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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.

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

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

	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

	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.

Actually, Katapayadi sankhya is a(n) (over-)simplification of Āryabhaṭa's Sanskrit numerals, due probably to Haridatta who lived at Kerala, c. 620-700.

Once the mela number is obtained, it is possible to derive the individual Swaras of the ragam. Here is how the SwaraSthanas are derived:

1. There is only one Sa in an Octave. so, 'Sa' is fixed.
2. 'Ri' and 'Ga' notes:
   • divide the melakarta number by 36 and note the remainder. The raga will have...
     1. Ri1 and Ga1 if remainder is less than 7 and greater than 0
     2. Ri1 and Ga2 if remainder is less than 13 and greater than 6
     3. Ri1 and Ga3 if remainder is less than 19 and greater than 12
     4. Ri2 and Ga2 if remainder is less than 25 and greater than 18
     5. Ri2 and Ga3 if remainder is less than 31 and greater than 24
     6. Ri3 and Ga3 if remainder is either zero or greater than 30
3. Melakartas 1 to 36 use Ma1 (shudhdha madhyamam) while 37 to 72 use Ma2 (prathi madhyamam)
4. 'Pa' is fixed as well.
5. 'Da' and 'Ni' notes:
   • divide the melakarta number by 6 and note the remainder. 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 melakarta#29, namely Dheerasankarabharanam. Its Melakarta number is 29. Lets apply the above Algorithm to obtain the swarasthanas of this ragam:

Since we know that 'sa' and 'pa' are fixed, we just need to determine Ri, Ga, Ma, Da and Ni.

Ri and Ga:

When dividing 29 by 36, the Remainder is 29. This is less than 31 and greater than 24. Hence using the above set of rules, we determine that Dheerasankarabharanam has Ri2 and Ga3.

Ma:

Since 29 is less than 37 this raga has Ma1.

Da and Ni:

On dividing 29 by 6 we get 5. This means that this raga has Da2 and Ni3.

To conclude, this raga's scale is: Sa Ri2 Ga3 Ma1 Pa Da2 Ni3 SA.

Thus, we have just derived the entire scale of this raga from its Melakarta number (see Melakarta Table).

• Katapayadi coding scheme