On the existence of the Shadja
KEDAR S NAPHADE
The question that motivates this posting is superficially somewhat stupid, but
given some thought, quite intriguing, and perhaps even rather philosphical.
I was trying to explain to a friend who has had no formal training in music, but a very good ear, how to identify the "Sa" in any song. When he asked the question, I had thought that it would be very easy to demonstrate the existence, and importance of the Sa using a couple of different songs; especially since he
has a very good ear. To my surprise however, it was not simple at all, and as
of now i still do not have the answers to his questions.
Consider trying to come up with a set of rules or guidelines that will
help a person to identify the Sa. This person can distinguish between the
notes he/she hears, and furthermore, once told to assume a certain note as a
Sa, can identify the other notes with respect to that Sa. With these
abilities, how do you train someone to define a Sa ? Is it the note with
which the song starts ? but that is not at all necessary; Is it the one on which there is a lot of emphasis ? well, other notes are resting places too ! Is it the note sung most frequently ? Obviously all these questions have no definite answer. So what is the question that will do the job ? Or perhaps
even a set of questions ? What is it that strikes most of us about the note
that we identify as a Sa in a song ?
Personally when I listen to a song, the Sa is obvious to me. But if
someone asks me how I arrived at that note as the Sa, I cannot profer a
logical explanation. Furthermore, given that if you referred to a different
Sa, and to the other notes in the song with respect to the new Sa, and then
sung or played the song, will it not still sound the same ? If it does, then
you could make the current Shuddha Re, or Komal Ga, or Teevra Ma as the new Sa,
change other notes accordingly and still play/sing the song. What is wrong
with doing this ? If it all sounds the same then do we really need a Sa ?
Regards,
Kedar
Unni Narayanan
>
>The question that motivates this posting is superficially somewhat stupid, but
>given some thought, quite intriguing, and perhaps even rather philosphical.
>
>I was trying to explain to a friend who has had no formal training in music, but a very good ear, how to identify the "Sa" in any song. When he asked the question, I had thought that it would be very easy to demonstrate the existence, and importance of the Sa using a couple of different songs; especially since he
>has a very good ear. To my surprise however, it was not simple at all, and as
>of now i still do not have the answers to his questions.
>
I am just a beginner at this game, but I identify SA as follows:
1) Identify the raga the song is in.
2) From some source get the arohanam and avarohanam of the raga.
3) Aribtrarily apply one of the notes in the scale of the
raga to a key phrase in the song (or just the first note in the song)
4) Sing the phrase, going up or down the scale of the raga -
as the song goes up or down in the pitch.
5) The moment there is an inconsistncy in what the next
note in the song is - and the next note up/or down is
in the scale - that means my inital guess was wrong.
And I go back to step 3.
This is a brute force method but, is still a tractable
algorithm. The key to reducing the time is a good guess
at the beginning - generally I can do it by the third try.
Of course, the simplest way to identify the SA is
to just listen to the Tambura in the background - an
identify the Sa PA and Sa. However, the former method is
more fun - because you can map the song to swarams.
Unni
Bhalchandra Thatte
Unni Narayanan <un...@ta20.cs.uiuc.edu> wrote:
>I am just a beginner at this game, but I identify SA as follows:
>
>1) Identify the raga the song is in.
>2) From some source get the arohanam and avarohanam of the raga.
>3) Aribtrarily apply one of the notes in the scale of the
> raga to a key phrase in the song (or just the first note in the song)
>4) Sing the phrase, going up or down the scale of the raga -
> as the song goes up or down in the pitch.
>5) The moment there is an inconsistncy in what the next
> note in the song is - and the next note up/or down is
> in the scale - that means my inital guess was wrong.
> And I go back to step 3.
>
>This is a brute force method but, is still a tractable
>algorithm. The key to reducing the time is a good guess
>at the beginning - generally I can do it by the third try.
>
>Of course, the simplest way to identify the SA is
>to just listen to the Tambura in the background - an
>identify the Sa PA and Sa. However, the former method is
>more fun - because you can map the song to swarams.
>
>Unni
I am almost sure that you do not identify the Sa by the above procedure.
I don't have doubt that you are able to identify Sa.
How do you somehow identify the raga?
Don't you feel a Sa in almost all songs (which are not necessarily
in any particular raga)?
Unless you identify the Sa, you cannot identify the raga.
Also, if you asked me to identify the Sa in some song, what I would
do is to hum that song (if I know it) and decide about the Sa. So
it means one can do it even without Tanpura.
If you listen to some western music piece which is composed in say
G major, the note which you feel as Sa is usually G.
I think it is a complex phenomenon, and it is likely that you wouldn't
have been able to identify the Sa if you were forced to listen to only
some random notes on a perfectly geometric scale for long enough time.
What do you netters think about the Sa in the songs:
1. sayonara sayonara ...
2. pankha hoteto ud ati re ...
3. (a Marathi song) Ya chimanyano parat fira re ...
Bhalchandra Thatte
Unni Narayanan
Hmmm - I guess I answered from the context of finding
Sa in a carnatic piece from which the Raga was given.
Let me see now...
>Don't you feel a Sa in almost all songs (which are not necessarily
>in any particular raga)?
This is a good question. I guess I don't always feel
the "SA" in lighter music (not meant disparagingly) -
and usually, I only try and find the SA in
classically based songs (in which case
the raga is very apparent)
As an aside - why does a song have to have a SA?
It is not vital, right? In a song, even if it
has a SA, SA might not be the most important note.
Like I said, if the song has a drone I can
gravitate to the SA. If the song is classically
based I can figure out the SA.
I guess, the general range of notes in a song
give some sort of intuition as to a scale - but,
then the song could be based on a PA to PA
thing. I guess I cannot really identify the
SA in songs that don't have a drone and are
not classically based.
>Unless you identify the Sa, you cannot identify the raga.
This is not true in my case. I have a pretty decent
hit rate at identifying the Raga first, and only
then do I identify the SA. I hope, however, as
my knowledge increases, I can do it in reverse order.
>Also, if you asked me to identify the Sa in some song, what I would
>do is to hum that song (if I know it) and decide about the Sa. So
>it means one can do it even without Tanpura.
That is pretty unique - again, if one knows the Raga I can
see this. But, without having a refernce pitch or
a reference of the Raga - I'm not sure how it is done.
>
>If you listen to some western music piece which is composed in say
>G major, the note which you feel as Sa is usually G.
Intersting. I don't find that true for myself.
From what I know about Western music, if a piece is
composed in the key of G Major - all that means, is that
the sharps and flats are applied to notes in the song
the same way sharps and flats are applied to a
diatonic scale (For the Carnatic people out there -
Shankarabharanam without Ghamakams) starting with G. That is, the G Major,
scale taken together still "sounds like" the C Major
scale - even though the first note (SA) is a G
and not a C. It just means the sharps and flats
in the rest of the scale are modified to
make the rest of the scale sound like Shankarabharanam -
kind of a pitch correction.
Maybe, the experts out there can clarify this.
However, I don't see any reason to feel
G in G Major.
>
>I think it is a complex phenomenon, and it is likely that you wouldn't
>have been able to identify the Sa if you were forced to listen to only
>some random notes on a perfectly geometric scale for long enough time.
>
I am not sure what a geomteric scale is, but I am
confused. What meaning is there to identify SA without
a reference pitch?
If you are talking about identifying on an absolute basis
whether a note is a C, D or whatever - then
that requires perfect pitch - and very few people
are born with it (I believe the pianist Vladami Horowitz
had perfect pitch - so did Mozart). Theer is no absolute SA - in
the Indian system - SA is not some fixed point. It is
only fixed within a context - so, identifying SA
within a random series of ntoes makes no sense.
>
>What do you netters think about the Sa in the songs:
>
>1. sayonara sayonara ...
>2. pankha hoteto ud ati re ...
>3. (a Marathi song) Ya chimanyano parat fira re ...
>
Sorry, can't help here - don't know any of the songs.
Hope this helps - or sparcs discussion.
Unni
V. Chandramouli
CAN NOT identify a raga without knowing the Sa. Of course, you can look up
a source that tells you the raga in which the song is and then you can
identify the Sa perhaps.
It is wrong to say that a scale (in the Indian sense) can be defined without the
Sa. All notes are defined relative to a fundamental frequency and that frequency
is the Sa. It is like saying can we have a coordinate system without (0,0),
which is silly. Sa may not be very heavily used; that is another matter.
Regarding a scale from Pa to Pa, you are now introducing the concept of
Sruti-bhedam. We have discussed this before and you can check the archives.
The key thing to note is that Indian music is based on the principle of
"relativity" :-). For eg, a vocalist assumes a frequency for Sa at which she is
comfortable with and the rest of the notes become automatically defined. A
different vocalist may have a different Sa (perhaps at the original singer's Ri).
Finally, I strongly feel that you cannot give an algorithm (i.e. a precise
step by step procedure) for identifying Sa. You just feel it. After all there
are certain things inherently human, isn't it ? :-) Love, emotions, music...
--Chandramouli
Rajan P. Parrikar
<deleted>
> Consider trying to come up with a set of rules or guidelines that will
>help a person to identify the Sa.
>This person can distinguish between the
>notes he/she hears, and furthermore, once told to assume a certain note as a
>Sa, can identify the other notes with respect to that Sa. With these
>abilities, how do you train someone to define a Sa ? Is it the note with
>which the song starts ?
The answer to the last question is, "need not be." As is well-known,
the Sa is the chassis which a melodic composition is built around
and it establishes a kind of baseline "pitch" in the melodic space.
Identifying the Sa in a classical music composition is relatively
easy because it is established a priori and sustained via the drone
of the tanpura. Even in a non-classical composition, the composer
almost always conceives his melody with Sa as the starting point.
But in the latter case, how do we smoke out the Sa? I do it instinctively
and have long lost my innocence in this regard. I suspect this to be
true of most of you who have been in this swara business for a while.
For the untrained, innocent ear, I don't know how to generate a set
of steps so that the Sa can be extracted unambiguously. But lemme suggest
a simple experiment.
All you need a tape recorder to play a melodic pattern repeatedly
and a tone generator (a Casiotone would do fine).
The idea is to offer the untrained ear two channels of music to compare,
one of which serves as a benchmark while the other tries to zero in on
consonance. The tyro must be instructed to indicate if and when he
"feels" the consonance between the two separate channels. (The assumption
is that your friend has a broad idea of what he is looking for, and
although untrained with no skills of swara-identification, has been
brought up listening to Indian melodic music).
a) Play the tape with the melodic pattern and allow some time for
your victim to get a feel for it.
b) In the background, with the tape still playing,
hold a fixed tone on the Casiotone (begin with
an arbitrary note). After a certain length of time, increment the
note by a semitone. Repeat the last step. My guess is that the
untrained ear will be sensitive to the Sa the minute you hit it.
If not, then at least it will be able to eliminate
all the dissonant notes (except perhaps the Ma or Pa with
reference to the correct Sa). Of course, this conjecture will have
to be tested.
Any suggestions?
Rajan Parrikar
==============
email: parr...@mimicad.colorado.edu
ra...@anteng.ssd.loral.com
ps: It will be interesting to see how people brought up in
different melodic systems react (the Chinese, for example,
whose scale sounds "besuraa to us).
V. S. Sridharan
It is a good question. In western music, at least in simple themes, the pieces end with either lower or upper Sa. In Indian Classical Music, it is hard to arrive at an algorithm. It will be great to hear from anyone who has worked on this.
The following can be easily dismissed as hogwash. Read on, at your own risk.
Personally speaking, Sa and Pa sound neutral in emotion. The notes slightly higher than Sa and Pa stir up the tranquility and transparency and introduce interrogation, anxiety, or pathos. I am referring to R1, R2, G1, D1 & D2. Closer, the more intense. The notes slightly lower than Sa and Pa appear to be yearning, distressful, pleading etc. Again, closer, the more intense. I am referring to M2 and N2, particularly. The ragas that avoid notes close to Sa and Pa appear to be more happy and peaceful.
Time for more hogwash. You have been warned.
Ragas with nyasa swaras other than Sa and Pa also cash in on this theory to create further emotions with respect to the position of the notes relative to the nyasa swaras. Ragas with vivadi swaras sound mysterious, enchanting or dark (to quote from another thread).
Speaking of the other thread, this might be a more fundamental discussion than the derivative ragas and their emotions.
The end.
Sridhar
Unni Narayanan
After some reflection, I have come to change my mind about
one thing. To identify a Raga one, must first identify
the SA. I realized that I implicilty do this by
humming what I feel to be the arohanam of the raga
I am trying to identify. Obviously, I will do
this in the "pitch" of the rendition I am listening
to. This means the first note
of the scale that I hum must be Sa.
The question is how I hone in on the
SA - I could say I feel it, but I think
for me, the more rational explanation is that I just hone
into the Thambura.
Regarding, the other posts, however, there seems to
be a consensus that you need a reference pitch to
identify the SA. Right?
>
>It is a good question. In western music, at least in simple themes, the pieces end with either lower or upper Sa. In Indian Classical Music, it is hard to arrive at an algorithm. It will be great to hear from anyone who has worked on this.
>
I don't thing an algo. for indian classical music is outrageous.
I mean if we know that a piece is strictly "in" a
particular Raga - then we know "legal" sequences of
notes in phrases of the songs (obviously, there are
jumps - but these are easy to see) - why can't
we just combinatorially try all starting notes - as I mentioned
earlier?
BTW, in western music there are tons of simple themes that
don't start and end with a SA.
>The following can be easily dismissed as hogwash. Read on, at your own risk.
>
>Personally speaking, Sa and Pa sound neutral in emotion. The notes slightly higher than Sa and Pa stir up the tranquility and transparency and introduce interrogation, anxiety, or pathos. I am referring to R1, R2, G1, D1 & D2. Closer, the more intense. The notes slightly lower than Sa and Pa appear to be yearning, distressful, pleading etc. Again, closer, the more intense. I am referring to M2 and N2, particularly. The ragas that avoid notes close to Sa and Pa appear to be more happy and peaceful.
>
Interesting.
>Time for more hogwash. You have been warned.
>
>Ragas with nyasa swaras other than Sa and Pa also cash in on this theory to create further emotions with respect to the position of the notes relative to the nyasa swaras. Ragas with vivadi swaras sound mysterious, enchanting or dark (to quote from another thread).
>
>Speaking of the other thread, this might be a more fundamental discussion than the derivative ragas and their emotions.
>
I agree with the above observation on the two ragas I am familiar with
that have vivadi swaras : Nattai and Vagadeeshwari.
Both of these ragas sound mysterious and dark (esp. Vagadeeshwari).
As a side note, they are especially easy to sing out
of tune!
Unni
Ajit K Ranganathan
i completely disagree with the concept that without knowing the Sa u cannot
identify the raga.
for example, my father can identify 100s of ragas .he has
no knowledge of the swarasthanas.he does not know where the Sa or Ri
is nor does he know the arohana and arovahana of a particular raga.
he has listened to the ragas before and he can find a
pattern and then say this is this raga or that.
and this is not only my father, i have seen many persons
like that.
i agree it is very difficult to place the shadja.
actually, in carnatic music i would say it is easy since
you have the tambura or sruthi box, but in film music,
i know keyboard players usually do it by trial and error.
ajit.
Todd Michel McComb
In classical music, it is the precise tuning which allows one to
identify the Sa -- the drone reference will give you the Sa, if
you pay attention (or, in many cases, people will make this
identification at the subconscious level; the singer's tone will
often be illuminating as well, because the physical production
of the notes is not invariant in pitch shifting). I "know" (at
the instantaneous level) many fewer ragas than many readers,
and if I don't know, I pick the Sa and then try for the raga; if
I do know, then the Sa just takes a moment from the raga (the
algorithm posted would work, but that's not how it goes in
practice...). (And, for me, even if I "know" the raga, it doesn't
mean I remember its name; it's easy to remember the name of Sa.)
Well, anyway.
The easiest way to identify Sa in Carnatic music? Why, wait
for the kalpana swara of course!
On Western G major and such....
G major is both a scale and a harmony. As a scale, it includes
the 7 notes of G major, and melodies need not end on G. As a
harmony, G will be the most important note and one can easily
sense it. The "chord of G major" is G-B-D and the harmonics
of those notes "point" to G; D is the next most important note;
and B is the next. All major scales are identical in interval,
and major-minor harmony emphasizes Sa-Ga-Pa. Of course, one
should remember that a piece which says it is in "G major" does
not usually remain in G major throughout.
So, G will always be the most important note (or nearly so).
This is only true in a sense for Sa in Indian music, because
Sa need not be the most important note for raga phrasing, yet
it retains a certain importance because of tuning.
Since all intervals are equal in Western music (equal temperament),
the tuning will not tell you the tonic (Sa). In fact, it could give
you the wrong impression on wind instruments, because these will
have a fundamental which is not necessarily the key of the piece.
But then, since notes are always tuned to the same pitch in Western
music, G will be at the same pitch, regardless of key.
T. M. McComb WWW ftp://ftp.netcom.com/pub/mc/mccombtm/home.html
Ajit Pendse
the technique of deriving of the Shadja.
I think that the process of finding the Shadja is a feedback response.
It starts with (unconscious) finding (or getting a feel) of the raga or more
loosly, the mood of the melody. The characteristic notes are then filtered
out and what remains is the Shadadja. Of course this is a rather poor
attempt at something that is difficult to describe. But try to
imagine hearing a raga very slowly, note by note -- it will
be more difficult to find the Shadja in that case. Hence I think it is
a top-down process.
I am curious to hear other descriptions of the process!
-Ajit Pendse
cmp...@lsuvm.bitnet
Suresh Krishnamoorthy
pattern recognition. i do it all the time. i can certainly identify the
obvious ones (about 50 - 60) and i have no knowledge of the scale or the
specific notes. i could not even tell you the arohanam avarohanam. but i
can pin down ragams like todi or kalyani or hamsanandi or revati, by
listening for 30 seconds. i do it by pattern recognition. i would love to
be able to recognize specific notes, but i think i may need some formal
training for that.
suresh
Bhalchandra Thatte
I take back my statement that a raga cannot be recognized without recognizing
the Shadja. In fact I also recognize them mostly by comparison with some
songs which I know to be in particular raga.
But many times I do this comparison based on the scale which
I recognize immediately. But my problem is I don't remember the names
of ragas corresponding to different scales. Since I listen to all the
classical music in terms of the association with specific notes, I do
not give importance to recognizing ragas.
Bhalchandra Thatte
V. Chandramouli
True, pattern recognition is what most people (including myself) use to
identify raagas. This, while being quite successful in practice, can fail in
the worst case, that being when somebody sings an hitherto unheard of raaga.
Consider the plight of the accompanying violinist who has to "decode" the notes
that a vocalist implicitly sings while doing an alapana. It is impossible to
do so without feeling the Sa.
By being able to identify ANY raga, I think one must pass the following
criterion. Suppose somebody provides you with an encyclopedia of all possible
ragas and their scales. Now when someone sings, you should be able to decode
the notes, look the list and name the raga.
Also, many film songs very rarely follow the characteristic phrases associated
with a raga though it may be in the scale of a well known raga like
Purvikalyani. While it will be incorrect to say that this song is based on
Purvikalyani, you might also mistakenly identify the song as being in some
other scale if you can't feel the Sa. As a case in point, we had a discussion
sometime back as to whether "Kahin deep jale kahin dil.." is based on the
scale of Shivaranjani or not. The ambiguity was caused by where you pin the
Sa.
Perhaps when we do pattern matching we implicitly feel the Sa at the subconscious
level since you always have the drone in a classical concert. I have to think
more on this. I think the concept of Srutibhedam is closely linked with this
problem. There you give the flavor of a different raga by shifting the Sa while
being in say, Todi. One of my friends, during a TNS concert, thought TNS had made
a mistake while doing the alapana, when in fact he was doing sruti-bhedam :-)
--Chandramouli
Ajit K Ranganathan
but the point is, people who have not learnt music dont know where the
shadja is and they also dont know all the ragas.i dont claim,
that they can identify all the ragas or any new raga for that matter.
its like a neural network.they hear ragas and get trained
by the pattern.so when they again hear the same raga they
are able to say the name.
they cannot identify a raga when they hear it for the first time.
as for accompanying, from my personal experience, i have found
it a lot easier when i know where the shadja is and this
is easy in the case of carnatic music.so i had no problems.
in the case of film music, i have a tough time trying to
find the sruthi, which is basically the shadja and since
flutes are tuned to a particular pitch, atleast
a range of flutes have to be tried .
i have found it difficult in that case to locate the shadja.
ajit.
Suresh Krishnamoorthy
to pin any raga down is correct. but i would go further. you need to be
able to recognize the others also, especially the difference between the
various 'Ri' and 'Ga' and so on. i attempted to do that a while ago and
gave up the effort. it was taking too much of my attention and i was
missing the flow of the alaapana.
sruti bedham is a differentt animal altogether. i can recognize (now,
after some effort) *when* a sruti bedham is in progress. but not much more.
my experience organizing concerts has led me to believe that most
artistes talk to the violinists before the concert and decide various key
poits - what the ragam tanam pallavi will be on, what the pallavi thalam
will be and so on. but some of the artistes of yesteryear (the likes of
ariyakudi and alathur) were known to 'put an accompanyist in his/her
place' by launching surprises at the poor accompanyist during the
concert. Prof TN Krishnan has some interesting stories on this.
suresh
Sarvjit Goraya
Many of you may remember me as the pest who has bothered you with private
e-mail in search for 'elusive Sa'. I am glad this is now being discussed in
open.
The results of my struggle are
1. With experience (repetitive and persistent listening) one starts
recognising Ragas. Some are easier than the others.
2. Positioning of Sa in a melody is not related to the feeling of the
music, although some ragas come out better when moved to higher or lower
scales.
3. In my recent experience, I have discovered that Sa (or the Key note) is
just there, waiting to be discovered. I thank Rajan Parrikar for
providing me the definition which helped immensely
'.......... Sa is the a most consonant note in the melody'
Now I play the music and listen to it carefully for a few moments. Then
decide on Sa and hit the note on my harmonium. Most of the time I find it
within coule of notes. When one plays this note along with the melody it
just resonates with it.
I would dearly love to do this without the aid of harmonium.
So at the moment I can only say ' Hey this song is in a rather high Sa'.
There are other clues too like many singers stick to their Sa.
But I am still confused about some folk tunes (punjabi) that use
only three or at the most four notes.
Comments and critique welcomed.
-Sarvjit Goraya
Pankaj Joshi
Sarvjit Goraya <gor...@citecuf.citec.qld.gov.au> wrote:
>
>'.......... Sa is the a most consonant note in the melody'
>
>Now I play the music and listen to it carefully for a few moments. Then
>decide on Sa and hit the note on my harmonium. Most of the time I find it
>within coule of notes. When one plays this note along with the melody it
>just resonates with it.
>
>I would dearly love to do this without the aid of harmonium.
I start humming with the song and in a few seconds I naturally hit the sa.
>
>So at the moment I can only say ' Hey this song is in a rather high Sa'.
>There are other clues too like many singers stick to their Sa.
>
>But I am still confused about some folk tunes (punjabi) that use
>only three or at the most four notes.
>
>Comments and critique welcomed.
>
>-Sarvjit Goraya
>
Pankaj
Dasanudas Adhikari
Interesting post. I'd like to offer some comments on it.
>>'.......... Sa is the a most consonant note in the melody'
Absolutely. Generally speaking, the lower the numbers used to express the
justly-intoned sruti ratio for a svara, the more harmonic or consonant the
note. Thus Sa, with a ratio of 1:1 or perfect unison, is the most consonant
note there is.
>>Now I play the music and listen to it carefully for a few moments. Then
>>decide on Sa and hit the note on my harmonium. Most of the time I find it
>>within coule of notes. When one plays this note along with the melody it
>>just resonates with it.
>>
>>I would dearly love to do this without the aid of harmonium.
>I start humming with the song and in a few seconds I naturally hit the sa.
Right. The Sa is always the harmonic 'center of gravity' of the music. This
intuitive feeling of Sa is the sensation of tonality, which is always present
to some extent even in 'atonal' music.
>>So at the moment I can only say ' Hey this song is in a rather high Sa'.
>>There are other clues too like many singers stick to their Sa.
>>
>>But I am still confused about some folk tunes (punjabi) that use
>>only three or at the most four notes.
The Sa is determined by taking all the notes in the thata and using the
formula mentioned above, (taking the harmonic ratios and comparing to
determine the one using the lowest numbers) calculating the harmonic center of
gravity. Then even in music that doesn't use tampura you can always find the
Sa.
Highly trained musicians do this instinctively. For example, let's say you
have a folk song with three notes: C, E flat and F. Assuming the singer is
using the most harmonic srutis for the intervals, the ratios are:
C - E flat Minor Third Komal Ga 6:5 6+5=11
C - F Perfect Fourth Shuddha Ma 4:3 4+3=7
E flat - F Major Second Suddha Ri 10:9 10+9=19
So the interval Sa to Ma would be the most consonant because its components
fall the lowest on the harmonic series. The upper tone of the perfect fourth
is its root, therefore F is the Sa of this song, unless other considerations
like constant repetition of the C would indicate that it is the root.
I hope this has shed some light on this intersting question.
Your ever well-wisher,
Dasanudas Adhikari,
Congregational Development Minister, ISKCON Chicago
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