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\centerline{\Large {\bf 
A Carnatic Music Primer
}}

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\centerline{\bf P. Sriram}
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\centerline{The Carnatic Music Association of North America, Inc.}
\centerline{375 Ridgewood Ave, Paramus, New Jersey}
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Published by: 
The Carnatic Music Association of North America, Inc.

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ABOUT THE AUTHOR
\medskip

Dr. Parthasarathy Sriram, is an aerospace engineer, with a
bachelors degree from IIT, Madras (1982) and a Ph.D. from
Georgia Institute of Technology where is currently a research
engineer in the Dept. of Aerospace Engineering.  The preface
written by Dr. Sriram speaks of why he wrote this monograph.  At
present Dr. Sriram is looking after the affairs of the
provisionally recognized South Eastern chapter of the Carnatic
Music Association of North America in Atlanta, Georgia.  CMANA
is very privileged to publish this scientific approach to
Carnatic Music written by a young student of music.

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\copyright CMANA, 375 Ridgewood Ave, Paramus, New Jersey

1990

Price: \$3.00


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\addcontentsline{toc}{section}{Preface}
\leftline{\large \bf Preface}

Om Sri Gurubhyo Namaha.

This booklet is aimed at music lovers everywhere who wish to
learn a little bit about the basic theory of Carnatic music. 
There are a large number of books on many aspects of Carnatic
music but I have found most of them to be of an advanced nature
- they have lots of good information but it is extremely
difficult for a novice to start learning about music using them.
 Once the basics are mastered, these books provide enormous
scope for intellectual enrichment.  This opinion is shared by
many of my music loving friends as evidenced by their expressing
a need for a simple booklet such as this one.  The primary
motivation in producing this booklet was to put together the
basics in one place so that a beginner can get started off
easily.  Except for the section on Grahabedam and Symmetries,
there is very little new material contained herein.  The
following books have been consulted to obtain much of the
material and interested readers are encouraged to further their
knowledge by reading them.

The New Groves Dictionary of Music and Musicians, under India.

Sri Krithi Mani Malai by R. Rangaramanuja Iyengar, 4 volumes.

Ganamrutha Varna Malika by A. S. Panchapakesa Iyer.

Abhyaasa Gaanam by A. Sundaram Iyer.

Karnataka Sangeetham by A. Sundaram Iyer.

Karnataka Sangeetham by Prof. P. Sambamoorthy, 3 volumes.

This book is intended to be read through (perhaps several times)
and it is inadvisable to delve into the later sections without
reading through the earlier sections.  Most of the terminology
is originally in Sanskrit and I have made no attempt to use a
standard transliteration scheme eg. Carnatic and Karnatic are
both used.  In fact, I have mixed Tamil and Sanskrit terms
freely (raga, ragas and ragams can all be found in the text) and
hope it is not a nuisance.  I have assumed little more than an
interest in Carnatic music on the part of the reader and thus,
the initial sections deal with basics like swaras, their names
etc.  Being a scientist and an engineer, I was tempted to
include mathematical ideas wherever possible.  Further, it is
very difficult to present anything other than an analytical
approach in a book like this.  Nevertheless, most of the
mathematical and physical concepts used are elementary and are
no more advanced than what one would encounter in high school.

A few words of advice to readers: Listen to as much music as you
can and find friends who share your interest.  Discuss what you
know and you will almost always end up adding to your knowledge.
 There is no question that is so silly that it does not deserve
to be asked.  The art of identifying ragas cannot be learned
from a book and it usually takes years of listening before one
begins to identify ragas reliably.  Patience and perseverance
are the key words here.

Inspiration for this work was provided by my uncle Valavanur N.
Jambunathan (who was born of parents who were neither musicians
nor musicologists and who did not have the benefit of any
musical education, whatsoever), who is our family musical
resource.  Further encouragement was provided by my cousins,
especially Basu (S. Baskaran, Dubai, U.A.E.), and many others
who expressed interest in a document such as this.  Special
thanks are due to my brothers of the Atlanta Panchapandavas,
Drs. Mahadevan (Nashville, Tennessee), Gajanan (Knoxville,
Tennessee), Chander (Washington, D.C.) and Kannan (Philadelphia,
Pennsylvania) for aiding me in my discovery of love for
classical music and (especially to Mahadevan) for reviewing and
contributing to the material in this book.

This work is dedicated to my Gurus Sri. Prathapam Natesa Iyer
(disciple of Ariyakkudi Ramanujam Iyengar) and Smt. Jayalakshmi
Ramaswamy (disciple of G.N. Balasubramanian).  Anything good you
see in this book is a consequence of the musical knowledge they
instilled in me while the errors you may come across are
entirely due to my inability to comprehend what I was taught.

I sincerely hope that reading this book accelerates your
understanding and appreciation of music.  This document is by no
means perfect and I welcome all suggestions and comments.

P. Sriram

Atlanta, U.S.A.

February 1989.


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\section{Introduction}


"Nature has endowed this universe with many beautiful life
forms, of so many different shapes, sizes and abilities.   Most
animal forms have the ability to produce sounds and some of them
even have the capability to communicate using varied sounds. 
Man is unique in that he can express his thoughts using sound." 
\ \ This is how Swami Jayendra Saraswathy, the  
Sankaracharya of
Kanchipuram, introduces the Kamalaambaa 
Navaavarna Kritis of
Muthu{}swamy Dikshithar.  The ability to express thoughts through
sounds has evolved into an art which we call music.  Music can
thus be defined as an art form that arranges sounds in a fashion
that follows certain natural principles and provides that
special inner feeling of happiness and contentment.  It is
important to note that the basic principles are natural and thus
the theory of music is only an attempt by man to rationally
explain what is already beautiful.  As a fringe benefit, this
rationalization helps in understanding the inherent beauty of
music and creates increasingly higher levels of appreciation in
the listener.

The most basic unit of music is the swara (or note) which simply
indicates the position in the audible spectrum occupied by a
particular sound or the pitch of the sound.  Actually, the
spectral position is better described as swara sthana. 
Inherently, certain sounds 'go together' and certain others do
not.  This property was realized by man thousands of years ago
and is indicated by the term harmony; lack of harmony is called
disharmony.  Before going any further, let me introduce, as a
practical tool, a keyboard, that will help us immensely as we go
along deeper into the fundamentals of Carnatic music.  Purists
may frown at this, but as long as we realize the limitations of
the keyboard and why the purists frown, we are committing no
sin.  

At first glance, a keyboard is simply an assortment of black and
white keys of two different lengths, usually the black  keys 
being the short ones.  A closer examination shows a pattern of
keys repeating a few times to produce the full keyboard.  The
repeating pattern is shown in the following figure.  Many
keyboards indicate the location of the 'C' key as shown in the
figure.  In any case, a C key can be identified as the white (or
long) key immediately to the left of a group of two black keys
or the first key in the above figure.  Evidently, there is more
than one C key (perhaps 4 or even more) on the keyboard.  The C
key is so called due to the notation used in western music for
the notes.  The successive white keys to the right of C are
labeled D, E, F, G, A and B.  As a first example of harmony,
play a C key and the  next C key simultaneously and listen
carefully (It is assumed here that the keyboard is polyphonic 
i.e., has the ability to produce more than one tone at a time.  Many
inexpensive keyboards lack this ability and are not suitable for
this demonstration).  The combined sound has an oneness.  Playing a C
key and the white key next to it (the D key) does not produce a
similar effect and the two tones stand out separately.  They do
not merge as in the case of the two C keys.  Total disharmony is
difficult to demonstrate using a keyboard due to the discrete
nature of the notes that can be played.  One would have to
produce a sound that is located 'between' two keys in order to
hear a set of highly disharmonious (abaswara) notes but the
preceding demonstration is a simple example of two levels of
harmony.

\begin{figure}
{\hspace*{1.in} \small 
\begin{verbatim}
C
====================================
|  |##| |##|   |  |##| |##| |##|   |
|  |##| |##|   |  |##| |##| |##|   |
|  |##| |##|   |  |##| |##| |##|   |
|  |##| |##|   |  |##| |##| |##|   |
|  |__| |__|   |  |__| |__| |__|   |
|    |    |    |    |    |    |    |  
|    |    |    |    |    |    |    |
|    |    |    |    |    |    |    |
|____|____|____|____|____|____|____|


\end{verbatim} 
\caption{
 Keyboard Layout:
Seven white keys and five black keys in between.}
\normalsize}
\end{figure}

Two successive C keys are separated by what is called an octave
which corresponds to a ratio of two in frequency.  That is, the
frequency of a C note is exactly double the frequency of the C
immediately below (to the left of) it and exactly half the
frequency of the C immediately above it.  Two sounds are
perceived to be very similar if they are separated by an octave
and the only explanation for this is that that is how mother
nature has made it!

The concept of harmony is closely related to the notion of
harmonics.  Consider a string fixed at both ends and vibrating
at a fundamental frequency f.  From basic physics, the upper
harmonics of the string are at integral multiples of f, namely,
2f, 3f, 4f etc.  Harmonious tones have common harmonics and this
implies that the tones have fundamental frequencies that are
related as a ratio of two integers.  A high degree of harmony is
associated with ratios involving powers of 2 (2:1, 4:1, 8:1
etc.) and small integers (eg. 3:2).  The ratio 3:2 signifies
that the second harmonic of the higher frequency tone coincides
the third harmonic of the lower frequency tone and such a
relationship is very easily detected by the human ear.  Two
tones related through a ratio 91:85 are not perceived as being
very harmonious because the common harmonics are the 91st and
85th.  Such high harmonics typically have very low intensity and
may even be beyond the frequency range of the human ear.  The
principle of integral ratios is inherent in our perception of
sound.  A tune is identified by the ratio of frequencies that
appear in succession to produce it and only special training
develops the ability to perceive the absolute pitch (frequency)
of sounds.

Next we observe that there are a total of twelve keys in the
repeating pattern (or twelve swara sthanas in an octave).  This
division of an octave into twelve swara sthanas has evolved over
a period of millennia.  This is evident from the fact that while
some ancient forms of music use fewer swara sthanas, the current
forms of many styles of classical music which evolved
independently (including Western, Hindustani and  Carnatic) use
only twelve swara sthanas to an octave.  In ancient Vedic
chantings, we have only three swara sthanas, denoted as normal,
low and high.  Interestingly, the pitch steps corresponding to
these three swara sthanas can be represented by the F, G and A
keys.  Vedic chants of later periods use as many as seven swaras
and are often described as the precursors of the raga system. 
The twelve swara sthanas are generally considered to be the
maximum number of sthanas that a normal human ear can perceive
to be different without too much difficulty.

Western music believes in specifying the absolute pitch of all
swaras and thus, the frequencies of all keys are fixed and the
same for all keyboards (in fact, all instruments, if one can
locate the corresponding notes).  Indian music is based on
relative positioning and thus, notes are not of fixed pitch. 
The note Sa is the analog of the note C.  The white key marked C
is called as one kattai and the successive white keys are
assigned values of two kattais, three kattais and so on.  The
black keys are assigned fractional values (one and a half, two
and half and so on).  Note that there is no three and a half
kattai pitch.  The sruthi accompaniment (tampoora or sruthi box)
provides the reference pitch and we indicate the reference pitch
by saying that somebody sings at one and half kattai pitch, or a
veena is tuned to four and half kattais.  This simply means that
the Sa has been set to that pitch and all other swaras occupy
corresponding sthanas.  The importance of the Sa is that it
provides the fixed foundation note upon which the rest of the
music is built.  Such a foundation note exists in classical
Western music also and is indicated by the scale name eg.
F-Major indicates that the tune is built using F as the base
note. The base note can be discriminated with a little practice
since the music generally returns to dwell on the base note
every now and then.



\section{Swaras and Swarasthanas}

There are seven swaras in Carnatic music, namely, Shadjam (Sa),
Rishabam (Ri), Gandharam (Ga), Madhyamam (Ma), Panchamam (Pa),
Dhaivatham (Da) and Nishadam (Ni).  There is some theoretical
basis for why there is an odd number (seven) of swaras and we
will deal with this subsequently.  For simplicity, let us fix
the Sa at one kattai and place the remaining swaras at the
successive white keys.  This provides us with a scale  or a raga
(in this case, containing all the seven swaras).  As mentioned
previously, ancient Vedic chants have but three swaras and
somewhat later forms of music (Indian as well as other forms,
eg. Chinese) use five swaras - eg. the Sa, Ri, Ga, Pa and Da of
the scale we just created.  Our present system is based on seven
swaras, and perhaps, a few thousand years from now, the human
race will advance to a point of  discriminating scales of more
swaras (unlikely).  The seven swaras are mythologically
associated with the sounds produced by certain animals and the
names of the swaras are related to the names of these animals. 
The name Madhyamam appears to be related to the central or 
madhya location in the seven notes and Panchamam is most
probably derived from the number five, denoting the position of
the note.

We observed earlier that doubling the pitch of a swara by a
factor of two results in going up in pitch by one octave.  Thus,
doubling the pitch of Sa (say Sa1) results in another Sa (Sa2)
which is one octave higher than our original Sa.  A further
doubling produces Sa3 which is one octave higher than Sa2 and
two octaves above Sa1.  Three times the original Sa produces the
Pa located between Sa2 and Sa3.  In other words, the pitch of
the swara Pa is one and half times the pitch of the Sa below it
(and three fourths the pitch of the Sa above it).  Now we come
to an important limitation of the keyboard - the way the octave
is divided into the twelve swara sthanas.  Since it is based on
current western music norms, the division is done on a
logarithmic basis (which is just a more technical way of saying
that the pitch values of the successive swara sthanas form a
geometric progression).  An octave is a factor of two and there
are twelve intervals in it.  If we make all the intervals equal
to a multiplicative factor x, then the pitch corresponding to
any key will be x times the pitch of the key (white or black)
immediately to the left of it.  Extending the procedure we
arrive at what the value of x should be.  The thirteenth swara
sthana results in an octave, or, stated mathematically, x12=2. 
Then, we have x to be the twelfth root of two or a factor of
approximately 1.06.  Using this logarthmic division procedure,
Pa (the 8th swara sthana) corresponds not to a ratio of 1.5 but
1.498.  Though the discrepancy is very small, a well trained ear
(eg. professional musician) can pick out this difference.  

Carnatic music is based not on logarithmic division but on
rational division.  An octave is based on the ratio 1:2; Pa is
located through the ratio 2:3; similar definitions exist for all
the twelve swara sthanas.  A few centuries ago, Western
classical music too was based on rational division (the
resulting scale was called as the natural scale), but this has
given way to the equally tempered (also called chromatic) scale
produced by logarithmic division.  The difference is subtle, but
quite important.  The rational division claim is supported by
the fact that tuning of instruments (for example, in setting the
frets of veena) is performed mostly by the ear and not by
reference to standards.  Further, the swara sthanas of Carnatic
music define only nominal locations for the swaras.  Depending
on the raga in which the swara is used, it manifests a deviation
from the nominal sthana.  Actually, the deviation from the
nominal sthana depends on the swara phrase in which the swara
occurs;  thus, a single swara in a given raga can appear at
different deviations from its nominal sthana when occuring along
with various other swaras of the same raga.  In a general sense,
this deviation is called gamaka.  Gamaka can refer to a constant
deviation  from  the nominal swara sthana or a time dependent
deviation or the path taken in reaching the nominal swara etc. 
Truly, gamaka is the life blood of Carnatic music and the raga
system.  Ragas are defined more by the gamakas and the way in
which certain swara phrases (chain of swaras) are used than by
the mere presence or absence of certain swaras.  Thus, playing
the keys corresponding to the swara sthanas of a certain raga
will not reproduce the true character of the raga but only
provide a general idea of what it sounds like.  This is the
reason why purists object to the use of keyboard instruments in
Carnatic music - the lack of gamaka, which leads to a mutilation
of the raga swaroopa.  The use of gamaka also implies that the
method used for defining nominal swara sthanas (rational or
logarithmic division) is not too critical as long the correct
raga swaroopam can be accommodated.

In the past, Hindustani music also had complex gamaka schemes,
but the acceptance of the Harmonium has caused their virtual
disappearance and only a few of the gamakas remain in use.  The
result is that the current form of Hindustani music has lost
some of its traditional character - perhaps forever.  Carnatic
music is one of the very few musical forms in the world that
have not lost their traditional character due to the influence
of western culture.  On the contrary, Carnatic music has
enhanced its traditional character by borrowing good things from
other systems of music.  The introduction of the violin is a
very good example of a positive influence.  The instrument and
its playing techniques have been successfully adapted to fit in
with the rest of the system.  This adaptation is so complete
that the present day listener can hardly imagine a concert
without a violin accompanying the singer.

The seven basic swaras occupy various swara sthanas and produce
a total of sixteen swaras that form the basis of the raga
scheme.  It should be emphasized that the swara sthanas are
nominal and in actual usage, depending on the raga, the swara is
not fixed at any one sthana but appears at various locations
around a nominal swara sthana in different swara phrases.  The
Shadja and Panchama swaras are like the foundations upon which
the rest of the melody is constructed.  So, these occupy fixed
sthanas.  This is denoted by naming these swaras as Prakruthi
swaras (all the other swaras are grouped under Vikruthi swaras).
 Further, these two swaras are usually employed without any
gamakas.  In order to identify the sthanas of the various
swaras, let us number the twelve sthanas.  The names of the
swaras and the swara sthanas they occupy are given in the
following table.

\begin{tabbing}
Numbered sthana	\ \ \=Name\hspace*{1.5in}\=   Notation/Common name\\
\\
1	  \>    Shadjam			\>	Sa\\
2	  \>    Suddha Rishabam		\>	Ra, Small Ri\\
3	  \>    Chatusruthi Rishabam	 \>       Ri, Big Ri\\
                 \>    Suddha Gandharam	\>        Ga\\
4	  \>    Shatsruthi Rishabam	 \>       Ru\\
                 \>    Sadharana Gandharam	\>	Gi, Small Ga\\
5	  \>    Anthara Gandharam	\>        Gu, Big Ga\\
6	  \>    Suddha Madhyamam	\>        Ma, Small Ma\\
7	  \>    Prati Madhyamam		\>	Mi, Big Ma\\
8	  \>    Panchamam		\>        Pa\\
9	  \>    Suddha Dhaivatham	\>        Da,Small Da\\
10	  \>    Chatusruthi Dhaivatham	\>	Di, Big Da\\
          \>    Suddha Nishadam			Na\\
11          \>    Shatsruthi Dhaivatham	\>	Du\\
          \>    Kaisika Nishadham       \>        Ni, Small Ni\\
12	  \>    Kakali Nishadham	\>        Nu, Big Ni\\

\end{tabbing} 

The numbering used above allows one to easily locate the swaras
on fretted string instruments (veena, mandolin etc.).  One
simply counts up the frets till the desired swara is reached. 
For example, if a Sa is played on a particular fret, to get a
Prati Madhyamam, one simply moves up 6 frets on the same string
(moving six steps from 1 results in 7, the number denoting the
Prati Madhyamam).  The  Ra-Ri-Ru  notation exists chiefly for
convenience and is not used very widely.  In conformance with
that practice, this document will point out when the notation is
being used.  In the absence of such an indication, Ra should be
taken to imply not Suddha Rishabam but a generic Rishabam.   
The following keyboard diagrams show the locations of the swaras
for one kattai and four and a half kattai reference pitch using
the ra-ri-ru notation.  A similar indication can be easily made
up for fretted string instruments simply by using the swara
sthana table and counting up the frets starting from Sa.

The use of sixteen swara names has led to some people describing
an octave as being divided into more than twelve swara sthanas
(as many as twenty two).  But, as the table and keyboard
diagrams show, there are only twelve sthanas and certain pairs
of swaras occupy the same nominal swara sthana (eg. Chatusruthi
Rishabam and Suddha Gandharam).  In an earlier era (or for that
matter, in contemporary Hindustani music), the duplicate name
swaras were not used i.e. each swara sthanam was associated with
one and only one swaram.  The swaras of the octave then read (in
Ra-Ri-Ru notation) Sa - Ra - Ri - Gi - Gu -  Ma - Mi - Pa - Da -
Di - Ni - Nu - Sa.  The remaining swaras, Ru, Ga, Du and Na,
were considered to be tainted ('Dhosham') and their use was to
be avoided.  These four swaras are called as Vivadi swaras and
their use is now generally accepted.  The occurrence of
combinations of swaras gives rise to melodies which can then be
classified on the basis of the swaras that are used.  This leads
to the scheme of ragas which is our next topic of discussion.

\begin{figure}
{\hspace*{1.in} \small 
\begin{verbatim}

====================================
|  |##| |##|   |  |##| |##| |##|   |
|  |##| |##|   |  |##| |##| |##|   |
|  |Ra| |Ru|   |  |Mi| |Da| |Du|   |
|  |##| |Gi|   |  |##| |##| |Ni|   |
|  |__| |__|   |  |__| |__| |__|   |
|    |    |    |    |    |    |    |  
| Sa | Ri | Gu | Ma | Pa | Di | Nu |
|    | Ga |    |    |    | Na |    |
|____|____|____|____|____|____|____|

\end{verbatim} 
\caption{
Swaras for one kattai reference pitch
}
\normalsize}
\end{figure}

\begin{figure}
{\hspace*{1.in} \small
\begin{verbatim}

=========================================================
|  |##| |##|   |  |##| |##| |##|   |  |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##| |##|   |  |##|
|  |##| |##|   |  |##| |Ri| |##|   |  |##| |Di|   |  |##|
|  |##| |##|   |  |Sa| |Ga| |Gu|   |  |Pa| |Na|   |  |##|
|  |__| |__|   |  |__| |__| |__|   |  |__| |__|   |  |__|
|    |    |    |    |    |    |    |    |    |    |    | 
|    |    |    |    |    | Ru |    |    |    | Du |    |
|    |    |    |    | Ra | Gi | Ma | Mi | Da | Ni | Nu |
|____|____|____|____|____|____|____|____|____|____|____|

\end{verbatim} 
\caption{
 Swaras for four and half kattai reference pitch
}
\normalsize}
\end{figure}



\section{Ragas}

Ragas are sometimes defined as melody types.  The raga system is
a method of organizing tunes based on certain natural
principles.  Tunes in the same raga use the same (nominal)
swaras in various combinations and with practice, the listener
can pick up the similarity.  Each raga has a swaroopam (a
musical form or image) that is defined by the swaras used, the
gamakas given to these swaras, the sequence in which the swaras
occur etc.  This definition is termed as the raga lakshanam.
(The magazine Sruthi usually contains a discussion of
ragalakshanam of one or two ragas in each issue). 
Raga lakshanam usually contains the arohanam, avarohanam,
details of raga chaya swaras (the swaras which are chiefly
responsible for the characteristic melody of the raga), gamakas,
characteristic swara phrases and general usage notes.  It is
intended more for the performer than for the listener.  We shall
first define arohanam and avarohanam.  Arohanam is the sequence
of swaras used in a raga in the ascending passages i.e. as the
pitch goes up.  Avarohanam is the sequence of swaras to be used
in descent.  The arohanam and avarohanam (or the scale) of a
raga provide only a skeletal outline upon which the rest of the
raga is formed.

Ragas are not simply abstract collections of swaras that occur
together to produce a tune.  Each raga has a distinct image or
swaroopam and it is this which defines a raga.  Arbitrary
selection of a set of swaras is unlikely to produce a distinct
raga swaroopam and this is the reason for attributing the
foundations of the raga system to nature.  The ragas that we
know of are the products of centuries of experimentation.  Each
ragam has associated with it a feeling that it induces in the
listener and the performer.  Hours of dedicated practice with a
single raga (Saathakam) results in the realization of the raga
swaroopa on the part of the performer and this is often referred
to as obtaining a Dharshan of that particular raga.  The
unfortunate consequence of this is that various performers have
slightly different mental concepts of a single raga and this is
manifest in their music.  But the good part is that it adds a
tremendous variety to the music.  This is also the reason why
Carnatic music (performance) can never really be learnt from a
book but needs a Guru who can portray the raga swaroopam in such
a manner that the pupil can pick it up.  From the viewpoint of
the listener, a realization of the raga swaroopam means that
some of the qualities of the music can be anticipated and this
contributes greatly to listening pleasure.

Ragas fall into two types, the base or melakarta ragas and the
derived or janya ragas.  Melakarta ragas have a formal structure
and follow a fairly rigid scheme of scientific organization
whereas the janya ragas are rooted in usage and are liable to
evolve with the music.  In fact many janya ragas change their
character over time.  Janya ragas are derived from the melakarta
ragas through various means as described subsequently. 
Melakarta ragas are identified by the fact that they use all
seven swaras and the arohanam and avarohanam are always
Sa-Ri-Ga-Ma-Pa-Da-Ni-Sa and Sa-Ni-Da-Pa-Ma-Ga-Ri-Sa.  This type
of arohanam and avarohanam is denoted by the term sampoornam,
indicating completeness.  The existence of multiple swara
sthanas for Ri, Ga, Ma, Da and Ni implies that by collecting
combinations of these, we can form a  system of melakartas. 
This concept will be developed in the succeeding section.  Any
raga that does not belong to the melakarta system is a janya
raga.  Janya ragas are characterized by missing notes in the
arohanam and/or avarohanam (eg. Sa-Ri-Ga-Pa-Da-Sa), the use of
twisted progressions (eg. Sa-Ga-Ri-Ma-Pa-Da-Ni-Sa) etc.  Janya
ragas and their classifications will be described subsequently.

The definition of melakarta given above is a currently accepted
one.  In the past, melakartas have been defined in other ways,
sometimes incompatible with the sampoornam characteristic.  The
present system is mathematically much more elegant and that
appears to be one of the reasons for its wide spread acceptance
and use in the past few centuries.


\section{The Melakarta Scheme}

Contemporary Carnatic music is based on a system of 72 melakarta
ragas.  These 'creator' ragas are also called janaka ragas and
thai (mother) ragas.  The current system can be traced to the
works of Venkatamakhi who appears to be the first to use 72
melakartas.  Earlier works generally contain fewer melakartas
and most have flaws in organization.  At that time, (16th
century) many of Venkatamakhi's melakartas were unknown and were
not assigned names.  Later, all 72 were given names and this
system is sometimes referred to as the Kanakaambari -
Phenadhyuthi system after the names of the first two melakartas
in it.  Muthuswamy Dikshithar's compositions are generally based
on the raga names and lakshanams (definitions) in this system
while Thyagaraja used a later scheme devised by Govindacharya in
the late 18th century.  Venkatamakhi did not believe that
melakartas must be of simple sampoorna arohanam - avarohanam but
favored the idea of calling a raga as a melakarta if all the
seven swaras occurred in either the arohanam or the avarohanam. 
Thus a raga  which went Sa-Ri-Ma-Pa-Ni-Sa, Sa-Da-Pa-Ga-Ri-Sa
could be a melakarta under this scheme.  Govindacharya's
insistence on sampoorna  arohanam - avarohanam leads to a system
which is more elegant from a mathematical viewpoint.  In this
scheme, the melakartas arise out of systematic permutation of
the seven swaras into the twelve swara sthanas.  Seen this way,
the melakarta scheme is a product of mathematical abstraction
and the naming of swaras (and the introduction of vivadi swaras)
is of no consequence as far as the organization of the
melakartas is concerned.  No wonder, Venkatamakhi is reputed to
have said that even Lord Maheswara could not create more
melakartas!

As we noted before, all melakartas employ a complete
(sampoornam) arohanam - avarohanam structure.  The purvangam of a
melakarta refers to the lower half of the Arohanam - Avarohanam,
namely Sa-Ri-Ga-Ma and uttarangam refers to the upper half or
Pa-Da-Ni-Sa.  First let us examine the possible variations in
the uttarangam.  Pa is fixed.  Da can occupy three sthanas and
so can the Ni.  But, the Ni has to be always above the Da and
that leaves us with the following six possible uttarangams.

(1)	Pa-Suddha Dhaivatham-Suddha Nishadam-Sa

(2)	Pa-Suddha Dhaivatham-Kaisika Nishadam-Sa

(3)	Pa-Suddha Dhaivatham-Kakali Nishadam-Sa

(4)	Pa-Chatusruthi Dhaivatham-Kaisika Nishadam-Sa

(Suddha Nishadam occupies the same swara sthana as Chatusruthi
Dhaivatham and hence the two cannot occur together)

(5)	Pa-Chatusruthi Dhaivatham-Kakali Nishadam-Sa

(6)	Pa-Shatsruthi Dhaivatham-Kakali Nishadam-Sa

These six uttarangam combinations are denoted by the names Pa,
Sri, Go, Bhu, Ma and Sha respectively.  The following series of
figures illustrate the keyboard locations of the swaras in these
six uttarangam combinations as also the corresponding numbered
swara sthanams (the number 13 refers to the Sa of the next
octave) for one kattai sruthi.

\begin{figure}
{\hspace*{1.in} \small 
\begin{verbatim}
==========================================
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |Da| |##|   |  |##|
|  |__| |__|   |  |__| |__| |__|   |  |__|
|    |    |    |    |    |    |    |    | 
|    |    |    |    |    |    |    |    |
|    |    |    |    | Pa | Ni |    | Sa |
|____|____|____|____|____|____|____|____|
\end{verbatim} } 
\caption{ Swara Locations for the 'Pa' uttarangam (8-9-10-13)}
\end{figure}

\begin{figure}
{\hspace*{1.in} \small
\begin{verbatim}
==========================================
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |Da| |Ni|   |  |##|
|  |__| |__|   |  |__| |__| |__|   |  |__|
|    |    |    |    |    |    |    |    | 
|    |    |    |    |    |    |    |    |
|    |    |    |    | Pa |    |    | Sa |
|____|____|____|____|____|____|____|____|
\end{verbatim} } 
\caption{ Swara Locations for the 'Sri' uttarangam (8-9-11-13)}
\end{figure}

\begin{figure}
{\hspace*{1.in} \small
\begin{verbatim}
==========================================
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |Da| |##|   |  |##|
|  |__| |__|   |  |__| |__| |__|   |  |__|
|    |    |    |    |    |    |    |    | 
|    |    |    |    |    |    |    |    |
|    |    |    |    | Pa |    | Ni | Sa |
|____|____|____|____|____|____|____|____|
 \end{verbatim} } 
\caption{ Swara Locations for the 'Go' uttarangam (8-9-12-13)}
\end{figure}

\begin{figure}
{\hspace*{1.in} \small
 \begin{verbatim}

==========================================
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |Ni|   |  |##|
|  |__| |__|   |  |__| |__| |__|   |  |__|
|    |    |    |    |    |    |    |    | 
|    |    |    |    |    |    |    |    |
|    |    |    |    | Pa | Da |    | Sa |
|____|____|____|____|____|____|____|____|
\end{verbatim} } 
\caption{ Swara Locations for the 'Bhu' uttarangam
(8-10-11-13)}
 \end{figure}

\begin{figure}
 {\hspace*{1.in} \small
\begin{verbatim}
==========================================
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |__| |__|   |  |__| |__| |__|   |  |__|
|    |    |    |    |    |    |    |    | 
|    |    |    |    |    |    |    |    |
|    |    |    |    | Pa | Da | Ni | Sa |
|____|____|____|____|____|____|____|____|
\end{verbatim} } 
\caption{
 Swara Locations for the 'Ma' uttarangam (8-10-12-13)}
 \end{figure}

\begin{figure}
 {\hspace*{1.in} \small
\begin{verbatim}
==========================================
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |Da|   |  |##|
|  |__| |__|   |  |__| |__| |__|   |  |__|
|    |    |    |    |    |    |    |    | 
|    |    |    |    |    |    |    |    |
|    |    |    |    | Pa |    | Ni | Sa |
|____|____|____|____|____|____|____|____|
\end{verbatim} } \caption{
 Swara Locations for the 'Sha' uttarangam (8-11-12-13)}
 \end{figure}
\normalsize 

As in the case of the Da and Ni uttarangam combinations, the Ri
and Ga provide six possible combinations.  Each of these can
occur with either of the two Madhyamams to yield a total of
twelve possible purvangams.  The twelve purvangam combinations
are each called as chakras.  The twelve chakras and the
corresponding purvangams are as follows.

\begin{figure*}[h]
{\hspace*{1.in} \small 
\begin{verbatim}
(1)	Indu	Sa, Suddha Rishabam, Suddha Gandharam, Suddha Madhyamam
(2)	Netra	Sa, Suddha Rishabam, Sadharana Gandharam, Suddha Ma
(3)	Agni	Sa, Suddha Rishabam, Anthara Gandharam, Suddha Ma
(4)	Veda	Sa, Chatusruthi Rishabam, Sadharana Gandharam, Suddha Ma
(5)	Bana	Sa, Chatusruthi Rishabam, Anthara Gandharam, Suddha Ma
(6)	Ruthu	Sa, Shatsruthi Rishabam, Anthara Gandharam, Suddha Ma
(7)	Rishi	Sa, Suddha Rishabam, Suddha Gandharam, Prati Madhyamam
(8)	Vasu	Sa, Suddha Rishabam, Sadharana Gandharam, Prati Ma
(9)	Brahma	Sa, Suddha Rishabam, Anthara Gandharam, Prati Ma
(10)	Disi	Sa, Chatusruthi Rishabam, Sadharana Gandharam, Prati Ma
(11)	Rudra	Sa, Chatusruthi Rishabam, Anthara Gandharam, Prati Ma
(12)	Aditya	Sa, Shatsruthi Rishabam, Anthara Gandharam, Prati Ma
\end{verbatim} 
\normalsize}
\end{figure*}

 The chakra names are associated with the chakra numbers they
represent.  For example, there are four Vedas, and Veda chakra
is the fourth chakra.  The following illustrations depict the
swara locations on the keyboard for the twelve chakras, along
with the numbered swaras.

\begin{figure}
{\hspace*{1.in} \small 
\begin{verbatim}
==========================================
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |Ri| |##|   |  |##| |##| |##|   |  |##|
|  |__| |__|   |  |__| |__| |__|   |  |__|
|    |    |    |    |    |    |    |    | 
|    |    |    |    |    |    |    |    |
| Sa | Ga |    | Ma |    |    |    |    |
|____|____|____|____|____|____|____|____|

\end{verbatim} 
\caption{
 Swaras of Indu Chakra (1-2-3-6)
}
\normalsize}
\end{figure}

\begin{figure}
{\hspace*{1.in} \small 
\begin{verbatim}


==========================================
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |Ri| |Ga|   |  |##| |##| |##|   |  |##|
|  |__| |__|   |  |__| |__| |__|   |  |__|
|    |    |    |    |    |    |    |    | 
|    |    |    |    |    |    |    |    |
| Sa |    |    | Ma |    |    |    |    |
|____|____|____|____|____|____|____|____|
\end{verbatim} 
\caption{
 Swaras of Netra Chakra (1-2-4-6)
}
\normalsize}
\end{figure}

\begin{figure}
{\hspace*{1.in} \small 
\begin{verbatim}

==========================================
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |Ri| |##|   |  |##| |##| |##|   |  |##|
|  |__| |__|   |  |__| |__| |__|   |  |__|
|    |    |    |    |    |    |    |    | 
|    |    |    |    |    |    |    |    |
| Sa |    | Ga | Ma |    |    |    |    |
|____|____|____|____|____|____|____|____|
\end{verbatim} 
\caption{  Swaras of Agni Chakra (1-2-5-6)
}
\normalsize}
\end{figure}
\begin{figure}
{\hspace*{1.in} \small 
\begin{verbatim}
==========================================
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |Ga|   |  |##| |##| |##|   |  |##|
|  |__| |__|   |  |__| |__| |__|   |  |__|
|    |    |    |    |    |    |    |    | 
|    |    |    |    |    |    |    |    |
| Sa | Ri |    | Ma |    |    |    |    |
|____|____|____|____|____|____|____|____|
\end{verbatim} 
\caption{  Swaras of Veda Chakra (1-3-4-6)
}
\normalsize}
\end{figure}

\begin{figure}
{\hspace*{1.in} \small 
\begin{verbatim}
==========================================
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |__| |__|   |  |__| |__| |__|   |  |__|
|    |    |    |    |    |    |    |    | 
|    |    |    |    |    |    |    |    |
| Sa | Ri | Ga | Ma |    |    |    |    |
|____|____|____|____|____|____|____|____|
\end{verbatim} 
\caption{
 Swaras of Bana Chakra (1-3-5-6)
}
\normalsize}
\end{figure}


\begin{figure}
{\hspace*{1.in} \small 
\begin{verbatim}
==========================================
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |Ri|   |  |##| |##| |##|   |  |##|
|  |__| |__|   |  |__| |__| |__|   |  |__|
|    |    |    |    |    |    |    |    | 
|    |    |    |    |    |    |    |    |
| Sa |    | Ga | Ma |    |    |    |    |
|____|____|____|____|____|____|____|____|
\end{verbatim} 
\caption{  Swaras of Ruthu Chakra (1-4-5-6) }
\normalsize}
\end{figure}

\begin{figure}
{\hspace*{1.in} \small 
\begin{verbatim}
==========================================
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |Ri| |##|   |  |Ma| |##| |##|   |  |##|
|  |__| |__|   |  |__| |__| |__|   |  |__|
|    |    |    |    |    |    |    |    | 
|    |    |    |    |    |    |    |    |
| Sa | Ga |    |    |    |    |    |    |
|____|____|____|____|____|____|____|____|
\end{verbatim} 
\caption{ Swaras of Rishi Chakra (1-2-3-7) }
\normalsize}
\end{figure}


\begin{figure}
{\hspace*{1.in} \small 
\begin{verbatim}
==========================================
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |Ri| |Ga|   |  |Ma| |##| |##|   |  |##|
|  |__| |__|   |  |__| |__| |__|   |  |__|
|    |    |    |    |    |    |    |    | 
|    |    |    |    |    |    |    |    |
| Sa |    |    |    |    |    |    |    |
|____|____|____|____|____|____|____|____|
\end{verbatim} 
\caption{ Swaras of Vasu Chakra (1-2-4-7) }
\normalsize}
\end{figure}

\begin{figure}
{\hspace*{1.in} \small 
\begin{verbatim}
==========================================
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |Ri| |##|   |  |Ma| |##| |##|   |  |##|
|  |__| |__|   |  |__| |__| |__|   |  |__|
|    |    |    |    |    |    |    |    | 
|    |    |    |    |    |    |    |    |
| Sa |    | Ga |    |    |    |    |    |
|____|____|____|____|____|____|____|____|
\end{verbatim} 
\caption{ Swaras of Brahma Chakra (1-2-5-7) }
\normalsize}
\end{figure}


\begin{figure}
{\hspace*{1.in} \small 
\begin{verbatim}
==========================================
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |Ga|   |  |Ma| |##| |##|   |  |##|
|  |__| |__|   |  |__| |__| |__|   |  |__|
|    |    |    |    |    |    |    |    | 
|    |    |    |    |    |    |    |    |
| Sa | Ri |    |    |    |    |    |    |
|____|____|____|____|____|____|____|____|
\end{verbatim} 
\caption{ Swaras of Disi Chakra (1-3-4-7) }
\normalsize}
\end{figure}



\begin{figure}
{\hspace*{1.in} \small 
\begin{verbatim}
==========================================
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |Ma| |##| |##|   |  |##|
|  |__| |__|   |  |__| |__| |__|   |  |__|
|    |    |    |    |    |    |    |    | 
|    |    |    |    |    |    |    |    |
| Sa | Ri | Ga |    |    |    |    |    |
|____|____|____|____|____|____|____|____|
\end{verbatim} 
\caption{ Swaras of Rudra Chakra (1-3-5-7) }
\normalsize}
\end{figure}



Each of the twelve purvangams can be combined with the six
uttarangams to obtain a total of 72 melakartas.  The melakartas
are then identified by combining the chakra name with the Pa -
Sri designation.  Thus, a melakarta described as Rudra-Ma (or
no. 65, Mechakalyaani) corresponds to an arohanam and avarohanam
containing Shadjam - Chatusruthi Rishabam - Anthara Gandharam -
Prati Madhyamam - Panchamam - Chatusruthi Dhaivatham - Kakali
Nishadam - Shadjam.  The following table lists all the 72
melakartas and the swaras used in each of them using the chakra
and Pa - Sri notation as described.  The first 36 melakartas use
Suddha Madhyamam and melakartas 37 through 72 use  Prati
Madhyamam.  These two groups are sometimes identified as Suddha
Madhyama melakartas or Purva melakartas and Prati Madhyama
melakartas or Uttara melakartas respectively.  The table is
organized in such a fashion that a Suddha Madhyama melakarta and
its Prati Madhyama pair (the melakarta which shares all swaras
except the Madhyama) occur on the same line.  Thus to find out
what is the Prati Madhyama (or Uttara melakarta) pair of
Maayaamaalavagowla, one just reads across the table to find
Kaamavardhani (which is also known as Pantuvaraali).  If it were
not for the gamakkas, such pairs would sound very similar and be
different only when the Madhyama occurs. 

\begin{figure}
{ \hspace*{1.in} \small 
\begin{verbatim}
==========================================
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |Ri|   |  |Ma| |##| |##|   |  |##|
|  |__| |__|   |  |__| |__| |__|   |  |__|
|    |    |    |    |    |    |    |    | 
|    |    |    |    |    |    |    |    |
| Sa |    | Ga |    |    |    |    |    |
|____|____|____|____|____|____|____|____|
\end{verbatim} 
\caption{ Swaras of Aditya Chakra (1-4-5-7) }
\normalsize}
\end{figure}

\newpage
\begin{table}[p]
\centerline{\bf Melakarta Ragas}
\begin{tabbing}
\hspace{.4in}\= \hspace{2.in}\=\hspace{.4in}\=\hspace{.7in}\=\hspace{0.4in}\= \hspace{2.75in}\= \hspace{.5in}  \\
No.\> Name	\>\>\>     \>     Name	     \> No.\\
\\
1 \>  Kanakaangi\>\>	Pa\> R\>Saalakam	 \> 37\\
2 \>  Rathnaangi\> I\>	Sri\>I\>	Jalaarnavam	 \> 38\\
3 \>  Gaanamurthy\> N\>	Go	\>S\>	Jhaalavaraali	 \> 39\\
4 \>  Vanaspathy\> D\>	Bhu\>H\>	Navaneetham	 \> 40\\
5 \>  Maanavathy\> U\>	Ma	\>I\>	Paavani	         \> 41\\
6 \>  Taanaroopi\>\>	Sha\>	\>	Raghupriya	 \> 42\\
7 \>  Senaavathy\> N\>	Pa	\>	\>	Gavaambhodhi\>	  43\\
8 \>  Hanumathodi\> E\>	Sri\>	V\>	Bhavapriya	 \> 44\\
9 \>  Dhenuka	\> T   \>  Go\>	A	\>Subhapantuvaraali\> 45\\
10\>  Naatakapriya \>R \>  Bhu\>	S	\>Shadvidhamaargini\> 46\\
11\>  Kokilapriya \>A\>	Ma\>	U\>	Suvarnaangi	 \> 47\\
12\>  Roopavathy\>\>	Sha	\>\>	Divyamani	\>  48\\
13\>  Gaayagapriya\>\>     Pa	\>	B\>	Dhavalaambari\>	  49\\
14\>  Vakulaabharanam\>      A\>  Sri\>	R\>	Naamanaaraayani\>	  50\\
15\>  Maayaamaalavagowla\>   G \> Go\>	A\>	Kaamavardhani	 \> 51\\
16\>  Chakravaaham   \>  N \> Bhu\>	H\>	Raamapriya	 \> 52\\
17\>  Sooryakaantham  \> I \> Ma\>	M\>	Gamanasrama	 \> 53\\
18\>  Haatakaambari\>	\> Sha\>	A\>	Visvambari	 \> 54\\
19\>  Jhankaaradhwani\>   \>  Pa	\>	\>	Shyaamalaangi\>	  55\\
20\>  Natabhairavi  \>   V \> Sri\>	D\>	Shanmugapriya	 \> 56\\
21\>  Kiravaani	    \>   E \> Go	\>	I\>	Simhendramadhyamam\>57\\
22\>  Kharaharapriyaa \> D \> Bhu\>	S\>	Hemavathy	 \> 58\\
23\>  Gowrimanohari  \>  A \> Ma\>	I\>	Dharmavathy	\>  59\\
24\>  Varunapriya  \>   \>  Sha\>	\>	Neetimathi	\>  60\\
25\>  Maararanjani \>  \>  Pa\>		R\>	Kaantaamani	\>  61\\
26\>  Chaarukesi \> B \> Sri\>	U\>	Rishabhapriya	 \> 62\\
27\>  Sarasaangi \> A\>  Go	\>	D\>	Lataangi	\>  63\\
28\>  Harikaambhoji\>     N\>  Bhu\>	R\>	Vaachaspathy	 \> 64\\
29\>  Dheerasankaraabharanam\>A \> Ma\>       A\>	Mechakalyaani	\>  65\\
30\>  Naagaanandini\>\>	Sha	\>\>	Chitraambari	 \> 66\\
31\>  Yaagapriya \>R \> Pa	\>	A\>	Sucharithram	\>  67\\
32\>  Raagavardhani\>   U\>  Sri\>	D\>	Jyotiswaroopini	 \> 68\\
33\>  Gaangeyabhooshani\> T\>  Go	\>	I\>	Dhaatuvarthini	\>  69\\
34\>  Vaagatheeswari  \>  H \> Bhu\>	T\>	Naasikaabhooshani \>70\\
35\>  Shoolini	    \>   U \> Ma	\>	Y\>	Kosalam	    \>      71\\
36\>  Chalanaata  \> \>  Sha        \>A	\>Rasigapriya	  \>72\\
\end{tabbing}
\end{table}

Many of the melakartas have alternate names like in the example
just cited and some of these are listed in the Appendix.  In
addition, some of the common ones (like Thodi) are listed with
prefixes (Hanumathodi).  This is in accordance with the so
called 'Katapayaathi' formula.  Using this formula, numerical
values are assigned to consonants as listed in the following
table (the devanagari script is the basis upon which this
assignment is done).  To find out what is the location of a
melakarta in the table, the first two consonants are deciphered
using the numerical assignment table and the resulting number is
inverted left to right.  For example, consider Hanumathodi - the
first two consonants being Ha and Na.  Ha is assigned 8 and Na
is zero.  The resulting number if 80 and after inversion, this
yields the number 8, which is the melakarta number corresponding
to Hanumathodi.  One must be careful in decoding prefixes - for
example, Thodi, Sankaraabharanam and Kalyaani are melakartas
which take on prefixes to identify their melakarta numbers but
Naata, Bhairavi and Kaambhoji are not melakartas but actually
janya ragas of Chalanaata, Natabhairavi and Harikaambhoji
respectively.  The naming of melakartas in accordance with the
Katapayaathi formula is generally attributed to Govindacharya. 
Govindacharya was well versed in astrology and the Katapayaathi
convention has been widely used in astrology for centuries.

Once the melakarta number is known, one can use the chakra
scheme to identify the swaras in it.  As an example, consider
Shanmugapriya.  The consonants are Sha and Ma.  Sha=6 and Ma=5
to yield the melakarta number 56.  Dividing 56 by 6 yields a
quotient of 9 and a remainder of 2.  This means that
Shanmugapriya belongs to the 10th (or Disi) chakra and is the
second (or Sri) raga in that chakra.  Thus Shanmugapriya is
identified as Disi-Sri.  Then, the swaras in Shanmugapriya are
(collecting the purvangam and uttarangam from the tables) Sa -
Chatusruthi Rishabam - Sadharana Gandharam - Prati Madhyamam -
Pa - Suddha Dhaivatham - Kaisika Nishadam - Sa.  Note that in
figuring out the chakra, we need to add one to the quotient to
obtain the chakra number.  We can use the melakarta table to
directly find that Shanmugapriya is Disi-Sri and end up with the
same swaras.   The following keyboard diagram illustrates the
location of the swaras in Shanmugapriya for one kattai sruthi.

\begin{figure}
{\hspace*{1.in} \small 
\begin{verbatim}

==========================================
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##|
|  |##| |Ga|   |  |Ma| |Da| |Ni|   |  |##|
|  |__| |__|   |  |__| |__| |__|   |  |__|
|    |    |    |    |    |    |    |    | 
|    |    |    |    |    |    |    |    |
| Sa | Ri |    |    | Pa |    |    | Sa |
|____|____|____|____|____|____|____|____|


\end{verbatim} 
\caption{
 Swaras in Raga Shanmugapriya
}
\normalsize}
\end{figure}


\begin{table}
{\hspace*{1.in} \small 
\begin{verbatim}
Table. Letter Values in Katapayaathi Formula

Values	Letters

        Ka series	Ta 	Pa 	Ya	

1	Ka	Ta (as in Tom)	Pa	Ya
2	Kha	Tha	Pha	Ra
3	Ga	Da (as in dumb)	Ba	La
4	Gha	Dha	Bha	Va
5	Nga (as in Bengal)	Na (as in Anna)	Ma	Sa (as in Siva)
6	Cha (as in chip)	Ta (as in with)		Sha(as in Shut)
7	Chha	Tha		Sa (as in Sea)
8	Ja	Da		Ha
9	Jha	Dha
0	Ngya	Na (as in Pen)
\end{verbatim} 
\normalsize}
\end{table}

It is worthwhile to observe here that the Pa, Sri, Go, Bhu, Ma,
Sha designation is also based on the Katapayaathi formula (with
Sri treated as ra).  The formal organization of the melakartas
provides some insights into the similarities between certain
ragas.  Ragas in the same chakra share their purvangam and thus,
sound similar in that portion.  This explains, for example, the
similarity between Kharaharapriya and Kiravaani.  Ragas whose
melakarta numbers differ by a multiple of six (meaning they have
the same Pa-..-Sha designation) have the same uttarangam and
this too causes similarity, as in the case of Lataangi and
Kaamavardhani.  One can find many pairs of melakarta ragas that
differ by a single swaram, as in the case of Lataangi and
Kaamavardhani (which differ only in Ri).  Locating such pairs is
often very instructive.  A good musician makes it a point not to
dwell on chains of swaras that are shared by various ragas, but
often introduces contrasting swaras that are designed to let the
listener identify the similarities and the differences
simultaneously.  This aspect can be used as a test of how good a
musician really is.  In a recent concert, a popular musician was
performing a composition in the raga Chaarukesi.  Chaarukesi can
be seen to have the same purvangam as Sankaraabharanam and the
same uttarangam as Shanmugapriya or Thodi.  However, singing the
purvangam portion of Sankaraabharanam and then the uttarangam of
Shanmugapriya or Thodi has very little to do with the true
swaroopam of Chaarukesi.  This is like arguing that glueing a
lion's head to a human torso results in the creation of a new
being, when all it really does is create neither a lion nor a
human being.  The resulting creature is a poor excuse for a
human or a lion and can be seen only as such.  The use of
gamakkas is also intricately connected to the concept of raga
swaroopam and even though swaras may be the same, the gamakkas
are often different, leading to ragas that are quite distinct in
character.

The melakarta ragas in which vivadi swaras appear are called as
vivadi melakartas.  Thus all melakartas of Indu, Ruthu, Rishi
and Aditya chakras as well as all melakartas with Pa or Sha
designation are vivadi melakartas.    The Pa and Sha designated
ragas have a vivadi swara in their uttarangam while the Indu,
Ruthu, Rishi and Aditya chakra ragas have a vivadi swara in
their purvangams.  Thus, there are 40 vivadi melakartas, out of
which 8 have two vivadi swaras and the rest one vivadi swara
each.  If a melakarta system is constructed without the vivadi
melakartas, a number of fairly common ragas will have to be
treated as being outside the system (eg. Gaanamurthy,
Jhaalavaraali).  Further, janya ragas like Naata will have no
associated melakarta, exposing the limitations of the
classification system.


\section{Janya Ragas}

Janya ragas, as we have seen before, are derived from the
melakarta ragas.  The simplest way to generate a janya raga is
to leave out one or more of the swaras in the arohanam and/or
avarohanam.  For example, if we drop out the Ma and Ni in the
arohanam of Dheerasankaraabharanam, we end up with Sa - Ri - Ga
- Pa - Da - Sa for the arohanam and a sampoorna avarohanam.  The
resulting raga is called Bilahari.  Thus, Bilahari is described
as a janya raga of the 29th melakarta Dheerasankaraabharanam
with an arohanam - avarohanam of Sa - Ri - Ga - Pa - Da - Sa, Sa
- Ni - Da - Pa - Ma - Ga - Ri - Sa.  This means that when going
up the scale, one may use only the notes of the arohanam,
namely, Sa, Ri, Ga, Pa, Da and Sa whereas, all seven notes can
be used in descent.  Thus, when a Ma or Ni is used, one has to
necessarily descend (using notes from the avarohanam).

Dropping out more than two swaras results in a scale that is
very limited and experience suggests that it is virtually
impossible to create a distinct raga swaroopam with the
remaining swaras.  However, there are some ragas which use only
four swaras in the arohanam or avarohanam as in the case of
Navarasa Kannada, derived from the 28th melakarta Harikaambhoji,
with a structure of Sa-Ga-Ma-Pa-Sa, Sa-Ni-Da-Ma-Ga-Ri-Sa.  Just
like a complete arohanam or avarohanam is called sampoornam, one
with a single swara dropped out is called shadava and one with
two swaras left out is termed oudava. Allowing the arohanam and
avarohanam to be sampoornam, shadava or oudava independently,
the following possible arohanam - avarohanam types can be
constructed.

{\hspace*{1.in} \small 
\begin{verbatim}
(1)	sampoorna - sampoorna 
(2)	sampoorna - shadava
(3)	sampoorna - oudava
(4)	shadava - sampoorna
(5)	oudava - sampoorna
(6)	shadava - shadava
(7)	shadava - oudava
(8)	oudava - shadava
(9)	oudava - oudava

\end{verbatim} 
\normalsize}

The first case evidently refers to the melakartas themselves and
does not generate any janya ragas.  The example of Bilahari
belongs to the 5th or oudava - sampoorna case.  Using the
sampoorna - shadava case as an example, there are 72 sampoorna
arohanams and six shadava avarohanams for each, leading to total
of 432 janya ragas of this type.  By the same argument, there
are 432 janya ragas of shadava - sampoorna type.  Following this
procedure, one can arrive at a total of about thirty thousand
independent janya ragas.  However, a large number of these are
not in use since they do not have distinct raga swaroopas.  This
brings us to the important observation that it is not just
mathematical jugglery that produces ragas.  As the saying goes,
'Ranjayathi ithi Raga' - that which is beautiful is a raga. 
Ragas are produced through experimenting with the possible
combinations, looking for distinct swaroopas.  This process has
been conducted for centuries by composers and musicians to
arrive at the few hundred or so janya ragas currently in use.

The type of janya raga we have considered so far, namely, what
is derived by simply dropping notes from a melakarta raga, is
called as an Upaanga raga.  There are alternate means of
generating janya ragas.  The arohanam and/or avarohanam can use
a twisted progression.  For example, we can construct a janya
raga from Dheerasankaraabharanam using the arohanam Sa - Ri - Ma
- Da - Ni - Ga - Pa - Sa and a simple sampoorna avarohanam.  The
resulting raga is called Katanakuthoohalam.  A janya ragam
employing a twisted arohanam and/or avarohanam is termed as a
Vakra ragam.  We can also mix notes from two melakartas in the
arohanam and avarohanam to produce janya ragas.  For example,
the ragam Bhairavi uses Chatusruthi Dhaivatham in its arohanam
and Suddha Dhaivatham in its avarohanam.   This type of
structure is indicated by the term Baashaanga ragam.  A ragam
can be Baashaangam or Upaangam but not both.  The Vakra 
characteristic can be combined freely with both types.  The
result is that a very large number of combinations are possible
and only the ability to create a distinct swaroopam dictates
what combinations are actually used in creating janya ragas. 
The description of a janya raga usually indicates the melakarta
from which it is derived, whether it Vakram or not, whether is
Upaangam or Baashaangam, and if it Baashaangam, the swaras which
make it so.  The arohanam and avarohanam provide further details
(like sampoorna, shadava or oudava).

The term varja is sometimes used to indicate missing swaras. 
For example, the raga Sriranjani has an arohanam - avarohanam of
Sa - Ri - Ga - Ma - Da - Ni - Sa, Sa - Ni - Da - Ma - Ga - Ri -
Sa and is derived from the 22nd melakarta Kharaharapriya.  It is
thus described as a Panchama varja raga, derived from
Kharaharapriya.  Consider another example, Malayamaarutham.  It
is a Madhyama varja raga derived from the 16th melakarta
Chakravaaham.  The designation of the parent ragam as
Chakravaaham is subjective since the Madhyama varja raga derived
from the 52nd melakarta Raamapriya is identical to
Malayamaarutham.  The problem is that Chakravaaham and
Raamapriya differ only in Ma and since Malayamaarutham is
Madhyama varja, it can be derived from either.  In such cases,
the gamakas used in the janya raga have to be studied to decide
which of the melakartas is appropriately described as the parent
raga.  This problem is compounded in the case of Baashaanga
ragas which are anyway derived from multiple melakartas.  In any
case, the assignment of a  parent melakarta is somewhat
subjective and various experts often ascribe different parents
for a given janya raga.  A well known example is the ragam
Mohanam, which has an arohanam - avarohanam of Sa - Ri - Ga - Pa
- Da - Sa, Sa - Da - Pa - Ga - Ri - Sa, using Chatusruthi
Rishabam, Anthara Gandharam and Chatusruthi Dhaivatham.  Various
authors have classified it as a janya ragam of Harikaambhoji
(melakarta no. 28) and Mechakalyaani (65) and more are possible.
 It is a matter of individual viewpoint as to which is the
parent ragam.  As long the distinct swaroopam is maintained, it
really does not matter what is assigned  as the parent ragam.


\section{Taalam}

We have seen that the term raga refers to the tune or melody
characteristics.  The analogous term referring to the rhythm or
beats of Carnatic music is taalam.  It indicates the pacing of
the music and the placement of syllables in the composition.  It
is vital to realize that the taalam system is essentially based
on a cyclic pattern; in other words, the rhythm is always
cyclic.  In Carnatic music, the singer indicates the taalam
using gestures.  There are three basic hand movements used in
keeping the rhythm - the downward beat with the palm facing
down, called thattu, the wave (sometimes the downward beat with
the palm facing up) called veechu and counts using one finger
for each count staring with the little finger (sometimes using
the thumb to indicate a finger or portions of a finger).  These
basic movements are combined into three groups, called Laghu,
Dhrutham and Anudhrutham.  A Laghu is one thattu followed by a
specified number of counts to make up the requisite number of
beats.  A Dhrutham is one thattu followed by one veechu while an
Anudhrutham is just one thattu.  Each beat or unit of taalam is
termed as an aksharam and thus, an Anudhrutham is one aksharam
long, a Dhrutham is two aksharams long and the Laghu is of
variable length.  There are several other movements but these
are rarely seen in practice.

The absolute duration of an aksharam is not fixed and it varies,
depending on the composition and the mood of the performer. 
This is similar to the way in which the absolute pitch of the
swaras is not fixed but defined only relative to the reference
pitch or sruthi.  The aksharam is further divided into a number
of swaras and this division is referred to as gathi or nadai. 
Four swaras per aksharam is standard and is termed Chaturasra
nadai.  The other standard divisions and the associated number
of swaras per aksharam are Tisra (three), Khanda (five), Misra
(seven) and Sankirna (nine).  These divisions apply to medium
tempo or Madhyama Kaalam.  The divisions can be doubled to yield
a fast tempo termed Dhuritha Kaalam or halved to yield the slow
Chowka Kaalam.  Further doubling and halving are also possible
but rarely heard.  Most of Dikshithar's compositions have the
last line of Anupallavi and Charanam (see Elements of Recital
section for definitions) set to Dhuritha Kaalam.

There are seven common taalams employing a mixture of the
movements just described.  In standard notation, the Laghu is
indicated by a |, the Dhrutham by a 0 and the anudhrutham by a
U.  The length of the Laghu is indicated by a subscript placed
after the |.  For example, |4 indicates a Laghu of length 4,
which comprises of a thattu followed by a three count on the
fingers for a total of four aksharams.  The seven common taalams
and their components are as follows:

{\hspace*{1.in} \small 
%\begin{verbatim}
\begin{tabular}{lllll}
Eka&	$|$&&&\\
Roopaka&0&$|$&&\\
Triputa&$|$&0&0&\\
Mattya&$|$&0&$|$&\\
Jhampa&$|$&U&0&\\
Dhruva&$|$&0&$|$&$|$\\
Ata&$|$&$|$&0&0
%\end{verbatim} 
\end{tabular}
\normalsize}

The length of the Laghu has not been specified in the
classification.  There are five possible Laghu lengths called
Tisra (length 3 aksharams), Chaturasra (4 aksharams), Khanda
(5), Misra (7) and Sankirna (9).  Each of these five Laghus can
occur in the seven basic taalams to produce a total of thirty
five taalams.  For example, Misra Jhampa taalam (|7 U 0) has a
Laghu of 7 aksharams, an Anudhrutham and a Dhrutham.  This would
be indicated by a thattu (counted one) followed by a six count
on the fingers (counts two through seven), two thattus and a
veechu, for a total of ten aksharams.  Each of these thirty five
taalams can be divided into the five nadais to yield 175 beat
patterns.  Sometimes, the taalam names are used without
indicating the length of the Laghu and are to be interpreted as
follows: Eka (Chaturasra Eka), Roopaka (Chaturasra Roopaka),
Triputa (Tisra Triputa), Jhampa (Misra Jhampa), Ata (Khanda
Ata).  Chaturasra Roopakam is usually indicated by two thattus
and a veechu (each of two akshara length) in order to economize
hand motion.

In addition to the taalams just described, there are three more
common taalams - Aadi, Khanda Chaapu and Misra Chaapu.  Aadi
taalam is just the name given to the most common taalam -
Chaturasra Triputa or |4 0 0.  Khanda Chaapu is a five beat
taalam also called arai Jhampa (or half Jhampa) and is usually
indicated 0 U 0, though there is really no fixed way of
indicating it.  One can also see a thattu of two aksharams
followed by two veechus of one and two aksharam durations. 
Khanda Chaapu is often used as a version of Misra Jhampa.  Misra
Chaapu is similar to Tisra Triputa and is sometimes used as an
alternative.  The usual indication consists of a thattu of three
aksharams followed by two veechus or two thattus of two
aksharams each, for a total of seven aksharams (and hence the
name).

There is another aspect of taalam which merits attention - the
starting point of the song in relation to the taalam or the
eduppu as it is called.  Many songs start simultaneously with
the beat and this is termed as sama eduppu indicating that the
start is level with the taalam.  Often, the song starts after
the taalam is started, leaving an empty rhythm pattern at the
beginning.  This gap allows the singer greater freedom in
improvisation (see also under the section titled Elements of a
Recital).  This is indicated by the term anaagatha eduppu. 
Sometimes, the song starts before the beat and this is termed 
atheetha eduppu.  This construction is often used to add a one
or two syllable prefix (eg. Hari, Sri, Amba) to the text of the
melodic line.  A peculiar eduppu is associated with a taalam
called Desadi taalam.  Though this taalam actually consists of
four movements, each of two aksharam duration, it is customary
to keep pace for this taalam using simple Aadi taalam.  Then,
the eduppu is at one and half aksharams from the start of the
taalam or three eighths way into the laghu.  An example for
Desadi eduppu is the song 'Bantu reethi kolu viya vayya Raama'
in the ragam Hamsanaadham.


\section{Elements of a Recital}

The exact form of a concert or recital changes with time,
adapting to the perceived needs of the listener and the
performer.  Much of the form as described here is generally
attributed to the tradition established by Sri Ariyakkudi
Ramanuja Iyengar.  There are two essential portions in any
Carnatic Music Recital - a composed portion and an extempore
portion.  The composed portion is fixed (more or less) while the
extempore or improvisational portion is heavily dependent on the
skills and imagination of the performer.  This extempore portion
is thus governed by the mind and is hence referred to as
manodharma sangeetham.  Recitals often start with a Varnam.  A
Varnam is a composed piece of fairly short duration usually set
to Aadi or Ata taalam.    It is usually performed at the start
of a recital as a warm up piece.  The lyrics are simple and
consist mostly of long syllables and swara phrases of various
lengths which bring out the essential features of the raga. 
There is usually a Pallavi and an Anupallavi, followed by a
Mukthaayiswaram and repetitions of a Charanam with various
Chittaswarams.  The Pallavi establishes a characteristic theme
of the raga, typically in the lower portion or purvangam of the
raga, while the Anupallavi provides a parallel or contrasting
theme in the upper portions (uttarangam).  The Mukthaayiswaram
and Chittaswarams both consist of chains of swaras rendered
using the swara syllables themselves (Sa, Ri, etc.).  The
Charanam is often composed on a raga theme related to the
Pallavi and the Anupallavi.

The recital then proceeds with the rendition of a number of
Krithis or Kirthanais (songs) in various ragas and taalams.
These songs, which are the main items of performance, are
composed pieces of various lengths.  Most compositions are of a
devotional nature due to the historically close relationship
between music and religion.  Generally, a few compositions of
The Trinity are included.  The Trinity refers to the three great
composers of Carnatic Music, Thyagaraja, Muthuswami Dikshithar
and Shyama Shastry.  The three were contemporaries who lived in
the late 18th and early 19th centuries in and around Tiruvarur
(near the South Indian City of Tanjore).  Thyagaraja is well
known for his five compositions in the ragas Naata, Gowla,
Aarabhi, Varaali and Sriragam, generally referred to as the
Pancharatnams.  Dikshithar's most famous compositions include
the Kamalaamba Navaavarna Krithis and the Navagraha Krithis. 
Thyagaraja and Shyama Shastry composed mainly in Telugu whereas
Dikshithar mostly used Sanskrit.  Dikshitar and Shyama Shastry
have often included the name of the raga also in their lyrics. 
The word Thyagaraja appears in Thyagaraja's compositions to
identify the composer.  Dikshithar used Guruguha as his
identifier while Shyama Shastry used Shyama Krishna.  The
identifiers for several other composers are listed in the
appendix.

Krithis formally have a Pallavi, an Anupallavi and one or more
Charanams.  A Kirthanai is similar to a Krithi but has no
Anupallavi. Often, a number of Sangadhis are used for each line
of the song.  Sangadhi is the repetition of a single line or
similar short portion of the song using various melodic tunes. 
Initially, the tune is simple and slowly, the structure of the
raga is revealed using more complicated structures.  This
portion is generally composed but many performers include their
own variations also.  A Swarajathi is sometimes included along
with the Krithis and Kirtanais in the main portion of the
concert.  A Swarajathi is like a Krithi but its Charanam section
is rendered first using the swaras and then the lyrics.  One of
the most dedicated Carnatic musicians of our times, Sri
Semmangudi Srinivasa Iyer, often used to sing Shyama Shastry's
Swarajathi composition in the raga Bhairavi beginning with the
words (Kanji) Kamakshi.  The Charanam sections of the Pancha
Ratna Keertanais of Thyagaraja are customarily sung in the
Swarajathi fashion i.e., first using the swarams and then with
the lyrics.

Some of the songs are preceded by an Aalaapanai, and may include
Niraval and/or Kalpanaaswaram.  An Aalapanai is an improvisation
in the same raga as the song.  It has no lyrics and only
abstract (meaningless) syllables are used (eg. Ta, Da, Ri, Na,
Nau).  There is no rhythm for this portion of the performance
which is essentially an extempore attempt by the performer to
convey the raga swaroopam as experienced by him/her.  The
Aalaapanai has a formal structure, similar to the Pallavi -
Anupallavi scheme.  It includes movements in all the three
sthaayis as the raga allows.  Sthaayi is the octave or register
of the swaras.  The normal or middle sthaayi is termed Madhya
sthaayi, the upper octave is Thaara sthaayi, the lower octave is
Mandhara sthaayi.  Similar names exist for further octaves.  An
Aalaapanai generally starts in the Madhya sthaayi, proceeds
upward into the Thaara sthaayi and then downward to the Mandhara
sthaayi before returning to end in the Madhya sthaayi.  This
structure is modified for ragas which are better exposed
otherwise.  For example, Aalaapanais in the raga Ataana are
often started in Thaara sthaayi.  Depending on the raga and the
imagination and skills of the performer, an Aalaapanai can take
up from a few minutes to a half hour or more.  In folklore,
there are stories of great performers who have rendered
Aalaapanai for a week, without any significant repetition of the
raga phrases used.

Niraval is similar to sangathi but performed in an extempore
manner.  The performer selects a single line or a similar short
portion of the song and renders it in various tunes, all within
the limits of the ragam and the taalam.  Kalpanaaswaram is to
Chittaswaram what Niraval is to Sangathi.  The performer renders
improvised swara phrases (in the same raga as the associated
song) while repeating a selected line from the song after each
chain of phrases, all the time staying within the constraints of
the taalam.  The empty space in the taalam for songs which have
an Anaagatha eduppu allows the performer to return to a fixed
short phrase at the end of each chain of Kalpanaaswarams with
great momemtum, adding to the graceful structure of the
performance.  Successful Kalpanaaswaram rendition requires
thorough study of the elements of the ragam.  Madurai Mani Iyer
was well known for his eagerness to sing Kalpanaaswarams with
every song.

Many recitals have a major item called Ragam - Thaanam -
Pallavi.  The Ragam portion is an elaborate Aalaapanai, a study
in the structure of the chosen ragam.  The Thaanam portion is
like an Aalaapanai but it has rhythm.  The rhythm is maintained
not by an explicit taalam, but by confining the voicing to
syllables of more or less fixed length.  Typical syllables used
in a Thaanam include Ta, Na and Nom.  Thaanam is an essential
part of veena playing due to the nature of the instrument.  The
Pallavi portion is often set to rare taalams and generally
consists of rendering a lyrical line at various speeds so as to
fit the taalam.  For example, the line can be rendered once for
each cycle of the taalam, twice per cycle, once every two cycles
etc.  This can be accomplished by keeping the rhythm at a fixed
speed and varying the pace of the melody or by varying the
rhythmic pace while the lyrical line is rendered at a constant
speed.  Pallavi rendition is intimately connected with the
performer's sense of rhythm.  When mentioning Pallavi singing
one can hardly forget Shatkaala Govindar, a contemporary of The
Trinity, whose title of Shatkaala was given due to his
exceptional ability to sing at six speeds.  It is also common to
make the Pallavi portion into a Ragamalika (garland of ragas),
meaning, a number of lines, each in a different raga.  The
Pallavi portion generally  includes Kalpanaswarams also.

Devotional items are quite common towards the end of the
recital.  These include slokas, Bhajans and compositions by or
in honor of the performer's Guru(s).  A Thillaana is performed
at or very near the end of the concert.  The Thillaana is a
composed piece intended mainly for dance.  Usually, there are no
lyrics and only certain syllables denoting division of the
taalam are used (Ta, Deem, Thom, Takadimi etc.).  The concluding
piece of the recital is called Mangalam and is generally in the
ragas Saurashtram, Madhyamavathy or Surati.


\section{Grahabedam and Symmetries}

The topics of this section are of fairly advanced nature and
somewhat abstract and mathematical.  Readers who are not
mathematically oriented may skip this section.  The basic
principles behind Grahabedam and symmetry are rooted in
mathematics.  Thus, a certain amount of mathematical notation is
almost unavoidable in any explanation of these concepts. 
Grahabedam is the process of modifying ragas by shifting the
base note Sa or the sruthi to various swara sthanas.  Symmetry
indicates certain types of similarities in the structure of the
swaras used in a ragam.  Grahabedam is defined for melakartas as
well as janya ragas.  Consider Dheerasankaraabharanam (Bana -
Ma), the 29th melakarta ragam.  The swara sthanas for it in one
kattai sruthi are as shown in the following keyboard diagram.

\begin{figure}
{\hspace*{1.in} \small 
\begin{verbatim}

=========================================================
|  |##| |##|   |  |##| |##| |##|   |  |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##| |##|   |  |##|
|  |__| |__|   |  |__| |__| |__|   |  |__| |__|   |  |__|
|    |    |    |    |    |    |    |    |    |    |    | 
|    |    |    |    |    |    |    |    |    |    |    |
| Sa | Ri | Ga | Ma | Pa | Da | Ni | Sa | Ri |    |    |
|____|____|____|____|____|____|____|____|____|____|____|


\end{verbatim} 
\caption{
Swaras in Dheerasankaraabharanam
}
\normalsize}
\end{figure}



Suppose we continue to use the same swara sthanas but shift the
sruthi to two kattais, what was Sankaraabharanam takes on a
different appearance.  The swara locations for two kattai sruthi
are given in the following figure.

\begin{figure}
{\hspace*{1.in} \small 
\begin{verbatim}

=========================================================
|  |##| |##|   |  |##| |##| |##|   |  |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##| |##|   |  |##|
|  |##| |##|   |  |##| |##| |##|   |  |##| |##|   |  |##|
|  |##| |Ra|   |  |Gu| |Mi| |Da|   |  |Nu| |##|   |  |##|
|  |__| |__|   |  |__| |__| |__|   |  |__| |__|   |  |__|
|    |    |    |    |    |    |    |    |    |    |    | 
|    |    | Ri | Ru |    |    | Di | Du |    |    |    |
|    | Sa | Ga | Gi | Ma | Pa | Na | Ni | Sa |    |    |
|____|____|____|____|____|____|____|____|____|____|____|


\end{verbatim} 
\caption{
Swaras for two kattai sruthi
}
\normalsize}
\end{figure}



Using this figure, we see that what used to be Chatusruthi
Rishabam now becomes Sa and Anthara Gandharam becomes
Chatusruthi Rishabam.  Continuing along, the Suddha Madhyamam
becomes Sadharana Gandharam, Pa becomes Suddha Madhyamam,
Chatusruthi Dhaivatham becomes Pa, Kakali Nishadam becomes
Chatusruthi Dhaivatham, Sa becomes Kaisika Nishadam.  Consulting
the melakarta tables, we see that the new swaras correspond to
the 22nd melakarta Kharaharapriya (Veda - Bhu).  Thus, moving
the sruthi to the swara Ri of Sankaraabharanam results in
Kharaharapriya.  It should be remembered that the absolute pitch
of the swaras continue to be the same;  it is only because of
the shifting of the origin of the scale (the Sa) that a
different raga is produced.  Evidently, one can carry out the
process for janya ragas also.

Consider a notation system for the swara and swara sthanas as
follows.  Let us represent the swara sthanas by a string of 12
digits, each one corresponding to the twelve swara sthanas into
which an octave is divided.  The presence of a swara sthana is
denoted by a one in the corresponding digit and the absence by a
zero.  Thus, in the above example of Sankaraabharanam, the
representation would be [101011010101].  The first 1 corresponds
to Sa; the next swara sthana corresponds to Suddha Rishabam
which does not occur in Sankaraabharanam and thus the
corresponding digit is 0.  The third digit is for Chatusruthi
Rishabam and Suddha Gandharam.  Since Chatusruthi Rishabam
occurs in our example, the third digit is set to 1.  The same
process can be continued to obtain all the twelve digits.  Note
that the first digit is always 1 to indicate the use of Sa.  In
the case of melakartas, Pa is always used and thus, the eighth
digit is always 1.  Further, all melakartas use seven and only
seven swaras and thus the notation always contains seven ones
and five zeros. In general, the number of ones in the notation
denotes the number of swaras used in that raga.  The following
list gives the number strings corresponding to the twelve
chakrams and the Pa-Sri.. designations.  Note that the Purvangam
is represented by seven digits and the uttarangam by five
digits.  The purvangam notations carry a 1 in parenthesis to
indicate that the next swara is Sa, which is always present.

\begin{center}
\begin{tabular}{llllll}
Indu&	1110010&	Rishi&	1110001&	Pa&	11100(1)\\
Netra&	1101010&	Vasu&	110100&	Sri&	11010(1)\\
Agni&	1100110&	Brahma&	1100101&	Go&	11001(1)\\
Veda&	1011010&	Disi&	1011001&	Bhu&	10110(1)\\
Bana&	1010110&	Rudra&	1010101&	Ma&	10101(1)\\
Ruthu&	1001110&	Aditya&	1001101&	Sha&	10011(1)
\end{tabular}
\end{center}


Using this notation, Grahabeda is very easy to handle.  One
simply moves digits from one end of the number to the other.  In
the example just considered, Sankaraabharanam is represented by
[101011010101].  To move the sruthi to Ri, we make the digit
corresponding to Ri as the first digit to get [1011010101].  The
two digits which were removed are moved over to the right end to
obtain [101101010110].  This can be easily verified to represent
Kharaharapriya.  This ability of a raga to generate other ragas
through Grahabedam is denoted by the term Murchanaakara.  The
absence of this characteristic is termed Amurchanaakara.  In
light of the above example, Dheeraankaraabharanam and
Kharaharapriya are  Murchanaakara ragas.  Sometimes, the process
of grahabedam on a ragam leads to non-existent scales.  For
example, if we take the Ni of Sankarabharanam as the base swara,
we get [110101101010].  This scale has two Madhyamas and no
Panchamam and such a scale is not allowable under the current
melakarta scheme.  Evidently, for a raga to be Amurchanaakara,
all the grahabeda derived scales of it should be somewhat like
this.  Jhaalavaraali (39) is an example of a melakarta which is
an Amurchanaakara ragam.

It is important to note that Grahabedam is necessarily a two way
process.  Instead  of generating Kharaharapriya from
Sankaraabharanam, we can start with Kharaharapriya and move the
sruthi to the Ni to get Sankaraabharanam.  Hence, it is
appropriate to group together ragas which can be derived from
each other and state, for example, that Kharaharapriya and
Sankaraabharanam are Grahabeda pairs instead of inappropriately
stating that Kharaharapriya can be derived from Sankaraabharanam
through Grahabedam.  The example just considered leads to the
most famous Grahabedam group of melakartas consisting of
Mechakalyaani (65), Dheerasankaraabharanam (29), Harikaambhoji
(28), Kharaharapriya (22), Natabhairavi (20) and Hanumathodi
(8).  This group possesses another interesting property. 
Mechakalyaani uses the 'big' variety of all the swaras (big Ri,
big Ga etc.) and proceeding down the group as it is written
above, the 'big' swaras are progressively replaced by
corresponding 'small' swaras.  Thus Dheerasankaraabharanam uses
'small' Ma ( and the rest, 'big'), Harikaambhoji uses 'small' Ma
and Ni and so on until we reach Hanumathodi, which uses the
'small' variety of all the swaras.

The Grahabedam process as above can be used on janya ragas also.
 The notation can handle only janya ragas with symmetric
arohanam and avarohanam (meaning the arohanam and avarohanam
should have the same swaras) and janya ragas with vivadi swaras
cannot be distinguished correctly.  The most famous Grahabedam
group of janya ragas includes Mohanam, Hindolam, Suddha
Dhanyaasi, Suddha Saaveri and Madhyamaavathy.  Some other groups
are listed in the Appendix.

The next logical question that arises is whether it is possible
for a raga (assumed to  have symmetric arohanam and avarohanam)
to be Grahabedam derivable from itself.  If the raga has five or
seven swaras (including the fixed Sa), then it turns out that it
cannot be Grahabedam derived from itself.  Thus, melakartas are
not self Grahabedam derivable since they all have seven swaras. 
If a ragam is self Grahabedam derivable, it can be confusing to
the listener since the same tune can belong to a single ragam at
two different sruthis!  Perhaps, it is no coincidence that we
see ancient systems of music with five note scales and the
current system with seven note scales, but no significant six
note scales.  The seven swara scale is most probably here to
stay since setting more than seven swaras into twelve swara
sthanas would allow very little room for the creation of
distinct base ragas especially if the Panchama sthana is
reserved and always present.

Consider the 1st melakarta, Kanakaangi (Indu - Pa).  It is
represented by the sequence [111001011100(1)].  Note the symmetry between the
lower and upper portions of the structure due to the repeating
sequence 111001.  This is an example of a class of symmetry,
where the lower and upper portions (not exactly the purvangam
and uttarangam, but close) of a raga have a similar structure. 
This characteristic is possessed by the following melakartas:
Hanumathodi (Netra - Sri), Maayaamaalavagowla (Agni - Go),
Kharaharapriya (Veda - Bhu), Dheerasankaraabharanam (Bana - Ma)
and Chalanaata (Ruthu - Sha).  The sixth melakarta Thaanaroopi
(Indu - Sha) is denoted by the string [111001010011(1)].  The
lower portion of this 111001 is the same as the upper portion
100111 written backwards.  This means that the swara steps in
the lower portion of the raga in the arohanam are similar to the
swara steps in the upper portion in the avarohanam, or these
ragas employ a similar swara step structure in the arohanam and
avarohanam.  This is another type of symmetry and the melakartas
which possess this property are Thaanaroopi (Indu - Sha),
Kokilapriya (Netra - Ma), Maayaamaalavagowla (Agni - Go),
Kharaharapriya (Veda - Bhu), Chaarukesi (Bana - Sri) and
Yaagapriya (Ruthu - Pa).

Note that Maayaamaalavagowla possesses both types of symmetries
we have looked at.  Further, it has no isolated swaras (denoted
by the ones all appearing in pairs).  This characteristic makes
a raga easier to sing (or play on an instrument) since pairs of
swaras occur together.  It is probably for this reason that this
ragam is almost invariably the first that a student is taught. 
In fact many of the initial lessons are set to this ragam.
(This practice is generally attributed to Purandara Dasa, who
is often called the father of modern Carnatic music). 
When an advanced stage is reached and students begin to render
Kalpanaaswaras, many find it convenient to sing first in
Maayaamaalavagowla or its Prati Madhyama pair Kaamavardhani.  A
systematic examination of the compositions of Muthuswamy
Dikshithar reveals a good degree of specialization in
Maayaamaalavagowla and its janya ragas.  (In fact, 
there is an interesting story in folklore about how
Dikshithar started composing songs.  From a very young age,
Dikshithar was a religious person and used to travel to many
temples.  On one such tour, he was at the temple of Lord
Subramanya in Thirutthani when an old man suddenly came up to
him, dropped a piece of sugar in his mouth and after blessing
him, disappeared mysteriously.  Dikshithar was inspired by this
incident and almost immediately composed the {some say his
first} song 'Sri Naathaathi Guruguho' in Maayaamaalavagowla.
Saint Thyagaraja's compositions exhibit a similar lean towards 
Kharaharapriya and its janya ragas.  Perhaps, these facts are related 
to the high degree of symmetry possessed by these two ragas.


\appendix

\section{Synonymous Ragas}

As we have seen before, different names have been assigned to
the same ragam by various sources, leading to some confusion on
the part of listeners and performers alike.  This problem is
very evident when one compares the compositions of Thyagaraja
and Muthuswamy Dikshithar, since the former used the
Kanakaangi-Rathnaangi scheme of Govindacharya while the latter
followed the Knakaambari-Phenadhyuthi scheme (which did not
require sampoorna melakartas).  In the case of Janya ragas also,
there are some discrepancies in the names as well as definitions
 used in the two systems.  The following list contains the names
of the melakartas in the Kanakaambari - Phenadhyuthi scheme. 
Some of the names are marked with an asterisk (*) to indicate
that they refer to the same raga as in the Kanakaangi -
Rathnaangi scheme.  Thus, Chaamaram, which is marked, is the
same as the corresponding (56th) melakarta, namely,
Shanmugapriya.  Detecting such correspondence is tricky since
different sources often offer conflicting definitions for the
same ragam.  The indicated correspondences were obtained after a
careful scrutiny of the songs as given in Rangaramanujam
Iyengar's Krithi Mani Malai.

{\hspace*{1.in} \small 
\begin{tabular}{llll}
1&	Kanakaambari			&37&Sougandhini   \\
2&	Phenadhyuthi			&38&Jaganmohanam   \\
3&	Gaanasaamavaraali		&39&Dhaalivaraali*   \\
4	&Bhaanumathi			&40&Nabhomani   \\
5	&Manoranjani*			&41&Kumbhini*   \\
6	&Thanukirthi			&42&Ravikriya*   \\
7	&Senaakrani			&43&Girvaani   \\
8	&Janathodi*			&44&Bhavaani*   \\
9	&Dhunibinnashadjam*		&45&Sivapantuvaraali*   \\
10	&Nataabharanam*			&46&Sthavaraajam*   \\
11	&Kokilaaravam*			&47&Sowveeram*   \\
12	&Roopavathy*			&48&Jeevanthini*   \\
13	&Geyahejjajji	*		&49&Dhavalaangam*   \\
14	&Vaativasanthabhairavi		&50&Naamadesi*   \\
15	&Maayaamaalavagowla*		&51&Kaasiraamakriya*   \\
16	&Toyaveghavaahini		&52&Ramaamanohari*   \\
17	&Chaayaavathi			&53&Gamakakriya   \\
18	&Jeyasuddhamaalavi	&	54&Vamsavathi*   \\
19	&Jhankaarabhramari		&55&Shyaamala   \\
20	&Naarireethigowla	&	56&Chaamaram*   \\
21	&Keeranaavali	&		57&Soomadhyuthi*   \\
22	&Sriraagam			&58&Desisimhaaravam*   \\
23	&Gowrivelaavali*	&	 59&Dhaamavathy*   \\
24	&Veeravasantham	&		60&Nishadham*   \\
25	&Sharaavathy		&	61&Kuntalam*   \\
26	&Tarangini	&		62&Ratipriya*   \\
27	&Sowrasena*			&63&	Geetapriya*   \\
28	&Harikedaaragowla	&	64&	Bhooshaavathi*   \\
29	&Dheerasankaraabharanam*	       & 65&	Saantakalyaani*   \\
30	&Naagaabharanam*			&66&	Chathurangini*   \\
31	&Kalaavathy			&67&	Santhaanamanjari*
\\
32	&Raagachudaamani*	&	68&	Jyothiraagam*
\\
33	&Gangaatarangini		&	69&	Dhowthapanchamam*
\\
34	&Bhogachaayaanaata*		&70&	Nasaamani*
\\
35	&Sailadesaakshi*		&	71&	Kusumaakaram*
\\
36	&Chalanaata*		&	72&	Rasamanjari*
\end{tabular}
\vspace*{.2in}

\noindent \# The following list indicates janya ragas which are known by
different names.

\noindent Suddha Dhanyaasi or Udaya Ravichandrikaa\\
\noindent Suddha Saaveri or Devakriya\\
\noindent Aabheri or Karnaataka Devagaandhaari\\

\normalsize} 

\section{Grahabeda Groups}

The following list contains groups of melakartas that are
Grahabeda derivable from each other within any group.  These are
thus Murchanakara melakarta ragas.

{\hspace*{1.in} \small 
\begin{verbatim}
Kanakaangi, Kaamavardhani
Rathnaangi, Gamanasrama, Jhankaaradhwani
Gaanamurthy, Visvambari, Shyaamalaangi
Vanaspathy, Maararanjani
Maanavathy, Kaantaamani
Senaavathy, Lataangi, Sooryakaantham
Hanumathodi, Mechakalyaani, Harikaambhoji, Natabhairavi, &
  Dheerasankaraabharanam, Kharaharapriya
Dhenuka, Chitraambari, Shanmugapriya, Shoolini
Naatakapriya, Vaachaspathy, Chaarukesi, Gowrimanohari
Kokilapriya, Rishabhapriya
Gaayagapriya, Dhaatuvardhani
Vakulaabharanam, Kosalam, Kiravaani, Hemavathy
Maayaamaalavagowla, Rasigapriya, Simhendhramadhyamam
Chakravaaham, Sarasaangi, Dharmavathy
Haatakaambari, Gavaambhodhi
Varunapriya, Raagavardhani
Naagaanandini, Bhavapriya, Vaagadheeswari
Gaangeyabhooshani, Neetimathy
Chalanaata, Subhapantuvaraali
Shadvidhamaargini, Naasikaabhooshani

# The following are the Amurchanaakara melakartas, meaning they
are not related to any other melakarta through Grahabedam.

Taanaroopi
Roopavathy
Yaagapriya
Saalagam
Jalaarnavam
Jhaalavaraali
Navaneetham
Paavani
Raghupriya
Suvarnaangi
Divyamani
Dhavalaambari
Naamanaaraayani
Raamapriya
Sucharithra
Jyotiswaroopini

# The following are Grahabeda related Janya raga groups and hence
it is appropriate to call these Janya ragas as Murchanakara
Janya ragas.
Suddha Saaveri, Suddha Dhanyaasi, Madhyamaavathy, Hindolam and
 Mohanam
Ghambeera Naata and Bhoopaalam
Kalkata and Lalitha
Naagaswaraavali and Hamsadwani
Aarabi, Mohana Kalyaani, Aabheri and Kedaara Gowla
Dhanyaasi and Saalaka Bhairavi
Aabhogi and Valagi
Kaambhoji and Desiya Thodi
Bilahari and Yadukula Kaambhoji
\end{verbatim} 
\normalsize}

In the preceding list, the first four groups possess symmetric
arohanam and avarohanam (use the same swaras in the arohanam and
the avarohanam) while the rest use asymmetric scales.

\section{Composers and thier identifiers}

The following list contains the names of a few composers and the
identifiers used by them.  The names are in no particular order.
\begin{tabbing}
\ \ \ \ \ \hskip 2.in \ \ \ \ \ \ \ \= \\ 
Composer	        \>Identifier\\
\\
Sadasiva Brahmendra	\>Paramahamsa\\
Jayadeva	        \>Jayadeva\\
Purandara Dasa	        \>Purandara Vittala\\
Bhadrachalam Rama Dasa	\>Bhadrachala Rama\\
Narayana Theerthar	\>Narayana Theertha\\
Annamacharya            \>  \\
Bhodendra	        \>Bhodendra\\
Thyagaraja	        \>Thyagraja\\
Muthuswamy  Dikshithar	\>Guruguha\\
Shyama Shastry	        \>Shyama Krishna\\
MaharajaSwathiThirunaal \>Padmanabha, Kamalanabha and other synonyms\\
Harikesanallur Muthiah  \>BhagavatharHarikesapura\\
Papanasam Sivan	        \>Ramadasan\\
Patnam Subramanya Iyer	\>Venkatesa, Venkateswara\\
Veenai Kuppaiyar	\>Gopaladasa\\
Mysore Vasudevacharya	\>Vasudeva\\
Tirupathi Narayanaswamy	\>Tirupathi (pura) Varada Venkatesa\\
Gopalakrishna Bharathi	\>Balakrishna\\
Vedanayagam Pillai      \> \\
\end{tabbing}
\vskip 0.2in
\vfill
\end{document}


