Katapayadi sankhya

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The katapayadi sankhya is a way of determining the number of a melakarta ragam from the first two syllables of the name of the raga.^[1]

Indian Music
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Concepts
Raga ·Thaat ·Melakarta · Katapayadi sankhya
Śruti · Swara · Saptak
Tala · Mudra ·Gharana

1 How to use it
- 1.1 Katapayadi sankhya
- 1.2 कटपयादि संख्या
  - 1.2.1 An Algorithm to derive the Swarasthanas
2 Links
3 References

[edit] How to use it

Following is the Katapayadi sankhya in the Roman alphabet and in Devanagari.

[edit] Katapayadi sankhya

	1	2	3	4	5	6	7	8	9	0
Kadi nava	ka	kha	ga	gha	nga	ca	cha	ja	jha	nya
Tadi nava	ṭa	ṭha	ḍa	ḍha	ṇa	ta	tha	da	dha	na
Padi pancha	pa	pha	ba	bha	ma
Yadi ashta	ya	ra	la	va	śha	sha	sa	ha

[edit] कटपयादि संख्या

	१	२	३	४	५	६	७	८	९	०
कादि नव	क	ख	ग	घ	ङ	च	छ	ज	झ	ञ
टादि नव	ट	ठ	ड	ढ	ण	त	थ	द	ध	न
पादि पंच	प	फ	ब	भ	म
यादि अष्ट	य	र	ल	व	श	ष	स	ह

To use the sankhya, take the first two syllables of the name of the ragam, and locate the corresponding columns on the table. Then take the two numbers and reverse them to get the mela number. The reversal is to account for the difference in endianness---the traditional Indian way of denoting numbers used the least significant bit first (little endian) while numbers today are written most significant bit first (big endian).

Katapayadi sankhya is a simplification of Āryabhaṭa's Sanskrit numerals, due probably to Haridatta from Kerala, c. 620-700.

[edit] An Algorithm to derive the Swarasthanas

The SwaraSthanas 'Sa' and 'Pa' are fixed, and here is how to get the other SwaraSthanas from the melakarta number:

Melakartas 1 through 36 have Ma1 and those from 37 through 72 have Ma2.
The other notes are derived by noting the (integral part of the) quotient and remainder when the melakarta number is divided by 6.
'Ri' and 'Ga' positions: the raga will have:
- 1. Ri1 and Ga1 if the quotient is 0
  2. Ri1 and Ga2 if the quotient is 1
  3. Ri1 and Ga3 if the quotient is 2
  4. Ri2 and Ga2 if the quotient is 3
  5. Ri2 and Ga3 if the quotient is 4
  6. Ri3 and Ga3 if the quotient is 5
'Da' and 'Ni' positions: the raga will have:
- 1. Da1 and Ni1 if remainder is 1
  2. Da1 and Ni2 if remainder is 2
  3. Da1 and Ni3 if remainder is 3
  4. Da2 and Ni2 if remainder is 4
  5. Da2 and Ni3 if remainder is 5
  6. Da3 and Ni3 if remainder is 0

Example:

Lets take the raga Dheerasankarabharanam. The katapayadi scheme associates dha $\leftrightarrow$ 9 and ra $\leftrightarrow$ 2, hence the raga's melakarta number is 29 (92 reversed).

Now $29\le36$ , hence Dheerasankarabharanam has Ma1. Divide 29 by 6, the quotient is 4 and the remainder 5. Therefore, this raga has Ri2,Ga3 (quotient is 4) and Da2,Ni3 (remainder is 5).

This raga's scale is: Sa Ri2 Ga3 Ma1 Pa Da2 Ni3 SA.

Now lets take the raga "MechaKalyani". From the coding scheme Ma $\leftrightarrow$ 5 Cha $\leftrightarrow$ 6, hence the raga's melakarta number is 65 (56 reversed).

65 is greater than 36. So MechaKalyani has Ma2.

If the raga's number is greater than 36 subtract 20 from it. 65-36=29. 29 divided by 6 : quotient=4, remainder=5 Ri2 Ga3 occurs. Da2 Ni3 occurs. So MechaKalyani has the notes: Sa Ri2 Ga3 Ma2 Pa Da2 Ni3 SA

You can play with the other ragas in the Melakarta Table.