Comparing Indian and western scales...
P. J. Narayanan
I have more questions/comments on Todd's reply on this topic. This is
from my reply to his mail...
-------------------------
I must confess at the outset that my smattering knowledge of
Western scales and systems come from the very little reading and even
less listening I have done. My analysis is almost only on a 'theoretical'
basis.
I don't know much about modes. I will certainly try to read a
book on western modality. It would be helpful if you can explain the
simiarity/difference between modes and ragas (they seem closer than
scales and ragas) as you understand both. I doubt if most books on
modality will discuss this stuff. I am also curious to know how modes
developed into "composite" major and minor scales as you put it. I see
your point about all white starting on C being Sankarabharanam and all
white keys starting on F being Kalyani -- it's another way of saying the
Ma-moorchhana of Sankarabharanam yields Kalyani in the grahabhedam
terminology.
->G Major: Kalyani (Yaman that)
->G natural minor: Kharaharapriya (Kafi that)
->G Harmonic minor: Hemavati (Kafi with tivra madhyamam)
->G Melodic minor: Vachaspati/Kharaharapriya
-
-This is an abuse of notation.
I agree this is an abuse of notation. I worked out the
correspondences between all major & minor scales -- but starting on C
always -- years back when I came to know of the raw scale structure
because it seemed an interesting thing to do "academically". Moreover,
scales with any note as the base sound identical to an Indian ear (by
shifting the tonic sa to that base note) and was not as interesting to
think about. I could rationalize these thought experiments because the
western system used absolute pitches and *should* (according to me) have
C as something special. My ear failed me in confirming these theories
though.
-Correspondences with Indian scales are difficult to use. That's for
-sure. Also, different composers will use the scales in quite different
-ways. What you have said makes some sense for Mozart, but even by
-Beethoven it is largely meaningless.
Again, I don't have the kind of listening experience to say this.
I would appreciate it if you can elaborate on the nature of differences
between the composers and how they came about. I was under the impression
that the equally tempered scale is in vogue (only system in vogue, but
for 'experimentalists') since around the time of Bach. You also write:
-Equal temperment
-is the most extreme version of this, but most keyboards (at least for
-serious performers) are not using equal temperment, though they use various
-other tunings (whose names I don't pay much attention to) which are close
-to equal temperment. Western players of wind or string instruments do not
-use equal temperment at all, except in an attempt to blend with keyboard
-when necessary.
I wasn't aware of this at all. Do you mean that concert pianists
tune their pianos differently and not according to the equally tempered
system? Are wind instruments tuned differently by classical players?
What I am curious to know is: Does this differently-tuned music belong to
the experimental class or can they be found in the `mainstream'? Can one
find a lot (majority ?) of solo concert pianists tuning their pianos
differently for Mozart and Beethoven (or for more later composers)?
I am sure many on the net will be interested in this topic. I am
sure there are many who can contribute also. Therefore, I will post
your mail and this mail of mine on the net. Hope that's OK.
PJN
P. J. Narayanan
I received this as a reply to my posting from Todd...
PJN
----------------------------------
To: p...@cs.umd.edu
Subject: Re: comparison
Newsgroups: rec.music.indian.classical
In-Reply-To: <PJN.92Ma...@mimsy.cs.umd.edu>
References: <1992May14.2...@menudo.uh.edu>
Organization: Rensselaer Mathematics Dept., Troy NY
Cc:
In article <PJN.92Ma...@mimsy.cs.umd.edu> you write:
>In the western system, these scales can be defined with respect to any
>base note. The intervals used in the scale are determined by the above
>numbers, no matter where it starts from. Unless you specify the
>starting note, correspondence with Indian scales cannot be made in the
>strictest sense. I guess this is a debatable point, as Indian music
>doesn't depend on absoulute frequencies or notes. If the base note of
>the scale is fixed as the tonic "sa", the above scales will default to
>those based on C. Correspondeces with C as the base are:
Yes, those numbers define a mode -- which can start on any base note.
The actual base note used gives the final name of the mode. Using C as
the default scale is fine; in piano terminology, this is the white keys
starting with C (as I'm sure you know.)
>C Major scale: Sankarabharanam (Bilawal that)
>C Natural/tonic minor: Natabhairavi (Asavari that)
>C Harmonic minor: Keerawani (No Hindustani that)
>C Melodic minor: Gowrimanohari ascending (No Hindustani that)
> Natabhairavi descending
>The correspondence with Indian ragams are only rough, as the western
>minor scales are defined with respect to an equally tempered scale
>where every semitone interval represents a fixed ratio of frequencies.
>They are loosely defined in the Indian system.
Western scales need not be based on equal temperment. More complicated
tuning systems were introduced in western music in order to play vertical
harmony in different keys on the same keyboard (re: Bach's Well-Tempered
Klavier, "well-tempering" is another sort of temperment.) Equal temperment
is the most extreme version of this, but most keyboards (at least for
serious performers) are not using equal temperment, though they use various
other tunings (whose names I don't pay much attention to) which are close
to equal temperment. Western players of wind or string instruments do not
use equal temperment at all, except in an attempt to blend with keyboard
when necessary.
Most westerners also seem to have the idea that everything is equal
temperment -- I suppose this is just easier to understand than the real
situation which is rather chaotic. Modern composers are paying an increasing
amount of attention to tuning.
>One can find correspondences between other western major/minor scales
>and Indian ragas, assuming that C is chosen as the tonic "sa". (Not
>a bad assumption as the western system holds C in a special place
>anyway).
Well, Ok, but this is not how it is done. If you are interested, find
a book on western modality -- what are often called "church modes" --
these modes are similar in concept to Indian ragas, and led eventually
to the 'composite' major and minor scales. The piano holds C in a special
place, since the white keys starting on C play the major mode. That's it.
>G Major: Kalyani (Yaman that)
>G natural minor: Kharaharapriya (Kafi that)
>G Harmonic minor: Hemavati (Kafi with tivra madhyamam)
>G Melodic minor: Vachaspati/Kharaharapriya
This is an abuse of notation. The notes of the G major scale, but
started at C, does define a mode -- but this is not the identification of
the mode, because the G is an unimportant note. All modes are identified
with their tonic (or final note) if they are to be so associated. The
common designation of 'g major scale, but starting on c' is 'white keys
starting on f' and I'll leave it to you to see that those are the same
mode. (And note the important fact that in this description, F<->Sa.)
This mode also has a name in western theory, but I must confess that I
never paid much attention to the names.
>We can work it out for other scales also, from the intervals. The
>important question is: Does it mean anything? I can't answer that very
>well. It isn't hard to see some similarity between G major and
>Kalyani. But, my efforts to find traces of Kharaharapiya in G minor
>hasn't exactly met with much success. May be someone else can comment
>on it.
Yes, it means something. It is a question of modality. It is your
'incorrect' description of the western modes that makes the similarity
that much harder to detect. Finding Kharaharapiya in G minor should
be no easier than finding it in Natabhairavi. Kalyani is somewhat easier,
because the tonic is deceptive and so your point of confusion is not
so obtrusive.
>When a western composition is in a major scale, it usually is faithful
>to the major scale (it might shift scales entirely, but won't "mix"
>them). However, a composition in a minor scale, I understand, could
>use any of the three minors, or even mix them up, making correspondeces
>with Indian scales difficult to make.
Correspondences with Indian scales are difficult to use. That's for
sure. Also, different composers will use the scales in quite different
ways. What you have said makes some sense for Mozart, but even by
Beethoven it is largely meaningless. Nowadays, there are thousands of
different ideas on how to use scales and modality.
>Does anyone have any comments on how wetern scales sound under an Indian
>system? Any comments about the situation wih the roles reversed?
Well, as you have said, the western scales can be identified with ragas,
and then they will sound exactly like indian music because they'll be
indian ragas. :-) A variety of western composers have used Indian scales,
starting early in the 20th century. Charles Tournemire was a real pioneer
in this regard. Olivier Messiaen (who recently passed away) gained quite
a bit of notoriety by using not only ragas but talas as part of his personal
style; his usage can be rather esoteric, and I am curious if an Indian
listener could identify the elements.
I'm not sure why I didn't post... if you want to follow-up to the group
and include parts of this, go ahead.
regards,
--
Todd McComb mcc...@turing.cs.rpi.edu [128.213.1.1]
William Alves
>
>I received this as a reply to my posting from Todd...
>
>tuning systems were introduced in western music in order to play vertical
>harmony in different keys on the same keyboard (re: Bach's Well-Tempered
>Klavier, "well-tempering" is another sort of temperment.) Equal temperment
>is the most extreme version of this, but most keyboards (at least for
>serious performers) are not using equal temperment, though they use various
>other tunings (whose names I don't pay much attention to) which are close
>to equal temperment.
Equal temperament is the standard tuning system in the West today. Virtually
all keyboard instruments are now tuned to it. Performers normally do not
make any choices about the way their piano is tuned, for example. There
are certain exceptions. Some "original instrument" performers who are con-
cerned about authentic performance practice for baroque and earlier music
tune their keyboard instruments to historically authentic tuning systems
such as a well temperament (really a class of tuning systems) or mean-tone.
Other exceptions include composers who are specifically interested in non-
standard tuning systems, such as Harry Partch, Lou Harrison, La Monte Young,
and Terry Riley.
With respect to the piano specifically, a complicating factor is that pianos
must be tuned to compensate for a phenomenon known as inharmonicity. Effec-
tively this means that strings are tuned progressively sharp as you go up
the keyboard. However, this is done to retain the sound of equal tempera-
ment despite the fact that the partials are relatively sharp of theoretically
pure frequency ratios.
>Western players of wind or string instruments do not
>use equal temperment at all, except in an attempt to blend with keyboard
>when necessary.
This is true to a certain extent, but it is misleading to be speaking of
tuning systems at all with these instruments. Precise tuning systems are
really only necessary on instruments that have one sounding body per note
(such as keyboard or mallet instruments) or fretted instruments. Western
wind instruments are constructed to play in tune with equal temperament,
but the players have a large amount of leeway in pitch on a given note.
Thus they can tune, within certain limits, to an instrument playing in
different tuning systems. Fretless strings and trombones can, of course,
play in any tuning system (theoretically).
>
>Most westerners also seem to have the idea that everything is equal
>temperment -- I suppose this is just easier to understand than the real
>situation which is rather chaotic. Modern composers are paying an increasing
>amount of attention to tuning.
>
I will agree that the situation is "chaotic" in that the range of fre-
quencies played by a symphony orchestra or sung by most choirs on what
is nominally a single pitch will easily span the difference between se-
veral tuning systems, so one cannot really say that it's equal tempera-
ment, well-temperament, just tuning, or whatever. A string quartet will
tend to tune the intervals beatless and hence approach just intonation,
but add a piano and it's a different story.
>
>>When a western composition is in a major scale, it usually is faithful
>>to the major scale (it might shift scales entirely, but won't "mix"
>>them). However, a composition in a minor scale, I understand, could
>>use any of the three minors, or even mix them up, making correspondeces
>>with Indian scales difficult to make.
>
I think that the idea that there are three minor modes is really incorrect.
Harmonic and melodic minor have found themselves included in theory
books even though I don't think they are really modes at all. What's
really happened in common-practice minor key pieces is that sometimes
the leading tone is raised in order to have a major dominant harmony
and that sometimes the sixth degree is raised in order to avoid the
augmented second between six and seven. These practices don't really
define new modes, just momentary inflections of the scale degrees to
accomodate harmony or voice leading, or "borrowed" chords, if you prefer.
>Correspondences with Indian scales are difficult to use. That's for
>sure.
Quite so.
On the subject of tuning systems, I might add that I read a dissertation
from UCLA some time ago about tuning systems used by various sitar players.
The author concluded that no "standard" tuning system exists for the in-
strument. Different teaching traditions use different tuning practices,
some tending towards just intonation, others toward temperament. As long
as the instrument is in tune with the pitches on the tambura (which is
presumably a pure 3/2 or 4/3) a "standard" isn't necessary. Thus the whole
question of tuning systems in Indian music is quite different than the
West, primarily because of the historical importance of keyboard instru-
ments in the West and having other instruments play with them.
Does anyone know of this dissertation or other references about this
question?
Bill Alves
Todd McComb
>Equal temperament is the standard tuning system in the West today. Virtually
>all keyboard instruments are now tuned to it. Performers normally do not
>make any choices about the way their piano is tuned, for example. There
>are certain exceptions.
I don't want to dwell on this, but isn't it true that performers tend to
prefer different 'styles' of tuning over others, or different piano tuners
over others? Equal temperament is the standard, and virtually all keyboards
are tuned *close* to it, but I just don't believe that strict parallel
intervals are the norm, as you go on to say.
Anyway, this is techinical stuff of rather little importance here.
>On the subject of tuning systems, I might add that I read a dissertation
>from UCLA some time ago about tuning systems used by various sitar players.
>The author concluded that no "standard" tuning system exists for the in-
>strument. Different teaching traditions use different tuning practices,
>some tending towards just intonation, others toward temperament. As long
>as the instrument is in tune with the pitches on the tambura (which is
>presumably a pure 3/2 or 4/3) a "standard" isn't necessary. Thus the whole
>question of tuning systems in Indian music is quite different than the
>West, primarily because of the historical importance of keyboard instru-
>ments in the West and having other instruments play with them.
>Does anyone know of this dissertation or other references about this
>question?
Since no one has picked up on this, I'll add some things. Perhaps someone
with better knowledge can correct me.
First of all, I believe there are two separate issues when one talks about
sitar tuning.
Different schools or gharanas of singing and playing have different
conventions for the precise pitch ratios in any given raga. This is
related to the 22 srutis posted some time ago, or various other theoretical
systems which people might use to describe what is actually sung. For
the moment, let me assume that a given school will sing a raga with the
same pitch ratios each time. This is what is supposed to happen, and in
this sense the tuning is fixed. Carrying this over to the sitar, different
players no doubt tune differently -- certainly differently based on the
raga, but also based on style.
Now assuming that one has decided on the precise tuning to be used for
a given raga, ie. the pitch ratios of each note, there is still a question
on the sitar of which notes to tune to. For this purpose, I will reproduce
a chart from a Sonodisc CD of Nikhil Banerjee. The author (Patrick Moutal)
discusses four leading sitar players, states that they use different numbers
of strings, and gives the following chart for which notes the strings are
tuned to:
Balaram Pathak 1-Ma, 2-Sa, 3-Pa., 4-Sa.., 5-Pa, 6-Sa, 7-Sa`
Ravi Shankar 1-Ma, 2-Sa, 3-Pa., 4-Sa.., 5- , 6-Sa, 7-Sa`
Vilayat Khan 1-Ma, 2- , 3-Sa, 4-Ga, 5-Pa, 6-Sa, 7-Sa`
Nikhil Banerjee 1-Ma, 2-Sa, 3-Pa., 4-Sa.., 5-Ga, 6-Sa, 7-Sa`, 8-Pa
(where I have placed register marks after the note)
It also seems likely to me that these artists will tune their instruments
to different notes depending on the raga in question, though the CD notes
do not mention this. My reasoning is that different notes are more important
in different ragas; the raga of this CD is Patdeep. Does anyone care
to comment?
I am totally ignorant of the paper mentioned, but I hope this helps to
clarify the situation somewhat.
William Alves
>
>I don't want to dwell on this, but isn't it true that performers tend to
>prefer different 'styles' of tuning over others, or different piano tuners
>over others? Equal temperament is the standard, and virtually all keyboards
>are tuned *close* to it, but I just don't believe that strict parallel
>intervals are the norm, as you go on to say.
>
slightly different results. However, these differences would be mistakes,
not different "styles." Now that virtually all piano tuners tune the instru-
ments with the aid of electronic devices, it is unlikely that there is even
that much difference. There is only one 12-tone equal temperament and you
either tune to it or you don't. When I learned to tune equal temperament
by ear, it was by learning such rules as the fifth F to middle C beats at
3 beats every 2 seconds, the third middle C to E beats 7 beats a second and
so on. That's because that's how equal temperament is defined.
Bill Alves