(April 1999)
Ajay Sathyanath
This is common for both Carnatic and Hindustani music, and
not suprisingly, because both stem from the same system
of music, and are the same in terms of raagas and swaras among
several other things.
Relax, for people who don't know what the
terminologies
are, start reading from the Appendix
section onwards. I have also worked out two
examples below, so you can get a feel.
It has 6 elements, at vertices given by
(1,1), (1,2), (1,3), (2,2), (2,3), and (3,3)
the first 3 elements occupy the top row,
the next 2 elements occupy the second row,
and the last element occupies the third row.
the vertices are given by
Numbering these elements from top down and from left to right
as numbers 1 to 6, we get:
(1,1) = 1, (1,2) = 2, (1,3) = 3, (2,2) = 4, (2,3) = 5, (3,3) = 6.
Much of the music was kept in its original/pure form, until the advent
of the Mughals in the 12th century AD. By virtue of the Mughal grasp of
all of North India and many parts of the South, classical music changed
to incorporate these influences. However, the South pretty much kept
with tradition and was thus called Carnatic music, where the word
Carnatic stands for tradition. The North added the Arabic and Persian
influence and called its version as Hindustani music, or in other words - the
music of India.
Though Indian classical music itself has two forms, each melodious in its
own way, the mathematics and the basics remain the same.
Each of the swaras/notes, appear in different frequencies.
There are 3 variations of Ri, denoted as R1, R2 and R3; 3 variations
of Ga, denoted as G1, G2 and G3; 2 variations of Ma, denoted as
M1 and M2; 2 variations of Da, denoted as D1 and D2; and two variations
of Ni, denoted as N1 and N2. The swaras Sa and Pa have no variations.
Arranging the swaras in order of increasing frequency we get:
S, R1, G1, R2, G2, R3, G3, M1, M2, P, D1, N1, D2, N2, D3, N3.
we now note why R and G are considered together as one group
and D and N as another group.
Melakartha raagas are raagas with a pattern, they can be split into
two portions, one called the Arohanam and the other called the
Avarohanam. The Avarohanam is the mirror image of the Arohanam, and
considered as a string of the constituent swaras, the Arohanam
plus the Avarohanam makes a palindrome!
Arohanam is a string/sequence of swaras whose frequencies
increase from left to right, in a strictly monotonic way.
Avarohanam is a string/sequence of swaras whose frequencies
decrease from left to right, in a strictly monotonic way.
Both the Arohanam and the Avarohanam must consist of all the
seven swaras/notes, of course these swaras will have different
variations in different Arohanams. For eg:
Since G2 > R2, and G1 is not greater than R2.
we can have "R2,G2" as a valid substring of an Arohanam,
but we CAN'T have "R2,G1" as a valid substring of an Arohanam.
It is called KaTaPaYadi, because all consonants can be partitioned
into 4 sets of numbers. consonants from Ka - Ta making one set,
Ta - Pa another, Pa - Ya a third, and everything after Ya constituting
the fourth.
Introduction
This is a method, part of which I discovered and part of which is
already known, to generate the entire raaga given
just the name
of the Melakartha Raaga. In other words this scheme/algorithm
makes it possible to generate the Arohanam and Avarohanam of
Melakartha raagas. This is a small 3 step procedure.
Disclaimer:
Though the Katapayadi number
generation is already
known in carnatic/hindustani circles, people do not
as yet know how to generate the raaga with this number, in ONE
CONSOLIDATED FORM. Usually they try remembering the whole
table of Melakartha Raagas, or through some other means, like
remembering certain properties of this table.
Notation
The seven Swaras or Notes viz.
Sa, Ri, Ga, Ma, Pa, Da, and Ni will be denoted by
S, R, G, M, P, D, N respectively.
Algorithm
Heres the Algorithm.
where x simply stands for either 1 or 2.
|1 2 3|
|- 4 5|
|- - 6|
|(1,1) (1,2) (1,3)|
| - (2,2) (2,3)|
| - - (3,3)|
ie. from the value of K1 find the vertex corresponding to it.
ie. from the value of K2, find the vertex corresponding to it.
and the Avarohanam as
and together they form the Raaga!!!!!!
Some Worked out Examples
Appendix
This section, apart from giving a fair introduction, explains some
basics of Indian classical music and certain terminologies concerning it.
Certain questions regarding the algorithm given above
are also answered in this section.
The Origins of Indian classical music can be traced back to the
time of the Vedas. The Vedas are four in number viz.
Rig, Sama, Yajur and Atharva Veda. The Yajur Veda talks about the
accompaniment of the veena for certain recitations.
The Sama Veda talks in detail about the seven basic notes - the swara.
Just like a language is composed of its alphabet, classical music is
composed of notes. There are seven basic notes (just like western
classical music) and each of them is called a Swara.
The notes are: Sa, Ri, Ga, Ma, Pa, Da, Ni
pretty much like Do, Re, Mi, Fa, So, La, Ti in the western world !!
A Raaga or a tone is a string of Swaras. In other words a combination
of the Swaras make a Raaga. There are 72 parent Raagas, combinations
and mutations of which result in all known Raagas in the world. These
72 parent Raagas are called Melakartha Raagas.
is one Arohanam and
is another.
In quite the same light as the ascii coding scheme of
modern computer science, the KaTaPaYadi scheme is a mapping of
letters in an alphabet to numbers. But unlike ascii, KaTaPaYadi
encodes only consonants of the sanskrit alphabet. All sanskrit
consonants correspond to a number between 0-9.
take the name of the Melakartha raaga
Hoping this was informative, and has helped you in anyway.
- Ajay Sathyanath