Universal Rhythmic Motifs

24 min readFeb 6, 2024

This article discusses rhythmic ideas in Carnatic Music—a classical tradition from South India—and assumes familiarity with some concepts.

TLDR

Universal Motifs are rhythmic patterns that you can use to create endings, korvais, and poruthams for any total duration. They are especially useful for creating samam to edam endings and korvais, even for challenging edams like rupaka thalam +2.

Terminology

beat: a “clap”; ex. Adhi thalam is 8 beats, misra chapu is 3.5 beats.
syllable: subdivisions of a beat; ex. chatusra nadai third speed corresponds to 4 syllables per beat.
samam: start of a thalam.
edam: the take-off point of a line of a composition.
karvai: a gap/silence with fixed duration.
korvai: rhythmic composition with two parts, purvangam and uttarangam, that is usually repeated 3 times.
porutham: a rhythmic pattern that resembles a melodic motif.

Motivation

Coming up with a rhythmic pattern that lasts n syllables is a common task in Carnatic music for vocalists, instrumentalists, and percussionists alike. Some examples of these:

Create a kalpana swaram ending that lasts n syllables and finishes at samam.
Create an ending that starts at samam and ends at an edam.
Given a purvangam, create an uttarangam such that the total korvai duration is n syllables.

To create such patterns, we often rely on rhythmic motifs. A motif is a representation of the numeric components in a rhythmic pattern. Some common motifs include:

AAA — here, A represents a pattern of some duration, and that pattern is repeated three times. This is usually the first motif that students learn. For example, if A=5 syllables, the total duration is 15.
ABABA — here, B can be a karvai. For instance, 26 can be represented as 6+(4)+6+(4)+6.
1+2+…+N — the total duration of this motif can be calculated using the formula for triangular numbers: Nx(N+1)/2. A few extensions of this: (1) 1+A+2+A+…+A+N — where A is a karvai, can be calculated with N*(N+1)/2 + A*(N-1). (2) 1+A+2+A+…+A+N+A can be calculated with N*(N+1)/2 + A*N. (3) N+A+…+A+1+A+A can be calculated with N*(N+1)/2 + A*(N+1). This one can work well for creating purvangams. Eg. we can set N=4 and A=3 to get a 25 syllable purvangam (in, say, kalyani): GRSN S,, RSN S,, SN S,, NS,, S,,

The challenge is that not all motifs work for all durations — in other words, not all motifs are “universal”. For example, the AAA motif cannot be used for 17, because 17 is not divisible by three.

The most well known universal motif is ABABA. This motif is universal because all numbers greater than 4 can be represented as ABABA (3A + 2B), where A is non-zero. This can be proved as follows:

Any even number can be represented as 2n = 6 + 2n-6 = 3(2) + 2(n-3) == 3A + 2B. And 3(2) + 2(n-3) = 3(4) + 2(n-6) = 3(6) + 2(n-9) and so on.
Any odd number can be represented as 2n + 1 = 3 + 2n-2 = 3(1) + 2(n-1) == 3A + 2B. And 3(1) + 2(n-1) = 3(3) + 2(n-4) = 3(5) + 2(n-6) and so on.

This raises the question: what other universal motifs exist?

Specifically, we are looking for motifs that have these desirable properties:

They should be truly “universal”—applicable to any total duration (above certain minimum durations). For example, there are some motifs that work only for even numbers — these are not truly universal.
They should be mathematically logical and musically aesthetic.
Ideally, they should be easy to calculate quickly.

Here, we will discuss some universal motifs with these properties:

AB…A
A1 A2 A3 where A1<A2<A3
A1 A2 A3 A4 where A1<A2<A3<A4
AAAA B AA B A
A B AA B {AAA, 3 per beat}
A B AA B {AAA, 6 per beat}
A+(A+1)…
A1 A2 A3 A2 A1 (Mridanga yati)
A3 A2 A1 A2 A3 (Damaru yati)
A // ABA // ABABA
ABABA // ABABA // {ABABA, 6 per beat}
A1 // A1 B A2A2 // A1 B A2A2 B A3A3A3

We will also discuss how these universal motifs can be applied:

Samam to samam/edam endings and korvais
Porutham endings and korvais
“Seamless” korvais
“Natural” korvais

Universal motifs

1) AB…A

Explanation: Any motif of the form AB…A (ABABA, ABABABA, ABABABABA, etc.) is universal for non-zero A, above a certain minimum number. For example, ABABA works for all numbers ≥5, and ABABABA works for all numbers ≥10.

Example: 32 == 5+4+5+4+5+4+5 == tha tha ka dhi na + thom , , , + tha tha ka dhi na + thom , , , + tha tha ka di na + thom , , , + tha tha ka dhi na

How to form: Let’s take ABABABA as an example. This boils down to 4A + 3B. Given a total duration T, find the largest multiple of 4 less than T such that T minus the multiple of 4 is divisible by 3. For the example above T=32, and 28 is the largest multiple of 4 smaller than 32, but 32–28=4 is not divisible by 3. Taking the next multiple of 4, 32–24=8 is also not divisible by 3. 32–20=12 is divisible by 3. So, 4A = 20 and 3B = 12, so A = 5 and B = 4.

2) A1 A2 A3 A4

Explanation: This motif is a series of four increasing numbers A1 A2 A3 A4 where A1<A2<A3<A4. We can extend this by adding karvais: A1 B A2 B A3 B A4. This motif can be boiled down to 4n + X where n is the duration of A1 and X is the sum of all the increments to A1 that are used to construct A2, A3, and A4, and the karvais B. To make this universal, we need at least one formulation of 4n + X such that X has remainder 0, 1, 2, and 3 when divided by 4.

Example: 32 == 5 + 7 + 9 + 11 == tha dhi ki na thom + thom , tha dhi ki na thom + tha , thom , tha dhi ki na thom + tha , dhi , thom , tha dhi ki na thom

How to form: Start with the total duration and divide by 4. Based on the remainder, find the corresponding row in the table below and form the motif using the value of n. Eg. if the total is 32, the remainder when divided by 4 is zero. Taking 32 == 4n + 12, we get n = 5 → 32 == 5 + 7 + 9 + 11.

3) A1 A2 A3

Explanation: In this motif, A1 < A2 < A3. This motif boils down to 3n + X where n is the duration of A1. To make this universal, we need at least one formulation of 3n + X such that X has remainder 0, 1, and 2 when divided by 3. This motif can be suitable for forming purvangams.

Example: 21 == 5 + 7 + 9 == dhin tha , thom , + tha , dhin tha , thom , + tha , dhi , dhin tha , thom ,.

How to form: Start with the total duration and divide by 3. Based on the remainder, find the corresponding row in the table below and form the motif using the value of n. Eg. if the total is 21, the remainder when divided by 3 is zero. Taking 21 == 3n + 6, we get n = 5 → 21 == 5 + 7 + 9.

4) AAAA B AA B A

Explanation: This motif boils down to 7A + 2B. To make this universal, we need at least one formulation of 7A + 2B such that 2B has remainder 0, 1, 2, 3, 4, 5, and 6 when divided by 7. This motif can also be framed as:

A B AA B AAAA OR
A B AA B {AAA, 3 per beat}

Example: 32 == 4 + 2 + (4+4) + 2 + {4+4+4, 3 per beat} = tha ka dhi na + thom , + tha ka dhi na tha ka dhi na + thom , + {tha ka dhi na tha ka dhi na tha ka dhi na, 3 per beat}.

How to form: Start with the total duration and divide by 7. Based on the remainder, find the corresponding row in the table below and form the motif using the value of n. Eg. if the total is 32, the remainder when divided by 7 is 4. Taking 32 == 7n+4, we get n = 4 → 32 == 4 + 2 + (4+4) + 2 + {4+4+4, 3 per beat}.

5) A B AA B {AAA, 6 per beat}

Explanation: This motif boils down to 5A + 2B (since AAA at 6 per beat == AA at 4 per beat). To make this universal, we need at least one formulation of 5A + 2B such that 2B has remainder 0, 1, 2, 3, and 4 when divided by 5.

Example: 32 == 6 + 1 + (6+6) + 1 + {6+6+6, 6 per beat} == tha dhi , ki na thom , tha dhi , ki na thom tha dhi , ki na thom , {tha thi , ki na thom tha thi , ki na thom tha thi , ki na thom}.

How to form: Start with the total duration and divide by 5. Based on the remainder, find the corresponding row in the table below and form the motif using the value of n. Eg. if the total is 32, the remainder when divided by 5 is 2. Taking 32 == 5n+2, we get n = 6 → 32 == 6 + 1 + (6+6) + 1 + {6+6+6, 6 per beat}.

6) A+(A+1)+…

Explanation: This motif consists of at least two consecutive terms A + (A+1) +… An integer that can be expressed as the sum of at least two consecutive integers is called a polite number. Those that cannot are called impolite numbers. The only impolite numbers are the powers of 2 (2, 4, 8, 16, 32, etc.). All other numbers are polite. Above, we saw the motif involving triangle numbers (1 + 2 +… + N), which are polite numbers that can be expressed as a sum of consecutive integers starting from 1.

Example: 33 = 3+4+5+6+7+8. This can be used as a purvangam with a 21 syllable (3x7) uttarangam to make a 54 syllable korvai (eg. in rupaka thalam 3 per beat, or khanda triputa 6 per beat): tha thom , (3) + tha ka thom , (4) + tha ki ta thom , (5) + tha ka dhi na thom , (6) + tha dhi ki na thom thom , (7) + tha dhi , ki na thom thom , (8) + (tha , dhi , ki na thom) x 3 (21)

How to form:

For polite numbers: given a number n, choose an odd divisor of n, d. Call the quotient n/d = q. The “polite” motif of n is given as the sum of d consecutive integers centered at q.

For example, if n = 35, we pick d = 5, then the motif is 5 consecutive integers centered at q=35/5=7 → 5+6+7+8+9.

Example: n = 39 and d = 3. Then the motif is q=39/3=13 consecutive integers centered at 3. This requires using negative integers and 0 which will eventually cancel out with some positive integers → -3 + -2 + -1 + 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 4+5+6+7+8+9

Note: for prime numbers, the polite motif will have only two terms. Ex. 37 = 18 + 19. This can be challenging to frame aesthetically.

For impolite numbers (powers of two), use the A1 A2 A3 A4 motif discussed above.

7) A1 A2 A3 A2 A1 (Mridanga Yati)

Explanation: This motif boils down to 5A1 + X. To make this universal, we need at least one formulation of 5A1 + X such that X has remainder 0, 1, 2, 3, and 4 when divided by 5.

Example: 32 == 4 + (3+4) + (6+4) + (3+4) + 4 == dhin tha thom , + tha , , dhin tha thom , + tha , , dhi , , dhin tha thom , + tha , , dhin tha thom , + dhin tha thom ,. It would be nice if the final “thom” ended on samam. To do this, we can create a pattern of length 34 and cut off the final two syllables: 34 == 6 + (1+6) + (2+6) + (1+6) + 6 == tha ka dhi na thom , + tha tha ka dhi na thom , + tha dhi tha ka dhi na thom , + tha tha ka dhi na thom , + tha ka dhi na (thom).

How to form: Start with the total duration and divide by 5. Based on the remainder, find the corresponding row in the table below and form the motif using the value of n. Eg. if the total is 32, the remainder when divided by 5 is 2. Taking 32 == 5n+12, we get n = 4 → 32 == 4 + (3+4) + (6+4) + (3+4) + 4.

8) A3 A2 A1 A2 A3 (Damaru Yati)

Explanation: This motif boils down to 5A1 + X. To make this universal, we need at least one formulation of 5A1 + X such that X has remainder 0, 1, 2, 3, and 4 when divided by 5.

Example: 32 == 5x4 + 12 == (4+4) + (2+4) + 4+ (2+4) + (4+4) == tha ka dhin tha dhin tha thom , + tha ka dhin tha thom , + dhin tha thom , + tha ka dhin tha thom , + tha ka dhin tha dhin tha thom ,. It would be nice if the final “thom” ended on samam. To do this, we can create a pattern of length 34 and cut off the final two syllables: 34 == (8+2) + (4+2) + 2 + (4+2) + (8+2) == tha tha ki ta tha ka dhi na thom , + tha ka dhi na thom , + thom , + tha ka dhi na thom , + tha tha ki ta tha ka dhi na (thom).

How to form: Start with the total duration and divide by 5. Based on the remainder, find the corresponding row in the table below and form the motif using the value of n. Eg. if the total is 32, the remainder when divided by 5 is 2. Taking 32 == 5n+12, we get n = 4 → 32 == 5x4 + 12 == (4+4) + (2+4) + 4+ (2+4) + (4+4).

Multi-Round Universal Motifs

Sometimes it’s helpful to have a motif that spans multiple “rounds”.

Suppose we want to make a korvai that starts at samam in rupaka thalam and ends 2 syllables after samam (edam) after three rounds. The overall structure is:

(samam)

Round 1: P(urvangam)1 + U(ttarangam)1

Round 2: P2 + U2

Round 3: P3 + U3

(edam)

Let’s fix P1 = P2 = P3 = 21 == 7x3 == (tha ka dhi na thom , ,) x 3.

So, P1+P2+P3 = 63. To end 2 syllables after samam, we need U1+U2+U3 to be equal to 12n + 2, so 74, 86, 98, 110, 122, 146, etc. Let’s pick 122. So, we need U1+U2+U3 = 122–63 = 59. It’s not immediately clear how to form three uttarangams that add up to 59.

This is where we can use multi-round Universal Motifs.

Using the A // ABA // ABABA motif (#9 below), we can easily make a samam to 2+ edam in rupaka thalam as follows:

P1: (tha ka dhi na thom , ,) x 3 (21)
U1: tha , thom , tha dhi ki na thom (9)
P2: (tha ka dhi na thom , ,) x 3 (21)
U2: tha , thom , tha dhi ki na thom , tha , thom , tha dhi ki na thom (19)
P3: (tha ka dhi na thom , ,) x 3 (21)
U3: tha , thom , tha dhi ki na thom thom , tha , thom , tha dhi ki na thom thom , tha , thom , tha dhi ki na thom (31)

All together, we have 21 + 9 // 21 + 19 // 21 + 31 == 30 + 40 + 52 = 122!

9) A // ABA // ABABA

Explanation: Because there are six As, this motif boils down to 6n + X. To make this universal, we need at least one formulation of 6n + X such that X has remainder 0, 1, 2, 3, 4, and 5 when divided by 6. We can play with X by incrementing A and by adding karvais (B).

Examples: 59 == 6x9 + 5 == 9 // 9+1+9 // 9+2+9+2+9 == tha , thom , tha dhi ki na thom // tha , thom , tha dhi ki na thom , tha , thom , tha dhi ki na thom // tha , thom , tha dhi ki na thom thom , tha , thom , tha dhi ki na thom thom , tha , thom , tha dhi ki na thom

How to form: Start with the total duration and divide by 6. Based on the remainder, find the corresponding row in the table below and form the motif using the value of n. Eg. if the total is 59, the remainder when divided by 6 is 5. Taking 59 == 6n+5, we get n = 9 → 59 == 6x9 + 5 == 9 // 9+1+9 // 9+2+9+2+9.

10) ABABA // ABABA // {ABABA, 6 per beat}

Explanation: This is a loose representation because we can increment the As and Bs in each round. Because there are 8 As (3 As in 6 per beat is 2 As in 4 per beat), this motif boils down to 8n + X. To make this universal, we need at least one formulation of 8n + X such that X has remainder 0, 1, 2, 3, 4, 5, 6, and 7 when divided by 8. We can play with X by incrementing A and by adding karvais (B).

Examples: 59 == 8x7 + 3 == 8+8+8 // 7+7+7 // {7+7+7, 6 per beat} == (tha thom , tha dhi ki na thom) x 3 // (tha , dhi , ki na thom) x 3 // {(tha , dhi , ki na thom) x 3, 6 per beat}

How to form: Start with the total duration and divide by 8. Based on the remainder, find the corresponding row in the table below and form the motif using the value of n. Eg. if the total is 59, the remainder when divided by 8 is 3. Taking 59 == 8n+3, we get n = 7 → 59 == 8x7 + 3 == 8+8+8 // 7+7+7 // {7+7+7, 6 per beat}.

11) A1 // A1 B A2A2 // A1 B A2A2 B A3A3A3

Explanation: In the formulations shown below, A3-A2 = A2-A1 = 1. In other words, A1, A2, A3 are consecutive. Because there are 10 As, this motif boils down to 10n + X. To make this universal, we need at least one formulation of 10n + X such that X has remainder 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 when divided by 10. We can play with X by incrementing A and by adding karvais (B).

Examples: 50 = 10x4 + 10 = 4 // 4+5+5 // 4+5+5+6+6+6. This can be used as a 60-syllable ending for khanda chapu with a 5-syllable karvai between each round: (tha ka dhi na) // (thom , tha , ,) // (tha ka dhi na) (tha tha ka dhi na) (tha tha ka dhi na) // thom , tha , , // (tha ka dhi na) (tha tha ka dhi na) (tha tha ka dhi na) (tha dhi tha ka dhi na) (tha dhi tha ka dhi na) (tha dhi tha ka dhi na)

How to form: Start with the total duration and divide by 10. Based on the remainder, find the corresponding row in the table below and form the motif using the value of n. Eg. if the total is 50, the remainder when divided by 10 is 0. Taking 50 == 10n+10, we get n = 4 → 50 = 10x4 + 10 = 4 // 4+5+5 // 4+5+5+6+6+6.

Applications

Samam to samam endings

Khanda chapu: Let’s make an ending that lasts 3 avarthanams (30 syllables). Using the A B AA B {AAA, 6 per beat} motif, we have 30 == 6+0+6+6+0+{6+6+6, 6 per beat} == (tha dhi , ki na thom)x3 + {(tha dhi , ki na thom)x3, 6 per beat}.

Misra jathi jhampa thalam: Let’s make an ending that lasts 1 avarthanam (40 syllables). Using the A1 A2 A3 A2 A1 (Mridanga yathi) motif, we can use a 42-syllable motif and cut off the final 2-syllable “thom ,”. 42 == 6 + (3+6) + (6+6) + (3+6) + 6 == tha ka dhi na thom , + tha , , tha ka dhi na thom , + tha , , dhi , , tha ka dhi na thom , + tha , , tha ka dhi na thom , + tha ka dhi na (thom ,).

Samam to samam korvais

Misra chapu thalam: Let’s fix the uttarangam as 3x7, so the purvangam should be 21. Using the A1 + A2 + A3 motif, 21 == 5 + 7 + 9 == dhin tha , thom , + tha , dhin tha , thom , + tha , dhi , dhin tha , thom ,. This can be followed by 3x7 == tha , dhi , ki na thom tha , dhi , ki na thom tha , dhi , ki na thom.

Khanda jathi thriputa thalam, thisra nadai: Let’s fix the uttarangam as 3x7 (21 syllables). To make a 54 syllable korvai, we need a 33 syllable purvangam. Using the A+(A-1)+… (polite numbers) motif, 33 = 3+4+5+6+7+8 == tha thom , (3) + tha ka thom , (4) + tha ki ta thom , (5) + tha ka dhi na thom , (6) + tha dhi ki na thom thom , (7) + tha dhi , ki na thom thom , (8) + (tha , dhi , ki na thom) x 3 (21)

Samam to edam endings

Adhi thalam 3 after: The total duration is 35. Using the AAAA B AA B A motif, we have 35 = 7x5 = 5x4 + 5x2 + 5 == tha , , , dhi , , , ki , , , na , , , thom , , , + tha , dhi , ki , na , thom , + tha dhi ki na thom.

Adhi thalam 6 after: The total duration is 38. Using the A1 A2 A3 A4 motif, we have 38 = 8+9+10+11 == tha , ka , dhi , na , + thom tha , ka , dhi , na , + tha ka tha , ka , dhi , na , + tha ki ta tha , ka , dhi , na ,

Rupaka thalam 2 after: Let’s take a total duration of 38. Using the A+(A-1)+… (polite numbers) motif, we have 38 = 19x2 == 19 numbers centered at 2 == -7 + -6 + … + 10 + 11 == 8+9+10+11 == tha , ki , ta , tha ka + tha , ki , ta , tha ki ta + tha , ki , ta , tha ka dhi na + tha , ki , ta , tha dhi ki na thom.

Misra chapu thalam after 4: Let’s take a total duration of 32. Using the ABABABA motif, we have 32 = 5+4+5+4+5+4+5 == tha dhi ki na thom thom , , , tha dhi ki na thom thom , , , tha dhi ki na thom thom , , , tha dhi ki na thom.

Samam to edam korvais

We saw an example of samam to edam korvais above in the “Multi-Round Universal Motifs” section.

Porutham endings

One way to structure a porutham ending is as follows:

Round 1 + porutham + Round 2 + porutham + Round 3 (edam)

Let’s create an ending with this structure for mishra chapu 3 syllables after samam for the edam “manasuna” in pakkala nilabadi (karaharapriya ragam). The porutham will be “tha tha , thom , , , ” (7 syllables).

The two repetitions of the poruthams will take up 7x2 = 14. The total ending should take up 14n + 3. Let’s pick 14x4 + 3 = 59 as the total. So Round 1 + Round 2 + Round 3 = 59–14 = 45. We can use the A // ABA // ABABA motif → 49 = 6x7 + 3 = 7 // 7+1+7 // 7+1+7+1+7. The full ending is:

Round 1: tha dhi , ki na thom + tha tha , thom , , ,
Round 2: tha dhi , ki na thom , tha dhi , ki na thom + tha tha , thom , , ,
Round 3: tha dhi , ki na thom , tha dhi , ki na thom , tha dhi , ki na thom (manasuna)

Similarly, we can create a porutham for paramaatmudu (vaagadhishwari ragam) that starts at samam and ends at edam (samam + 4) for a total of 68 syllables. The porutham will consist of 3 rounds with an 7-syllable pattern dhin , tha , thom , , (paramaa…) after each round. The overall structure will be: Round 1 + 7 + Round 2 + 7 + Round 3 (paramaa). The three rounds need to sum to 68–14 = 54 == 8x6 + 6 == (6+2+6+2+6) + (6+1+6+1+6) + {6+6+6, 6 per beat}. All together, the entire porutham is:

Round 1: tha dhi , ki na thom tha , tha dhi , ki na thom tha , tha dhi , ki na thom + dhin , tha , thom , ,

Round 2: tha dhi , ki na thom , tha dhi , ki na thom , tha dhi , ki na thom + dhin , tha , thom , ,

Round 3: {tha dhi , ki na thom tha dhi , ki na thom tha dhi , ki na thom, 6 per beat} (paramaa…)

Porutham korvais

One way to structure a porutham korvai is

P1 + porutham // P2 + (porutham)x2 // P3 + (porutham)x3

where the last porutham is the edam.

We can do this for “krupajesi na” in aparadhamulanniyu (lathangi ragam), where the porutham is “thom , thom , , tha , , tha ,” (10 syllables). The edam is 6 syllables after samam in one kalai adhi thalam. The total duration is 32n + 6. We can pick n = 3, for a total duration of 102.

In total, the porutham will appear 5 times before the edam, so P1 + P2 + P3 = 102–50 = 52. We can use the A // ABA // ABABA motif to form 52 as 8 // 8+9 // 8+9+10. The full korvai is:

Round 1: tha thom , tha dhi ki na thom + thom , thom , , tha , , tha ,

Round 2: tha thom , tha dhi ki na thom + tha , thom , tha dhi ki na thom + thom , thom , , tha , , tha , + thom , thom , , tha , , tha ,

Round 3: tha thom , tha dhi ki na thom + tha , thom , tha dhi ki na thom + tha , , thom , tha dhi ki na thom + thom , thom , , tha , , tha , + thom , thom , , tha , , tha , (krupajesi na)

“Seamless” korvais

Seamless korvais, a term coined by Chitravina Ravikiran, are korvais whose total duration is not divisible by 3 and whose uttarangam has no karvais. Example (composed by Ravikiran): [7+(3)+6+(3)+5+(3)+4+(3)+3+(3)+2+(3)+1+(3)] + [5+5+5] = 64. This is a seamless korvai because the total duration of 64 is not divisible by 3 and the uttarangam has no karvais.

The beauty of seamless korvais comes in large part from the karvai-less uttarangam. But setting this constraint makes creating a suitable poorvangam challenging, especially using common rhythmic motifs. Universal motifs can be employed here to easily create purvangams of any duration for seamless korvais.

For example, take 2 kalai adi thalam with 64 syllables, and set the uttarangam as three 5s (as in the example above). This leaves 64–15 = 49 for the poorvangam. We can now use several universal motifs to create a 49-syllable purvangam.

First, we can see that Ravikiran’s seamless korvai is an application of the A+(A+1)+… motif:

49 can be expressed as a sum of 7 numbers centered at 7
49 = 4+5+6+7+8+9+10
Tha ka thom , (4)
Tha ki ta thom , (5)
Tha ka dhi na thom , (6)
Tha tha ka dhi na thom , (7)
Tha ka tha ka dhi na thom , (8)
Tha ki ta tha ka dhi na thom , (9)
Tha tha ki ta tha ka dhi na thom , (10)
(Tha dhi ki na thom) x 3 (15)

Using the A1 A2 A3 A4 motif:

49 = 10 + 11 + 13 + 15
Tha, dhi , ki , na , thom , (10)
Gu tha , dhi , ki , na , thom , (11)
Thaangu tha, dhi , ki , na , thom , (13)
Tha , thaangu tha , dhi , ki , na , thom , (15)
(Tha , thaangu) x 3 (15)

Using the A1 A2 A3 motif:

49 = 13 + (2+13) + (8+13)
Ta , tom , , ta di ki na tom ta , , (13)
Ta ka ta , tom , , ta di ki na tom ta , , (15)
Ta , ka , di , ku , ta , tom , , ta di ki na tom ta , , (17)
(Ta di ki na tom) x 3 (15)

Using the AAAA B AA B A motif:

Ta ka ta di ki na tom (7)
Ta , ka , ta , di , ki , na , tom , (14)
Ta , , , ka , , , ta , , , di , , , ki , , , na , , , tom , , , (28)
(Ta di ki na tom) x 3 (15)

“Naturals”

Naturals, a term coined by Patri Satish Kumar, are endings or korvais that follow an asymmetric progression, usually in 3 rounds or parts. For example here, he demonstrates 5 // 6+6 // 7+7+7 == 38 as a possible ending for rupaka thalam 2 syllables after samam. This is a simple application of the A // ABA // ABABA motif.

We can use motifs 9–11 to create Natural korvais as well — korvais whose total duration in each of the three rounds follows an asymmetric progression.

Example in rupaka thalam 2 syllables after samam:

First let’s fix the purvangam, picking a simple 3x7: tha ka dhi na thom , , // tha ka dhi na thom , , // tha ka dhi na thom , , (21)
The total across all three rounds must be 12n + 2, so let’s pick 122 as an example.
The three purvangams will take up 21x3 = 63. Remaining for the three uttarangams is 122–63 = 59.
We can form using the A // ABA // ABABA motif as 59 == 9 // 9+1+9 // 9+2+9+2+9
Round 1: tha ka dhi na thom , , // tha ka dhi na thom , , // tha ka dhi na thom , , (21) // tha ka dhi ku tha dhi ki na thom (9)
Round 2: tha ka dhi na thom , , // tha ka dhi na thom , , // tha ka dhi na thom , , (21) // tha ka dhi ku tha dhi ki na thom , tha ka dhi ku tha dhi ki na thom (19)
Round 3: tha ka dhi na thom , , // tha ka dhi na thom , , // tha ka dhi na thom , , (21) // tha ka dhi ku tha dhi ki na thom tha , tha ka dhi ku tha dhi ki na thom tha , tha ka dhi ku tha dhi ki na thom (31)
Total == 21+9 // 21+19 // 21+31 == 30 + 40 + 52 == 122

Example in misra chapu four syllables after samam:

First let’s fix the purvangam, picking a simple 3x7: tha ka dhi na thom , , // tha ka dhi na thom , , // tha ka dhi na thom , , (21)
The total across all three rounds must be 14n + 4, so let’s pick 144 as an example.
The three purvangams will take up 21x3 = 63. Remaining for the three uttarangams is 144–63 = 81.
We can form using the A1 // A1 B A2A2 // A1 B A2A2 B A3A3A3 motif as 81 == 5 // 5+(7)+6+6 // 5+(7)+6+6+(7)+7+7+7.
Round 1: tha ka dhi na thom , , // tha ka dhi na thom , , // tha ka dhi na thom , , (21) // tha dhi ki na thom (5)
Round 2: tha ka dhi na thom , , // tha ka dhi na thom , , // tha ka dhi na thom , , (21) // tha dhi ki na thom (thom , thom , tha , ,) tha , dhi ki na thom tha , dhi ki na thom (24)
Round 2: tha ka dhi na thom , , // tha ka dhi na thom , , // tha ka dhi na thom , , (21) // tha dhi ki na thom (thom , thom , tha , ,) tha , dhi ki na thom tha , dhi ki na thom (thom , thom , tha , ,) tha , , dhi ki na thom tha , , dhi ki na thom tha , , dhi ki na thom (52)
Total == 21+5 // 21+24 // 21+52 == 26 + 45 + 73 == 144

Conclusion

If you made it this far, thank you for your attention. I hope you found these ideas interesting and helpful. Of course, it is easy to write out patterns as numbers on a page — it is much harder to deploy them in performance aesthetically!

If you discover other Universal Motifs, please write to me at akshay325[AT]gmail.com and I will add them here.