More 5ths/3rds/4ths and 53 eq

Hey Gene...I'm pretty happy with 31 and 34, but I think I'd be ok with a 53 tone guitar, although I've never tried it yet. The real issue for me, is, what sort of music would I want to play on it? I've been told that Eduardo Sabat's sons have a site where they are playing jazz standards in 53, but I've not heard it yet. At this point, jazz in 19 eq is super hip for me, cause it twists it just enough to make it intriguing, and the frets are far enough apart to facilitate complex chords, walking basslines, and the general sound of standard jazz (of course, I also like non standard jazz). If I had more $$$, I'd have a lot more guitars, so if money becomes available I'd have to be real picky about which tuning system I want to get into next. 53 has not interested me to this point, but who knows.
On the subject of the 22 srutis, I am reading a book that Haresh sent me, and according to this author the srutis are arrived at by mixing cycles of 5ths and 4ths...then they tweak a couple of notes by a couple of cents to make them 5 limit. And, this ties in with what Yahya just said; when does such activity become just an intellectual exercise in tuning theory, and when is it meaningful to real playing? I mean, I just mentioned that myself, that an interval of 2 cents, in the real world on acoustic instruments, is meaningless. So, if the spiral of 5ths maj 3rd is 384 cents, with a high ratio, and the 5/4 is only 2 cents sharper, who cares? On paper maybe it means something, but 2 cents is 2/100's of a fret, pretty teensy indeed for actual music.
And, you know, we all chat a lot about ancient theories from India and Arabia and elsewhere, but lately, more than ever, I've been wondering if, in fact, all sorts of tunings were tried out over the centuries in these, and other, countries, by curious and brilliant folks who wanted to see what was possible. Why not? In fact, although the 7 limit doesn't seem to be a part of Indian music, somewhere a while back I seem to recall someone saying that Erv Wilson had visited with an Indian musician who had, indeed, used 7 limit in his music...was that you, Kraig? If not, is this a real incident? Danielou said in his "Music and the Power of Sound" that Indian musicians avoided the 7th harmonic for spiritual reasons, but I'd be surprised if it hasn't been used at some time or another.
Which brings me to another question that just occurred to me recently...in Barbour's Tuning and Temperament, there are a number of Greek scales with the dreaded 7 limit; so, why did the 3 limit, so called Pythagorean tuning, become so popular, when all these other rather interesting scales were around as well? And, why, indeed, IS the 7th harmonic often absent from the storied scales of India, Arabia, and Europe? It sure sems to add a lot of depth to music, period, so was Danielou's hypothesis correct? Were folks a bit scared of the 7th harmonic? I realize there may not be any one ansewr to these sorts of questions, but would like to see what folks here think about this...best...HHH

--- In tuning@yahoogroups.com, "Neil Haverstick" <microstick@m...> wrote:

> If I had more $$$, I'd have a lot more guitars, so if money becomes
> available I'd have to be real picky about which tuning system I want
to get
> into next. 53 has not interested me to this point, but who knows.

53 is good for the schismatic/garibaldi tuning system we were talking
about, but it does other things. It does something you are probably
familiar with from 34; it supports the hanson/kleismic chains of minor
thirds. It also does chains of subminor thirds, 12 steps out of 53,
which is orwell. I was claiming a while back that this tended to have
a vauguely jazzy quality to it.

> On the subject of the 22 srutis, I am reading a book that Haresh
sent me,
> and according to this author the srutis are arrived at by mixing
cycles of
> 5ths and 4ths...then they tweak a couple of notes by a couple of
cents to
> make them 5 limit.

Well, I've heard that a lot and it makes sense. The only trouble with
it is that I can't fit it with other things I read about srutis. I
think it probably represents an attempt to understand the srutis
theoretically, but I am inclined to doubt it has much to do with how
they originated.

> Danielou said in his "Music and the Power of Sound" that Indian
musicians
> avoided the 7th harmonic for spiritual reasons, but I'd be surprised
if it
> hasn't been used at some time or another.

Same here.

> Which brings me to another question that just occurred to me
> recently...in Barbour's Tuning and Temperament, there are a number
of Greek
> scales with the dreaded 7 limit; so, why did the 3 limit, so called
> Pythagorean tuning, become so popular, when all these other rather
> interesting scales were around as well?

It represents a simplifying phase in music, apparently. Perhaps it
just came to seem more suitable for as a theoretical basis for
monophonic chant.

And, why, indeed, IS the 7th
> harmonic often absent from the storied scales of India, Arabia, and
Europe?
> It sure sems to add a lot of depth to music, period, so was Danielou's
> hypothesis correct? Were folks a bit scared of the 7th harmonic?

European music made a great deal of the dominant seventh, which has
something of the sound of an out-of-tune septimal tetrad; and
augmented sixth intervals and tritones were prevalent. So, they dipped
the toe in the water, without really embracing the concept.

Amiya Dasgupta ( who BTW worked with the Beatles before going to cal arts) worked with Erv quite a bit on examining the srutis.
Supposedly 7th harmonics were used in Erotic ragas , but being the case, they don't talk about it much. or so Amiya said.
They concluded that most Indian music now uses only 17 of these pitches for the most part. which corresponds with the 17 Erv works with elsewhere
On the subject of the srutis being equal, this would be difficult mainly when one is working with a drone as the slightest deviation becomes very very noticeable.
Indian Musicians , of which Haresh is a great example in test conducted here, tend to quite sensitive to deviations in the range of 2 cents.
Erv would attempt to fool both Amiya and later Supramaniam with other pitches of said size over a weeks time and they would notice immediately.
On the other hand Erv found that when he would play subharmonic analogs of many of the raga scales these same p artists would recognize the scale immediately.
This supports along empirical lines the idea that possibly these scales originated in this form first , later being changed to Pythagorean interpretation
Neil wrote
And, you know, we all chat a lot about ancient theories from India and Arabia and elsewhere, but lately, more than ever, I've been wondering if, in fact, all sorts of tunings were tried out over the centuries in these, and other, countries, by curious and brilliant folks who wanted to see what was possible. Why not? In fact, although the 7 limit doesn't seem to be a part of Indian music, somewhere a while back I seem to recall someone saying that Erv Wilson had visited with an Indian musician who had, indeed, used 7 limit in his music...was that you, Kraig? If not, is this a real incident? Danielou said in his "Music and the Power of Sound" that Indian musicians avoided the 7th harmonic for spiritual reasons, but I'd be surprised if it hasn't been used at some time or another.

>
>
> -- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

Hi Neil,

--- In tuning@yahoogroups.com, "Neil Haverstick" <microstick@m...> wrote:

> <snip> ... In fact, although the 7 limit doesn't seem to be
> a part of Indian music, somewhere a while back I seem to
> recall someone saying that Erv Wilson had visited with an
> Indian musician who had, indeed, used 7 limit in his music
> ...was that you, Kraig? If not, is this a real incident?
> Danielou said in his "Music and the Power of Sound" that
> Indian musicians avoided the 7th harmonic for spiritual
> reasons, but I'd be surprised if it hasn't been used at
> some time or another.

I've certainly heard what sounded like 7-limit pitches
and intervals in a lot of the Indian music i've listened to.
Ravi Shankar used them all the time.

> Which brings me to another question that just occurred
> to me recently...in Barbour's Tuning and Temperament, there
> are a number of Greek scales with the dreaded 7 limit; so,
> why did the 3 limit, so called Pythagorean tuning, become
> so popular, when all these other rather interesting scales
> were around as well? And, why, indeed, IS the 7th harmonic
> often absent from the storied scales of India, Arabia, and
> Europe?
> It sure sems to add a lot of depth to music, period, so was
> Danielou's hypothesis correct? Were folks a bit scared of
> the 7th harmonic? I realize there may not be any one ansewr
> to these sorts of questions, but would like to see what
> folks here think about this...best...HHH

My book

http://tonalsoft.com/monzo/book/book.htm

... is arranged first by prime-limit, then chronologically
within each prime-limit. This makes for a history of tuning
with a perspective that is different from those you'll
get anywhere else.

There are separate chapters for 3-limit, 5-limit, 7-limit,
and 11-limit, but then i group all higher prime-limits into
the closing chapter. It's interesting to see Ptolemy's
tunings near the end of the book, with 31 as a factor.

What really happened is that there were all sorts of
prime-factors described by various ancient theorists,
but then around 505 AD Boethius translated the musical
books by Nicomachus, ps-Euclid, and Ptolemy into Latin,
specifying one particular tuning for each of the 3 genera
(diatonic, chromatic, and enharmonic).

Boethius's diatonic was the ancient pythagorean version;
his chromatic used 19-limit ratios, and his enharmonic
used 499 as a factor.

I've written here before about how music theory changed
between Boethius and the "Carolingian Renaissance" of
c.800 AD. Obviously the Germanic tribes which conquered
the western Roman Empire barely had a grasp of Latin,
and no knowledge at all of Greek -- thus ensued the
so-called "dark ages", in which there really was very
little written ... the only significant book i know of
from this period is _History of the Franks_ by Gregory
of Tours.

Anyway, my guess is that by this time the chromatic
and enharmonic genera of the ancients had proved too
subtle and/or complicated for the Germanic tribes to
understand ... and i also have a pet theory that perhaps
the Germans really had a fondness for singing and
playing music with 5-limit ratios -- 5-limit singing
was first documented in England, and it seems to me
that it may have come into England from Denmark.

So Boethius's pythagorean diatonic genus became the
basis of European tuning (at least in the theory treatises)
when music-theory began to be written in Latin again
around 800 AD, and it stayed that way at least until 1300.
Theorists were not willing to accept 5-limit ratios until
Ramos published his monochord division in 1482.

The only significant non-pythagorean proposal before
this was Marchetto of Padua in 1318 -- and his theory
is vague enough to leave lots of scholars sratching
their heads over exactly what he meant.

But hmm ... looking at Boethius again, i only noticed just
now that his chromatic genus supplies the ratios in my first
interpretation of Marchetto of Padua's curious "fifth-tones":

http://tonalsoft.com/monzo/marchet/marchet.htm

Combining Boethius's diatonic and chromatic genera,
one gets a "whole-tone" divided exactly according to
the specifications given in my diagram of Marchetto's
"enharmonic" and "diatonic" semitones.

So anyway, once 5-limit ratios were acknowledged in Europe,
the music being composed had already become complicated
enough harmonically that both composers and theorists
recognized that there could be problems connected with
the syntonic-comma, and it was only a few decades before
meantone temperament was invented.

I'd guess that it was these kinds of complications which
made musicians and theorists cautious about using 7-limit
ratios. But what's ironic is that the augmented-6th in
1/4-comma meantone is almost exactly the harmonic-7th,
so augmented-6th chords became a sort of doorway into
the 7-limit while meantone tuning was in practice.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
>
> Amiya Dasgupta ( who BTW worked with the Beatles before going to
cal arts) worked with Erv quite a bit on examining the srutis.

What conclusions did he draw about their actual numerical tuning?

Latin accustomed Germanic tribes lacking comprehension of Greek treatises
and seeking a simplification of the sesquitertial division is reminiscent of
Urmevi's work during the 13th century. There may be hidden parallels here
monz.

Oz.

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 24 Ocak 2006 Sal� 19:53
Subject: [tuning] historical prime-limits (was: More 5ths/3rds/4ths and 53
eq)

> Hi Neil,
>
>
> --- In tuning@yahoogroups.com, "Neil Haverstick" <microstick@m...> wrote:
>
> > <snip> ... In fact, although the 7 limit doesn't seem to be
> > a part of Indian music, somewhere a while back I seem to
> > recall someone saying that Erv Wilson had visited with an
> > Indian musician who had, indeed, used 7 limit in his music
> > ...was that you, Kraig? If not, is this a real incident?
> > Danielou said in his "Music and the Power of Sound" that
> > Indian musicians avoided the 7th harmonic for spiritual
> > reasons, but I'd be surprised if it hasn't been used at
> > some time or another.
>
>
> I've certainly heard what sounded like 7-limit pitches
> and intervals in a lot of the Indian music i've listened to.
> Ravi Shankar used them all the time.
>
>
> > Which brings me to another question that just occurred
> > to me recently...in Barbour's Tuning and Temperament, there
> > are a number of Greek scales with the dreaded 7 limit; so,
> > why did the 3 limit, so called Pythagorean tuning, become
> > so popular, when all these other rather interesting scales
> > were around as well? And, why, indeed, IS the 7th harmonic
> > often absent from the storied scales of India, Arabia, and
> > Europe?
> > It sure sems to add a lot of depth to music, period, so was
> > Danielou's hypothesis correct? Were folks a bit scared of
> > the 7th harmonic? I realize there may not be any one ansewr
> > to these sorts of questions, but would like to see what
> > folks here think about this...best...HHH
>
>
> My book
>
> http://tonalsoft.com/monzo/book/book.htm
>
> ... is arranged first by prime-limit, then chronologically
> within each prime-limit. This makes for a history of tuning
> with a perspective that is different from those you'll
> get anywhere else.
>
> There are separate chapters for 3-limit, 5-limit, 7-limit,
> and 11-limit, but then i group all higher prime-limits into
> the closing chapter. It's interesting to see Ptolemy's
> tunings near the end of the book, with 31 as a factor.
>
>
> What really happened is that there were all sorts of
> prime-factors described by various ancient theorists,
> but then around 505 AD Boethius translated the musical
> books by Nicomachus, ps-Euclid, and Ptolemy into Latin,
> specifying one particular tuning for each of the 3 genera
> (diatonic, chromatic, and enharmonic).
>
> Boethius's diatonic was the ancient pythagorean version;
> his chromatic used 19-limit ratios, and his enharmonic
> used 499 as a factor.
>
> I've written here before about how music theory changed
> between Boethius and the "Carolingian Renaissance" of
> c.800 AD. Obviously the Germanic tribes which conquered
> the western Roman Empire barely had a grasp of Latin,
> and no knowledge at all of Greek -- thus ensued the
> so-called "dark ages", in which there really was very
> little written ... the only significant book i know of
> from this period is _History of the Franks_ by Gregory
> of Tours.
>
> Anyway, my guess is that by this time the chromatic
> and enharmonic genera of the ancients had proved too
> subtle and/or complicated for the Germanic tribes to
> understand ... and i also have a pet theory that perhaps
> the Germans really had a fondness for singing and
> playing music with 5-limit ratios -- 5-limit singing
> was first documented in England, and it seems to me
> that it may have come into England from Denmark.
>
> So Boethius's pythagorean diatonic genus became the
> basis of European tuning (at least in the theory treatises)
> when music-theory began to be written in Latin again
> around 800 AD, and it stayed that way at least until 1300.
> Theorists were not willing to accept 5-limit ratios until
> Ramos published his monochord division in 1482.
>
>
> The only significant non-pythagorean proposal before
> this was Marchetto of Padua in 1318 -- and his theory
> is vague enough to leave lots of scholars sratching
> their heads over exactly what he meant.
>
> But hmm ... looking at Boethius again, i only noticed just
> now that his chromatic genus supplies the ratios in my first
> interpretation of Marchetto of Padua's curious "fifth-tones":
>
> http://tonalsoft.com/monzo/marchet/marchet.htm
>
> Combining Boethius's diatonic and chromatic genera,
> one gets a "whole-tone" divided exactly according to
> the specifications given in my diagram of Marchetto's
> "enharmonic" and "diatonic" semitones.
>
>
> So anyway, once 5-limit ratios were acknowledged in Europe,
> the music being composed had already become complicated
> enough harmonically that both composers and theorists
> recognized that there could be problems connected with
> the syntonic-comma, and it was only a few decades before
> meantone temperament was invented.
>
> I'd guess that it was these kinds of complications which
> made musicians and theorists cautious about using 7-limit
> ratios. But what's ironic is that the augmented-6th in
> 1/4-comma meantone is almost exactly the harmonic-7th,
> so augmented-6th chords became a sort of doorway into
> the 7-limit while meantone tuning was in practice.
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
>

Neil,

Eduardo Sabat's Dinarra scale has 53 tones per octave,
but it isn't 53-ET! His book on the subject will soon
be available in english. He has recently come up with
a way to adapt a 53 tone per octave Dinarra fretboard
to a de-fretted guitar neck. He says that it sounds
OK and doesn't buzz.

-- Mark
Rankin

--- Neil Haverstick <microstick@msn.com> wrote:

> Hey Gene...I'm pretty happy with 31 and 34, but I
> think I'd be ok with a
> 53 tone guitar, although I've never tried it yet.
> The real issue for me, is,
> what sort of music would I want to play on it? I've
> been told that Eduardo
> Sabat's sons have a site where they are playing jazz
> standards in 53, but
> I've not heard it yet. At this point, jazz in 19 eq
> is super hip for me,
> cause it twists it just enough to make it
> intriguing, and the frets are far
> enough apart to facilitate complex chords, walking
> basslines, and the
> general sound of standard jazz (of course, I also
> like non standard jazz).
> If I had more $$$, I'd have a lot more guitars, so
> if money becomes
> available I'd have to be real picky about which
> tuning system I want to get
> into next. 53 has not interested me to this point,
> but who knows.
> On the subject of the 22 srutis, I am reading a
> book that Haresh sent me,
> and according to this author the srutis are arrived
> at by mixing cycles of
> 5ths and 4ths...then they tweak a couple of notes by
> a couple of cents to
> make them 5 limit. And, this ties in with what Yahya
> just said; when does
> such activity become just an intellectual exercise
> in tuning theory, and
> when is it meaningful to real playing? I mean, I
> just mentioned that myself,
> that an interval of 2 cents, in the real world on
> acoustic instruments, is
> meaningless. So, if the spiral of 5ths maj 3rd is
> 384 cents, with a high
> ratio, and the 5/4 is only 2 cents sharper, who
> cares? On paper maybe it
> means something, but 2 cents is 2/100's of a fret,
> pretty teensy indeed for
> actual music.
> And, you know, we all chat a lot about ancient
> theories from India and
> Arabia and elsewhere, but lately, more than ever,
> I've been wondering if, in
> fact, all sorts of tunings were tried out over the
> centuries in these, and
> other, countries, by curious and brilliant folks who
> wanted to see what was
> possible. Why not? In fact, although the 7 limit
> doesn't seem to be a part
> of Indian music, somewhere a while back I seem to
> recall someone saying that
> Erv Wilson had visited with an Indian musician who
> had, indeed, used 7 limit
> in his music...was that you, Kraig? If not, is this
> a real incident?
> Danielou said in his "Music and the Power of Sound"
> that Indian musicians
> avoided the 7th harmonic for spiritual reasons, but
> I'd be surprised if it
> hasn't been used at some time or another.
> Which brings me to another question that just
> occurred to me
> recently...in Barbour's Tuning and Temperament,
> there are a number of Greek
> scales with the dreaded 7 limit; so, why did the 3
> limit, so called
> Pythagorean tuning, become so popular, when all
> these other rather
> interesting scales were around as well? And, why,
> indeed, IS the 7th
> harmonic often absent from the storied scales of
> India, Arabia, and Europe?
> It sure sems to add a lot of depth to music, period,
> so was Danielou's
> hypothesis correct? Were folks a bit scared of the
> 7th harmonic? I realize
> there may not be any one ansewr to these sorts of
> questions, but would like
> to see what folks here think about this...best...HHH
>
>
>

__________________________________________________
Do You Yahoo!?
Tired of spam? Yahoo! Mail has the best spam protection around
http://mail.yahoo.com

--- In tuning@yahoogroups.com, Mark Rankin <markrankin95511@y...> wrote:
>
> Neil,
>
> Eduardo Sabat's Dinarra scale has 53 tones per octave,
> but it isn't 53-ET!

I think it's 1/9-schisma Schsimatic[53]. This is the minimax tuning of
5-limit schismatic.

Hi Gene.

> --- In tuning@yahoogroups.com, Mark Rankin <markrankin95511@y...> wrote:
> >
> > Neil,
> >
> > Eduardo Sabat's Dinarra scale has 53 tones per octave,
> > but it isn't 53-ET!
>
> I think it's 1/9-schisma Schsimatic[53]. This is the minimax tuning of
> 5-limit schismatic.

Has this been documented somewhere? If it is really like that, I'd be very
much interested in the history of this scale. Recently I came with an idea
of a 48-tone chain of 1/9-schisma tempered fifths and one of you (either
yourself or Paul, I'm not sure) notified me about this similarity.

Petr

Kraig Grady wrote:
> > On the subject of the srutis being equal, this would be difficult mainly when one is working with a drone as the slightest deviation becomes very very noticeable.
> Indian Musicians , of which Haresh is a great example in test conducted here, tend to quite sensitive to deviations in the range of 2 cents.
> Erv would attempt to fool both Amiya and later Supramaniam with other pitches of said size over a weeks time and they would notice immediately.
> On the other hand Erv found that when he would play subharmonic analogs of many of the raga scales these same p artists would recognize the scale immediately.
> This supports along empirical lines the idea that possibly these scales originated in this form first , later being changed to Pythagorean The music originally described by Bharata as making use of 22 srutis did not use a drone. When looking for the origins of the srutis, forget the drone. Then again, the modern srutis probably have no connection with the original ones except for the name and number. Quite possibly the original 22 were close to equal spacing.

The value of Pythagorean tuning is that it's easy to describe. That doesn't mean the fifths would have been tuned strictly so as to preserve the 2 cent errors in the thirds.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@g...> wrote:

>Then again, the modern srutis probably have no connection with
> the original ones except for the name and number. Quite possibly the
> original 22 were close to equal spacing.

If so, they weren't anything like Pythagorean.

Hi Graham,

On Wed, 25 Jan 2006 Graham Breed wrote:
[snip]
>
> The music originally described by Bharata as making use of 22 srutis did
> not use a drone. When looking for the origins of the srutis, forget the
> drone. ...

Quite extraordinary! Not at all what Ravi Shankar
thought when writing his introduction to north Indian
classical music, which I read some decades ago, so
can't quote you an exact title. In his view, the drone
was foundational.

Because of the extreme simplicity of the tuning of
the drone instruments, eg ekatara, dotara, there
would hardly be much call for any theorist or
historian to spend much time or many words on
them, would there?

I'd like to know what evidence you have for saying
categorically that the music that Bharata described
did not use drones.

> Then again, the modern srutis probably have no connection with
> the original ones except for the name and number. Quite possibly the
> original 22 were close to equal spacing.

Why would you think so?

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Free Edition.
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--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:
An legend reports in the old sanscrit Natyasastra the story:
Once Bhararta-muni had tunded in an acoustic experiment
from base tone SADJA on one Sitar 26 times 5ths in one direction
upwards, and on an other second Sitar also from same SADJA on 26 *
4ths downwards too in the other direction,
recognizing by that the 5ths/4ths cycle closes nearly almost
after the sum of 1+26+26=53 tuning-steps, when putting all the 5ths
accurate just pure by ear one after the other that first way.
In an other experiment he tuned that both Instruments
in the fix distance of an PC, incldung an correct
numerical determination of the PC=531441/524288=3^12/2^19 by
calculation, yielding as result the same 53 scale/gamut.

The old hindu 26-tone sitars had once probably 4 tone/oct.
more than the actual modern ones, containing only 22 tones/oct,
may be that the lacking 4 tones went lost probably over the
centuries.

>> > The music originally described by Bharata as making use of 22
srutis did
> > not use a drone. When looking for the origins of the srutis,
then above 2 experiments of the major shruti-inventor should be
considered:
Formerly old: 26 shruti-steps out of 53 commata.
Today: 22 out of 53, but still in a chain of 21 consecutive 5ths,
as modern masters me reassured again and again,
that they tune their instuments only alone in the 3-limit concept,
considering 5-limit as foreign strange approximation.
The traditionalists even prefer and esteem
8192/6561 3rds of ~384 cents as more consonant,
than the biger syntonic 5/4 3rd of ~386 cents,
because an shisma 32805/32768=5*3^8/2^15 to sharp,
incomprehensible for 12et western ears, used to ~13 cents sharp 3rds,
even about ~15cent to sharp detuned for my hindu friend-musicians,
damading precision.

> I'd like to know what evidence you have for saying
> categorically that the music that Bharata described
> did not use drones.
There exist several doubtful editions, partially contradicting
each other in detail, but not in the 4th/5th construction principle.
Now we don't know any more which of them is the original Adibharata.
The material changed very much due to several comiplations
over the centuries, like
Saradaytanayas: author of Bhavaprkasa
Dattila 7th century: author of Sangutameru,
Kohala: Uttaratantra
or by commentators from 6th century like
Bhattalollata, Sankuka, Udbhata, Bhattanayaka, Kritihara

espical the comments: Abhinavabharati by Abhinavagupas 12th century
and the king of Mithila: Nanyavedain his famous lectures
Bharatabhasya also called Sarasvatihrdayalakamkara,
just to call only a few.

> > Then again, the modern srutis probably have no connection with
> > the original ones except for the name and number. Quite possibly
the
> > original 22 were close to equal spacing.
As far as i do know at the moment from my own research:
I found in historic indian sources no evidence for the
european concept of logarithmic division 2^(1/22) into
equidistant equal steps before the age of colonization
in the 18-19th century.

Hope that helps.
A.S.

>
> Why would you think so?
>
>
> Regards,
> Yahya
>
> --
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25/1/06
>

Yahya Abdal-Aziz wrote:
> Hi Graham,

Hi Yahya!

>>The music originally described by Bharata as making use of 22 srutis did >>not use a drone. When looking for the origins of the srutis, forget the >>drone. ...
> > Quite extraordinary! Not at all what Ravi Shankar > thought when writing his introduction to north Indian
> classical music, which I read some decades ago, so > can't quote you an exact title. In his view, the drone
> was foundational.

Either he didn't think what you thought he thought, or he was wrong. He isn't an expert on ancient theatre that I'm aware of.

> Because of the extreme simplicity of the tuning of
> the drone instruments, eg ekatara, dotara, there > would hardly be much call for any theorist or > historian to spend much time or many words on > them, would there?

If the drone were as important as it is in modern Indian classical music, I would certainly expect it to be mentioned.

> I'd like to know what evidence you have for saying > categorically that the music that Bharata described
> did not use drones.

I'm following the received wisdom as I'm aware of it. My best source is Widdess: "The Ragas of Early Indian Music: Modes, Melodies, and Musical Notations from the Gupta Period to c. 1250" OUP 1996 and I think I'm remembering it correctly.

>>Then again, the modern srutis probably have no connection with >>the original ones except for the name and number. Quite possibly the >>original 22 were close to equal spacing.
> > Why would you think so?

Bharata defined intervals being consonant or dissonant according to the number of srutis that made them up. That's an elaborate structure if he was only talking about notes against a drone. And there'd be wolves if the srutis were supposed to be Pythagorean.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@g...> wrote:

> Bharata defined intervals being consonant or dissonant according to the
> number of srutis that made them up.

Which numbers of srutis were consonant?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@g...> wrote:
>
> > Bharata defined intervals being consonant or dissonant according
to the
> > number of srutis that made them up.
>
> Which numbers of srutis were consonant?
>

The consonance 5th is 13-shruti-difference.
The consonance 4th is 9-shruti-difference.

The farther you go from these differences, the
greater is the dissonance -- except, of course, 22 shruti-s.

Regards,
Haresh.

--- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...> wrote:

> > Which numbers of srutis were consonant?
> >
>
> The consonance 5th is 13-shruti-difference.
> The consonance 4th is 9-shruti-difference.

With a chain of pure fifths, you end up with three wolves and nineteen
pure fifths this way. I don't know that that rules out the Pythagorean
interpretaion of srutis.

Hi Andreas,

On Thu, 26 Jan 2006 "a_sparschuh" wrote:
>
> --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:

No, that was you! :-)

[a_sparschuh]
> An legend reports in the old sanscrit Natyasastra the story:
> Once Bhararta-muni had tunded in an acoustic experiment
> from base tone SADJA on one Sitar 26 times 5ths in one direction
> upwards, and on an other second Sitar also from same SADJA on 26 *
> 4ths downwards too in the other direction,
> recognizing by that the 5ths/4ths cycle closes nearly almost
> after the sum of 1+26+26=53 tuning-steps, when putting all the 5ths
> accurate just pure by ear one after the other that first way.

Interesting anecdote. But is the maths accurate?

[a_sparschuh]
> In an other experiment he tuned that both Instruments
> in the fix distance of an PC, incldung an correct
> numerical determination of the PC=531441/524288=3^12/2^19 by
> calculation, yielding as result the same 53 scale/gamut.

Not to bore the anti-maths squad, but I calculate
the PC as:
k = 3^12/2^19 = 1.0136432647705078125
whence:
k^53 = 2.0507483371543738333598823813537
k^52 = 2.0231460203296176778693891023748
k^51 = 1.9959152205166229046964503561184

so I get more nearly 51 commas to the octave.
What's wrong with this picture?

[a_sparschuh]
> The old hindu 26-tone sitars had once probably 4 tone/oct.
> more than the actual modern ones, containing only 22 tones/oct,
> may be that the lacking 4 tones went lost probably over the
> centuries.

Just speculation? Or do we have, say, carvings
of sitars showing a 26-fold division of the octave ?

[Graham Breed]
> >> > The music originally described by Bharata as making use of 22
> srutis did
> > > not use a drone. When looking for the origins of the srutis,

[a_sparschuh]
> then above 2 experiments of the major shruti-inventor should be
> considered:
> Formerly old: 26 shruti-steps out of 53 commata.
> Today: 22 out of 53, but still in a chain of 21 consecutive 5ths,
> as modern masters me reassured again and again,
> that they tune their instuments only alone in the 3-limit concept,
> considering 5-limit as foreign strange approximation.
> The traditionalists even prefer and esteem
> 8192/6561 3rds of ~384 cents as more consonant,
> than the biger syntonic 5/4 3rd of ~386 cents,
> because an shisma 32805/32768=5*3^8/2^15 to sharp,
> incomprehensible for 12et western ears, used to ~13 cents sharp 3rds,
> even about ~15cent to sharp detuned for my hindu friend-musicians,
> damading precision.

[Yahya]
> > I'd like to know what evidence you have for saying
> > categorically that the music that Bharata described
> > did not use drones.

[a_sparschuh]
> There exist several doubtful editions, partially contradicting
> each other in detail, but not in the 4th/5th construction principle.
> Now we don't know any more which of them is the original Adibharata.
> The material changed very much due to several comiplations
> over the centuries, like
> Saradaytanayas: author of Bhavaprkasa
> Dattila 7th century: author of Sangutameru,
> Kohala: Uttaratantra
> or by commentators from 6th century like
> Bhattalollata, Sankuka, Udbhata, Bhattanayaka, Kritihara
>
> espical the comments: Abhinavabharati by Abhinavagupas 12th century
> and the king of Mithila: Nanyavedain his famous lectures
> Bharatabhasya also called Sarasvatihrdayalakamkara,
> just to call only a few.

[Graham Breed]
> > > Then again, the modern srutis probably have no connection with
> > > the original ones except for the name and number. Quite possibly
> the
> > > original 22 were close to equal spacing.

[a_sparschuh]
> As far as i do know at the moment from my own research:
> I found in historic indian sources no evidence for the
> european concept of logarithmic division 2^(1/22) into
> equidistant equal steps before the age of colonization
> in the 18-19th century.
>
> Hope that helps.
> A.S.

Thanks.

Regards,
Yahya

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Hi again Graham,

On Thu, 26 Jan 2006 Graham Breed wrote:
>
> Hi Yahya!
>
> >>The music originally described by Bharata as making use of 22 srutis did
> >>not use a drone. When looking for the origins of the srutis, forget the
> >>drone. ...
> >
> > Quite extraordinary! Not at all what Ravi Shankar
> > thought when writing his introduction to north Indian
> > classical music, which I read some decades ago, so
> > can't quote you an exact title. In his view, the drone
> > was foundational.
>
> Either he didn't think what you thought he thought, or he was wrong. He
> isn't an expert on ancient theatre that I'm aware of.

I'll bite ... Theatre?

> > Because of the extreme simplicity of the tuning of
> > the drone instruments, eg ekatara, dotara, there
> > would hardly be much call for any theorist or
> > historian to spend much time or many words on
> > them, would there?
>
> If the drone were as important as it is in modern Indian classical
> music, I would certainly expect it to be mentioned.

To "be mentioned" may still not be "many words".

> > I'd like to know what evidence you have for saying
> > categorically that the music that Bharata described
> > did not use drones.
>
> I'm following the received wisdom as I'm aware of it. My best source is
> Widdess: "The Ragas of Early Indian Music: Modes, Melodies, and Musical
> Notations from the Gupta Period to c. 1250" OUP 1996 and I think I'm
> remembering it correctly.

I'll have a look for it.

> >>Then again, the modern srutis probably have no connection with
> >>the original ones except for the name and number. Quite possibly the
> >>original 22 were close to equal spacing.
> >
> > Why would you think so?
>
> Bharata defined intervals being consonant or dissonant according to the
> number of srutis that made them up. ...

That doesn't make the srutis equal.

For example, n steps of m cents may be not quite
enough to fill some desired consonant interval
of p cents, whereas another step of m cents may
overshoot that interval:
n*m < p < (n+1)*m

So in this example there may be n srutis of one
size and 1 sruti of another required to fill the
given consonant interval - in exactly the same
way as it takes two meantone wholetones and
one meantone semitone to make a meantone
fourth.

Besides, didn't Bharata recognise as consonant
only those intervals the West calls perfect - the
fourth, fifth and octave?

Further, saying, for example, that the fourth is
that interval which comprises 9 srutis, is after
the fact, exactly as we might say that the fourth
is that interval which comprises 5 semitones. We
might come to that conclusion after tuning a
keyboard in 12-EDO, or equally, after tuning the
same keyboard in some well-temperament,
meantone or 5-limit JI. In the first case, the 5
semitones that comprise the fourth are equal by
definition; but that is not the case for 5-limit JI.
So the fact, that we can characterise an interval
by the count of tuning steps included in it, is no
guarantee that those steps are equal. If it were,
then all meantone and well-temperaments would
necessarily be equal ... ! To conclude that the
22 srutis were equal because Bharata counted
them is a bizarre leap of logic.

But I do hope there is a stronger case than that,
perhaps involving "facts not in evidence".

> ... That's an elaborate structure if he
> was only talking about notes against a drone. ...

"only"???

> ... And there'd be wolves if
> the srutis were supposed to be Pythagorean.

I smell, not a wolf (sorry Daniel!), but something
fishy ... as my wife is wont to say: "Life is just a
bowl of red herrings".

>
>
Graham,

Thanks for your reply. Your sources are clearly more
recent than mine - and who knows, your memory may
be better, too!

Regards,
Yahya

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--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:

> Not to bore the anti-maths squad, but I calculate
> the PC as:
> k = 3^12/2^19 = 1.0136432647705078125
> whence:
> k^53 = 2.0507483371543738333598823813537
> k^52 = 2.0231460203296176778693891023748
> k^51 = 1.9959152205166229046964503561184
>
> so I get more nearly 51 commas to the octave.
> What's wrong with this picture?

Nothing, but it has nothing to do with the near-closure of the cicle
of fifths after 53, either. For that, you should compute 3^53/2^84,
which is about 1.002. To find the number of Pythatorean commas in the
octave, find log_k(2) = 1/log_2(k) = 51.15087.

Yahya Abdal-Aziz wrote:

> I'll bite ... Theatre?

Bharata wrote an extensive account of a particular kind of devotional theatre. As music was an intrinsic part of it, a lot of his account is about music. But it doesn't claim to speak about Indian music in general. There's another account from around the same time that mentions srutis, and is purely about devotional music. So the nearest modern equivalent could well be Vedic chant rather than classical music -- but it's such a long time ago that the lines of influence are hopelessly tangled.

Many Indian writers talk about Bharata as if he were describing classical music similar to their own time. You have to be careful about this.

> To "be mentioned" may still not be "many words".

There's no evidence for drones in Indian music before the 15th Century. The instruments that could have supported them were being introduced around the 12th Century, and the classical music was generally going through changes at this time that would have made drones more appropriate. There are suggestions that flutes might have been used as a drone, but I have no idea how plausible. The earliest sources for srutis (which quote earlier texts) are probably Fourth Century.

> That doesn't make the srutis equal.
> > For example, n steps of m cents may be not quite
> enough to fill some desired consonant interval
> of p cents, whereas another step of m cents may
> overshoot that interval:
> n*m < p < (n+1)*m
> > So in this example there may be n srutis of one
> size and 1 sruti of another required to fill the
> given consonant interval - in exactly the same
> way as it takes two meantone wholetones and
> one meantone semitone to make a meantone
> fourth.

You're assuming that the srutis were supposed to exactly give the actual intervals, which I don't think Bharata said. Of course, without a complete translation I have no idea what he didn't say. He certainly didn't have a concept of cents. No Indian sources from this time mention a relationship between string-length ratios and consonances which makes it much harder to do the calculations. Neither do we know that Bharata was a mathematician.

But no, we don't know the srutis weren't equal. We don't know very much at all. But the simplest explanation is that they were supposed to be equal. Widdess says "nominally equal" -- presumable that they were treated equal, even if they couldn't have been tuned equally.

> Besides, didn't Bharata recognise as consonant
> only those intervals the West calls perfect - the
> fourth, fifth and octave?

Yes, but only certain tunings of the fourth and fifth, which we recognise as being the 3-limit ratios. That's probably what the srutis were brought in to explain. Why the 7-note diatonics, which they knew contained three different step sizes, had fourths and fifths that didn't sound good in harmony.

> Further, saying, for example, that the fourth is
> that interval which comprises 9 srutis, is after
> the fact, exactly as we might say that the fourth
> is that interval which comprises 5 semitones. We
> might come to that conclusion after tuning a
> keyboard in 12-EDO, or equally, after tuning the
> same keyboard in some well-temperament,
> meantone or 5-limit JI. In the first case, the 5
> semitones that comprise the fourth are equal by
> definition; but that is not the case for 5-limit JI.
> So the fact, that we can characterise an interval
> by the count of tuning steps included in it, is no
> guarantee that those steps are equal. If it were,
> then all meantone and well-temperaments would
> necessarily be equal ... ! To conclude that the
> 22 srutis were equal because Bharata counted
> them is a bizarre leap of logic.

If you say that any interval of 5 semitones is a consonance you'll be bitten by a meantone wolf -- if you tune up all 12 notes. If you're only tuning up pentatonics then, yes, the semitones are pretty much equal. You aren't likely to guess their inequality by ear. We -- or, at least, I -- don't even know that Bharata (or anybody at that time) did tune up all 22 srutis.

Also, when you say "meantone and well-temperaments would necessarily be equal" that misses the point. Bharata wasn't talking about these fine-tuning distinctions. He only needed his diatonic scales to contain two different sizes of whole tone. He probably didn't know himself what the exact ratios of interval size should be. He also specified that certain notes should be played with vibrato on the flute -- so he specifically wasn't talking about precise tuning.

> But I do hope there is a stronger case than that,
> perhaps involving "facts not in evidence".

No, there's no strong case for any specific interpretation of Bharata's srutis but many people searching for one. If there are early sources describing tuning 22 srutis by fifths, or showing that the cycle of fifths closes at 53 notes, that would imply Pythagorean tuning. But I haven't seen any such facts in published sources. You can chase it down if you want. It's a lot of trouble and ultimately pointless. We don't need vague 4th Century texts to tell us about 22-equal, or schismatic temperament, or 5-limit diatonics. It's much easier to consider them on their own merits with the much superior musical and mathematical tools we now have available.

>>... That's an elaborate structure if he
>>was only talking about notes against a drone. ...
> > "only"???

One of the interpretations is that when he said "9 and 13 srutis are consonances" he meant the notes 9 and 13 srutis from the tonic, not all notes of 9 and 13 srutis.

>>... And there'd be wolves if
>>the srutis were supposed to be Pythagorean.
> > I smell, not a wolf (sorry Daniel!), but something
> fishy ... as my wife is wont to say: "Life is just a
> bowl of red herrings".

> Graham,
> > Thanks for your reply. Your sources are clearly more
> recent than mine - and who knows, your memory may
> be better, too!

I checked the book in the library yesterday. Mostly it's about reconstructing notated melodies. He does note that the earliest pieces (from the 8th Century) don't show any preference for the intervals that Bharata considered consonances over their comma-separated neighbours. So the tonal structure Bharata was explaining had probably died out by then or was only ever theoretical. During the same time zither-like instruments had replaced harp-like instruments and so musicians weren't constrained by a fixed tuning.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@g...> wrote:

> But no, we don't know the srutis weren't equal. We don't know very
much
> at all. But the simplest explanation is that they were supposed to be
> equal. Widdess says "nominally equal" -- presumable that they were
> treated equal, even if they couldn't have been tuned equally.

It seems to me this is contradicted a bit ny what you say below.

> > Besides, didn't Bharata recognise as consonant
> > only those intervals the West calls perfect - the
> > fourth, fifth and octave?
>
> Yes, but only certain tunings of the fourth and fifth, which we
> recognise as being the 3-limit ratios. That's probably what the srutis
> were brought in to explain.

The only way to tune them to be roughly equal is to sharpen the fifth.
If you sharpen it all the way up to 13/22 of an octave, of course you
are looking at exactly equal. If Bharata recognized *only* pure fifths
as consonant, and not slightly sharp ones, then we seem to be back at
the Pythagorean tuning, where most of time 13 sruits give you a nice,
pure fifth but the spacing is far from equal.

> I checked the book in the library yesterday. Mostly it's about
> reconstructing notated melodies. He does note that the earliest pieces
> (from the 8th Century) don't show any preference for the intervals that
> Bharata considered consonances over their comma-separated neighbours.

Ah ha! So there is at least one more layer here.

Gene Ward Smith wrote:

> The only way to tune them to be roughly equal is to sharpen the fifth.
> If you sharpen it all the way up to 13/22 of an octave, of course you
> are looking at exactly equal. If Bharata recognized *only* pure fifths
> as consonant, and not slightly sharp ones, then we seem to be back at
> the Pythagorean tuning, where most of time 13 sruits give you a nice,
> pure fifth but the spacing is far from equal.

No. Firstly, I don't know any mention of Bharata specifying the exact tuning of the fifths, or even how he could have done that. You seem to be assuming Pythagorean tuning and using that to prove Pythagorean tuning. All Bharata had to measure intervals with were srutis.

Secondly, the tuning of the notes needn't determine the tuning of the srutis. Nowhere that I know of (and my knowledge could always be incomplete) does Bharata say that the srutis have to add up to exactly the ideal interval you'd want to tune. You could have 22 roughly equal (and why does this word "exact" keep sneaking into replies when I explicitly avoid it?) srutis and specify each interval by the nearest whole number of them.

>>I checked the book in the library yesterday. Mostly it's about >>reconstructing notated melodies. He does note that the earliest pieces >>(from the 8th Century) don't show any preference for the intervals that >>Bharata considered consonances over their comma-separated neighbours. > > > Ah ha! So there is at least one more layer here.

One more layer of what on top of how many layers you thought there were before? Nigh on every theorist since has decided to add their own layer of interpretation. There are two millenia of layers between what a musician today would understand as a sruti and whatever Bharata might have intended.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@g...> wrote:

>You seem to
> be assuming Pythagorean tuning and using that to prove Pythagorean
> tuning.

All I was assuming was that when you said "pure fifths" it meant "pure
fifths". If it meant "13 srutis", obviously conclusions will differ.

> Secondly, the tuning of the notes needn't determine the tuning of the
> srutis. Nowhere that I know of (and my knowledge could always be
> incomplete) does Bharata say that the srutis have to add up to exactly
> the ideal interval you'd want to tune. You could have 22 roughly equal
> (and why does this word "exact" keep sneaking into replies when I
> explicitly avoid it?) srutis and specify each interval by the nearest
> whole number of them.

You certainly could, but this will lead to a lot of sharp fifths.

> > Ah ha! So there is at least one more layer here.
>
> One more layer of what on top of how many layers you thought there were
> before? Nigh on every theorist since has decided to add their own
layer
> of interpretation.

Then please don't add your own. If you say "pure fifths", what am I to
assume?

--- In tuning@yahoogroups.com, "Neil Haverstick" <microstick@m...>
wrote:

> Danielou said in his "Music and the Power of Sound" that Indian
musicians
> avoided the 7th harmonic for spiritual reasons,

Danielou makes a lot of far-fetched "spiritual" claims in his book,
such as on which times of day are appropriate for which ragas, and
mostly they seem to be there purely to support his personal set of
mystical/aesthetic/mathematical correspondences, without any regard
to actual practice in the musical cultures in question.

> but I'd be surprised if it
> hasn't been used at some time or another.
> Which brings me to another question that just occurred to me
> recently...in Barbour's Tuning and Temperament, there are a number
of Greek
> scales with the dreaded 7 limit;

They sure did and no one dreaded them!

> so, why did the 3 limit, so called
> Pythagorean tuning, become so popular, when all these other rather
> interesting scales were around as well?

One guess would be the ease with which the pitches in the modes
derived from rotation and from transposition would agree with one
another in Pythagorean.

> And, why, indeed, IS the 7th
> harmonic often absent from the storied scales of India, Arabia, and
> Europe?

Part of the reason is that for millenia, musicians had a subset of
the Greek texts available to them -- emphasizing Pythagorean lore
about the tetrakys, etc. -- and had no means to actually measure the
frequencies they were using, so they simply forced all their scales
into a Pythagorean bed -- the set of ratios they were used to reading
about and calculating.

> It sure sems to add a lot of depth to music, period, so was
Danielou's
> hypothesis correct? Were folks a bit scared of the 7th harmonic?

I think the hypothesis was put there to fit Danielou's mystical
prejudices, rather than to fit any facts.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, Mark Rankin <markrankin95511@y...>
wrote:
> >
> > Neil,
> >
> > Eduardo Sabat's Dinarra scale has 53 tones per octave,
> > but it isn't 53-ET!
>
> I think it's 1/9-schisma Schsimatic[53].

That's correct. Eduardo was a frequent contributor here back when you
could only be reached by snail-mail, Mark.

> This is the minimax tuning of
> 5-limit schismatic.

Eduardo had 7-limit in mind, which is why I named the "7-limit
schismatic" temperament class after him. His "Beta" intervals, such as
5120:5103, vanish in this system.

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@c...> wrote:
>
> Hi Gene.
>
> > --- In tuning@yahoogroups.com, Mark Rankin <markrankin95511@y...>
wrote:
> > >
> > > Neil,
> > >
> > > Eduardo Sabat's Dinarra scale has 53 tones per octave,
> > > but it isn't 53-ET!
> >
> > I think it's 1/9-schisma Schsimatic[53]. This is the minimax
tuning of
> > 5-limit schismatic.
>
> Has this been documented somewhere?

Yes, Eduardo himself mentioned it here on several occasions. You can
try a search on the archives, though some of his posts may have been
back in the Mills days, before the present archive begins.

> If it is really like that, I'd be very
> much interested in the history of this scale.

As we've been discussing, schismatic thirds were used in 15th century
Europe, but the first time the fifths were actually *tempered* to
acheive better schismatic thirds was probably Helmholtz.

> Recently I came with an idea
> of a 48-tone chain of 1/9-schisma tempered fifths and one of you
(either
> yourself or Paul, I'm not sure) notified me about this similarity.
>
> Petr

On a guitar, I can see why you might want 41 tones from this chain,
or 53, but not 48.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> > And, why, indeed, IS the 7th
> > harmonic often absent from the storied scales of India, Arabia, and
> > Europe?
>
> Part of the reason is that for millenia, musicians had a subset of
> the Greek texts available to them -- emphasizing Pythagorean lore
> about the tetrakys, etc. -- and had no means to actually measure the
> frequencies they were using, so they simply forced all their scales
> into a Pythagorean bed -- the set of ratios they were used to reading
> about and calculating.

In other words, possibly they aren't absent.

I don't know if your Modern Indian Gamut is the same as what Scala
calls indian_12, the North Indian Gamut or modern Hindustani gamut,
but if it is I pointed out a while back that this is equivalent under
225/224 equivalence to Kraig Grady's very much 7-limit Centaur scale.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> > This is the minimax tuning of
> > 5-limit schismatic.
>
> Eduardo had 7-limit in mind, which is why I named the "7-limit
> schismatic" temperament class after him. His "Beta" intervals, such as
> 5120:5103, vanish in this system.

My 5120/5103-planar piece has fifths sharp by a cent, and flattening
them does not help the 7-limit aspect. I was struck, however, by how
fifth-relationship oriented it is; in that respect very much in line
with 32805/32768.

--- In tuning@yahoogroups.com, "a_sparschuh" <a_sparschuh@y...> wrote:
>
> --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...>
wrote:
> An legend reports in the old sanscrit Natyasastra the story:
> Once Bhararta-muni had tunded in an acoustic experiment
> from base tone SADJA on one Sitar 26 times 5ths in one direction
> upwards,

Bharata made no reference to chains of fifths, let along 26 of them.

> and on an other second Sitar also from same SADJA on 26 *
> 4ths downwards too in the other direction,
> recognizing by that the 5ths/4ths cycle closes nearly almost
> after the sum of 1+26+26=53 tuning-steps, when putting all the 5ths
> accurate just pure by ear one after the other that first way.
> In an other experiment he tuned that both Instruments
> in the fix distance of an PC, incldung an correct
> numerical determination of the PC=531441/524288=3^12/2^19 by
> calculation, yielding as result the same 53 scale/gamut.

You have completely distorted the Bharata story, and fabricated a
different story because it fits your theories better.

> The old hindu 26-tone sitars

Reference?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...>
wrote:
>
> > > Which numbers of srutis were consonant?
> > >
> >
> > The consonance 5th is 13-shruti-difference.
> > The consonance 4th is 9-shruti-difference.
>
> With a chain of pure fifths, you end up with three wolves and nineteen
> pure fifths this way.

I don't think this is what you meant to say, or at least you could
havge said it more clearly. Two of the fifths, rather than being
wolves, are represented by 12 shrutis (or fourths as 10 shrutis).
Neither of them are wolves in any acoustical sense.

You should re-read the section on Indian music in my paper _Tuning,
Tonality, and Twenty-Two-Tone Temperament_ now.

> I don't know that that rules out the Pythagorean
> interpretaion of srutis.
>

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:

> > If the drone were as important as it is in modern Indian classical
> > music, I would certainly expect it to be mentioned.
>
> To "be mentioned" may still not be "many words".

I spent a long time in the Harvard music library reading every book on
Indian music. The picture that clearly emerged was that the drone was
specifically introduced for the first time well after Bharata's time. I
wish I had some specific references for you but all those books are
still in the library.

> > > I'd like to know what evidence you have for saying
> > > categorically that the music that Bharata described
> > > did not use drones.

Paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> Danielou makes a lot of far-fetched "spiritual" claims in his book,
> such as on which times of day are appropriate for which ragas, and
> mostly they seem to be there purely to support his personal set of
> mystical/aesthetic/mathematical correspondences, without any regard
> to actual practice in the musical cultures in question.

I just want to clear up something in my own education: I recall that
when I had studied ragas (and this was not in great depth) one
interesting facet was the use of particular rags at certain times of
the day. It was a feature more of the Hindustani school/culture (I
think) and I note in just a cursory glance a couple of similar
indications:

http://www.musicalnirvana.com/introduction/raaga_basics2.html
http://chandrakantha.com/articles/indian_music/samay.html

Is your quote above refuting Danielou's particular claims, or are you
saying that the use of rags at certain times was never a practice?

Cheers,
Jon

Jon Szanto wrote:

>Paul,
>
>--- In tuning@yahoogroups.com, "wallyesterpaulrus"
><wallyesterpaulrus@y...> wrote:
> >
>>Danielou makes a lot of far-fetched "spiritual" claims in his book, >>such as on which times of day are appropriate for which ragas, and >>mostly they seem to be there purely to support his personal set of >>mystical/aesthetic/mathematical correspondences, without any regard >>to actual practice in the musical cultures in question.
>> >>
>
>I just want to clear up something in my own education: I recall that
>when I had studied ragas (and this was not in great depth) one
>interesting facet was the use of particular rags at certain times of
>the day. It was a feature more of the Hindustani school/culture (I
>think) >

That's right.

--
* David Beardsley
* microtonal guitar
* http://biink.com/db

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
>
> > > And, why, indeed, IS the 7th
> > > harmonic often absent from the storied scales of India, Arabia,
and
> > > Europe?
> >
> > Part of the reason is that for millenia, musicians had a subset
of
> > the Greek texts available to them -- emphasizing Pythagorean lore
> > about the tetrakys, etc. -- and had no means to actually measure
the
> > frequencies they were using, so they simply forced all their
scales
> > into a Pythagorean bed -- the set of ratios they were used to
reading
> > about and calculating.
>
> In other words, possibly they aren't absent.

?

> I don't know if your Modern Indian Gamut

1/1
16/15 (or 135/128)
9/8
6/5
5/4
4/3
45/32
3/2
8/5
27/16
9/5
15/8

> is the same as what Scala
> calls indian_12, the North Indian Gamut or modern Hindustani gamut,
> but if it is I pointed out a while back that this is equivalent
under
> 225/224 equivalence to Kraig Grady's very much 7-limit Centaur
scale.

Things look kind of different when you take the drone into account.
Normally the drone would consist of 1/1 and 3/2 for the gamut above.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> > --- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...>
> wrote:

> > > The consonance 5th is 13-shruti-difference.
> > > The consonance 4th is 9-shruti-difference.

> > With a chain of pure fifths, you end up with three wolves and nineteen
> > pure fifths this way.
>
> I don't think this is what you meant to say, or at least you could
> havge said it more clearly. Two of the fifths, rather than being
> wolves, are represented by 12 shrutis (or fourths as 10 shrutis).
> Neither of them are wolves in any acoustical sense.

Neither of them are 13 srutis either, so as stated they don't count as
consonances. By "wolves" I meant the three non-fifth intervals which
appear among the 13-sruti intervals.

--- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@c...> wrote:
>
> Paul,
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
> > Danielou makes a lot of far-fetched "spiritual" claims in his
book,
> > such as on which times of day are appropriate for which ragas,
and
> > mostly they seem to be there purely to support his personal set
of
> > mystical/aesthetic/mathematical correspondences, without any
regard
> > to actual practice in the musical cultures in question.
>
> I just want to clear up something in my own education: I recall that
> when I had studied ragas (and this was not in great depth) one
> interesting facet was the use of particular rags at certain times of
> the day.

Absolutely!

> It was a feature more of the Hindustani school/culture (I
> think) and I note in just a cursory glance a couple of similar
> indications:
>
> http://www.musicalnirvana.com/introduction/raaga_basics2.html
> http://chandrakantha.com/articles/indian_music/samay.html
>
> Is your quote above refuting Danielou's particular claims,

Yes -- that's why I said *which* times of day are appropriate for
*which* ragas.

> or are you
> saying that the use of rags at certain times was never a practice?

It's been a practice for at least as long as I've been going to
concerts and master classes of Indian music, where this practice is
often mentioned -- usually by saying "This rag is normally performed
at night" or whatever time it is normally performed.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
> > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > > --- In tuning@yahoogroups.com, "Haresh BAKSHI"
<hareshbakshi@h...>
> > wrote:
>
> > > > The consonance 5th is 13-shruti-difference.
> > > > The consonance 4th is 9-shruti-difference.
>
> > > With a chain of pure fifths, you end up with three wolves and
nineteen
> > > pure fifths this way.
> >
> > I don't think this is what you meant to say, or at least you
could
> > havge said it more clearly. Two of the fifths, rather than being
> > wolves, are represented by 12 shrutis (or fourths as 10 shrutis).
> > Neither of them are wolves in any acoustical sense.
>
> By "wolves" I meant the three non-fifth intervals which
> appear among the 13-sruti intervals.

Aha, so this is what you meant -- sorry.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> Yes -- that's why I said *which* times of day are appropriate for
> *which* ragas.

A very small specificity that I just wanted to make sure on. I'm
guessing his choices were completely out, as opposed to a rag that
should have been at 9:00 a.m. was mistakenly put at 11:30 a.m. :)

> > or are you
> > saying that the use of rags at certain times was never a practice?
>
> It's been a practice for at least as long as I've been going to
> concerts and master classes of Indian music, where this practice is
> often mentioned -- usually by saying "This rag is normally performed
> at night" or whatever time it is normally performed.

Right, that is how I understood it as well.

Cheers,
Jon

Hi Paul.

You wrote:

> On a guitar, I can see why you might want 41 tones from this chain,
> or 53, but not 48.

Well, I'm mostly a piano/flute player so I can't judge for a guitar. My idea
was a large keyboard consisting of four 12-key-per-octave keyboards. The
reason why I chose 48 tones is that the interval achieved by stacking 47
fifths (and then removing some octaves) is nicely close to 7/5.

Petr

--- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@...> wrote:
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
> > Yes -- that's why I said *which* times of day are appropriate for
> > *which* ragas.
>
> A very small specificity that I just wanted to make sure on. I'm
> guessing his choices were completely out, as opposed to a rag that
> should have been at 9:00 a.m. was mistakenly put at 11:30 a.m. :)

Right. His choices follow a strict mathematical/aesthetic logic of his
own devising.