कटपयादि संख्या

मुक्त ज्ञानकोश विकिपीडिया से
यहाँ जाएँ: भ्रमण, खोज

कटपयादि संख्या कर्नाटक संगीत में मेलापक राग की संख्या ज्ञात करने के काम आती है। इसके लिये राग के नाम के प्रथम दो सिलैबल्स के संगत कटपयादि संख्या निकालनी पड़ती है।[1]

इसका प्रयोग कैसे करें[संपादित करें]

कटपयादि संख्या[संपादित करें]

नीचे की सारणी में देवनागरी वर्णों के संगत कटपयादि संख्याएं दी गयी हैं।

कादि नव
टादि नव
पादि पंच
यादि अष्ट

To use the sankhya, take the first two syllables of the name of the raga, and locate the corresponding columns on the table. Then take the two numbers and reverse them to get the mela number. This is according to the following sutra: अंकानां वामतॊ गतिः (read numbers in the leftward (वामतः) direction)।

कटपयादि संख्या is a simplification of Āryabhaa's Sanskrit numerals, due probably to Haridatta from Kerala, c. 620-700.

स्वरस्थानों का निर्धारण करने की कलनविधि[संपादित करें]

मेलकर्ता (कटपयादि संख्या) चार्ट

The Swaras 'Sa' and 'Pa' are fixed, and here is how to get the other swaras from the melakarta number.

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

कुछ उदाहरण[संपादित करें]

राग धीरशंकरभरणम

The katapayadi scheme associates dha9 and ra2, hence the raga's melakarta number is 29 (92 reversed)।

Now 29 36, hence Dheerasankarabharanam has Ma1. Divide 28 (1 less than 29)by 6, the quotient is 4 and the remainder 4. Therefore, this raga has Ri2, Ga3 (quotient is 4) and Da2, Ni3 (remainder is 4)।

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

राग मेचकल्याणी

From the coding scheme Ma 5, Cha 6. Hence the raga's melakarta number is 65 (56 reversed)।

65 is greater than 36. So MechaKalyani has Ma2.

Since the raga's number is greater than 36 subtract 36 from it. 65-36=29. 28 (1 less than 29) divided by 6 : quotient=4, remainder=4 Ri2 Ga3 occurs. Da2 Ni3 occurs.

So MechaKalyani has the notes Sa Ri2 Ga3 Ma2 Pa Da2 Ni3 SA.

अपवाद: सिंहेन्द्रमाध्ययम

You can see that, as per the above calculation we should get Sa 7, Ha 8 giving the number 87 instead of 57 for Simhendramadhyamam. This should be ideally Sa 7, Ma 5 giving the number 57. So it is believed that the name should be written as Sihmendramadhymam (As in the case of Brahmana in Sanskrit)।

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

बाहरी कड़ियाँ[संपादित करें]

सन्दर्भ[संपादित करें]

  1. http://citeseer.ist.psu.edu/532626.html Katapayadi coding scheme