdns,) as A and (g,r,snd r,s,ndp d,p,mgr) as B

3. Inverted progression in 3 parts:
A=3,3,3 + 5X1, B= 3,3+7X2, C= 3+9X3
(g,, r,, s,, + grsns) as A and( r,, s,, + g,r,sns r,s,ndn) as B
and (s,, + g,r,grsns r,s,rsndp d,p,dpmgr) as C

Another example:
A=2,2,3 + 7x1; B=2,3 + 7x2; C=3 + 7x3(tishra gati)

4. Progressive in second part: A= 6, 6, 6; B = (3x9) + (2x7) + (1x5). Impressive when B is rendered 3 times with A alternating between the 9, 7 and 5s.

( gr,s,, rs,n,, sn,d,,) + (g,, ,,, r,, ,,, g,, r,, s,, n,, d,, r,, ,,, s,, ,,, r,, s,, n,, d,, p,, s,, ,,, n,, ,,, s,, n,, d,, p,, m,,) first time

then (gm,p,, mp,d,, pd,n,,) + (g, ,, m, ,, p, d, p, m, ,, p, ,, d, n, d, p, ,, d, ,, n, s, n,) as second time

and (gr,s,, rs,n,, sn,d,, ) +( grsnd rsndp dpmgr) as third time

5. Progressive in each part:
A = (5x3karvais)+(5x2karvais)+5x1;
B= (6x3karvais)+(6x2karvais)+6x2
C = (7x3karvais)+(7x2karvais)+7x3

6. 3-speed korvais (example for 4 after samam):
(A=7, 2+7, 4+7; B=9x3)x3 karvais;
(A=7, 2+7, 4+7; B=9x3)x2 karvais;
A=7, 2+7, 4+7; B=9x3
(g,, ,,, r,, ,,, s,, ,,, ,,, s,, n,, g,, ,,, r,, ,,, s,, ,,, ,,, d,,n,,s,,n,, g,, ,,, r,, ,,, s,, ,,, ,,,) as A and (g,, ,,, r,, ,,, g,, r,, s,, n,, d,, r,, ,, s,, ,, r,, s,, n,, d,, p,, s,, ,,, n,, ,,, s,, n,, d,, p,, m,,) as B;
(g, ,, m, ,, p, ,, ,, p, m, g, ,, m, ,, p, ,, ,, n,d,p,m, g, ,, m, ,, p, ,, ,, ) as A and (g,m,g,m,p,d,p, m,p,m,p,d,n,d, p,d,p,d,n,s,n,) as B;
(g,r,s,, sn g,r,s,, dnsn g,r,s,,) as A and (g,r,grsnd r,s,rsndp d,p,dpmgr) as B

Another example, employing second part progression also (samam to samam):
6+2, 5+2, 4+2, 3+2, (3x5)x3; 6+2, 5+2, 4+2, 3+2, (2x7)x3; 6+2, 5+2, 4+2, 3+2, (1x9)x3

Seamless korvais – dovetailing patterns

The beauty of these are part of A will dovetail into B in a seamless manner.

(a) G,R,S,, R,S,N,, - G,R,SND - GR,S,, RS,N,, - GR,SND - GRS,, RSN,, - GRSND RSNDP SNDPM
(b) GR, S, N, S,,, R,,, - GRSND – R,SN, S,,, R,,, - GRSND – SN, S,,, R,,, - GRSND RSNDP SNDPM
(c) G,,,,, R,,,,, G,, R,, S,, N,, D,, - G,,, R,,, G, R, S, N, D, - G,R, GRSND RSNDP SNDPM
(d) G,,, R,,, S,,, N,,, D – GRSND – R,, S,, N,, D,, P – RSNDP – S,N,D,P,D - GRSND RSNDP SNDPM

It would be obvious that some are 13+5, 13+5 and 13+(3 times 5) in various ways. If song starts after +6, various manifestations of 15+5, 15+5 and 15+(3 times 5) can be created.

Let’s look at the sequence of numbers: (a) 7, 12, 15, 16….
(b) 6, 10, 12, 12... What are the next numbers?

Typically, these are not part of general math textbooks and do not make sense to most mathematicians. But they are fine examples of how Carnatic music can transcend science and math. Remarkably, the series will turn back on itself. I call these Double layered progressive sequences which boomerang. The first few numbers are formed using multiplication progression in (a) are: 7x1, 6x2, 5x3, 4x4. Thus, the next few numbers are 15, 12 and 7. Similarly, in (b), they are 10 and 6.

An example of a korvai with this: A= 6x2, 5x3, 4x4; B = 7x3
(Ta….. Ki…..), (Ta,,,, ki,,,, ta,,,,) , (Ta,,, ka,,, di,,, mi,,,) as A and (Ta.di.kitatom Ta.di.kitatom Ta.di.kitatom ) as B

Another ex: A= 7, 12, 15, 16, 15, 12 or 7x1, 6x2, 5x3, 4x4, 5x3, 6x2 and B= 3 mishrams C= 3x10 (which can be said as ta.. Ti.. Ki ta. Tom (to give an illusion of 7)

(g,,,,,, r,,,,,s,,,,, n,,,,d,,,,p,,,, m,,,g,,,r,,,s,,, r,,g,,m,,p,,d,, m,p,d,n,s,r,) as A and (g,r,snd r,s,ndp p,d,nsr) as B and
(g,,r,,sn,d r,,s,,nd,p s,,n,,dp,m ) as C

The concept of Keyless korvais

At times, one stumbles upon korvais with no apparent mathematical relationship. These cannot be logically deciphered or developed by locking on to their key (usually the average of their various parts/2nd repeat out of 3). Yet, these are elegant beyond words in their simplicity.

1. A 3-part korvai over 2 cycles (128 units): A stunning set of patterns found in nature.

A= [(5+2), (4+2), (3+2)] + (3x5); B = [(5+2), (4+2), (3+2), (2+2)] + (3x7)
C = [(5+2), (4+2),(3+2), (2+2), (1+2)] + (3x9).

[( gmpdn s,) (mpdn s,) (pdn s,)] + grsnd rsndp sndpm as A
[( gmpdn s,) (mpdn s,) (pdn s,) (dn s,)] + (g,r,snd r,s,ndp
d,p,mgr) as B and
[( gmpdn s,) (mpdn s,) (pdn s,) (dn s,) (n s,)] + (g,r,grsnd
r,s,rsndp d,p,dpmgr) as C

2. A 3-part Korvai in 3 speeds: The amazing aesthetics of this is mind-boggling – simple when rendered but looks a jungle of numbers when expressed as below!

A = (8+3)x3 + (1x5)x3
B = (6+3)x2 + (2x7) x 2
C = (4+3)x1 + (3x9) x1

(Ta.. … Di.. … Ta.. Ka.. Di.. Na.. Tam.. … …) + (Ta.. Di.. Ki.. Ta..tom.. ) – A

(Di. .. Ta. Ka. Di. Na. tam. .. ) +( Ta. .. Di. .. Ki. Ta. Tom. Ta. .. Di. .. Ki. Ta. Tom.) – B

( Takadina Tam..) +( Ta.di.tatikitatom Ta.di.tatikitatom Ta.di.tatikitatom) - C

Keyless korvais extensions to other talas

Keyless methods give scope to execute amazing finishes in seemingly impossible situations. For instance, a tala like Khanda Triputa @ 8 units per beat (72 units) or Rupakam, which is already divisible by 3, can hardly offer scope for a samam to + 2 or + 4 finish… Let’s look at a couple of aesthetic solutions.

1. Khanda triputa – samam to +2 (out of 8) in 2 cycles
A= [(5+2), (4+2), (3+2), (2+2)] + (3x5), B = [(5+2), (4+2), (3+2), (2+2), (1+2)] + (3x8), C = [(5+2), (4+2), (3+2), (2+2), (1+2), (0+2)] + (3x11).

[Takatakita tam. Takadina tam. Takita tam. Taka tam.] + (Tadikitatom Tadikitatom Tadikitatom) – A

[Takatakita tam. Takadina tam. Takita tam. Taka tam. TaTam.] + (Tadi . Ki . Ta . tom Tadi . Ki . Ta . tom Tadi . Ki . Ta . tom ) - B

[Takatakita tam. Takadina tam. Takita tam. Taka tam. TaTam. Tam.] + (Ta di .. Ki.. Ta.. Tom Ta di .. Ki.. Ta.. Tom Ta di .. Ki.. Ta.. Tom ) - C

2. A 3-part Korvai in 3 speeds for same landing as above

A = (11+3)x3 + (1x5)x3 (Can be rendered as G, R, GRSN DPD N,, - GRSND in a raga like Vachaspati)
B = (9+3)x2 + (2x7) x 2
C = (7+3)x1 + (3x9) x1

A = (g,, ,,, r,, ,,, g,, r,, s,, n,, d,, p,, d,, n,, ,, ,,) +( g,, r,, s,, n,, d,,)
B = ( r, ,, g, r, s, n, d, p, d, n, ,, ,, ) + (g,,, r,,, s, n, d, r,,,s,,,n,d,p,)
C= (grsndpd n,,) + (g,r,grsnd r,s,rsndp s,n,sndpm)

3. Khanda triputa – samam to +3 (out of 8)
[A= 7+3 (karvais), 6+3…..1+3, 0+3 B= 7x3] (To be rendered 3 times or change B as 5x3, 7x3 and 9x3 each time etc).
A= Takadimitakita tam.. Takadimitaka tam.. Takatakita tam..
Takadina tam.. Takita tam.. Taka tam.. Ta tam.. Tam..)
B = (Ta.di.kitatom Ta.di.kitatom Ta.di.kitatom )

4. Mishra Chapu: Samam to -1
[(5x4)+1]x3, [(4x4)+1]x3, [(3x4)+1]x3, [(2x4)+1]x3, [(1x4)+1]x3 (for landings like Suvaasita nava javanti in Shri matrubhootam)
(Ta…. Di…. Ki…. Ta…. Tom Ta…. Di…. Ki…. Ta…. Tom Ta…. Di…. Ki…. Ta…. Tom ),
(Ta... Di... Ki… Ta… Tom Ta... Di... Ki… Ta… Tom Ta... Di... Ki… Ta… Tom ),
(Ta.. Di.. Ki.. Ta.. Tom Ta.. Di.. Ki.. Ta.. Tom Ta.. Di.. Ki.. Ta.. Tom),
(Ta. Di. Ki. Ta. Tom Ta. Di. Ki. Ta. Tom Ta. Di. Ki. Ta. Tom) ,
(Tadikitatom Tadikitatom Tadikitatom )

5. Roopakam: Samam to +2
A= [(5+2), (4+2), (3+2)] + (3x5), B = [(5+2), (4+2), (3+2), (2+2)] + (3x9), C = [(5+2), (4+2), (3+2), (2+2), (1+2)] + (3x13).
(The 3x(5/9/13) can be rendered as just 3x5 all 3 times. Or as 3x9, 3x13, 3x17 etc.

Seamless korvais for other talas

ADI 1 kalai (32 units)

Most korvais in this smaller space require patch work. Some of the most famous ones are even mathematically incorrect. (ta, tom… taka tom.. Takita tom.. + 3x5).

1. Simple progressive: A few years ago, I had introduced
A = 2, 3, 4, 5; B = 6x3.
(Tam. TaTam. TakaTam. TakiTaTam.) – A
(Tadi.kitatom Tadi.kitatom Tadi.kitatom ) - B

ADI 1 kalai (32 units)

2.Single part apparently wrong but actually correct korvai:


GR,-GRS,-GRSN,-GRSNP,-GRSNPG,-GRSNPGR
Typical hearing will make it seem like 1+2 karvais… 5+2 karvais and final phrase illogically being 7. In reality, it is 2+1, 3+1…6+1 ending in 7.

ADI 1 kalais = 32 units

3. An elegant solution in 3 cycles for songs starting after 6 (34 units/cycle)

A = (3x5) x3; B= (2x6)x3; C = (1x7) x3
(G,, r,, s,, n,, d,, r,, s,, n,, d,, p,, d,, p,, m,, g,, r,,) – A
(g, m, ,, p, d, p, m, p, ,, d, n, d, p, d, ,, n, s, n,) – B
(gr,,snd rs,,ndp dp,,mgr) - C

4. Several other progressive solutions work beautifully for samam to songs starting after 6:
7+7 (karvais), 6+7….2+7 +1 (landing on the song)

The same one can be rendered with 6 karvais for songs starting on samam.

5. A simple 3-speed solution for 6 after samam:
A = (6x3 + 5x3)x3; B = (6x3 + 5x3)x2
C = (6x3 + 5x3)x1

6. A progressive 3-speed korvai for 6 after samam:
(7+7+3; 5)x3 karvais; (GR,S,N, DP,D,N, S,, - GRSND)X3
(6+6+3; 5)x2 karvais;

5+5+3; 5,5,5
(G,, r,, ,,, s,, ,,, n,, ,,, + d,, p,, ,,, d,, ,,, n,, ,,, + s,, ,,, ,,, ; g,, r,, s,, n,, d,,) for the first part
(g, r, ,, s, n, ,, + d, p, ,, d, n, ,, + s, ,, ,, ; g, r, s, n, d, ) for second part
(grsn, + dpdn, + s,,) ; grsnd rsndp dpmgr for third part

Roopakam from samam to +3
A= [6, (2+6), (4+6)] B = (5 x 4 karvais + 3x5)
C = [6, (2+6), (4+6)] D = (7 x 4 karvais + 3x7)
E= [6, (2+6), (4+6)] B = (9 x 4 karvais + 3x9)
Note: A, C and E can be any combination divisible by 12

Seamless korvais in other gatis

Just as many korvais for Adi can be extended to other talas, they can be extended to other gatis too. For instance, Adi - Khanda gati (double speed) = 80 units

Eg: GR, SN, DP, DN, S,, - G, R, SND – RS, ND, PM, P D, N,,- R,S | ,NDP – SN, DP, MG, MP, D,, - G | ,R,SND – R,S,NDP – S,N,DPM ||

But there are highly interesting possibilities which are original for this like the one I had presented in my solo concert at the Academy 2-3 years ago: A = (4x5) + (3x7) + (2x9); B= 5+7+9
(Ta… Ka… Ta… Ki… Ta… ) + ( Ta.. .. Di.. .. Ki.. Ta.. Tom..) + (Ta. .. Di. .. Ta. Di. Ki. Ta. Tom. ) as A

And (Tadikitatom Ta.di.kitatom Ta.di.Tadikitatom) as B

There is a lovely possibility in 3 gatis:
G,R, SN, S,, - GRSND (tishram)
GR, SN, S,, - G, R, SND (Chaturashram)
GRSN, S,, - G,R,GRSND – R,S,RSNDP – S,N,SNDPM

Seamless korvais with other approaches

I had remarked in a mrdanga arangetram about how most of our music is elementary arithmetic and why percussionists must focus on aesthetics once they have got the patterns right. This got me into thinking about experimenting with korvais that represent some other math concepts such as a couple below:

1. Fibonachi series:  Leonardo of Pisa, known as Fibonacci in 1200 AD but attributed to a much earlier Indian mathematician Pingala (450-200 BC). The series is any two initial numbers like 3, 4 which are added to get 7. Now, add the last two numbers (4+7) to get 11 and so forth. A korvai in that sequence (in say, Kalyani):
A = G,, - R,,, - G,R,SND – GRSNDPMGRSN – DN,R,, GM,D,, MD,N,,
B= G,R,SND – R,S,NDP – D,P,MGR

2. A simple korvai using squares of numbers as first part (3)2+(4)2+(5)2:
A= G,,R,,S,, - G,,, R,,, S,,, N,,, - G,,,, R,,,, S,,,, N,,,, D,,,,
B= 3 mishrams in tishra gati double speed.

Creating Seamless korvais

Happy exploring!!!

Laya Terms in Carnatic Music

Terminology

BACK TO LAYA

Learn the terminologies used in Laya in Carnatic Music such as Aksharas, Gatis, Kalais, Jatis and many other terms.

Avarta – a cycle of tala.

Akshara – Fundamental units that make up a tala. A tala can be expressed in terms of the number of Aksharas. Normally Adi tala would be considered to have 8 Aksharas. When no other details are specified, we assume that the Adi tala is in Chaturashra gati and rendered with 4 subunits in each Akshara.

 

Note that Aksharas are just measuring units for tala. An Akshara can carry any number of subunits within it , upon which depends the classification of the gati of the tala. A good analogy is just as one litre is a measuring unit for volume , an Akshara is a measuring unit for Tala. One litre could be a measurement for any liquid, water, milk or juice. Similarly the Akshara could contain a variety of subunits that represent a Tishra gati, Chaturashra gati, Khanda gati, Mishra gati or Sankeerna gati.

 

Subunits – The units contained within an akshara. These are erroneously referred to as ‘matras’ by some, but we will avoid that connotation in the interest of adhering to the original definition in musical treatises . The term ‘matra’ actually refers to duration of 4 Aksharas. It is not too relevant here, but we will adhere to the convention of referring to the subunits of Aksharas as ‘subunits’ and not ‘matras’.

 

Gati or Nadai – Pulse or gait of the tala. Gati is the Sanskrit term while ‘Nadai’ is the Tamil term and refer to the same entity.

The number of subunits within an Akshara determine the Gati or Nadai.

 

Number of Subunits ----------> Type of Gati or Nadai

4 or multiples of 4 ---------> Chaturashram
3 or multiples of 3 ---------> Tishram
7 or multiples of 7 ---------> Mishram
5 or multiples of 5 ---------> Khandam
9 or multiples of 9 ---------> Sankeernam

 

Kalai – The number of branches in a beat of a tala. Typically we might say a 2-kalai Adi Tala contains 16 Aksharas with 2 kalais in each beat.

 

 

JAti - Another attribute of a tala which determines the number of counts in the laghu of the tala. These can be one of 5 varieties,

• chaturashra jAti (4 counts)
• tishra jAti (3 counts)
• mishra jAti (7 counts)
• khanda jAti (5 counts)
• sankeerna jAti (9 counts)
jAti can also refer to a count which is any one of the numbers 3, 4,5, 7 or 9.

 

Jati – A rhythmic pattern represented by a ‘sol’. ( Rhythmic syllable)
Example:
A pattern of 3 could be represented by a Jati , ‘Ta ki ta’ .
A pattern of 5 could be expressed as Jati , ‘Ta ka ta ki ta’.

 

 

Yati – The progression of rhythmic patterns can be one of following:

• Sama or Pipilikam (Ants) – Constant progression like ants following one behind another.
• Gopuchham (cow’s tail) – Gradually tapering.
• Srotovaham (flow of river) – Gradually increasing.
• Mridanga ( following contours of a mridangam shape) – This is actually a Srotovaham + Gopucham -> small to big to small
• Veda Madhyamam or Damaru (following contours of a ‘damaru’ shape) – This is actually a Gopuchham + Srotovaham. -> big to small to big.
• Vishama – Random

 

kArvai – Silent space represented by a comma or dot in notation. Although silent, kArvais form the beauty of many rhythmic constructions and demand lot of practice to execute with precision and beauty.

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