Shrutis/Intonation Theory (was: Composition)(LONG!)
WARVIJ
>:>:Warren Senders (WARVIJ) wrote:
::>Leaving aside other problems, the 22-shruti system is the object of
::>enormous controversy. No two authors agree on the validity of the
::>system; those who assert its existence do not agree on whether it
::>is equally tempered or not.
Batish responds:
>This is true. But since I am not familiar with what has been
>discussed to date on the 22 Shruti system, I think it would
>be nice to bring forth the existing theory on this topic.
Warren Senders responds, at length:
The problem is that there are as many 22-shruti theories as there
are writers on the subject. In my initial post I suggested that
interested
readers investigate Mark Levy's "Intonation in North Indian Music."
For Ashwin's benefit and for those others who may be curious I
will recapitulate some of Levy's summarizations of the various
theories re: shruti-s.
Levy comments first on "Differing Modern Interpretations of Bharata."
"While Bharata describes 22 shrutis to the octave, researchers disagree
on whether these were all equal or of different sizes. Those belonging
to the latter school also have numerous opinions regarding the precise
values for these different varieties. In addition, Bharata's wording
leaves
ample opportunity for diverse interpretations concerning the precise
relationships of svaras and shrutis in each *grama*. One reason for this
uncertainty is that some regard his svaras Sa, Ri, Ga etc., as pitches (as
they are considered in modern terminology), while others regard them
as intervals."
Levy then discusses the varying interpretations of Bharata by scholars
including Hornbostel, Lachmann, Poply, Bake, Jairazbhoy, Deva, Powers and
Clements -- and summarizes thusly:
"...Bharata describes in relative detail a melodic system based on a
division
of the octave into 22 shrutis, but leaves room for a great variety of
differing interpretations concerning their precise nature and
relationships.
It should be emphasized that nowhere in the *Natyashastra* is there a
mathematical definition of shrutis involving precise divisions of a string
length or interval ratios. The human ear is considered by Bharata as the
sole judge of shruti size. Arguments of succeeding authors utilizing
mathematical and acoustical formulations to interpret sections of this
treatise are all later additions externally imposed on Bharata's work."
Levy discusses each of the ancient writers on music, and moves into the
modern period, examining in turn such writers as Fox-Strangways (who
leans strongly towards a just intonation system with both major and]
minor whole-tones providing a variety of alternate pitch choices),
Kolinski
(who applies unrelieved Pythagoreanism to shruti theory to create a
virtually unsingable chromatic made of continuous perfect 5ths), and Bake
&
Jairazbhoy (who, reflecting a study of the relevant Vedic materials,
suggest
that Bharata's shrutis were equal in size).
Levy summarizes, thusly:
"The three origin theories...all agree that Bharata's 22 shrutis most
likely
did not arise from a conscious division of the octave. Fox-Strangways
believes that they evolved rather from a need to describe the intervals
of Just intonation. Kolinski hypothesizes their evolution from the
various interval combinations of the Pythagorean scale, modified to
retain the consonances of the fourth and fifth within a single octave.
Bake and Jairazbhoy also emphasize the fundamental importance of
these consonances, but believe that Bharata's shruti formulation was
based on an attempt to describe the three interval sizes of Vedic chant,
and apply them to a theory of secular music."
Levy continues in the chapter titled "Modern Interpretations and
Expansions of the Sruti System," examining in turn the assertions
of K.B. Deval, Clements, Danielou (whose bizarre theories are
*comprehensively* refuted -- cf. earlier posts on this subject), N.K.
Bose,
Antsher Lobo, Goswami, Swami Prajnanananda and H.V. Modak. He
summarizes:
"With few exceptions, then, the majority of the theorists discussed in
this
chapter visualize an unbroken continuity of musical tradition from ancient
to modern times. A corresponding reverence for the old treatises results,
along with a desire to reconcile ancient theory with modern musical
practice. Fears are expressed concerning the encroachment of Western
tempered tuning on Indian music. While these authors seek to defend
the continued applicability of a system of 22 shrutis, they also construct
complex expanded formulations involving an increased number of
microintervals. These constructs result from the imposition of Western
acoustical, mathematical and notational concepts. Numerous references
to the Western just and Pythagorean tuning systems are made, along
with the harmonic series. Precision and consistency of intonation in
contemporary musical practice are stressed. The arguments of many of
these writers are unconvincing, however, due to subjective views,
contrived formulations, and a lack of documentation."
(WS note: sock it to 'em! We're behind you all the way!)
Levy concludes this section of his book with a look at the writings
of contemporary musicologists who eschew sruti theory. These writers
include Bhatkhande, M.R. Telang, Herbert Popley, G.H. Ranade, A.A. Bake,
Amiya Nath Sanyal, Rabindralal Roy, S.N. Ratanjankar, Harold S. Powers,
Nazir Jairazbhoy, Walter Kaufmann, Purnima Sinha, B.C. Deva and H.V.
Modak. He summarizes:
"The writers...oppose the view that intonation in modern musical
performance is mathematically precise and consistent. While they
acknowledge the existence and importance of subtle microtonal
inflections (especially with respect to ornamentation) they emphasize
the flexible and subjective nature of these phenomena. Several of these
theorists discuss the possible influences of melodic movement,
tetrachord symmetry, and subjective human perception on intonation.
These writers wish to discontinue the application of the ancient sruti
theory to contemporary musical practice, since they do not acknowledge
a continuity of tradition from ancient to modern times. They emphasize
that North Indian raags are not differentiated from one another on the
basis of microtonal alteratios. Most of these authors recognize the
general
twelve-semitone character of modern North Indian music. Some
vague attempts, however, are made to reconcile it with the 22-sruti
system. The majority of the Indian writers here are influenced by
Western scientific methods and acoustical theory, and frequently have
some difficulty in dealing with these approaches within the framework
of their traditional Indian outlook."
The second half of Levy's book consists of laboratory measurements of
famous musicians' intonation in actual performance context. The artists
sampled include: Amir Khan, Niaz & Faiyaz Ahmed Khan, Nazakat &
Salamat Ali Khan, Kishori Amonkar, Bismillah Khan, and Z.M. Dagar.
His summary is too long for me to type in, but I will reproduce germane
excerpts:
"The laboratory results do not corroborate the insistence of many
theoreticians on extreme precision and consistency with respect to fine
microtonal differentiations in North Indian Music. In each of the ten
recordings analyzed, every note showed a relatively high degree of
flexibility in its intonation. Even the ground-note Sa tended to vary,
although it was almost always considerably more stable than the
other notes. Most stable after Sa were the consonant secondary ground-
notes Ma and Pa. Shuddha or natural notes tended to be somewhat more
stable than vikrit or altered ones. Notes with greatest flexibility were
those
exhibiting pitch oscillation and leading tone functions, and were often
associated with tetrachordal imbalance."
"The numerous constructs of some ancient and modern theorists
involving systems of 22 or more shrutis to the octave were seen to have
little in common with the basically twelve-semitone (not necessarily
tempered) character of the music analyzed here.....On the whole, the data
supported only those views which allowed for flexibility in intonation."
Senders again:
As a practicing musician none of this seems strange to me. We all strive
for beauty in our performance, and one of our sources of beauty is
the artistic rendering of melodic gesture within a relatively defined
range of intonational probabilities. Even those musicians whose
pitch was considered as "faultless" by their contemporaries varied
their intonation depending on melodic context, emotional involvement,
the pitch of accompanying instruments and hundreds of other variables.
This is as true in Western music as it is in Hindustani music.
------now, on to Ashwin's next paragraphs:-------------
>>There is nothing demonic or strange about this crucial
aspect of Indian music. It is controversial only because
we tend to look at this theory from the Western, equal
temperament, 12 tone chromatic, perspective.
Note: 12-tone chromatic does *not* mean equally-tempered. This
is a common fallacy. Furthermore, consultation with any professional
piano tuner will reveal that they frequently stretch tunings on pianos
*away* from equal temperament (putting fifths in tune, expanding
octaves, etc.) -- it was remarked by a student of mine who tunes and
performs on the clavichord that equal temperament in its pure form is
only heard in electronic contexts!
>>>This is perhaps because this intonational system
>is the dominant one today thanks to the marketing
>success of Western pop worldwide.
The suggestion that Western pop is based on equal temperament is
reasonable only if one ignores the prevalence of bent notes, slides,
slurs, glissandi, "blue notes" etc., many of which are derived from the
African musical traditions that survived in the West. Since it is
precisely
these elements that have ensured the continuing prevalence of Western
pop music, Sri Batish's assertion is groundless --
in fact, 12-tone equal temperament is only found on electronic keyboards
(and irregularly even there); thus calling it the "dominant" intonational
system of the present day is erroneous. It's a grave error to confuse
"musical system based on harmonic structures
in motion" with "intonational system based on logarithmic division of
the octave."
AB:
>>>But one should not forget equal temprament is Bach's gift to
>us all. Although, from what I understand, even he wasn't
>serious about its use for performances. The 22 shrutis are
>derived from the Just Intonation tuning system. The
>purity of note is the issue here.
The "Just Intonation" tuning system was developed in the west,
centuries after the development of the 22-shruti theory. Presumably
what Shri Batish means is that (in his opinion) shrutis emerged through
the application of overtonal relationships from a central generative
tone, using the preference for small whole-number ratios as the guiding
principle.
Just Intonation is practiced regularly today by any competent string
quartet, barbershop quartet or chamber ensemble that does not
include a piano or tempered keyboard instrument. For a lengthy and
detailed exegisis of Just Intonation, I recommend Harry Partch's
"Genesis of a Music" and Llewelyn Lloyd's "Intervals, Scales and
Temperaments." I am providing a separate post in a few days' time
that gives some basic information on Just Intonation.
Batish:
>>>For the practical performing musician, the 22 shruti theory
>complicates his spotaniety (sic) and is often sacrificed for
>instant pleasure. But the question is - does
>the theory take precedence over performance? Not in my book.
>The theoretician must be subordinated to the performer.
True. But note that Levy's results conflict with your own assertions
about shrutis. Where do these assertions come from if not from your
work as a performer? If they are not backed up by experience they're
just idle "chhed-chhad."
>>>It is the job of the theoretician to explain and
>analyse what makes the performer and his music
>tick. Herein lies the problem, the controversy, and
>the diversity of answers.
Well, actually the problem is that for centuries theoreticians have
been trying to explain things in terms of 5th century Sanskrit
dramaturgy -- while the music has changed totally around them!
It's only post-Bhatkhande theorists who have tried to discuss
any elements of contemporary practice at all!
>>>For the student and layman, trying to make sense of
>all this is perhaps too wierd.
Weird is a charitable word.
>>>After all the seven notes in our Sargam are derived
>from the 12 in an octave so why
>are classical theorists pushing the 22 note philosophy?...
I'm not sure what you mean. Are you now repudiating your
earlier assertion about the derivation of the 22 shrutis from
an Indian version of Just Intonation?
>>>They then tend to discard and redicule this. Some
>even go as far as to suggest that these are quarter tones???
The term "quarter tones" is frequently used by members of the lay
audience to refer to "any musical interval smaller than the accepted
Western semitone."
Obviously a 22-note-to-the-octave scale, if equally tempered, would
yield "semi-ektadecitones" (my Latin diminutives may be off, but you
get the idea). Equally-tempered 22 is a really gruesome set of intervals
with nothing to recommend it.
Western music in "quarter tones" has been composed, of course; see
Ives, Haba, Carillo, Krenek, Penderecki and many others.
---------- moving on ------------------
WS:
>Ajoy Chakrabarty explained his concept to me:
>
>"Leave aside Sa and Pa -- they never change. The 10 other notes are
>Komal & Shuddh Re, K&S Ga, Shuddh & Tivra Ma, K&S Dha, K&S Ni. For
>each of these notes there can be a slightly higher position and a
slightly
>lower position, making a total of 20 notes in all -- for example:
>*low* komal Re / *higher* komal Re /
>*low* shuddh Re / *higher* shuddh Re.
>Thus there are a total of 22!"
AB:
>>>This explanation is very popular amongst most
>singers. This is probably all they
>need to state. We have a popular saying in India..
>"if you are gifted with a
>beautiful singing voice you are already striking the right
>shrutis" Ajoy certainly
>holds that status.
>
WS:
>But he never offered to sing them for me in chromatic sequence!
AB:
>>>This is not the goal of the 22 shruti system.
>They are never sung in a "chromatic"
>sequence. To do so would be a disaster.
To do so would be a chromatic sequence. The word "disaster" is a bit
strong, don't you think? If, for the purposes of demonstration or art,
you
play or sing a 12-note chromatic scale (as indeed many do in the course
of their peregrinations through Bhairavi), then surely it is within your
capability to render a 22-note chromatic?
(Note: that doesn't mean you'd want to hear it in performance. But if
they exist and are used regularly by modern performers, why hasn't
*somebody* done it at a SPIC-MACAY function?)
AB:
>Instead 7 notes are selected for the raga to
>be performed.
Or however many are involved, right? Like Jaijaivanti, Pilu,
Basanti Kanada, etc., etc., etc.
WS:
>>>Maharashtrian junior musicians all assert that Feroze Dastoor can
>sing 22 notes in sequence. I asked him and he looked irritated and
>changed the subject.
AB:
>No comment.
No comment on that "no comment."
>
WS:
>It's said that Bade Ghulam Ali was listening to a learned discussion
>about shrutis; exasperated, he got up and shouted: "all this is
nonsense,
>*this* (singing a typical BGAK taan) is the only thing that matters!"
AB:
>>>Again, performers have little patience with theory.
>This does not substantiate their non-existense.
Performers' lack of patience with theory seems to me to have little to
do with whether they exist or not. Bade Ghulam Ali Khan certainly
existed, no? Or did you mean the non-existence of shrutis?
In that case we need to know what the term "shruti" means,
which is what this whole discussion is about.
AB:
>>>In Bade Gulam Aliji's case, one has to respect his view point.
>He is right also... He, like many other top musicians, was a practical
>performer. To him "the music is really the only thing that mattered."
When you say "He is right also..." are you confirming that intonation is
variable in performance, and that whatever notes he chose to suit
his own artistic purposes were the right ones? I hope so!
AB:
>>>But, where knowledge of shrutis "matters" is with
>instrumentalists. You have to put this question to sitarists,
>sarodists, dilrubha players etc. They are the ones facing
>the intonation nightmare. They have to constantly battle
>note purity. They cannot fudge notes as they are
>confined by frets and hence have to have some idea
>of intonational purity.
I don't understand. Do you mean to suggest that vocalists don't have
to "battle note purity?" This seems bizarre to me. A string player
(and I am one as well as a vocalist so I speak from experience) can
look at the instrument, can feel the tension on the string, can adjust
the frets (if frets there be) to get the right pitch. But vocalists can't
look at anything; *all* they have to rely on is their aural sensitivity.
WS:
>>>Clements designed a 22-shruti harmonium in the early years of this
>century, but nobody wanted to use it. I've seen one in Pune, but it's
>gone completely out of whack, and nobody knows what the original
>tuning was -- probably a just-intonation structure with a significant
>fudge factor.
>
AB:
>>>It was not designed to be "used." the idea was
identification of the 22 notes.
Well, this instrument was sitting on a shelf in the harmonium room
of a music school. It wasn't in a museum, and there was a manufacturer's
label attached to it -- all suggesting that the instrument was made to
be sold and used.
>>>The ancient shruti experiments gave rise to the
>"achal veena" similar to the swarmandal
>of today. Here the twenty two shrutis would
>be tuned in sequence. This was done so
>that difference ragas in the three gramas
>could be properly identified and tunings
>noted.
Where are these instruments now? Why does nobody retain this
knowledge? My personal opinion is that it's irrelevant to contemporary
performance practice. As the tuning of the Turkish baglama suggests,
adding frets to render microtones required by performance practice
is quite easy. If Indian musicians needed these notes, they would
have added them.
WS:
>Yusuf Mirajkar of Pune tunes using exclusively 5ths, creating what
>would be a Pythagorean tuning were it not that the traffic noise outside
>his workshop makes it impossible to hear the beating of two slightly
>mistuned notes. This sort of thing is why so many harmoniums are
>covered with thick cloth in concert!
AB:
>>>The harmonium gets bashed every time ;-)....
Now wait a second! I like harmoniums; a reasonably sweetly tuned
harmonium is certainly more consistent and definitely less obtrusive
than any but the most sensitive sarangiya.
>The ever popular Indian harmonium is
>tuned to the Western equal temprement scale.....
No, it's not. See my note re Mirajkar, above. See also Jairazbhoy, who
pointed out considerable variance in tuning from harmonium to
harmonium (and that's not just the absolute pitches involved, but
also their intervallic distances). I don't really believe that harmonium
tuners in India went through the whole rigamarole of tuning each
3/2 to give exactly 3 difference beats in each 5 seconds -- or any of
the other pre-electronic methods used to arrive at approximations
to equal temperament. Furthermore the harmonium's pitches also
distort depending on the volume and pressure of air going through
the reeds. Just because somebody *says* they tune to equal temp.
doesn't mean that they actually *do.*
>...so even while many in the classical
>community shut their eyes from the 22 note
>shruti system, yet, they give credit to
>its obvious merritts by recommending the
>tanpura over the harmonium!
The tanpura is a drone instrument and has nothing to do with the
22-shruti system. Unless you know of a chromatic 22-note tamboura?
;-)
What are the "merits" of a system of intonation that nobody
actually seems to use (as Levy demonstrates very ably) but everybody
gives lip-service to?
AB:
>>>But I really like the harmonium. It has its beauty.
>An interesting aspect of harmonium tuning is
>the fact that the ones classified as "bass/treble"
>reed type have their reeds
>slightly out of tune so they create a
>"shimmering" effect. This also has the effect
>of camouflaging the exact note. But a bad
>tuning job can make listening a sickening
>experience!
WS:
But faced with a sensitive player on a badly tuned instrument vs.
an earless fellow on a perfectly tuned one, I'd unhesitatingly go for
the sensitive player.
I was told by Jayant Joshi that Appasaheb Jalgaonkar has a number of
harmoniums which have been tuned to a single Sa; therefore, he chooses
the instrument which fits a particular singer's key-note. Certainly I
recall that the shadja-panchama bhava of his harmonium is quite pure
(though sometimes he forgets to listen to the performer and goes off
on distracting flights of his own!).
>
WS:
>>>Anyway, notation in Hindustani music can either be descriptive, in
which
>case it will be useful to analytical musicologists -- or prescriptive,
>in which case it will function as it always has: as a spur to the memory
>of the artist.
AB:
>>>I like the last definition. I use notation as a
>skeletal means of writing melodies.
>Application of gamaks should then be left to the player.
As it has always been. Whither shrutis now?
Warren Senders
Original music blending Indian and Western traditions;
Songs of Myth and Magic;
Hindustani vocal music -- Khyal & Thumri --
for info:
http://challenge.tiac.net/users/joisprng/Senders.html
also check out:
http://www.rootsworld.com/rw/
"Beauty in music is too often confused with something
that lets the ears lie back in an easy chair."
-- Charles Ives --
Vidyasankar Sundaresan
>
>Levy comments first on "Differing Modern Interpretations of Bharata."
>"While Bharata describes 22 shrutis to the octave, researchers disagree
>on whether these were all equal or of different sizes. Those belonging
>to the latter school also have numerous opinions regarding the precise
>values for these different varieties. In addition, Bharata's wording
>leaves
>ample opportunity for diverse interpretations concerning the precise
>relationships of svaras and shrutis in each *grama*. One reason for this
>uncertainty is that some regard his svaras Sa, Ri, Ga etc., as pitches (as
>they are considered in modern terminology), while others regard them
>as intervals."
My 2 c. on this. Bharata's description of the determination of 22 Srutis using
a cala vINA and an acala vINA needs careful understanding. In the beginning, he
tells you to "tune both vINAs to shaDja grAma and then on the acala vINA,
reduce pancama to be in samvAda with rishabha instead of with shaDja". It is
clear that here shaDja, rishabha, pancama etc. refer to pitches (as used in
modern terminology) and not to intervals. When finally he describes nishAda as
"having" 4 Srutis and so on, there might be some ambiguity in whether he is
referring to a pitch or an interval. Here too, the problem may really be one of
translation from the Skt. original. I don't think there are many modern
musicologists who have read and understood Bharata in the original.
But even otherwise, in the context of the cala vINA - acala vINA experiment,
sa, ri, ga etc. refer not to intervals but to notes, which then determine
intervals characterized by consonance (samvAda) or otherwise. If there is a
modern musicologist out there who thinks there is ambiguity within this
specific context, he is certainly wrong.
>Levy then discusses the varying interpretations of Bharata by scholars
>including Hornbostel, Lachmann, Poply, Bake, Jairazbhoy, Deva, Powers and
>Clements -- and summarizes thusly:
>
>"...Bharata describes in relative detail a melodic system based on a
>division
>of the octave into 22 shrutis, but leaves room for a great variety of
>differing interpretations concerning their precise nature and
>relationships.
>It should be emphasized that nowhere in the *Natyashastra* is there a
>mathematical definition of shrutis involving precise divisions of a string
>length or interval ratios. The human ear is considered by Bharata as the
>sole judge of shruti size. Arguments of succeeding authors utilizing
True. All attempts to fix integer-ratios to the Srutis that Bharata describes
are acts of external retrofitting. But then it is very tempting and also the
least unreasonable to suppose that Bharata implies sa:pa = 1:1.5, (at least
approximately, as judged by the human ear) when he says there is a samvAda
between these two in the shaDja grAma. The absolute pitches of these notes need
not matter, it is the ratio that determines samvAda. The fact that precise
mathematical ratios are not defined in the nATyaSAstra does not mean that some
rudimentary mathematics is not implicit in it. Beyond that however, there will
always be uncertainty, and therefore controversy, in "fixing" a ratio value to
each of the 22 Srutis that Bharata mentions.
--- deleted ---
>
>"The three origin theories...all agree that Bharata's 22 shrutis most
>likely
>did not arise from a conscious division of the octave. Fox-Strangways
>believes that they evolved rather from a need to describe the intervals
>of Just intonation. Kolinski hypothesizes their evolution from the
>various interval combinations of the Pythagorean scale, modified to
>retain the consonances of the fourth and fifth within a single octave.
>Bake and Jairazbhoy also emphasize the fundamental importance of
>these consonances, but believe that Bharata's shruti formulation was
>based on an attempt to describe the three interval sizes of Vedic chant,
>and apply them to a theory of secular music."
If you take the historic setting of the nAtyaSAstra into account, all these
beliefs are quite presumptuous, I must say. It is very clear that Bharata is
describing a system of music based on the grAma-mUrchanA system. Bharata
clearly talks of a shaDja grAma and a madhyama grAma. The three (two, actually)
interval sizes of Vedic chant are quite geography dependent today, and I don't
believe there was any conscious attempt at any point of time to fix these sizes
or to describe them in terms of Srutis. Even the terms used for the pitches in
the Vedic chant (udAtta, anudAtta and svarita) do not enter into musicological
decriptions to any significant extent. Kolinski, I suspect, is one of those who
derive quite a few things Indian from Greek precursors. There seems little
justification for this. Nor is there any need to believe that the Sruti system
is specifically designed to describe intervals of just intonation. Bharata
starts by assuming that the experimenter can tune the cala vINA and the acala
vINA to the shaDja grAma, which is supposed to be today's melakartA
kharaharapriyA = thAT kAfI. Whether this basic tuning conforms to Just
Intonation is anyone's guess. Taking the human ear (and a reasonably sensitive
human ear, I presume!) to be the judge however, the tuning may just approximate
to just intonation, within limits of human error. But who can say that for
sure? Some of the pitches that I hear in Iranian music sound extremely odd to
me, but they may have sounded perfectly beautiful to some ancestor of mine! So
there is no guarantee that the shaDja grAma of Bharata's time was in fact tuned
according to what we call just intonation today.
>
>Levy continues in the chapter titled "Modern Interpretations and
>Expansions of the Sruti System," examining in turn the assertions
>of K.B. Deval, Clements, Danielou (whose bizarre theories are
>*comprehensively* refuted -- cf. earlier posts on this subject), N.K.
>Bose,
>Antsher Lobo, Goswami, Swami Prajnanananda and H.V. Modak. He
>summarizes:
>
>"With few exceptions, then, the majority of the theorists discussed in
>this
>chapter visualize an unbroken continuity of musical tradition from ancient
>to modern times. A corresponding reverence for the old treatises results,
>along with a desire to reconcile ancient theory with modern musical
Aha, therein lies the crux of the matter. In fact, there is ample evidence that
even some of the medieval writers in Sanskrit are aware that substantial change
if not a break has occured. There is no reason to believe that grAma and
mUrchanA based music as desribed in the nATyaSastra necessarily used a fixed sa
at all. In fact, from Bharata's description of the madhyama grAma, the "pa" of
the madhyama grAma is not in consonance with "sa", where "sa" and "pa" refer to
these notes as in shaDja grAma. On the other hand, madhyama grAma is reckoned
from ma and not from sa. Visualized in terms of intervals, the "sa" of shaDja
grAma becomes the fifth wrt "ma" and is in consonance. Clearly, in performing
madhyama grAma, the reference note is ma, not sa. So, I guess one could say
with some confidence that grAma based music was probably not based on the
concept of a fixed reference note. Somewhere along the line, this has given way
to the concept that sa and pa should both be "fixed" notes, while others can
take different pitch values. This is invariably explained away as due to the
madhyama grAma falling out of use. It is quite fashionable to say that nowadays
only the shaDja grAma is performed. This does not seem a very satisfactory
explanation to me. I would rather say that grAma based music has given way to
AdhAra shaDja based music. Change or break? In any case, not much continuity
can be postulated. No wonder then that the 22 Sruti theory described by Bharata
causes lots of problems for modern interpreters.
None of the modern interpreters of ancient Indian music theory explain
adequately the fact that among Bharata's 22 Srutis is a "panchama" that is not
consonant with the "shaDja". It is facetious to claim that this note that
Bharata calls a "panchama" is now a "more tIvrafied" variety of tIvra (prati)
madhyama. I see no justification for this in current Hindustani music practice
- my ear (the sole judge :-)) hears only one tIvra ma in contemporary
Hindustani music. Carnatic music practice may be a different issue in this
regard. There are different shades of prati madhyama in use e.g. prati madhyama
in ranjanI vs. prati madhyama in varALI. Not that it is any easier to fit 22
Sruti theory to contemporary Carnatic music practice - the 72 melakartA system
prevents that quite admirably.
---- deleted ----
Re: Ajoy Chakraborty's explanation of 22 Srutis:
>WS:
>
>>But he never offered to sing them for me in chromatic sequence!
>
>AB:
>>>>This is not the goal of the 22 shruti system.
>>They are never sung in a "chromatic"
>>sequence. To do so would be a disaster.
>
>To do so would be a chromatic sequence. The word "disaster" is a bit
>strong, don't you think? If, for the purposes of demonstration or art,
>you
>play or sing a 12-note chromatic scale (as indeed many do in the course
>of their peregrinations through Bhairavi), then surely it is within your
>capability to render a 22-note chromatic?
I doubt that it was even Bharata's intention to have 22 Srutis sung in
chromatic sequence. The presence of 22 Srutis in an octave, as per Bharata's
description, is an abstracted explanation of what happens within an octave when
the shaDja grAma and madhyama grAma are both taken into account. It seems to me
that the shaDja grAma, when being performed, would preclude that of the
madhyama grAma. It is highly unlikely that a musician in Bharata's time was
called upon to render both shaDja and madhyama grAmas simultaneously. Also,
note that Ajoy Chakraborty's explanation is performance-based. The slightly
higher version and slightly lower version of each vikrita note do not occur in
and of themselves, but in the context of the rAga being sung. A given rAga
might call for one of these two versions predominantly. Or it might even call
for both varieties of the same vikrita note, but rarely in sequential order. In
other words, the musician decides whether the aesthetics of the situation
demands the higher or lower version of say the komal rishabha. Rendering the
two in sequential order would obviously lead to vivAda, which Indian musicians
avoid by and large, or else mask with great ingenuity. Again the magic number
22 exists only as a theoretical superset of possibilities, never actually sung
in sequential order. It is in this context that I understand Ashwin's comment
that it would be a "disaster". The 12-note sequence in some renderings of
Bhairavi always sounds trite to me, no matter who does it. Who knows, some day
in the future it may be fashionable to sing 22-notes in sequential order!
S. Vidyasankar
ps. Have people heard of the "22 Srutis/7 notes = pi" explanation? :-)
pps. Most lists of retro-fit ratio values to "Bharata's 22 Srutis" rely on a
perfect fifths cycle. But these lists also include values like 5/4 and 5/3 for
gAndhAra and dhaivata respectively. These numbers could not have come from a
pure fifths cycle, but this fact is rarely, if ever, appreciated by most modern
Indian writers.
ppps. Many thanks to Srini Pichumani for discussions in the past on this issue,
and also for copies of articles from various music related journals. I've even
put in ps, pps and ppps in his honor here!
Vidyasankar Sundaresan
>My 2 c. on this. Bharata's description of the determination of 22 Srutis using
>a cala vINA and an acala vINA needs careful understanding. In the beginning, he
>tells you to "tune both vINAs to shaDja grAma and then on the acala vINA,
>reduce pancama to be in samvAda with rishabha instead of with shaDja". It is
Sorry about that. It should have been "on the cala vINA, reduce pancama" etc.
The acala vINA, true to its name, is left untouched in the course of Bharata's
demonstration, once it has been tuned to shaDja grAma. It is the cala vINA that
gets retuned.
>pps. Most lists of retro-fit ratio values to "Bharata's 22 Srutis" rely on a
>perfect fifths cycle. But these lists also include values like 5/4 and 5/3 for
>gAndhAra and dhaivata respectively. These numbers could not have come from a
>pure fifths cycle, but this fact is rarely, if ever, appreciated by most modern
>Indian writers.
>
There are a few more interesting aspects to this issue. Bharata starts by
assuming that the tuning of the acala vINA to the shaDja grAma is well-known.
As far as my knowledge goes, the nAtyaSAstra does not explain how to do it.
That is why assuming that shaDja grAma was tuned according to just intonation,
leads to conroversy. A related controversy is whether the 22 Srutis were equal
in size or not.
On the other hand, any aspect of Indian culture is always studied through
samskr.ta sources, and tamizh sources are relatively neglected. One of the
prime sources of information on music in the tamizh regions is the classic
Silappadikaram. This, along with its commentary, provides us with a different
picture of the state of music and music theory in India. An analysis of the
musical references in the Silappadikaram has been done by S. Ramanathan in his
doctoral thesis.
It is evident from these works that the cycle of fifths was indeed used to tune
the yAzh (harp-like?). Consonance and dissonance relationships between notes
are described in terms of naTpu (friendship) and pakai (enmity). kural (shaDja)
and iLi (pancama) are said to be in naTpu. The process of taking repeated
fifths is known in tamizh as iLikramam. The description of tuning pAlaiyAzh
(equivalent to harikAmbhoji - khamAj) leaves no room for doubt that the cycle
of fifths is used to tune the strings of the instrument. What is even more
interesting is that there is evidence that the tamizh musicians also modified
this cycle in the case of the kaikkiLai (= gAndhAra) and viLari (= dhaivata).
This is done because the iLikramam would give a third that is dissonant with
the tonic. aTiyArkunallar clearly describes the reduction of the pitch of the
kaikkiLai (gAndhAra) to bring it into consonance with the tonic (kural), so
that the pakai is removed and naTpu is re-established. The viLari (dhaivata) is
also correspondingly reduced, in order to be in naTpu with the reduced
kaikkiLai. If we were to attach a simple ratio of integers to this verbal
description, it is clear that only a value of 5/4 could be meant for the new,
reduced kaikkiLai. The presence of the fifth harmonic is very pronounced,
especially in vibrations of thick strings, and it is obvious that the reduction
of the kaikkiLai (gAndhAra) is to bring it in resonance with this harmonic. The
corresponding value for the reduced viLari (dhaivata) would then be 5/3. What
strikes me in this description is that the modification of the cycle of fifths
is done not to maintain the consonance of the uzhai (madhyama), but that of the
kaikkiLai (gAndhAra). The consonance of the uzhai is ensured because the
iLikramam is started from tAram (nishAda), so that uzhai is determined as the
fifth of tAram and kural as the fifth of uzhai. It has always puzzled me that
the notes in Indian references have always been reckoned from the nishAda.
There is even a story that originally there were only six notes, and that the
shaDja was introduced because it was given by Siva. It may be that the
reckoning from nishAda is just a way of maintaining the consonance of the
fourth even while determining notes using a cycle of fifths. On the other hand,
I haven't seen such an explicit description of gAndhAra consonance with shaDja
in any samskr.ta source. Of course, this does not mean that it wasn't
recognized in practice.
There is also evidence in tamizh sources for derivation of new scales by what
is called kural tiripu i.e. shift of tonic from pAlaiyAzh. This shift of tonic
is called mUrchanA in samskr.ta sources. Ramanathan also gives the Greek modes
(Dorian, Ionian etc.) corresponding to these scales. However, what is unclear
to me from a reading of S. Ramanathan's work is whether the tamizh sources
themselves explicitly mention 22 intervals in an octave or whether he is
unconsciously reading the popular 22 Sruti theory into them. He quotes a few
original verses from aTiyArkunallar in his thesis, but my knowledge of old
tamizh is almost nil, so that I can't say for sure. The reason I am doubtful
about it is because unlike in Bharata's case, the tamizh sources do not mention
anything equivalent to a madhyama grAma.
There always remains the question of influence from the Greeks, which I won't
go into now.
S. Vidyasankar
Varanus gouldii
>It should have been "on the cala vINA, reduce pancama" etc.
>The acala vINA, true to its name, is left untouched in the
>course of Bharata's demonstration, once it has been tuned to
>shaDja grAma. It is the cala vINA that gets retuned.
Vidya, what are these types of vINA?
Ramki
Vidyasankar Sundaresan
>Vidyasankar Sundaresan <vi...@cco.caltech.edu> wrote:
>
>>It should have been "on the cala vINA, reduce pancama" etc.
>>The acala vINA, true to its name, is left untouched in the
>>course of Bharata's demonstration, once it has been tuned to
>>shaDja grAma. It is the cala vINA that gets retuned.
>
>
>Ramki
Some kind of stringed instrument, that much is for sure. I don't know
if they were supposed to be fretted or not. But frets are not necessary for
Bharata's demonstration. It is clear from his description that there is one
string per note.
The cala vINA and acala vINA are identical instruments. Both are tuned
identically to begin with, to shaDja grAma. The tuning of the acala vINA
remains unchanged and that of the cala vINA is changed to modify the samvAda
relationships between various pairs of notes over the course of the experiment.
Vidya
ChristianAMR
> Vidyasankar Sundaresan <vidya> wrote:
> The acala vINA, true to its name, is left untouched in the course of Bharata's
> demonstration, once it has been tuned to shaDja grAma. It is the cala vINA that
> gets retuned.
> >pps. Most lists of retro-fit ratio values to "Bharata's 22 Srutis" rely on a
> >perfect fifths cycle. But these lists also include values like 5/4 and 5/3 for
> >gAndhAra and dhaivata respectively. These numbers could not have come from a
> >pure fifths cycle, but this fact is rarely, if ever, appreciated by most modern
> >Indian writers.
> about it is because unlike in Bharata's case, the tamizh sources do not mention
> anything equivalent to a madhyama grAma.
> There always remains the question of influence from the Greeks, which I won't
> go into now.
>
> S. Vidyasankar
Interesting to read about shadja-gandhar conosonance in old Tamil shastras .
This site talks about Shadaj-Gandhar Bhav :
https://www.chandraveena.com/blog/grammar-of-music/
Dr Oke ( 22 shruti reasearch + harmonium ) also writes extensively about the Shadja Gandhar relationship :
http://www.22shruti.com/research_topic_31.asp
http://www.22shruti.com/research_topic_12.asp --- importance of Ga
Dharambir Singh goes into the details :
http://www.dharambir.com/indian-classical-music-research/svara-and-tunings/
" Starting with the tonic Shadaj the fourth tone was tuned as a perfect fourth interval called Madyam. This Madyam was used to establish its perfect fourth the last note in the series called Nishãd. This Nishad helped to establish the third tone called Gandhãr a perfect fifth down. From Madyam as reference a perfect third was tuned and called Dhaivat. From this Dhiavat the second tone Rishab was tuned as a perfect fifth below. The perfect fifth was tuned from Shadaj as reference to complete the basic seven tone basic Grãma (tuning reference).
In a perfectly tuned Tānpūrā, the perfect third overtone heard in the Mandra Shadaj string of the 5/4 ratio is Bharata’s Antra Gandhār. Though Bharata did not include this interval as Samvād but in the establishment of the Grāma he has highlighted the importance of Antra Gandhār. This importance will be evident in the proceeding couplets. It is important to remember that Matanga has mentioned the seven shrūti interval in Madhyama Grāma as samvād and that is same as the S –G interval. In Brhaddeshi (page 16) this interval has been given more prominence than the shadaja pancham and shadaja madhyama. One reason for this is that in the overtones this note is the most prominent and second that in the establishment of the Grāma’s the use of this is worth looking at. In the next couplets both samvād are mentioned.
The only method to tune Dhaivat on the sixth string is through the Seven Shruti Shadaj Gandhār samvād. From this Dhaivat tune the Rishab on the second string through avroh Shadaj pancham samvād. "
It seems that somehow or other the Shadja Gandhar samvaad was there in ancient North Indian texts also . ( ma Dha tuning in Shadja Grama )