The Katapayadi system

During my early years, when I was trying to learn Carnatic music, my teacher talked about how a melakarta raga’s notes can be determined by the full name of the raga, essentially from the first two syllables. This was amazing to me then, and it continues to be fantastic. This was based on the Katapayadi system. 

Like it’s said, the best way to learn something is to teach it; at least, Richard Bach said it; and I’m guessing it was in his book “Jonathan Livingston Seagull.”

So, what exactly is the Katapayadi system? Let’s dive into it, er…with a little bit of help from my friends, Wiki and Chat GPT, and the internet in general. 

What is the Katapayadi system?

The Katapayadi system is a numerical notation system used in ancient India to represent numbers using letters of the alphabet. The system is believed to have originated in the Vedic period and was used for various purposes, such as writing poetry, mathematical calculations, and representing numbers in inscriptions.

Origins of the Katapayadi System

The origins of the Katapayadi system can be traced back to the Vedic period in India. The Vedas, the oldest Hindu scriptures, contain verses that use letters to represent numbers. This system was later developed and refined by Indian scholars and mathematicians to create the Katapayadi system.

Practical Usage of the Katapayadi System

The Katapayadi system was used for various purposes, such as writing poetry, mathematical calculations, and representing numbers in inscriptions. In poetry, the system was used to create numerical codes for words and phrases, which allowed poets to write poems that were easy to remember and recite. In mathematics, the system was used to represent numbers more compactly, making calculations easier. Finally, in inscriptions, the system was used to represent numbers in a way that was easy to understand, even for those unfamiliar with the numerals used in India at the time.

Examples of the Katapayadi System

The Katapayadi system is an integral part of India’s cultural heritage. It is a testament to ancient India’s mathematical and linguistic prowess and continues to be studied and appreciated by scholars and enthusiasts alike. Although the system is no longer in widespread use, it remains an essential part of India’s rich history and cultural legacy.

Cracking the Melakarta Raga Codes with the Katapayadi System in Carnatic Music

In Carnatic music, the Katapayadi system offers an intriguing way to decode the Melakarta ragas, the foundational scales that form the backbone of this rich musical tradition. Named using specific syllables, the first two syllables of a Melakarta raga reveal its number when decoded using this ancient Indian numerical system.

The process of decoding the ragas and understanding their structure involves several steps. First, the two constant notes in every raga are ‘Sa’ and ‘Pa.’ The remaining notes, ‘Ri,’ ‘Ga,’ ‘Ma,’ ‘Da,’ and ‘Ni,’ are derived from the Melakarta number.

The first 36 Melakarta ragas feature ‘Ma1,’ while the remaining 36, numbered 37 through 72, include ‘Ma2.’

To determine the positions of the ‘Ri’ and ‘Ga’ notes, subtract one from the Melakarta number and divide the result by six. The integral part of the quotient provides the ‘Ri’ and ‘Ga’ positions. If the Melakarta number exceeds 36, subtract 36 before performing this calculation.

The remainder from the same division operation determines the ‘Da’ and ‘Ni’ positions.

Let us illustrate these rules with a couple of examples:

1. Raga Dheerasankarabharanam: The Katapayadi system assigns the value of 9 to ‘Dha’ and 2 to ‘Ra,’ resulting in a Melakarta number of 29 (reversing ’92’). As 29 is less than 36, Dheerasankarabharanam has ‘Ma1.’ When 28 (1 less than 29) is divided by 6, the quotient is 4, and the remainder is 4. Hence, this raga features ‘Ri2,’ ‘Ga3,’ ‘Da2,’ and ‘Ni3.’ Therefore, the full scale of this raga is ‘Sa Ri2 Ga3 Ma1 Pa Da2 Ni3 SA.’
2. Raga Mechakalyani: According to the coding scheme, ‘Ma’ corresponds to 5 and ‘Cha’ to 6, yielding a Melakarta number of 65 (reversing ’56’). As 65 is greater than 36, Mechakalyani features ‘Ma2.’ Subtracting 36 from 65 gives us 29. Dividing 28 (1 less than 29) by 6 gives a quotient and remainder of 4, leading to ‘Ri2,’ ‘Ga3,’ ‘Da2,’ and ‘Ni3.’ Thus, Mechakalyani’s note sequence is ‘Sa Ri2 Ga3 Ma2 Pa Da2 Ni3 SA.’

An interesting exception to these rules is the raga Simhendramadhyamam. Using the conventional calculation, ‘Sa’ (7) and ‘Ha’ (8) would result in the number 87 rather than the correct Melakarta number 57. To correct this anomaly., the name should be ‘Sihmendramadhyamam,’ treating ‘Ma’ as 5, yielding the correct Melakarta number, 57.

In summary, the Katapayadi system offers a unique method to understand the structure of Melakarta ragas in Carnatic music, blending language, mathematics, and music fascinatingly. 

Despite occasional exceptions, this system remains essential for Carnatic music enthusiasts and practitioners.