The Equivalences

Hello ALL tuners,

I have a very important query:

Can you name the source where the equivalence between 9 shruti-s and
Sa-Ma interval, the 13 shruti-s and Sa-Pa interval, and the existence
in Indian music of the octave doubling was first suggested? And
conclusively proved?

I have been going through sangitaratnakara for quite some time
recently, and it does not even remotely mention those equivalences --
obviously, because the ratios, cents and savarts did not exist then.

Thanks.
Haresh.

--- In tuning@y..., "Haresh BAKSHI" <hareshbakshi@h...> wrote:
> Hello ALL tuners,
>
> I have a very important query:
>
> Can you name the source where the equivalence between 9 shruti-s
and
> Sa-Ma interval, the 13 shruti-s and Sa-Pa interval, and the
existence
> in Indian music of the octave doubling was first suggested?

Wasn't it in Bharata were these specifications were found? Except
that the names of the notes have been rotated since Bharata's time,
so that today's Sa was his Ni, etc . . . ?

> And
> conclusively proved?

What do you mean by "conclusively proved"?

>
> I have been going through sangitaratnakara for quite some time
> recently, and it does not even remotely mention those equivalences -
-
> obviously, because the ratios, cents and savarts did not exist then.

I don't see why one would need ratios, cents, or savarts to simply
notice octave equivalence and to roughly measure the fifth and fourth
as 13 and 9 parts, respectively.

Haresh BAKSHI schrieb:
>
> Hello ALL tuners,
>
> I have a very important query:
>
> Can you name the source where the equivalence between 9 shruti-s and
> Sa-Ma interval, the 13 shruti-s and Sa-Pa interval, and the existence
> in Indian music of the octave doubling was first suggested? And
> conclusively proved?
>
> I have been going through sangitaratnakara for quite some time
> recently, and it does not even remotely mention those equivalences

In my edition it's in section 8 of book 3 (or rather, section 3,
viii, in their terms under the heading "Sonant, consonant, dissonant
and assonant notes: 47c-51" (this last probably being the most
pertinent pointer). It says, "The notes having an interval [i.e.,
add 1 for the real number] of eight or twelve sruti-s are mutually
consonant." What is consonant must be inferred from the actual
practice here.

Another hint: wherever you find the sruti steps of the different
gramas enumerated (e.g. Natya Sastra 28; 24-28), you will find that
Sa-Ma will consist of 2, 3, and 4 (=9) sruti in some order and that
another 4 will give you Sa-Pa.

It is almost a consolation for me to see an Indian having trouble in
unearthing the original theoretical sources. As I mentioned in an
earlier post, I never even have a clue whether to place a statement
in the northern or southern tradition, and my knowledge of the
musical practice is very superficial and not likely to change much.
There is a little book that I found pretty helpful for an overview
of the history since Dravidic times: "Svaras and Srutis in Indian
Music" by one Sri Satyaban Chakraborty, published by Kalyani House
in Santragachi (? if that's a place name...), no date, obviously
anything but recent. The English is a bit funny (but I've seen much
worse!). He mentions a lot of the old writings, seems to know the
extant ones and supplies original quotes in the footnotes (where I,
of course, can't even read the letters).

What is the octave doubling? Has it got anything to do with the 66
sruti that I saw mentioned in Danielou (adding up the srutis of
three octaves), but never in Indian sources?

Klaus

--- In tuning@y..., klaus schmirler <KSchmir@z...> wrote:

>There is a little book that I found pretty helpful for an overview
>of the history since Dravidic times: "Svaras and Srutis in Indian
>Music" by one Sri Satyaban Chakraborty, published by Kalyani House
>in Santragachi (? if that's a place name...), no date, obviously
>anything but recent. The English is a bit funny (but I've seen much
>worse!). He mentions a lot of the old writings, seems to know the
>extant ones and supplies original quotes in the footnotes (where I,
>of course, can't even read the letters).

Klaus, it's been a few years since I saw it, but this book was a
major source for my own paper, and my own footnote reads as follows:

Chakraborty, Satyaban. 1990. _Svaras and Srutis in Indian Music_.
Kalyani Prakashani, West Bengal.

Other sources I found valuable or at least quotable included:

Rowell, Lewis. 1992. _Music and Musical Thought in Early India_.
University of Chicago Press.

Deva, B. Chaitanya. 1980. _The Music of India: A Scientific Study_.
Munshiram Manoharlal, New Delhi.

Ramanathan, S. Feb. 1973. "The Sruti Veena," in _Musical Scales:
Report of Symposium_. Sangeet Natak Akademi, New Delhi.

And, of course, discussions on this list, especially with Manuel Op
de Coul.

A book that hasn't been mentioned yet is:

Mark Levy
Intonation in North Indian Music
A Select Comparison of Theories with Contemporary Practice
Biblia Impex Private Ltd
New Delhi, 1981

It has an overview of the sruti through history, and reports original
experiments done to see what really gets played. Perhaps Chakraborty
superseeds it, I wouldn't know.

FWIW, if you ignore the complications, the following general 12-note
scale comes out:

S 0 cents
Rb 98 cents
R 198
Gb 311
G 410
M 498
M# 611
P 701
Db 820
D 895
Nb 1005
N 1111

Other things I found in it: there is evidence of narrowed leading
tones, sharp octaves (a few cents) and pitch drift during a piece
(9-44, typically 22 cents).

Graham

Graham!
Statistics are not a good method of measurements. Nor are the musician picked of equal
quality. It can't be reduced to a 12 tone scale.

Graham Breed wrote:

> A book that hasn't been mentioned yet is:
>
> Mark Levy
> Intonation in North Indian Music
> A Select Comparison of Theories with Contemporary Practice
> Biblia Impex Private Ltd
> New Delhi, 1981
>
> It has an overview of the sruti through history, and reports original
> experiments done to see what really gets played. Perhaps Chakraborty
> superseeds it, I wouldn't know.
>
> FWIW, if you ignore the complications, the following general 12-note
> scale comes out:
>
> S 0 cents
> Rb 98 cents
> R 198
> Gb 311
> G 410
> M 498
> M# 611
> P 701
> Db 820
> D 895
> Nb 1005
> N 1111
>
> Other things I found in it: there is evidence of narrowed leading
> tones, sharp octaves (a few cents) and pitch drift during a piece
> (9-44, typically 22 cents).
>
> Graham

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

> Graham!
> Statistics are not a good method of measurements. Nor are the
musician picked of equal
> quality. It can't be reduced to a 12 tone scale.

Kraig!

These are fairly gnomic statements. I don't even know if you're
objecting to the research or my presentation of it. I presume you're
objecting to something.

Statistics is not a method of measurements. It's what you do with the
measurements. As such, it is very good indeed. Do you have a better
idea? Otherwise, what you say is pure intellectual anarchy, and I'm
having none of it.

Musicians are never of equal quality. Are you suggesting there's an
important distinction between good and bad musicians that gets lost
when you average them out?

What can't be reduced to a 12 tone scale? North Indian music or the
book? If the latter, of course not. The former looks like it can be.
Modern practice is clearly notated using 12 notes to the octave.
It's a fairly obvious step to ask how those notes are tuned. As there
is some level of consistency (G and Nb being the exceptions) surely
the averages are worth reporting!

If you're trying to prod me into checking the evidence more closely,
sorry but that won't do any good. I don't have the book for
reference. If you have anything to add to Levy's conclusions, I
suggest you come right out with it.

Graham

Graham !

Graham Breed wrote:

> > Graham!
> > Statistics are not a good method of measurements. Nor are the
> musician picked of equal
> > quality. It can't be reduced to a 12 tone scale.
>
> Kraig!
>
> These are fairly gnomic statements. I don't even know if you're
> objecting to the research or my presentation of it. I presume you're
> objecting to something.

I find this book not a good reference on indian music

>
>
> Statistics is not a method of measurements. It's what you do with the
> measurements. As such, it is very good indeed. Do you have a better
> idea? Otherwise, what you say is pure intellectual anarchy, and I'm
> having none of it.

Take the statistical average of all pentatonics and you end up with 5 equal. Same with pebbles in
a stream. Let's say your result says the average size in one inch. You can spend the rest of the
day not finding one that is one inch in size. Apply the analogy to scales and I think you sense my
objections. There are ways statisticians work around this I am told but don't think it applies to
the measurements taken in the book. This is far from pure intellectual anarchy. There are so many
things that effect intonation. The presence of a drone or not. I don't know if you have ever
handled a sitar but the slightest difference in pressure changes the intonation drastically. They
can not be measured by fret placements alone and maybe intonation samples should occur after a few
minutes into the raga if not the end.

> Musicians are never of equal quality. Are you suggesting there's an
> important distinction between good and bad musicians that gets lost
> when you average them out?

Yes! Some musicians have better ears than others do. Let's take all musicians in L.A. and test the
tuning. The result would not be 12 ET yet it doesn't mean this isn't what they are trying to tune.
Well actually if you took any 12 tones within the octave and took the average the result would be
12 et.

> What can't be reduced to a 12 tone scale? North Indian music or the
> book? If the latter, of course not. The former looks like it can be.
> Modern practice is clearly notated using 12 notes to the octave.

This ignores the fact that they say they use 22 shutis. How can you average something out unless
you understand which Shuti is being attempted.
The British influence in South India where the tuning is much more influenced by 12 ET had had
it own effect on those areas bordering with North Indian Practice. These where not isolated in
this study. Which from memory was a Masters thesis at UCLA in 1970 but I could be quite wrong
about this.

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

Kraig Grady wrote:

> I find this book not a good reference on indian music

Okay.

> Take the statistical average of all pentatonics and you end up with 5
> equal. Same with pebbles in
> a stream. Let's say your result says the average size in one inch. You
> can spend the rest of the
> day not finding one that is one inch in size. Apply the analogy to
> scales and I think you sense my
> objections. There are ways statisticians work around this I am told but
> don't think it applies to
> the measurements taken in the book. This is far from pure intellectual
> anarchy. There are so many
> things that effect intonation. The presence of a drone or not. I don't
> know if you have ever
> handled a sitar but the slightest difference in pressure changes the
> intonation drastically. They
> can not be measured by fret placements alone and maybe intonation
> samples should occur after a few
> minutes into the raga if not the end.

Yes, statistics itself addresses the issues you raise. Maybe Levy was
using poor statistics. Without having the book to hand, that's difficult
to check. The simplest way of saying how closely your average represents
the data is to take the standard deviation. I think Levy did this at
times, although obviously not in the table I copied.

The drone is always there in North Indian classical music. I haven't
handled a sitar, no. Were sitar players being tested here? I don't think
the data I posted came from fret placements. That a pitch drift was
measured during the performance shows that samples can't all have been
taken from the beginning.

I can see your objections, which is why I added a caveat before posting
the general scale. If you have a generalized scale more characteristic of
Indian music, please post it.

Incidentally for all this talk of "averaging out" I don't know what
average was being taken. It may be a subjective generalization.

> > Musicians are never of equal quality. Are you suggesting there's an
> > important distinction between good and bad musicians that gets lost
> > when you average them out?
>
> Yes! Some musicians have better ears than others do. Let's take all
> musicians in L.A. and test the
> tuning. The result would not be 12 ET yet it doesn't mean this isn't
> what they are trying to tune.
> Well actually if you took any 12 tones within the octave and took the
> average the result would be
> 12 et.

You can take all the musicians in LA if you want. When you do, I'll
consider what you find. Until then, I'll have to make do with what
evidence has been published. Do you know of any better?

> > What can't be reduced to a 12 tone scale? North Indian music or the
> > book? If the latter, of course not. The former looks like it can be.
> > Modern practice is clearly notated using 12 notes to the octave.
>
> This ignores the fact that they say they use 22 shutis. How can you
> average something out unless
> you understand which Shuti is being attempted.

Some theorists claim 22 shrutis are used. I've never known a musician
give a clear explanation of what the 22 shrutis mean. One thing this
study shows is that different schools interpret the same ragas differently
to such an extent that claiming them to be the same notes taken from 22
shrutis doesn't hold water. The evidence is really against those 22
shrutis in recorded music.

In some cases I'm sure the theoretical shruti is taken into account. But
we won't get any further with this unless one of us checks, which is
unlikely from my side. In most cases, where the musician doesn't know
what shruti is being attempted, what hope does the poor theorist have?

I think the generalized scale quoted is supposed to be representative of
the basic pitches before shruti shifts are made.

> The British influence in South India where the tuning is much more
> influenced by 12 ET had had
> it own effect on those areas bordering with North Indian Practice.
> These where not isolated in
> this study. Which from memory was a Masters thesis at UCLA in 1970 but
> I could be quite wrong
> about this.

Where is your evidence for those first two claims? That South India had a
stronger British influence, and that tuning is closer to 12-equal.

I think motorised transport had reached India by 1970, so I'm not sure
what value a regional analysis of tuning practice would have. But, if you
have evidence to support this, please present it.

Graham

Graham!

graham@microtonal.co.uk wrote:

> The drone is always there in North Indian classical music.

I would sense weather the drone was present or not would influence the accuracy of the intonation

> I can see your objections, which is why I added a caveat before posting
> the general scale. If you have a generalized scale more characteristic of
> Indian music, please post it.

I think there has been quite a few people who have put up the 22 shutis. I have not seen much
disagreement on what the Shutis are rom Erlich to Wilson (see
http://www.anaphoria.com/trans22.PDF page 3 no.1) which was worked out with Amiya Dasgupta (North
Indian Teacher at Cal Arts). Hopefully this book will go up soon as an addition to the Wilson
archive.

>
>
> Some theorists claim 22 shrutis are used. I've never known a musician
> give a clear explanation of what the 22 shrutis mean. One thing this
> study shows is that different schools interpret the same ragas differently
> to such an extent that claiming them to be the same notes taken from 22
> shrutis doesn't hold water. The evidence is really against those 22
> shrutis in recorded music.

I was talking to a Palestinian Musician who told me he could tell where a player was from by
differences in intonations and ornaments . He explained that they varied from provence to
provence. As the 22 tone shuti system was influenced, if not derived from Persian influence
(occupation in the north) in the 13th century
one might expect the same fluctuations one finds elsewhere. Still it appears they do not confuse
comma differences such as 81/64 and 5/4. They say different things but you are correct that within
these they fluctuate also. Possibly India is too general of Area to get at what people are really
doing

> In some cases I'm sure the theoretical shruti is taken into account. But
> we won't get any further with this unless one of us checks, which is
> unlikely from my side. In most cases, where the musician doesn't know
> what shruti is being attempted, what hope does the poor theorist have?

Well in Amiya and Erv case they realized they needed each other

> > The British influence in South India where the tuning is much more
> > influenced by 12 ET had had
> > it own effect on those areas bordering with North Indian Practice.
> > These where not isolated in
> > this study. Which from memory was a Masters thesis at UCLA in 1970 but
> > I could be quite wrong
> > about this.
>
> Where is your evidence for those first two claims? That South India had a
> stronger British influence, and that tuning is closer to 12-equal.

you find more western instruments and western derived instruments such as the 12 ET shuti box
(harmonium) and the violin which is only know making it into North indian music.

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

>I think there has been quite a few people who have put up the 22
>shutis. I have not seen much disagreement on what the Shutis are
>rom Erlich to Wilson (see http://www.anaphoria.com/trans22.PDF
>page 3 no.1) which was worked out with Amiya Dasgupta (North Indian
>Teacher at Cal Arts). Hopefully this book will go up soon as an
>addition to the Wilson archive.

Dasgutpa's book? Cool!

As for this debate, i think every good Indian musician i've ever
heard uses a major third at 5/4 in most ragas. Haresh Bashki and i
engaged in an intensive off-list conversation about this and, though
we were both looking for a positive outcome, neither of us could feel
justified in claiming that commatic differences between one raga and
another in Indian musical practice, which are clearly observed, are
equivalent to the outcome of any of the theoretical frameworks that
have been proposed. Rather they appear to vary widely from one
musical ghanara (or school) to another and different theories of
what "22" is all about seem to have crystallized according to local
expressive tendencies. 22 is an interesting outcome of one musician's
(Bharata's, if I recall correctly) experiment over a thousand years
ago. The particular sruti ratios usually proposed have the
double "advantage" of an interpretation as a chain of 22 fifths, and
as a 22-tone periodicity block in the 5-limit lattice (and the fact,
maybe unrelated, that of 7-limit periodicity blocks, the greatest
number seem to have either 22 or 171 notes). I wonder if perhaps a
thousand other musicians contributed to modern Indian musical
practice.