Sarvalaghu(flow of rhythm) and Kanakku(arithmetic) in Carnatic music

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KavyaVriksha

8 min readFeb 7, 2020

In ‘the hidden maths in great art’, Marcus du Sautoy eloquently says “Art and mathematics. For many, this would appear to be synonymous with chalk and cheese. One is the domain of emotional expression, passion and aesthetics. The other, a world of steely logic, precision and truth. And yet scratch the surface of these stereotypes and one discovers that the two worlds have much more in common than one might expect.”

In Carnatic (South Indian Classical) music, the oft-debated rhythmic concepts of Sarvalaghu (seamless,steady flow,hidden math) vs Kanakku (calculated,rapids and pauses,explicit math) come to mind. It is like debating which type of painting resonates the most. The answer is of course, it depends.

Before we take a deeper dive into these two aspects from the perspective of percussion accompaniment in a Carnatic concert, let us first look at how they apply in the singing of svaras(musical notes). We are going to look at examples in :

musical compositions such as Varnams and Kritis (songs)
and improvisations such as Kalpana Svaras(on the spot singing or playing of svara patterns for a particular line of a song adhering to its underlying tala). It is referred to as multiple rounds of kalpana svaras since “a rhythmic meter in Carnatic music is called tala and each tala has certain total number of beats per cycle.”[8]

Sarvalaghu Patterns in Varnam Svaras

Varnams are a genre of compositions in Carnatic music that are usually learned in various ragas prior to learning kritis or compositions. They contain multiple sections of lyrics called Pallavi , AnuPallavi and Charanam similar to kritis; additionally, varnams contain sections with just svaras . The multiple lines of svaras after the charanam are called ‘ettukada svaras’.

“Sarvalaghu literally means all brief and Subbarama Dikshitar in the Sangita Sampradaya Pradarshini gives the heading of Sarvalaghu for such ettukada svaras in some of the varnams.”[5]

As you can see in the example below, the various patterns of Sarvalaghu svaras just flow without any pauses or breaks.

Source : Appendix of Subbarama Dikshitar’s Sangita Sampradaya Pradarshini English Translation

In most varnams, the first two ettukada svaras contain kaarvai(spacing or elongation of a particular svara to two or more subunits) while the third or sometimes the fourth ettukada svara has Sarvalaghu svaras, as seen above, with no elongations or gaps in between. [5]

You can check this out by listening to or looking at the notations of multiple varnams.

Listening to Sarvalaghu Svaras in Varnams

Abhogi raga varnam, tala Adi (in third ettukada svara)
Saveri raga varnam, tala Adi (in third ettukada svara)
Thodi raga varnam, tala Adi (in fourth ettukada svara)

Sarvalaghu Patterns in Kalpana Svaras

For percussion accompaniment David Nelson describes Sarvalaghu as `the shaping of time’, while Trichy Sankaran uses the term ‘flow patterns’ .[6]

In the varnam, the Sarvalaghu patterns we heard were created by the composer. In a concert, the artist improvises the multiple rounds of varying Sarvalaghu kalpana svaras in real time and these are also ‘flow patterns’ aligned with the melody of the song.

Multiple Carnatic music legends have spoken about how they have been greatly inspired by the Nadaswaram legend T N Rajaratnam Pillai. Radhika Balakrishnan explores this further in her research and states :”Nagaswaram Vidwan TN Rajatathinam Pillai (TNR) was known for his speedy sarvalaghu which showed not only high levels of spontaneity but also scholarship in their arrangement. He made a huge impact on all his contemporaries both instrumentalists and vocalists.”[2]

Listening to Sarvalaghu Kalpana Svaras

svaras in raga Abheri on the Nadaswaram, tala Adi , each cycle 8 beats
svaras in raga Kapinarayani, tala Desadi,each cycle 8 beats
svaras in raga Kharaharapriya, tala Mishra Chapu,each cycle 7 beats
svaras in raga Khamas, tala Adi 2 Kalai, each cycle 16 beats
svaras in raga Sankarabaranam, tala Adi 2 Kalai ,each cycle 16 beats
svaras in raga Kalyanavasantam, tala Khanda Chapu, each cycle 5 beats
svaras in raga Saramati on violin, tala Adi,each cycle 8 beats
svaras in raga Abheri on violin, tala Adi,each cycle 8 beats
svaras in raga Mohana Kalyani on flute and violin, tala Adi ,each cycle 8 beats

In this lecdem, Kunnakudi M Balamuralikrishna explains how converting the phrases, sung during a madhyama kala (faster tempo) alapana (improvisation) of a raga, into their equivalent svaras, results in Sarvalaghu pattern svaras :

Raga phrases and equivalent Sarvalaghu pattern svaras

Korvais in Syama Sastri’s Svarajathis

While Varnams frequently contain Sarvalaghu patterns, the landmark Svarajathis of Syama Sastri, that are renowned for capturing the quintessence of the raga, also contain intricate korvais (rhythmic patterns that are strung together) in their svaras.

Researcher Manju Gopal says : “ the application of laya korvais in the svarajatis is complicated. Set in misra chapu tala(each cycle 7 beats), the svarajatis in Yadukulakambhoji and Bhairavi consist of intricate rhythmic patterns formed by combining elongated svaras .”[Manju Gopal, Concept of laya and gamaka in syamasastri s compositions]

Amba Kamakshi Svarajathi in Raga Bhairavi
Kamakshi Svarajathi in Raga Yadukulakambodhi

Korvais in Kriti Chittasvaras

Kritis are musical compositions in Carnatic music that contain lyrics and can sometimes also include one or more lines of svaras called Chittasvaras.

These Chittasvaras can sometimes include rhythmic patterns or Korvais .

R Vedavalli shares this interesting example from one of Poochi Srinivasa Iyengar, 19th century composer’s renowned composition Saruguna Palimpa in Raga Kedaragowla set to Tala Adi 2 kalai(each cycle 16 beats) :
“For many of his kritis, he composed the chittaswaras himself. Several kritis have korvais for the chittaswaram, which are exquisite. For example, the Kedaragaula kriti, Saraguna palimpa, has an interesting chittaswara pattern. It is said that in those days, a korvai that is structured in threes was not in vogue; it would be in fours or twos.
In this kriti, Saraguna palimpa, the end of the chittaswaram has a pair of similarly constructed patterns, which is the same as in the beginning of the kriti — resulting in a korvai of twos in the swaram and one from the sahityam — thus making it a korvai of threes.
The pattern of chittaswaram and the beginning of the pallavi is described below.
RS, NDP | DP, MGR | Sa(1)Ra(2) Gu(1)Na(1)a(1)”[R Vedavalli, Sruti Magazine — A great lakshana vidwan]

So, the rhythmic pattern of the korvai repeats 3 times, twice via svaras and third time via starting lyric SaRaGunaa (syllables broken into Sa(1 subunit), Ra(2 subunits) Gu Na a(1 subunit each, hence the same pattern of 12111 subunits as the svara korvai).

It is much clearer when we listen to it:

Chittasvarams followed by Saraguna

This is a significant example because today, it is the established practice to repeat the korvai pattern three times to finish the multiple rounds of improvised kalapana svaras.

Blend of Sarvalaghu and additional patterns in Kalpana Svaras

Many artists blend multiple patterns including Sarvalaghu when singing kalpana svaras. These non-Sarvalaghu patterns can have elongations, kaarvai(pauses), intricate korvais(rhythmic patterns) and/or nadai changes (changes in gait) The overall goal still remains to not sacrifice the melody in the pursuit of more rhythmic complexity.

Listening to blended patterns in Kalpana Svaras

svaras in raga Saramati, tala Adi,each cycle 8 beats
svaras in raga Thodi, tala Jhampa, each cycle 10 beats, including Kuraippu(reduction) where svara length gets successively reduced to half from full avartana or 10 beats to 5 and so on
svaras in raga Vasantha, tala Ata, each cycle 14 beats,including Nadai or time signature changes
svaras in raga Varali, tala Adi, each cycle of 8 beats, including Nadai or time signature changes
svaras in raga Saranga, tala Khanda Chapu, each cycle of 5 beats, cross rhythm of svaras in chatusra (4) and other patterns for a tala that is in 5

Kanakku

Kanakku means arithmetic in Tamil. Robbert van Hulzen says “ While in Sarvalaghu patterns the calculations take the shape of syncopation as we know it in western music, which serves to emphasize the steadiness of the beat, in kanakkus the flow of the tala is broken by musical events that entirely ignore the pulse, and instead assume a pulse function themselves.”[1]

Many artists like to culminate the multiple rounds of kalpana svaras with a flourish by repeating a korvai three times. And, there is definitely math involved to ensure that this korvai fits into the total number of subunits of the tala cycles. When this complex arithmetic becomes front and center, the kannakku or math also becomes an adjective to describe the kalpana svaras !

In this lecdem, Kunnakudi M Balamuralikrishna first demonstrates how to create a korvai for a simpler scale based raga like raga Simhendramadyamam which permits resting on any of its notes :

Korvai in Raga Simhendramadhyamam, Mishra Chapu Tala, each Cycle 7 beats

On the other hand, it is much more complex to sing korvais for a raga like Begada because it is shaped by specific characteristic phrases; and these will need to be fitted within the mathematical boundaries of the korvai without losing their musicality. Kunnakudi M Balamuralikrishna demonstrates how a korvai can be created from the outline of the ascent and descent and then embellished to ensure that the gamakas(oscillations) and melodic beauty of the raga are still intact. Then he deconstructs the math involved.

Korvai in Raga Begada, Adi Tala, each cycle 8 beats and explanation of calculation

In a south Indian concert, the audience also puts the tala and can hence gauge the accuracy of the artist’s math even if they are not tracking all aspects of these real time calculations. The expected climax happens, when after finishing the 3 rounds of the korvai, all the artists on stage (the singer, the violinist and the percussionist) precisely arrive at the correct starting point in the line of the song !