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
- Numbers have fascinated man for millennia.
- India’s contributions in this area is mammoth in general.
- It is therefore unsurprising that Indian rhythm has led the way in world music when it comes to musical mathematics.
- Even between Indian’s two major classical systems, Carnatic culture stands out for not just rhythmic virtuosity but in its sophisticated approach towards structured mathematical patterns.
- Level I: Any number taken after appropriate units after samam to end as required. Ex: (3+3, 5+3, 7)x3 after 1. My very first attempt at a korvai at age 5…
- Level II: Taken from samam to end at samam with 1 or 2 karvais between patterns to fill out the remaining units (in say 32/64/28/40 units in Adi 1/2 kalais, Mishra chapu/Khanda chapu etc)
- Level III: Same as II but to end a few units after or before samam.
- Level IV: Same as I or II but with different gatis thrown in.
All these can be termed as man-made korvais
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.
- In other words, these do not have remainder of any number of units not divisible by 3 (like 2 or 4) which have to be patched up as 1 or 2 karvais it in between patterns. These have a grace or sophistication in the numbers that are obvious only when one is inspired.
- Intellectually, they require multi-layered thinking rather than just conventional approaches.
Some of them involve precise and logical patterns but not found in mathematical text books.
I literally stumbled upon most them as some of them are not accessible through intuitive methods.
- A couple of them have been in vogue for decades – 6, 8, 10 (or 8+8+8) as first part then 3×5, 2×5, (1×5) x3.
Typically, they are in one gati though there are exceptions (but overuse of multiple gati will make it a different concept.)
ADI 2 kalais = 64 units
Challenges: To get 3 khandams (3×5) in Part B, Part A has to be 49. Similarly, for 3×6, 3×7 or 3×9 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 5×3 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 5×3 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=7×3.
(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
A=2,2,3 + 7×1; B=2,3 + 7×2; C=3 + 7×3(tishra gati)
4. Progressive in second part: A= 6, 6, 6; B = (3×9) + (2×7) + (1×5). 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)+5×1;
C = (7x3karvais)+(7x2karvais)+7×3
6. 3-speed korvais (example for 4 after samam):
(A=7, 2+7, 4+7; B=9×3)x3 karvais;
(A=7, 2+7, 4+7; B=9×3)x2 karvais;
A=7, 2+7, 4+7; B=9×3
(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, (3×5)x3; 6+2, 5+2, 4+2, 3+2, (2×7)x3; 6+2, 5+2, 4+2, 3+2, (1×9)x3
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: 7×1, 6×2, 5×3, 4×4. 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= 6×2, 5×3, 4×4; B = 7×3
(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 7×1, 6×2, 5×3, 4×4, 5×3, 6×2 and B= 3 mishrams C= 3×10 (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
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= [fusion_builder_container hundred_percent=”yes” overflow=”visible”][fusion_builder_row][fusion_builder_column type=”1_1″ background_position=”left top” background_color=”” border_size=”” border_color=”” border_style=”solid” spacing=”yes” background_image=”” background_repeat=”no-repeat” padding=”” margin_top=”0px” margin_bottom=”0px” class=”” id=”” animation_type=”” animation_speed=”0.3″ animation_direction=”left” hide_on_mobile=”no” center_content=”no” min_height=”none”][(5+2), (4+2), (3+2)] + (3×5); B = [(5+2), (4+2), (3+2), (2+2)] + (3×7)
C = [(5+2), (4+2),(3+2), (2+2), (1+2)] + (3×9).
[( 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 + (1×5)x3
B = (6+3)x2 + (2×7) x 2
C = (4+3)x1 + (3×9) 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 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)] + (3×5), B = [(5+2), (4+2), (3+2), (2+2), (1+2)] + (3×8), C = [(5+2), (4+2), (3+2), (2+2), (1+2), (0+2)] + (3×11).
[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 + (1×5)x3 (Can be rendered as G, R, GRSN DPD N,, – GRSND in a raga like Vachaspati)
B = (9+3)x2 + (2×7) x 2
C = (7+3)x1 + (3×9) 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= 7×3] (To be rendered 3 times or change B as 5×3, 7×3 and 9×3 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
[(5×4)+1]x3, [(4×4)+1]x3, [(3×4)+1]x3, [(2×4)+1]x3, [(1×4)+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)] + (3×5), B = [(5+2), (4+2), (3+2), (2+2)] + (3×9), C = [(5+2), (4+2), (3+2), (2+2), (1+2)] + (3×13).
(The 3x(5/9/13) can be rendered as just 3×5 all 3 times. Or as 3×9, 3×13, 3×17 etc.
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.. + 3×5).
1. Simple progressive: A few years ago, I had introduced
A = 2, 3, 4, 5; B = 6×3.
(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:
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 = (3×5) x3; B= (2×6)x3; C = (1×7) 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 = (6×3 + 5×3)x3; B = (6×3 + 5×3)x2
C = (6×3 + 5×3)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;
(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 + 3×5)
C = [6, (2+6), (4+6)] D = (7 x 4 karvais + 3×7)
E= [6, (2+6), (4+6)] B = (9 x 4 karvais + 3×9)
Note: A, C and E can be any combination divisible by 12
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 = (4×5) + (3×7) + (2×9); 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
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.
- It now would be obvious that anyone can create seamless korvais with the thinking and methods I have shared.
- I have used mostly familiar sounding easy patterns to create these, mainly with melodic aesthetics in mind
- I have shown only a few small samples here, even from the ones I have discovered/presented. Pure rhythmic seamless korvais can deal with typical patterns suited for percussion.
- This is a vast exciting new world with tremendous scope to expand the horizons both melodically and rhythmically.
- Each door I’ve opened leads to exhilarating worlds…