Yahoo Tuning Groups Ultimate Backup tuning Magic[22] as srutis

Hi Hans,

--- In tuning@yahoogroups.com, "hstraub64" <hstraub64@...> wrote:
>
> From time to time, I am combing the archives searching
> for stuff to put into our xenharmonic Wiki. I am
> currently thinking the posting below would be a good
> one. The point why I am posting here is that I am no
> expert in shruti theory so I cannot really judge the
> relevance of the article. So I would like to ask here:
> Are there objections against putting this into the
> xenharmonic wiki, in the context of indian music theory?

I don't really have a comment on Gene's posting, as i
haven't really examined the magic tuning yet, but
upon first reading what he says seems to make sense
and agree with what i know of the Indian tuning schemes.

But i do have a comment on the subject in general.
I also haven't seen the wiki article, so maybe you
have this in there already ...

I think it's important to point out that historically
the 22-sruti system derives from a pythagorean tuning
which is large enough to contain schismatic equivalents
of 5-limit intervals, 3^-10...3^11. I describe this
in my old webpage:

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

As i was writing this, it originally turned into a much
longer commentary about the work i'm currently doing
regarding the Greek-letter notation described by Boethius.
Since that is mostly unrelated to this and i still
have more to write on it, i decided to separate it
and post it later when i'm finished with it. But
note that i said *mostly unrelated* ... i do indeed
perceive a connection that i think folks here will
find interesting.

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

🔗hstraub64 <hstraub64@telesonique.net>

🔗ma1973 <marcsavage73@mchsi.com>

The listing of the srutis of Indian classical music given below is
based on decades of study of the srutis, study with several masters
of Indian classical music, pitch analysis of recordings by several
masters of raga performance, and the following quote by Ali Akbar
Khan:

"I am still learning about the srutis. They reach to your heart and
help you feel the ragas and the notes. In old theory, they say that
there are twenty-two in number, but right now I feel that there are
more like twenty-three and a half. There is only one sa and one pa.
Komal re, komal ga, and komal dha all have three. Shuddha ma, tivra
ma, shuddha dha, and komal ni each have two. And shuddha re, shuddha
ga, and shuddha ni each have one and a half." Ali Akbar Khan

This quotation yields many insights... Below I have just listed the
twenty-three and a half srutis he is referring to.

In brief summary, Khansahib's list is basically the usually-given
twenty-two srutis plus the three "ati ati komals" (ati ati komal re;
ati ati komal ga; and ati ati komal dha). Though not on the usual
list of 22 srutis, it is well-known that these notes do appear is
some ragas. So really there are twenty-five notes on Khansahib's
list. It's reduced to twenty-three and half because he gives "half"
status to three notes that are usually considered srutis -- the
lesser-used versions of shuddha re, shuddha ga, and shuddha ni. I
think this is the most illuminating aspect of his comment.

With each set of srutis associated with a given note, the principal
sruti is listed first, the others in descending order of
significance. Ratios given are exact. Cent values given are rounded
to the nearest whole cent:

Sa (1): [1/1; 000)

komal re (3):
komal re: [16/15; 112]
ati komal re: [256/243; 090]
ati ati komal re: [25/24; 070]

Re (1 1/2):
shuddha re: [9/8; 204]
"half"-status shuddha re: [10/9; 182]

komal ga (3):
komal ga: [6/5; 316]
ati komal ga: [32/27; 294]
ati ati komal ga: [75/64; 274]

Ga (1 1/2):
shuddha ga: [5/4; 386]
"half"-status shuddha ga: [81/64; 408]

Ma (2):
shuddha Ma: [4/3; 498]
ekasruti Ma: [27/20; 520]

tivra Ma (2):
tivra Ma: [45/32; 590]
tivratar Ma: [729/512; 612]

Pa (1): [3/2; 702]

komal dha (3):
komal dha: [8/5; 814]
ati komal dha: [128/81; 792]
ati ati komal dha: [25/16; 772]

Dha (2):
shuddha dha: [5/3; 884]
shuddha dha: [27/16; 906]

komal ni (2):
komal ni: [9/5; 1018]
komal ni: [16/9; 996]
(these two hard to prioritize; maybe a toss-up)

Ni (1 1/2):
shuddha ni: [15/8; 1088]
"half"-status shuddha ni: [243/128; 1110]

🔗monz <monz@tonalsoft.com>

Hi Marc,

--- In tuning@yahoogroups.com, "ma1973" <marcsavage73@...> wrote:

> "I am still learning about the srutis. They reach to
> your heart and help you feel the ragas and the notes.
> In old theory, they say that there are twenty-two in
> number, but right now I feel that there are more like
> twenty-three and a half. There is only one sa and one pa.
> Komal re, komal ga, and komal dha all have three.
> Shuddha ma, tivra ma, shuddha dha, and komal ni each
> have two. And shuddha re, shuddha ga, and shuddha ni
> each have one and a half." Ali Akbar Khan
>
> This quotation yields many insights... Below I have
> just listed the twenty-three and a half srutis he is
> referring to.
>
> In brief summary, Khansahib's list is basically the
> usually-given twenty-two srutis plus the three "ati
> ati komals" (ati ati komal re; ati ati komal ga; and
> ati ati komal dha). Though not on the usual list of
> 22 srutis, it is well-known that these notes do appear
> is some ragas. So really there are twenty-five notes
> on Khansahib's list. It's reduced to twenty-three and
> half because he gives "half" status to three notes that
> are usually considered srutis -- the lesser-used versions
> of shuddha re, shuddha ga, and shuddha ni. I think this
> is the most illuminating aspect of his comment.

Ignoring the skhisma (~2 cents), the set of ratios you
give can mostly be tuned as a pythagorean chain by the method
of "tuning-by-concords" (i.e., all 4ths and 5ths, easily tuned
by ear), with one other interval needed to reach the three
"ati ati" srutis, which can then also be tuning "by concords".
The result is the set of ratios i give at the beginning of
my webpage with a disjunction and then the other three, thus:

(arranged here in order of exponent of 3)

3^x .. ~cents

.. 11 ... 522 .. Ekasruti Ma
.. 10 .. 1020 .. Komal ni
... 9 ... 318 .. Komal ga
... 8 ... 816 .. Komal dha
... 7 ... 114 .. Komal re
... 6 ... 612 .. Tivratar Ma
... 5 .. 1110 .. "half"-status shuddha ni
... 4 ... 408 .. "half"-status shuddha ga
... 3 ... 906 .. Shuddha dha
... 2 ... 204 .. Shuddha re
... 1 ... 702 .. Pa
... 0 ..... 0 .. Sa
.. -1 ... 498 .. Shuddha Ma
.. -2 ... 996 .. Komal ni
.. -3 ... 294 .. Ati komal ga
.. -4 ... 792 .. Ati komal dha
.. -5 .... 90 .. Ati komal re
.. -6 ... 588 .. Tivra Ma
.. -7 .. 1086 .. Shuddha ni
.. -8 ... 384 .. Shuddha ga
.. -9 ... 882 .. Shuddha dha
. -10 ... 180 .. "half"-status shuddha re
.
.
.
. -15 ... 271 .. Ati ati komal ga
. -16 ... 769 .. Ati ati komal dha
. -17 .... 67 .. Ati ati komal re

Given the way that most of the names group together
in this tuning, i submit that this is probably the
origin of the system you describe.

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

🔗ma1973 <marcsavage73@mchsi.com>

> Ignoring the skhisma (~2 cents), the set of ratios you
> give can mostly be tuned as a pythagorean chain by the method
> of "tuning-by-concords" (i.e., all 4ths and 5ths, easily tuned
> by ear), with one other interval needed to reach the three
> "ati ati" srutis, which can then also be tuning "by concords".
> The result is the set of ratios i give at the beginning of
> my webpage with a disjunction and then the other three, thus:
>
> (arranged here in order of exponent of 3)
>
> 3^x .. ~cents
>
> .. 11 ... 522 .. Ekasruti Ma
> .. 10 .. 1020 .. Komal ni
> ... 9 ... 318 .. Komal ga
> ... 8 ... 816 .. Komal dha
> ... 7 ... 114 .. Komal re
> ... 6 ... 612 .. Tivratar Ma
> ... 5 .. 1110 .. "half"-status shuddha ni
> ... 4 ... 408 .. "half"-status shuddha ga
> ... 3 ... 906 .. Shuddha dha
> ... 2 ... 204 .. Shuddha re
> ... 1 ... 702 .. Pa
> ... 0 ..... 0 .. Sa
> .. -1 ... 498 .. Shuddha Ma
> .. -2 ... 996 .. Komal ni
> .. -3 ... 294 .. Ati komal ga
> .. -4 ... 792 .. Ati komal dha
> .. -5 .... 90 .. Ati komal re
> .. -6 ... 588 .. Tivra Ma
> .. -7 .. 1086 .. Shuddha ni
> .. -8 ... 384 .. Shuddha ga
> .. -9 ... 882 .. Shuddha dha
> . -10 ... 180 .. "half"-status shuddha re
> .
> .
> .
> . -15 ... 271 .. Ati ati komal ga
> . -16 ... 769 .. Ati ati komal dha
> . -17 .... 67 .. Ati ati komal re
>
> Given the way that most of the names group together
> in this tuning, i submit that this is probably the
> origin of the system you describe.

From a strictly theoretical point of view, what you
say has some theoretical appeal, but I don't think
it passes "Occam's Razor". Why force the system into
a 3-limit paradigm when there is no such bias among
Indian musicians, either historically or in the present,
and when the 5th harmonic is so clearly audible?
Acknowledging the role of the 5th harmonic makes
the whole system readily perceivable, simple and
straightforward, and also just happens to correspond
to what can be observed and measured in actual use,
as well is what is actively taught by masters of
raga to their students.

There is another point that should be mentioned which
is probably stronger than either your argument or the
caveat to it I have mentioned above. The tamboura is
the principal drone instrument in Indian music and most
tambouras have a VERY pronounced 5th harmonic. I have
heard super-expensive concert tambouras in which the
5th harmonic is so strong that it almost overwhelms the
tonic! I have sometimes found it difficult to sing a
6/5 komal ga in the presence of such a strong 5/4!

With such a strong 5th harmonic audibly present in
the fundamental drone from which the shrutis naturally
arise, it just doesn't make sense to impose a 3-limit
Pythagorean paradigm on Indian music. In fact, the
many masters of Indian music that I have had the good
fortune to associate with seem to have a love affair
with the 5th harmonic. In some forty years of investigation
I have yet to see the slightest empirical evidence that
the Indian system is based on a 3-limit paradigm. It just
doesn't fit the observable facts.

I have seen some theoreticians to who, like you, seem
to think that the Indian system is based on the 3-limit,
such as Alain Danielou. Mr. Danielou bases his conclusions on
extremely limited exposure, however. Though I'm sure
he was well meaning, he just didn't hear enough
of the music to draw any decisive conclusions. (He
worked with a few musicians in Varanasi in the 30's and
had almost no exposure to other musicians or to recordings.
It's also questionable how he decided which intervals he
was hearing. As an example, Danielou claims that the
third (shuddha ga) of Raga Yaman is 81/64. In my extensive
study of this raga I have yet to find a single musician who uses
81/64. They use 5/4 in all cases that I have studied.)

And, for example, why posit a 384 cent
shuddha ga based on a theoretical pythagorean sequence,
when the 386 cent 5/4 shuddha ga is blasting in your ear
from the tamboura and forms such a prominent part of the
soundscape in which Indian music is created? Again, the
Indian musicians have not the slightest bias against
the 5th harmonic nor do they make any effort to avoid it.
Rather, it is fully embraced.

Further, the Indian scale and indeed all of
Indian music, has its root in vocal music. It
would require a rather sophisticed musical
instrument to accurately generate a long chain
of pythagorean intervals based on perfect fifths
(or fourths). Instead, Indian music is based
on the simple relationship of each tone to the
tonic (sa).

Of course tonal relationships within the scale are
also significant, but secondary to the fundamental
relationship with the tonic. Again using the example
of Raga Yaman. This raga has no natural fourth
(ma) but rather uses the raised fourth (tivra ma).
Because of this, the 5/4 relationship usually
favored in Indian music between the natural fourth
(4/3) and the major sixth (shuddha dha = 5/3) is
not present. This "frees up" shuddha dha and in
most cases musicians prefer the 27/16 shuddha dha in
Yaman. But even so, they still use the 5/4 shuddha ga
even though it does not make a nice 3/2 with 27/16
as it does with 5/3. Thus, musicians place the inner
relationship between shuddha ga and shuddha dha second
to their sense of which tones are most desirable
melodically in relation to the tonic, which is always
heard in the constantly sounding drone. In ragas that
use the natural fourth (4/3) and the major sixth
(shuddha dha), the preferred pitch for shuddha dha
is generally 5/3.

Even such a "5th harmonic phobic" composer
as La Monte Young embraces the 5th harmonic
fully in his very advanced practice of Indian
vocal music.

I am not interested in proving anything here, nor of
convincing those who wish to apply a different
theoretical paradigm. I just know from
experience, first hand and without any doubt,
of the role of the 5th harmonic in Indian raga.
Just listen to singers such as Pandit Pran
Nath blend his voice seamlessly with the 5th harmonic
of the tamboura drone and I think you won't have
any doubts either.

🔗Mark Rankin <markrankin95511@yahoo.com>

Dear All,

It's really a shame and a pity.

Not because "you were raised up in the city", if you
even were, but because our sweetly detested Portal
Tenders, Yahoo.com, think that they know better than
their users what their users want and need.

To wit (and please listen up Yahoo Board of
Directors):

A picture is worth every iota of those well known
"thousand words".

I am a musical tuning theorist. At precisely this
moment, as I type this message, I am right in the
middle of trying to describe to my musical tuning
cohorts, especially the newer, younger ones, something
that would be a hell of alot easier to describe with a
picture, or a mathematical table, rather than with
text.

I have tried to type out little mathematical tables
using Yahoo Mail several times, thinking it would make
things much easier for my readers to understand, but
No Deal!

Yahoo automatically re-arranged my carefully crafted
number tables, to the point of unreadability, a thing
that has made me curse their owners and managers
bitterly.

In the old days, when computers had limited memory,
brevity was required. But these days, the length of
an e-mail is not, or should not, be an issue. A few
years back my very own Yahoo upped every user's
personal stash of memory from 600 KB to 1 million
Bytes.

And yet, in the past year or so, Yahoo has revamped
our service to "save space" (or some such excuse), and
has now alienated all users who try to be creative
with the e-mail interface by making shapes or pictures
or designs or number tables with our keyboards in
order to make things easier for our readers to
understand.

If anyone reading this message knows how to send it to
both the President and the CEO of Yahoo.com, please do
so!

In the meantime I'm going to try to communicate to my
musical tuning theorist friends, in deadly dull linear
pictureless tableless designless text, that years ago
I came to realize that the Hindu 22-tone per octave
"Sruti" scale appeared to be incomplete, and that a
25-tone per octave "Sruti" scale appeared to make more
sense, or at least more symmetry.

Later I met a Dutch-Canadian tuning theorist named
Siemen Terpstra who had made the same discovery, and
he had gone even further and had drawn a 25-tone per
octave "tuning diagram" which I would dearly love to
create for you using the Yahoo's e-mail keyboard.

Unfortunately, miserable experience has taught me that
any attempt to create the 25-tone per octave tuning
diagram using my Yahoo e-mail keyboard will only lead
me to anger, hostility and alienation.

All I can do is describe it to you with poor man's
prose - here goes:

Draw an 8 inch long horizontal line on a sheet of
paper and mark the beginning of the line as 0, the
middle of the line as 4, and the end of the line as 8,
then mark 1 inch measurements at 1, 2, 3, 5, 6, and 7
inches in between.

We can call each of the eight 1 inch 'gaps' between
each of the 9 marks (0-8) a "musical fifth". We can
also call each of the 9 'marks' on the sheet a
"musical fifth" and designate it with a small "f",
except for the one fifth that's in the center of the 9
fifths. We can call that central fifth the "starting
keynote" and we can give it any of the 18 keynames.
For now, lets call it "D".

Imagine a second horizontal line of musical fifths
that is eight fifths long, and imagine that each of
these eight fifths are also one inch apart.

Finally, imagine a third horizontal line of musical
fifths that, like the second line, is eight fifths
long and, like both of the previous lines of fifths,
has all it's fifths lined up one inch apart.

Now, imagine taking the three separate horizontal
lines of fifths and laying them out horizontally, with
one of the lines of eight fifths on top, with the line
of eight fifths and the "starting keynote" in the
center, and with the second line of eight fifths
underneath.

Our final alignment will be to make the layout
perfectly symmetrical by centering all 25 fifths
(8+9+8), around the "D" in the center of the central
line of 9 fifths. This centering maneuver will entail
placing the upper 8 fifths directly above the eight
one inch wide gaps in the central line of 9 fifths,
and placing the lower 8 fifths directly under the
eight one inch wide gaps in the central line of 9
fifths.

And there we have it, a 25 tone per octave stack of
three horizontal lines of fifths arranged in perfect
symmetry around the Starting Keynote of D.

Please hear me Yahoo, your e-mail service could be so
much better if you gave your subscribers better
choices for personalizing their e-mails.

It would help your bottom line, if only you would pay
attention to what your subscribers want!

My name is Mark Rankin, I like to place my name alone,
three lines below the end of the text above it. But
Yahoo software automatically moves my name two lines
northward, every time, as if to say "We know better".
But you don't. You know worse, and in's obvious you
don't care what your subscribers want.

--- monz <monz@tonalsoft.com> wrote:

> Hi Marc,
>
>
> --- In tuning@yahoogroups.com, "ma1973"
> <marcsavage73@...> wrote:
>
> > "I am still learning about the srutis. They reach
> to
> > your heart and help you feel the ragas and the
> notes.
> > In old theory, they say that there are twenty-two
> in
> > number, but right now I feel that there are more
> like
> > twenty-three and a half. There is only one sa and
> one pa.
> > Komal re, komal ga, and komal dha all have three.
> > Shuddha ma, tivra ma, shuddha dha, and komal ni
> each
> > have two. And shuddha re, shuddha ga, and shuddha
> ni
> > each have one and a half." Ali Akbar Khan
> >
> > This quotation yields many insights... Below I
> have
> > just listed the twenty-three and a half srutis he
> is
> > referring to.
> >
> > In brief summary, Khansahib's list is basically
> the
> > usually-given twenty-two srutis plus the three
> "ati
> > ati komals" (ati ati komal re; ati ati komal ga;
> and
> > ati ati komal dha). Though not on the usual list
> of
> > 22 srutis, it is well-known that these notes do
> appear
> > is some ragas. So really there are twenty-five
> notes
> > on Khansahib's list. It's reduced to twenty-three
> and
> > half because he gives "half" status to three notes
> that
> > are usually considered srutis -- the lesser-used
> versions
> > of shuddha re, shuddha ga, and shuddha ni. I
> think this
> > is the most illuminating aspect of his comment.
>
>
> Ignoring the skhisma (~2 cents), the set of ratios
> you
> give can mostly be tuned as a pythagorean chain by
> the method
> of "tuning-by-concords" (i.e., all 4ths and 5ths,
> easily tuned
> by ear), with one other interval needed to reach the
> three
> "ati ati" srutis, which can then also be tuning "by
> concords".
> The result is the set of ratios i give at the
> beginning of
> my webpage with a disjunction and then the other
> three, thus:
>
> (arranged here in order of exponent of 3)
>
> 3^x .. ~cents
>
> .. 11 ... 522 .. Ekasruti Ma
> .. 10 .. 1020 .. Komal ni
> ... 9 ... 318 .. Komal ga
> ... 8 ... 816 .. Komal dha
> ... 7 ... 114 .. Komal re
> ... 6 ... 612 .. Tivratar Ma
> ... 5 .. 1110 .. "half"-status shuddha ni
> ... 4 ... 408 .. "half"-status shuddha ga
> ... 3 ... 906 .. Shuddha dha
> ... 2 ... 204 .. Shuddha re
> ... 1 ... 702 .. Pa
> ... 0 ..... 0 .. Sa
> .. -1 ... 498 .. Shuddha Ma
> .. -2 ... 996 .. Komal ni
> .. -3 ... 294 .. Ati komal ga
> .. -4 ... 792 .. Ati komal dha
> .. -5 .... 90 .. Ati komal re
> .. -6 ... 588 .. Tivra Ma
> .. -7 .. 1086 .. Shuddha ni
> .. -8 ... 384 .. Shuddha ga
> .. -9 ... 882 .. Shuddha dha
> . -10 ... 180 .. "half"-status shuddha re
> .
> .
> .
> . -15 ... 271 .. Ati ati komal ga
> . -16 ... 769 .. Ati ati komal dha
> . -17 .... 67 .. Ati ati komal re
>
> Given the way that most of the names group together
> in this tuning, i submit that this is probably the
> origin of the system you describe.
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
>
>
>

____________________________________________________________________________________
Luggage? GPS? Comic books?
Check out fitting gifts for grads at Yahoo! Search
http://search.yahoo.com/search?fr=oni_on_mail&p=graduation+gifts&cs=bz

🔗monz <monz@tonalsoft.com>

Hi Marc,

--- In tuning@yahoogroups.com, "ma1973" <marcsavage73@...> wrote:
>
> > Ignoring the skhisma (~2 cents), the set of ratios you
> > give can mostly be tuned as a pythagorean chain by the method
> > of "tuning-by-concords" (i.e., all 4ths and 5ths, easily tuned
> > by ear), with one other interval needed to reach the three
> > "ati ati" srutis, which can then also be tuning "by concords".
> > The result is the set of ratios i give at the beginning of
> > my webpage with a disjunction and then the other three, thus:
> >
> > [table snipped]
>
> From a strictly theoretical point of view, what you
> say has some theoretical appeal, but I don't think
> it passes "Occam's Razor". Why force the system into
> a 3-limit paradigm when there is no such bias among
> Indian musicians, either historically or in the present,
> and when the 5th harmonic is so clearly audible?
> Acknowledging the role of the 5th harmonic makes
> the whole system readily perceivable, simple and
> straightforward, and also just happens to correspond
> to what can be observed and measured in actual use,
> as well is what is actively taught by masters of
> raga to their students.

I understand perfectly well everything that you wrote
in response to me. But please note that i'm invoking
the schisma equivalence, which means that for all
intents and purposes what would have been tuned as
a pythagorean system actually doesn't function that
way at all, but rather functions as a 5-limit JI system.

My main reason for fitting this scheme into a pythagorean
framework is my (admittedly speculative) search for
historical accuracy. Pythagorean tuning is as old as
dirt, and my hunch is that Indian tuning has precursors
in the music of the Sumerians and Babylonians, whose
music-theory descriptions are almost certainly "pythagorean"
(centuries before Pythagoras, of course).

As i wrote briefly in my first post in this thread,
i've recently been working again on my hypothesis that
the Greek-letter notation used by Boethius in his
description of the Graeco-Roman modal system fits
an extended pythagorean tuning which recognizes
schismic equivalence but has pairs of pitches separated
by the syntonic/pythagorean comma. The Indian system
works exactly this same way. So i'm interested in the
possibility that something which i always believed
originated with the Sumerians, found later reflections
not only in Greece but also in India.

The skhisma is an imperceptible difference in all but
the most stringent laboratory listening experiments,
so even if a musician tuned his instrument to an
extended pythagorean system, his ears would be telling
him that he's working with 5-limit JI.

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

🔗monz <monz@tonalsoft.com>

🔗ma1973 <marcsavage73@mchsi.com>

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗ma1973 <marcsavage73@mchsi.com>

> THE ORIGIN OF THE INDIAN 22-TONE SCALE by MIECZYSLAW KOLINSKI

A good example of academic text-torturing
utterly divorced from the actual practice
of Indian music. Ridiculous methodology
and equally ridiculous conclusions.

The author seem to have no connection to the
world of Indian music, and doesn't take actual
music into account at all. He also seems to
suggest that the origin of the
Indian scale is related to some ancient
harp-like instrument. This ignores the
central and originating role of vocal music
as emphatically stated by all masters of
Indian music and by the historical texts
as well.

Though I don't think it would necessarily
be productive to discuss it on this forum,
the deeper roots of Indian music in Indian
spirituality are of primary significance.
That is also ignored in this paper.

If the old texts are interpreted literally, as if they
were modern Western scientific documents, they are
misunderstood. It requires a deep sensitivity to the
Indian character, and a broad study of ancient Indian
texts, especially the philosophical works, to begin
to understand the mentality and assumptions that
underlie the texts. These are entirely different
from the modern Western scientific mentality.

For all its academic pretensions, this paper
is a joke.

a selection from SOUTH INDIAN MUSIC: BOOK 4. BY P. SAMBMOORTHY

Coming from an Indian who has a much stronger sense
of the music he is discussing, this paper comes to
much more sensible conclusions. However, the author's
attempt to make his arguments in Western academic style
detracts from the actual understanding of Indian music.

Study with a master. Understand that the svaras and
srutis have their origin in the relationship of the voice
to a drone. Then the real potency and character of
Indian music emerges. The origin of the shrutis is
not lost in the engimatic ancient Indian texts. It
is alive today in the practice of the great masters.
When you hear the svaras in the drone, and produce
them with your voice immersed deeply in the drone,
then you know instantly and intuitively where the
notes MUST come fromm if the character (rasa) of the
raga is the be evoked and preserved. Evoking and
sustaining the rasa is what Indian music is all about.
This is never done by applying an abstract
intellectual system and then trying to conform
one's practice to it.

Of course applying an abstract intellectual
system and then conforming one's practice to
it is exactly what is done in Western music,
at least since the advent of tempered scales,
and so it is easy to see how some scholars
attempt to apply this paradigm to Indian music,
where it doesn't fit at all.

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗ma1973 <marcsavage73@mchsi.com>

> The conclusion are the same.

I don't think so. Certainly there is a distinction between intervals
derived solely from the 3rd harmonic and those derived from both the
3rd and 5th harmonics. That's the distinction we've been discussing.

> India got their tuning from !4th century Persian theory. From the
mouth of a master BTW, Amiya Dusgupta.

Even if this is true it does not apply to the tunings used in Indian
music today, which are derived from the drone. Have you studied with
a master of Indian vocal music? They will invariably teach you to
find the notes in the drone -- to tune your voice to the harmonics
you hear in the drone -- to actually merge your voice in the drone.
In real practice, this is where the notes come from.

> The first shows Indian tuning in terms of the Pythagorean
> series. The second with it schismatic equivalents. Not all of India
> does things the same way. They call it a subcontinent for a reason.

These two approaches to identifying intervals are different, and
thus they're not talking about the same tunings. I have previously
stated my arguments for "the second" being the more accurate
representation of the intevals used in North Indian music today.

Perhaps I should have made it clearer that I have been talking about
North Indian classical music all along. The South Indian Carnatic
melakarta system is different. Though the book by P. SAMBMOORTHY
is ostensibly about South Indian Music, he also discusses the tunings
used in North Indian "Hindustani" music.

I admit I was too hasty in making a slight criticism of Sambmoorthy's
work. Looking at it further I think it is quite good. Kolinski's
work is indeed trash however.

> The drone came later in Indian music.

All my comments have been about the system of tuning used in North
Indian classical music. I don't have too many recordings in my
collection made a couple thousand years ago, nor even a couple
hundred! (Recording technology seems to have been somewhat lacking
in those days!) And the ancient Indian texts are, generously
speaking, less than precise on the tuning issue.

If it is the case that "the drone came later" than the tuning theory
you wish to discuss, then it is also probably fair to say that none
of the speculated derivations of ancient tunings have even the
slightest relevance to the tunings used today. If it is true that
some contrived pythagorean tunings system was used in India PRE-
DRONE, then the advent of the drone would have overthrown the old
tuning system completely and supplanted it with a tuning system based
on the audible harmonics within the drone, which is what is used
today.

So in talking about tunings used in North Indian classical music
today (the topic of my disccusion) and tunings that MAY (or may not,
no recordings to check!) have once anciently been used, we're talking
about "apples and oranges".

> But there is a big variety about the theoretical tunings and the
practice.

This is true, and is an area I've avoided getting into in my
discussion. Even today the actual practice may vary significantly
from any coherent theory. One huge limitation in our discussion (and
in the theory) is that the essential technique of evoking and
sustaining the "rasa" of a given raga involves the use of all the
pitches "between the notes". The pitch areas between the notes
comprise much of the actual Indian music heard in performance. The
svaras (notes) are the nodal points -- the points of maximum
resonance -- that demarcate the broader pitch areas. In a full
performance of any raga it is almost certain that all points on the
entire pitch spectrum within an octave are sounded at some point or
other in the performance.

> erotic ragas where you find the 7th harmonic
> used for instance.

The 7th harmonic doesn't figure in theory, nor in common practice,
but certainly may appear in the performances of some artists who
probably have no idea they they're singing notes derived from the
seventh harmonic. I don't know of any raga that uses these tones as
principal notes consistently however. The singer is permitted a
great deal of freedom to use whatever tones they feel invoke the
spirit of the raga, though if they get too idiosyncratic with this,
other artists may feel that they have moved outside the scope of the
raga.

> Much of India has been only using 17 of the 22 for a
> while, according to this one master.

I think this is true, though I haven't pinned it down to precisely
17. It does seem like the full range of shrutis is rarely used, but
of course no one is suggesting that all the shrutis are used in any
one performance in any case. The notion is that the full array of
shrutis constitute the fundamental pitch palette of the entire art
form, not a single performance.

If those of you interested in discussing this topic are primarily
interested in what you believe might be the ancient origins of scales
once used in India but which are no longer in use (perhaps since the
advent of the drone?), then the discussion has moved outside the area
of my knowledge and interest. I joined the discussion to provide
some information and insights about the shrutis as used in North
Indian classical music today, and at least since the age of
recording, and probably for at least some time before.

Because there are no recordings of the ancient music, you can
speculate to your heart's content about what pitches they may have
been using in actual practice, but you can never prove your points
nor can anyone disprove them. At best you can argue about what you
think the ancient (rather enigmatic) texts are saying.

But if you want to understand the practice of Indian music today, I
think you will have to confine yourself to considering the singable
tones. Pitches derived theoretically from long strings of compounded
ratios are neither audible nor singable within the soundscape of the
sa-pa drone of the tamboura and are thus outside the scope of Indian
music in practice.

I think this discussion has had some value up to this point, but if
it is going to degenerate into unprovable speculations about what
tunings were used by ancient Indian musicians in their practice, I am
no longer interested.

However, if anyone has anything of substance to add
about the use of tunings in North Indian raga today, that would be
interesting. For example, can you give me an example of any
recordings by any acknowledged master who uses pitches derived from
the seventh harmonic as a regular part of his or her musical
vocabulary? Now that would be interesting!

🔗monz <monz@tonalsoft.com>

Hi Marc,

--- In tuning@yahoogroups.com, "ma1973" <marcsavage73@...> wrote:
>
> > The conclusion are the same.
>
> I don't think so. Certainly there is a distinction
> between intervals derived solely from the 3rd harmonic
> and those derived from both the 3rd and 5th harmonics.
> That's the distinction we've been discussing.

You're ignoring the idea of schismatic equivalence.
Sure, if you focus only on the numbers in the ratios,
then there's a huge difference between these two
tuning systems. But if you *listen*, you'll find
that an *extended* pythagorean system has intervals
which are essentially indistinguishable from 5-limit JI.

Since i know that you have Tonescape running, i was
going to make a .tuning file combining both versions
of the Indian system: the 5-limit version you posted,
and the 3-limit version i posted ... but right now
i have to take care of my baby girl, so i'll have to
do it later.

But in the meantime, there is a file you already have
which gives schismatic 3rds and 6ths -- in the Tonescape
File|Open dialog-box, go to the "My Tonescape" folder
on your hard-drive (if you used the default install
location, it will be under "My Documents"), and under
the "Samples" folder and the "Tunings" subfolder, load
this file: "3-limit pythagorean ji, 17-tone.tuning" .

Right-click on the blue Lattice background, and choose
"Select notation" from the pop-up menu, and choose either
"Logarithmic" (and "OK") to use cents, or "Logical Meantone"
to view letter-names. Because the letters are calculated
for meantone and not pythagorean, some of them will be off:
for example, if you keep "A" as your reference note, you'll
get "B#" where "C" should be. But you'll see that some pairs
of ratios are separated by 384 cents -- try listening to
those and see if they don't sound like 5/4 ratios to your
ears.

> I think this discussion has had some value up to this point,
> but if it is going to degenerate into unprovable speculations
> about what tunings were used by ancient Indian musicians in
> their practice, I am no longer interested.

Well, *i'm* still interested in "unprovable speculations"!

I think a very good argument can be made that pythagorean
tuning was used by the Sumerians and their successors.
I won't go into it all now, but here are two websites that
will give anyone interested a lot to chew on:

http://kingmixers.com/Terp.html

http://members.aol.com/ricdum/mane.htm

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

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗ma1973 <marcsavage73@mchsi.com>

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗ma1973 <marcsavage73@mchsi.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "ma1973" <marcsavage73@> wrote:
> > --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@>
> > wrote:
>
> > > If they were really basing everything on listening to the
drone,
> it
> > > ought to be in there.
> > >
> >
> > Huh??? Just because the svaras used in Indian music are derived
> from
> > the drone (and the interaction between the voice and the drone,
see
> > below) why does this require the musician to use every possible
> tone
> > audible within the drone? It's a total non-sequiter.
>
> You went on and on about how it was all based on the overtone
series
> of the drone, and you must listen to the drone. You hit 7 pretty
> early on if you do that. If you skip over it, something other than
> listening to the drone is clearly at work.

Why not quote me instead of paraphrasing what you think I said? Why
does avoding the seventh harmonic mean that something other than the
overtone series is at work? Does relating to the overtone series
mean that you must include EVERYTHING in that series? Why?

As I type these words, all the letters I use are from the alphabet.
However, I am not using every letter of the alphabet. Does that mean
that I am drawing on some source of letters outside the alphabet to
create these words? What would that thing be? I don't know any
source of letters to use here outside the alphabet, yet I have no
trouble skipping over some of the letters without going outside the
alphabet at all.

> > To my ears, and many others (though probably not all), the tones
> > derived from the 7th harmonic don't mix particularly well in a
> scale
> > along with tones derived from the 5th harmonic.
>
> It mixes just fine, but it adds a quality not found in 5, just as 5
> adds something to 3. But again, here you are saying it really isn't
> just a matter of the overtone series, which was my point.

I guess it's a matter of taste and aesthetics. I would dispute your
claim that tones derived from the seventh harmonic mix as well with
those derived from the fifth harmonic as those from the 5th harmonic
do with those from the 3rd harmonic. I think that the plethora of
musical systems found throughout the world that are in essence 5-
limit, including Western music, demonstrates this. But if you hear
otherwise, fine, I won't argue.

But the more significant point is that deriving tones from the
harmonic series in no way requires one to use every possible
harmonic, nor even every possible audible harmonic. Indian music
does indeed derive from the audible harmonic series, but is under no
obligation to include every possible tone that can be derived from
audible harmonics.

Now, if there were tones included in the Indian system that had no
discernable relationship to the harmonic series, then we might begin
to consider that something else was at work -- some kind of tempering
or whatever. But this is not the case. As there are no svaras in
the Indian system that cannot be easily understood in terms of the
audible harmonic series, we certainly don't need to go outside of the
harmonic series to explain the origin of those tones.

🔗ma1973 <marcsavage73@mchsi.com>

> You're ignoring the idea of schismatic equivalence.

Indeed I am, because it has no application to the subject under
discussion -- the tones used in contemporary North Indian classical
music.

> Sure, if you focus only on the numbers in the ratios,
> then there's a huge difference between these two
> tuning systems. But if you *listen*, you'll find
> that an *extended* pythagorean system has intervals
> which are essentially indistinguishable from 5-limit JI.

Do you realize that you can do this with ANY ratio? You can take the
17th harmonic, if you wish, and "extend" it (indefinitely) to the
point where you will generate tones, which if you LISTEN to them,
will be the "equivalent" of any other tone -- including the octave!

By this reasoning you could readily claim that the octave is NOT
derived from a ratio of 2/1, but rather from an extended series of
compounded 17th harmonics! Or any other harmonic.

All you're doing is compounding the 3rd harmonic to the extent that
you finally arrive at pitches which are close to those derived from
the fifth harmonic without all the extensions. Big deal! As stated
above, you can do this with ANY harmonic and derive equivalents for
ALL the tones derived from EVERY POSSIBLE harmonic. So what? It
doesn't imply anything about where strong scale tones actually come
from? Do you really think that the octave actually derives from an
extended series of 3rd harmonics, or 17th harmonics, rather than 2/1?

Unless you're going to claim that the octave actually does derive
from the 3rd harmonic (or whatever), your claim that, for example,
the consonant major third that is derived from the universally heard
5th harmonic is actually a derivitive of an extended sequence of 3rd
harmonics -- extended to the point where it is inaudible and
unsingable is not tenable. And if you do make such a claim about the
octave, no one will take you seriously (I don't think!).

> Since i know that you have Tonescape running, i was
> going to make a .tuning file combining both versions
> of the Indian system: the 5-limit version you posted,
> and the 3-limit version i posted ... but right now
> i have to take care of my baby girl, so i'll have to
> do it later.
>
> But in the meantime, there is a file you already have
> which gives schismatic 3rds and 6ths -- in the Tonescape
> File|Open dialog-box, go to the "My Tonescape" folder
> on your hard-drive (if you used the default install
> location, it will be under "My Documents"), and under
> the "Samples" folder and the "Tunings" subfolder, load
> this file: "3-limit pythagorean ji, 17-tone.tuning" .
>
> Right-click on the blue Lattice background, and choose
> "Select notation" from the pop-up menu, and choose either
> "Logarithmic" (and "OK") to use cents, or "Logical Meantone"
> to view letter-names. Because the letters are calculated
> for meantone and not pythagorean, some of them will be off:
> for example, if you keep "A" as your reference note, you'll
> get "B#" where "C" should be. But you'll see that some pairs
> of ratios are separated by 384 cents -- try listening to
> those and see if they don't sound like 5/4 ratios to your
> ears.

Of course 384 cents sounds close to 386 cents, but so what? Are you
seriously proposing that we ignore the obvious, audible, 5th harmonic
as the source of the consonant major third (shuddha ga) and instead
compound eight layers of 3rd harmonics to a tone which can neither be
heard nor sung relative to a drone (it would be overwhelmed by the
nearby 5th harmonic if it were even audible at all. As a reciprocal
interval however, it's not even in the overtone series!).

Are you seriously suggesting that the "real" origin of the consonant
major third is 8192/6561 and not 5/4? Can you hear and sing
8192/6561 without actually hearing and singing 5/4? If you have to
resort to the audible 5/4 to sing shuddha ga maybe that's where it
actually comes from? If it sounds like 5/4 just maybe it IS 5/4!
You know, if it walks like a duck...

Your system still flunks Occam's Razor, and you also have not
answered my earlier question about why you would prefer to guess that
the svaras derive from highly extended compounded sequences of ratios
which can neither be heard nor sung when the actual notes are right
in front of you, clearly audible and singable?

When a master of Indian vocal music teaches students the svaras, they
don't discuss any theory, never propose extended sequences of ratios,
never mention ratios at all, never discuss 3rd and 5th harmonics,
etc. They simply call attention to naturally occurring points of
resonance between the voice and the drone. That's all.

🔗monz <monz@tonalsoft.com>

Hi Marc,

--- In tuning@yahoogroups.com, "ma1973" <marcsavage73@...> wrote:
>
> > You're ignoring the idea of schismatic equivalence.
>
> Indeed I am, because it has no application to the subject
> under discussion -- the tones used in contemporary
> North Indian classical music.

No, incorrect.

The post by Hans which started this discussion:

/tuning/topicId_63593.html#72682

was asking a specific question about the relevance of
an observation that Gene made regarding the possible
connection of magic[22] with the sruti system. I responded
to Hans saying that i hadn't seen the wiki article but
that it probably should mention the historical priority
of an extended pythagorean tuning as the original basis
of the sruti system. *You* seem to be the person who insists
on discussing "contemporary North Indian classical music".

Nothing wrong with discussing that here as well, but this
discussion was never limited to that topic except by you.

>
> > Sure, if you focus only on the numbers in the ratios,
> > then there's a huge difference between these two
> > tuning systems. But if you *listen*, you'll find
> > that an *extended* pythagorean system has intervals
> > which are essentially indistinguishable from 5-limit JI.
>
> Do you realize that you can do this with ANY ratio?
> You can take the 17th harmonic, if you wish, and "extend"
> it (indefinitely) to the point where you will generate
> tones, which if you LISTEN to them, will be the
> "equivalent" of any other tone -- including the octave!

Of course. That's exactly what my concept of
"xenharmonic-bridge" is all about:

http://tonalsoft.com/enc/x/xenharmonic-bridge.aspx

> All you're doing is compounding the 3rd harmonic to the
> extent that you finally arrive at pitches which are close
> to those derived from the fifth harmonic without all the
> extensions. Big deal! As stated above, you can do this
> with ANY harmonic and derive equivalents for ALL the tones
> derived from EVERY POSSIBLE harmonic. So what? It doesn't
> imply anything about where strong scale tones actually
> come from? Do you really think that the octave actually
> derives from an extended series of 3rd harmonics, or 17th
> harmonics, rather than 2/1?

You say "Big deal" in what seems to me to be a condescending
tone. But for me, it is exactly that, a very big deal.

Of course, JI theory states that the ratios with the
smallest integers in their numerator and denominator are
going to equate to the most consonant for that intervallic
_gestalt_ -- thus, 2/1 = "octave", 3/2 = "5th", 4/3 = fourth,
5/4 = "major-3rd", etc.

But almost every sophisticated ancient tuning scheme i've
studied began its life as a pythagorean system, and it was
only when the chain-of-5ths was extended far enough that
intervals which are similar to higher-prime-limit (but
lower-integer numerator and denominator) ratios were found
that the theorists were willing to include those higher-prime
ratios in their theoretical tuning systems.

The discovery of the pythagorean-comma, which takes notice
of the near-equivalence of 3^12 and 2/1, is what led to
12-edo tuning. Similarly, the discovery of the mercator-comma,
where 3^53 == 2/1, led to 53-edo.

The schismatic equivalence of 3^-8 with 5/4 was made a
basis of tuning and compositional practice in the 1400s,
where the pythagorean Gb, Db, Ab, Eb were used as
close substitutes for the 5-limit F#, C#, G#, D#; see:

http://tonalsoft.com/enc/s/schismic-tuning.aspx

But obviously this schismatic equivalence was noticed
far earlier, and this is just another case of medieval
Europe emerging from the "Dark Ages" with knowledge that
had already been in use centuries earlier but was
forgotten in Europe after the Germanic migrations.

My point is that in cultures outside Europe this
knowledge may not have been forgotten: India is one
such place, and the "Arab world" via the Greek
Byzantine Empire is another.

I'm absolutely certain that the ancient Greek musical
notation, as described by Boethius and Alypius, was
based on an extended pythagorean system with schismatic
equivalences. In fact, 53-edo is an excellent tuning
to use for this notation; but the pythagorean tuning
with the actual 3-limit ratios would work just as well
in terms of what is actually audible.

And i'm also certain that the Greeks did not invent this,
but that they got it from either the Persians who got it
from the Babylonians, or directly from the Babylonians,
and that the Babylonians got it from the Sumerians.
This would make it a music-theoretical idea which goes
all the way back to the beginning of recorded history.
And to me, that's very significant.

I've read various accounts that state that the most
ancient Indian tuning was done as an extended pythagorean
system, and i see no reason to doubt it.

> Your system still flunks Occam's Razor, and you also
> have not answered my earlier question about why you
> would prefer to guess that the svaras derive from
> highly extended compounded sequences of ratios which
> can neither be heard nor sung when the actual notes
> are right in front of you, clearly audible and singable?

I provided the answer to that question before you asked
it, right in the first post i sent which had the
pythagorean tuning:

/tuning/topicId_63593.html#72706

>> "Ignoring the skhisma (~2 cents), the set of ratios
>> you give can mostly be tuned as a pythagorean chain
>> by the method of "tuning-by-concords" (i.e., all 4ths
>> and 5ths, easily tuned by ear), with one other interval
>> needed to reach the three "ati ati" srutis, which can
>> then also be tuning "by concords"."

The method of "tuning-by-concords" was first described
explicitly by Aristoxenos (c. 350 BC), in a situation
very much like this one here, where i would be
"the pythagoreans" and you would be Aristoxenos,
decrying the attempts by the pythagoreans to use their
ratios to describe what every musician knows how to do
by ear.

http://tonalsoft.com/enc/t/tuning-by-concords.aspx

In fact, this method is essentially the one described
in the Babylonian tablet "UET VII 74":

http://kingmixers.com/Franklin%20PDF%20files%20copy/Franklin%20Dissertation.%20PDF/UET%20774.pdf

http://members.aol.com/ricdum/morphology.htm

Now i've gone and written most of what i was going
to put into my post about the Boethius Greek notation,
and i haven't finished that yet. Oh well ...

Anyway, i understand that you are interested in
describing contemporary North Indian classical music,
and that you are backing up your statements with
those of respected teachers in that tradition.
And good for you for all of that. I'm describing
something related but different, and i will continue
to maintain its validity.

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

🔗ma1973 <marcsavage73@mchsi.com>

🔗monz <monz@tonalsoft.com>

Hi Marc,

It's OK, no harm done, and thanks for the apology.
I didn't really take any of too strongly to heart,
because being a very frequent poster to many
internet lists (particularly *this* one with its
highly-opinionated membership), i've developed a
really tough skin over the cyber-years.

Since you have a copy of Tonescape running (which
is something that a lot of folks who have tried it
were not able to accomplish, and my apologies to
all of them) i'd be very happy to continue correspondence
with you about that, either in private email, or on
the Yahoo group if you'd like to join:

/tonescape_denhaag/

If you could send me either a score or MIDI-file
(or something similar) of a North Indian piece with
all the appropriate tuning information, i'd be willing
to create a Tonescape file of it. That would probably
be the best way for me to show you what Tonescape is
capable of.

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

--- In tuning@yahoogroups.com, "ma1973" <marcsavage73@...> wrote:
>
> Hi monz,
>
> I apologize to you. You're right about the origin of the thread and
> the original subject matter. I was wrong. I just got caught up in
> what I thought the discussion had become. Sorry.
>
> Thank you for your detailed post about your understanding of the
> history of tuning systems and your interest in the extended
> pythagorean tuning. These are interesting ideas.
>
> I'm extremely sorry for the demeaning tone of some of my remarks. I
> see that you are very serious and responsible in the development of
> your theories. Though I feel that your theories miss the mark in
> some important ways, they certainly merit serious consideration.
> I'll bet we could have a great conversation if we could sit down
> comfortably somewhere with time on our hands, and we'd end up good
> friends.
>
> But the internet doesn't seem to foster that kind of communication,
> at least not in my experience. I've run into this before -- these
> dialogs exhaust and depress me. I just don't have a thick enough
> skin for the internet age, I'm afraid. Every time I override my
> reluctance and get into one of these conversations I regret it.
>
> Since our dialog was public, I felt that my apology should be
> likewise. But unless anyone else feels offended by my remarks
> (please raise your hand so I can apologize now!) I really am
> retiring. And again my thanks to all
>

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗Cameron Bobro <misterbobro@yahoo.com>

Here's the thing, Joe- tuning by pure fifths is practical
as all get out. Going as far along the spiral as you
propose is certainly feasible, the question would be why?
Because the spiral is then "justified" by something
that predates the "pythagorean" approach by billions
of years, namely the harmonic series. I don't doubt
that what you say happened, happened, but I believe you've
got the cart before the horse. The ancients were
probably tickled pink to find that an elegant and
numerologically delightful manmade system could
"square the circle" to coincide with the proportions of
nature staring them in the ear. But 5/4 sure as hell
didn't ORIGINATE in a spiral of fifths, that's just plain
nuts.

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Marc,
>
>
> --- In tuning@yahoogroups.com, "ma1973" <marcsavage73@> wrote:
> >
> > > The conclusion are the same.
> >
> > I don't think so. Certainly there is a distinction
> > between intervals derived solely from the 3rd harmonic
> > and those derived from both the 3rd and 5th harmonics.
> > That's the distinction we've been discussing.
>
>
> You're ignoring the idea of schismatic equivalence.
> Sure, if you focus only on the numbers in the ratios,
> then there's a huge difference between these two
> tuning systems. But if you *listen*, you'll find
> that an *extended* pythagorean system has intervals
> which are essentially indistinguishable from 5-limit JI.
>
> Since i know that you have Tonescape running, i was
> going to make a .tuning file combining both versions
> of the Indian system: the 5-limit version you posted,
> and the 3-limit version i posted ... but right now
> i have to take care of my baby girl, so i'll have to
> do it later.
>
> But in the meantime, there is a file you already have
> which gives schismatic 3rds and 6ths -- in the Tonescape
> File|Open dialog-box, go to the "My Tonescape" folder
> on your hard-drive (if you used the default install
> location, it will be under "My Documents"), and under
> the "Samples" folder and the "Tunings" subfolder, load
> this file: "3-limit pythagorean ji, 17-tone.tuning" .
>
> Right-click on the blue Lattice background, and choose
> "Select notation" from the pop-up menu, and choose either
> "Logarithmic" (and "OK") to use cents, or "Logical Meantone"
> to view letter-names. Because the letters are calculated
> for meantone and not pythagorean, some of them will be off:
> for example, if you keep "A" as your reference note, you'll
> get "B#" where "C" should be. But you'll see that some pairs
> of ratios are separated by 384 cents -- try listening to
> those and see if they don't sound like 5/4 ratios to your
> ears.
>
>
> > I think this discussion has had some value up to this point,
> > but if it is going to degenerate into unprovable speculations
> > about what tunings were used by ancient Indian musicians in
> > their practice, I am no longer interested.
>
> Well, *i'm* still interested in "unprovable speculations"!
>
> I think a very good argument can be made that pythagorean
> tuning was used by the Sumerians and their successors.
> I won't go into it all now, but here are two websites that
> will give anyone interested a lot to chew on:
>
> http://kingmixers.com/Terp.html
>
> http://members.aol.com/ricdum/mane.htm
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>

🔗monz <monz@tonalsoft.com>

Hi Cameron (and Marc Savage),

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...>
wrote:
>
> Here's the thing, Joe- tuning by pure fifths is practical
> as all get out. Going as far along the spiral as you
> propose is certainly feasible, the question would be why?
> Because the spiral is then "justified" by something
> that predates the "pythagorean" approach by billions
> of years, namely the harmonic series. I don't doubt
> that what you say happened, happened, but I believe you've
> got the cart before the horse. The ancients were
> probably tickled pink to find that an elegant and
> numerologically delightful manmade system could
> "square the circle" to coincide with the proportions of
> nature staring them in the ear. But 5/4 sure as hell
> didn't ORIGINATE in a spiral of fifths, that's just plain
> nuts.

Right, you've got it exactly. I guess i wasn't clear
enough about this with Marc, but the way you put it
is exactly how i see it too.

Of course we don't know what tuning systems musicians
used before the dawn of writing, other than to examine
the spacing of holes on bone-flutes etc. But from the
earliest written music-theory, we can see that pythagorean
tuning was developed as a standard means of scale-building.

It's logical to think that musicians have always heard
5- and 7-limit (and higher-prime?) harmonies and liked
them. But i think recent experience, with the nearly
universal acceptance of 12-edo to the exclusion of
teaching any other tuning data to most music students,
shows us how strongly a theoretical idea/ideal can
be ingrained, which makes it very hard to "go outside
the box" into other tuning systems. The same would have
been true in the past about pythagorean tuning -- indeed,
its hegemony lasted for *millennia*, compared to a century
or two for 12-edo.

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

🔗Aaron K. Johnson <aaron@akjmusic.com>

monz wrote:
> Hi Cameron (and Marc Savage),
>
>
> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> > wrote:
> >> Here's the thing, Joe- tuning by pure fifths is practical
>> as all get out. Going as far along the spiral as you
>> propose is certainly feasible, the question would be why?
>> Because the spiral is then "justified" by something
>> that predates the "pythagorean" approach by billions
>> of years, namely the harmonic series. I don't doubt
>> that what you say happened, happened, but I believe you've
>> got the cart before the horse. The ancients were
>> probably tickled pink to find that an elegant and >> numerologically delightful manmade system could >> "square the circle" to coincide with the proportions of >> nature staring them in the ear. But 5/4 sure as hell >> didn't ORIGINATE in a spiral of fifths, that's just plain >> nuts.
>> >
>
> Right, you've got it exactly. I guess i wasn't clear
> enough about this with Marc, but the way you put it
> is exactly how i see it too.
>
> Of course we don't know what tuning systems musicians
> used before the dawn of writing, other than to examine
> the spacing of holes on bone-flutes etc. But from the
> earliest written music-theory, we can see that pythagorean
> tuning was developed as a standard means of scale-building.
>
> It's logical to think that musicians have always heard
> 5- and 7-limit (and higher-prime?) harmonies and liked
> them. But i think recent experience, with the nearly
> universal acceptance of 12-edo to the exclusion of
> teaching any other tuning data to most music students,
> shows us how strongly a theoretical idea/ideal can
> be ingrained, which makes it very hard to "go outside
> the box" into other tuning systems. The same would have
> been true in the past about pythagorean tuning -- indeed,
> its hegemony lasted for *millennia*, compared to a century
> or two for 12-edo.
> At least in the west....

The other thing is this....we've had a 300 year reign of meantone, which favors 5/4 at the slight expense of 3/2.

My own explanation of the genesis of meantone is that the schismatic near 4:5:6 triads (3 of them) in a 12-tone fixed-pitch Pythagorean scale seduced musicians on the same instruments (e.g. keyboards) to go to the sweet 5/4 that they probably intuitively sung in adaptive JI.

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗Cameron Bobro <misterbobro@yahoo.com>

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Cameron (and Marc Savage),
>
>
> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@>
> wrote:
> >
> > Here's the thing, Joe- tuning by pure fifths is practical
> > as all get out. Going as far along the spiral as you
> > propose is certainly feasible, the question would be why?
> > Because the spiral is then "justified" by something
> > that predates the "pythagorean" approach by billions
> > of years, namely the harmonic series. I don't doubt
> > that what you say happened, happened, but I believe you've
> > got the cart before the horse. The ancients were
> > probably tickled pink to find that an elegant and
> > numerologically delightful manmade system could
> > "square the circle" to coincide with the proportions of
> > nature staring them in the ear. But 5/4 sure as hell
> > didn't ORIGINATE in a spiral of fifths, that's just plain
> > nuts.
>
>
> Right, you've got it exactly. I guess i wasn't clear
> enough about this with Marc, but the way you put it
> is exactly how i see it too.

I think it's related to how a sphere and half a cone make
a head and a nose, but ancient sculpture doesn't look like '50s
robots, and how the ancients could have idealized and
stereotyped sculptural proportions and yet do portraits
of individuals (which are amazingly accurate according
to the forensics documentaries I've seen).

>
> Of course we don't know what tuning systems musicians
> used before the dawn of writing, other than to examine
> the spacing of holes on bone-flutes etc. But from the
> earliest written music-theory, we can see that pythagorean
> tuning was developed as a standard means of scale-building.

I think it's important to remember that the first steps,
of tuning up an instrument don't necessarily dictate the
final scale, and I see no reason why a character/mood-based
tetrachordal approach, like what Ozan calls "maqam" music,
isn't downright antedeluvian. Pure fifths do the blocking,
the specific flavors are learned by ear, that kind of thing.

-Cameron Bobro

🔗hstraub64 <hstraub64@telesonique.net>

--- In tuning@yahoogroups.com, "ma1973" <marcsavage73@...> wrote:
>
> However, the author's
> attempt to make his arguments in Western academic style
> detracts from the actual understanding of Indian music.
>
> Study with a master. Understand that the svaras and
> srutis have their origin in the relationship of the voice
> to a drone. Then the real potency and character of
> Indian music emerges. The origin of the shrutis is
> not lost in the engimatic ancient Indian texts. It
> is alive today in the practice of the great masters.
> When you hear the svaras in the drone, and produce
> them with your voice immersed deeply in the drone,
> then you know instantly and intuitively where the
> notes MUST come fromm if the character (rasa) of the
> raga is the be evoked and preserved. Evoking and
> sustaining the rasa is what Indian music is all about.
> This is never done by applying an abstract
> intellectual system and then trying to conform
> one's practice to it.
>
> Of course applying an abstract intellectual
> system and then conforming one's practice to
> it is exactly what is done in Western music,
> at least since the advent of tempered scales,
> and so it is easy to see how some scholars
> attempt to apply this paradigm to Indian music,
> where it doesn't fit at all.
>

At the risk of being another reason for you to quit (which I would
regret, though): You are not saying that applying an (any) abstract
intellectual system absolutely cannot fit indian music, are you?

If this were the case, I would strongly doubt that, even with my very
limited knowledge of indian music.

The paragraph above does, to me, not appear to describe a difference
between the western and indian paradigm but rather the notorious
"theory lover" vs. "theory hater" debate, which I keep coming across
again and again, inside western music as well.

I cannot judge the theoretical texts - they may well be as wrong as
you said. However, to me this is not a sign that abstract intellectual
systems do not fit at all but rather that an appropriate, fitting
system has not been found yet.

Just my two unqualified percents...

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

Hans,

----- Original Message -----
From: "hstraub64" <hstraub64@telesonique.net>
To: <tuning@yahoogroups.com>
Sent: 15 Aï¿½ustos 2007 ï¿½arï¿½amba 13:55
Subject: [tuning] Re: Magic[22] as srutis

> --- In tuning@yahoogroups.com, "ma1973" <marcsavage73@...> wrote:
> >
> > However, the author's
> > attempt to make his arguments in Western academic style
> > detracts from the actual understanding of Indian music.
> >
> > Study with a master. Understand that the svaras and
> > srutis have their origin in the relationship of the voice
> > to a drone. Then the real potency and character of
> > Indian music emerges. The origin of the shrutis is
> > not lost in the engimatic ancient Indian texts. It
> > is alive today in the practice of the great masters.
> > When you hear the svaras in the drone, and produce
> > them with your voice immersed deeply in the drone,
> > then you know instantly and intuitively where the
> > notes MUST come fromm if the character (rasa) of the
> > raga is the be evoked and preserved. Evoking and
> > sustaining the rasa is what Indian music is all about.
> > This is never done by applying an abstract
> > intellectual system and then trying to conform
> > one's practice to it.
> >
> > Of course applying an abstract intellectual
> > system and then conforming one's practice to
> > it is exactly what is done in Western music,
> > at least since the advent of tempered scales,
> > and so it is easy to see how some scholars
> > attempt to apply this paradigm to Indian music,
> > where it doesn't fit at all.
> >
>
> At the risk of being another reason for you to quit (which I would
> regret, though): You are not saying that applying an (any) abstract
> intellectual system absolutely cannot fit indian music, are you?
>
> If this were the case, I would strongly doubt that, even with my very
> limited knowledge of indian music.
>
> The paragraph above does, to me, not appear to describe a difference
> between the western and indian paradigm but rather the notorious
> "theory lover" vs. "theory hater" debate, which I keep coming across
> again and again, inside western music as well.
>

Believe it or not, that is exactly what transpired in a huge Turkish Music
discussion platform I took part in these recent days. You could not guess
the animosity certain people harbor against the notion of temperament in the
name of preserving tradition.

> I cannot judge the theoretical texts - they may well be as wrong as
> you said. However, to me this is not a sign that abstract intellectual
> systems do not fit at all but rather that an appropriate, fitting
> system has not been found yet.
>

79/80 MOS 159-tET: try it, you'll love it.

> Just my two unqualified percents...
>
>

Oz.

🔗hstraub64 <hstraub64@telesonique.net>

🔗Klaus Schmirler <KSchmir@online.de>

Mark,

you seem to insist that sruti are used to make music. In Bharata's text, they are the unit of measurement, and Bharata describes the two genera of Shadja Grama and Madhyama Grama in terms of sruti. Measuring units should have some objective foundation, for which the chain of fifths is a good candidate, and Kolinski gives reasons why other measurements (monochord) are unlikely. Nothing wrong with that. And no claim that rounding is forbidden, either.

As to the spirit vs. letter of old texts, do you really think the rules of Sanskrit don't follow Panini's letter?

There are good sources that the practice of Indian court music changed drastically under Persian rule, and the system you use (with names for the inflected svara) is newer still. It might be advisable to forget about the notion of sruti, or its association with the number 22, in these cases. Of course, that is not what a society proud of its cultural history does.

klaus

ma1973 schrieb:
>> The conclusion are the same. > > I don't think so. Certainly there is a distinction between intervals > derived solely from the 3rd harmonic and those derived from both the > 3rd and 5th harmonics. That's the distinction we've been discussing.
> >> India got their tuning from !4th century Persian theory. From the > mouth of a master BTW, Amiya Dusgupta. > > Even if this is true it does not apply to the tunings used in Indian > music today, which are derived from the drone. Have you studied with > a master of Indian vocal music? They will invariably teach you to > find the notes in the drone -- to tune your voice to the harmonics > you hear in the drone -- to actually merge your voice in the drone. > In real practice, this is where the notes come from.
> >> The first shows Indian tuning in terms of the Pythagorean >> series. The second with it schismatic equivalents. Not all of India >> does things the same way. They call it a subcontinent for a reason. > > These two approaches to identifying intervals are different, and > thus they're not talking about the same tunings. I have previously > stated my arguments for "the second" being the more accurate > representation of the intevals used in North Indian music today.
> > Perhaps I should have made it clearer that I have been talking about > North Indian classical music all along. The South Indian Carnatic > melakarta system is different. Though the book by P. SAMBMOORTHY
> is ostensibly about South Indian Music, he also discusses the tunings > used in North Indian "Hindustani" music. > > I admit I was too hasty in making a slight criticism of Sambmoorthy's > work. Looking at it further I think it is quite good. Kolinski's > work is indeed trash however.
> >> The drone came later in Indian music. > > All my comments have been about the system of tuning used in North > Indian classical music. I don't have too many recordings in my > collection made a couple thousand years ago, nor even a couple > hundred! (Recording technology seems to have been somewhat lacking > in those days!) And the ancient Indian texts are, generously > speaking, less than precise on the tuning issue. > > If it is the case that "the drone came later" than the tuning theory > you wish to discuss, then it is also probably fair to say that none > of the speculated derivations of ancient tunings have even the > slightest relevance to the tunings used today. If it is true that > some contrived pythagorean tunings system was used in India PRE-
> DRONE, then the advent of the drone would have overthrown the old > tuning system completely and supplanted it with a tuning system based > on the audible harmonics within the drone, which is what is used > today.
> > So in talking about tunings used in North Indian classical music > today (the topic of my disccusion) and tunings that MAY (or may not, > no recordings to check!) have once anciently been used, we're talking > about "apples and oranges".
> >> But there is a big variety about the theoretical tunings and the > practice. > > This is true, and is an area I've avoided getting into in my > discussion. Even today the actual practice may vary significantly > from any coherent theory. One huge limitation in our discussion (and > in the theory) is that the essential technique of evoking and > sustaining the "rasa" of a given raga involves the use of all the > pitches "between the notes". The pitch areas between the notes > comprise much of the actual Indian music heard in performance. The > svaras (notes) are the nodal points -- the points of maximum > resonance -- that demarcate the broader pitch areas. In a full > performance of any raga it is almost certain that all points on the > entire pitch spectrum within an octave are sounded at some point or > other in the performance.
> >> erotic ragas where you find the 7th harmonic >> used for instance. > > The 7th harmonic doesn't figure in theory, nor in common practice, > but certainly may appear in the performances of some artists who > probably have no idea they they're singing notes derived from the > seventh harmonic. I don't know of any raga that uses these tones as > principal notes consistently however. The singer is permitted a > great deal of freedom to use whatever tones they feel invoke the > spirit of the raga, though if they get too idiosyncratic with this, > other artists may feel that they have moved outside the scope of the > raga.
> >> Much of India has been only using 17 of the 22 for a >> while, according to this one master.
> > I think this is true, though I haven't pinned it down to precisely > 17. It does seem like the full range of shrutis is rarely used, but > of course no one is suggesting that all the shrutis are used in any > one performance in any case. The notion is that the full array of > shrutis constitute the fundamental pitch palette of the entire art > form, not a single performance.
> > If those of you interested in discussing this topic are primarily > interested in what you believe might be the ancient origins of scales > once used in India but which are no longer in use (perhaps since the > advent of the drone?), then the discussion has moved outside the area > of my knowledge and interest. I joined the discussion to provide > some information and insights about the shrutis as used in North > Indian classical music today, and at least since the age of > recording, and probably for at least some time before.
> > Because there are no recordings of the ancient music, you can > speculate to your heart's content about what pitches they may have > been using in actual practice, but you can never prove your points > nor can anyone disprove them. At best you can argue about what you > think the ancient (rather enigmatic) texts are saying.
> > But if you want to understand the practice of Indian music today, I > think you will have to confine yourself to considering the singable > tones. Pitches derived theoretically from long strings of compounded > ratios are neither audible nor singable within the soundscape of the > sa-pa drone of the tamboura and are thus outside the scope of Indian > music in practice.
> > I think this discussion has had some value up to this point, but if > it is going to degenerate into unprovable speculations about what > tunings were used by ancient Indian musicians in their practice, I am > no longer interested. > > However, if anyone has anything of substance to add > about the use of tunings in North Indian raga today, that would be > interesting. For example, can you give me an example of any > recordings by any acknowledged master who uses pitches derived from > the seventh harmonic as a regular part of his or her musical > vocabulary? Now that would be interesting!

🔗Andreas Sparschuh <a_sparschuh@yahoo.com>

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> .... even the Greeks thought beyond 5 limit.
>.... we are up to 18-19 and beyond.

Here comes an 53-ADO that contains exactly the harmonic
overtone series:

21 : 19 : 17 : 15 : 13 : 11 : 9 : 7 : 5 : 3 : 1 on the pitches
E/ : D//: Db\: A#/: Ab : F :D\\: A/: D#:G\\: C\\

Legenda of 2 types of accidentials:

1.Commatic:
'/' elevation about an comma sharper up
'\' depression about an comma flattened down

2. Major halftone
'#' ~ ///// ~ 3^7/2^11 = 2187:2048 apotome
'b' ~ \\\\\ ~ 1:# reverse apotome

Additional lower case letters in []s correspond to indian note names.

Pitch-classes as circle of 5ths

abs.name.rel.
256 C\\ _1:1_ middle C\\ unison
284 G\\ _3:2_
288 D\\ _9:8_
432 A\\ 27:16
324 E\\=Fb\ 81:64
486 B\\=Cb\ 243:128
364 Gb\ (729>)728 364 182 91:64
272 Db\ (273>)272 136 68 34 _17:16_
410 Ab\ (51 102 204<)205:128
306 Eb\ (615<)616 308154 77:64
462 Bb\ 231:128
347 F\ (693<)694 347:256
260 C\ (1041>)1040 520 260 130 65:64
390 G\ 195:128
293 D\ (585<)586 293:256
440 A\ (879<)880 440 220 110 55:32 http://en.wikipedia.org/wiki/A440
330 E\=Fb 165:128
495 B\=Cb 495:256
371 Gb (1485>)1484 742 371:256
278 Db (1113>1112 556 278 139:128
416 Ab (417>)416 208 104 52 26 _13:8_
312 Eb 39:32
468 Bb 117:64
352 F (351<)352 176 88 44 22 _11:8_
264 C 33:32
396 G 99:64
297 D 297:256
445 A (891>)890 445:256
334 E (1335<)1336 668 334 167:128
500 B (501>)500 250 125:64 = 5^3:2^8
375 F# 375:256
281 C# (1125>)1124 562 281:256
422 G# (843<)844 422 211:128
317 D# (633<)634 317:256
475 A# (951>)950 475:256
356 F/=E# (1425>)1424 712 356 178 89:64
267 C/=B# 267:256
400 G/ (801>)800 400 200 100 50 25:16
299 D/ (75 150 300>)299:128 [g]
448 A/ (897>)896 448 224 112 56 28 14 _7:4_ [n]
336 E/ _21:16_
504 B/ 63:32
378 F#/ 189:64
284 G#/ (567<)568 284 172 71:64
426 G#/ 213:128
320 D#/ (639>)640 320 160 80 40 20 10 _5:4_ [m]
480 A#/ _15:8_ [s]
360 F//=E#/ 45:32 [p]
270 C//=B#/ 135:128 [r]
405 G// 405:256 [d]
304 D// (1215<)1216 608 304 152 76 38 _19:16_
456 A// 57:32
342 E//=F\\ 171:128
512 B//=C\\ (513>)512 256 128 64 32 16 8 4 2 _1:1_ unison

that's in ascending order:

abs.name.rel.
256 C\\ _1:1_ middle C\\ unison
260 C\ 65:64
264 C 33:32
267 C/ 267:256
270 C// 135:128 [r]
272 Db\ _17:16_
278 Db 139:128
281 C# 281:256
284 C#/ 71:64
288 D\\ _9:8_
293 D\ 293:256
297 D 297:256
299 D/ 299:256 [g]
304 D// _19:16_
308 Eb\ 77:64
312 Eb 39:32
317 D# 317:256
320 D#/ _5:4_ [m]
324 E\\ 81:64
330 E\ 165:128
334 E 167:128
336 E/ _21:16_
342 E// 171:128
347 F\ 347:256
352 F _11:8_
356 F/ 89:64
360 F// 45:32 [p]
364 Gb\ 91:64
371 Gb 371:256
375 F# 375:256
378 F#/ 189:128
384 G\\ _3:2_
390 G\ 195:128
396 G 99:64
400 G\ 25:16
405 G// 405:256 [d]
410 Ab\ 205:128
416 Ab _13:8_
422 G# 211:128
426 G#/ 213:128
432 A\\ 27:16
440 A\ 55:32 http://en.wikipedia.org/wiki/A440
445 A 445:256
448 A/ _7:4_ [n]
456 A// 57:32
462 Bb\ 231:128
468 Bb 117:64
475 A# 475:256
480 A#/ _15:8_ [s]
486 B\\ 243:128
495 B\ 495:256
500 B 126:64
504 B/ 63:32
512 B//=C// 2:1

Indian music uses today 22-28 shruthis
http://forums.chandrakantha.com/viewtopic.php?t=1681&start=15&sid=4b177186546a592d78f549d61b3e4ce1
"explore all the posibilities for intonation for each of the notes,
you'll find the missing sruti-s. i'm reluctant to write it out because
it would take a while. there are actually 28 differnt pitches you can
get overtonally staying true to only one version of sa, shuddh ma, and
pa. then, because of the 3 overtones that we're using (from the
harmonics of sa-pa and ga and their recipricols), we get 3 options for
both re-s, komal ga, tivra ma, both dha-s and both ni-s. that adds up
to 28. now some of those are weird intervals, so the asthetics of
hindustani music says that 5 of those aren't used. leaving you the
magic number of 22"
.....
"Frightening though it may be, the 53 tone scale is very nearly
"pythagorean" - meaning the tones are almost completely symetrical
according to "just temperament" - what we use in Indian music."

Back to the original ancient sources:
Who in that group knows more about the historically vague
http://en.wikipedia.org/wiki/Bharata_Muni
's alleged experimental discovery of 53?
http://www.exoticindiaart.com/book/details/IDG155/
Is the corresponding chapter there understandable in that way?

How far can the questionable claims be taken as serious
that appear in an old legendary story
that he once would had tuned starting from SAdja
on the one hand: 26 times 5ths
on the other hand: 26 times 4ths
in order to yield as result an returning 53-chain of 5ths that
gets closed by matching at distance of 26 from SAdja in both directions?

Was Bahratha-muni really an independent predecessor of
http://en.wikipedia.org/wiki/Jing_Fang
http://en.wikipedia.org/wiki/53_equal_temperament#History
?
or even of the old greek
http://en.wikipedia.org/wiki/Philolaus
who divided according
http://en.wikipedia.org/wiki/Anicius_Manlius_Severinus_Boethius
's "de musica" the apotome into almost 5 Pyth.-Commata?

Quest:
Hence may we conclude from that:
That's the reason why the later (modern?)
22-tone subset extrated from
its 53 origin background appears
today to be somehow as incomplete alike
Newton's 14 out of 53 drawing:
http://www.societymusictheory.org/mto/issues/mto.93.0.3/mto.93.0.3.lindley.art
?
/tuning/topicId_71935.html#72165

But back from Newton's 53 to the indian nomenclature:
Attend the absolute shruti to Hz conversion of
south-indian pitches by P.Sambamoorthy's (1954 Madras)
http://anaphoria.com/sruti.PDF
on p.18 "114, TABLE X: Sankarabharana Just-Intonation"

240 [s] A#/
270 [r] C//
300 [g] D/ 299
320 [m] D#/
360 [p] F//
405 [d] G//
450 [n] A/
480 [s]'A#'

Have a lot of fun
in identifying the others 15=22-7 missing srutis.

A.S.

🔗monz <monz@tonalsoft.com>

Hi Cameron,

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:

> > [monz:]
> > Of course we don't know what tuning systems musicians
> > used before the dawn of writing, other than to examine
> > the spacing of holes on bone-flutes etc. But from the
> > earliest written music-theory, we can see that pythagorean
> > tuning was developed as a standard means of scale-building.
>
> I think it's important to remember that the first steps,
> of tuning up an instrument don't necessarily dictate the
> final scale, and I see no reason why a character/mood-based
> tetrachordal approach, like what Ozan calls "maqam" music,
> isn't downright antedeluvian. Pure fifths do the blocking,
> the specific flavors are learned by ear, that kind of thing.

Yes, again i think you're right on the mark here.

The ancient Greek tetrachord theory had the _hestotes_
(fixed notes) bounding the tetrachords, and these
were all 4/3 and 9/8 ratios, and there was never any
question about that. These equate to our modern notes
A B E a b e in the GPS and A B E a d in the LPS.

http://tonalsoft.com/enc/g/gps.aspx

http://tonalsoft.com/enc/l/lps.aspx

Then the two inner notes of the tetrachords were moveable,
and that's what all of the Greek tuning literature is about.

Originally, the moveable notes were certainly found by
means of pythagorean tuning, and thus the diatonic genus,
which later became known as the A-natural-minor scale,
was tuned in pythagorean form and lasted all the way
to the 1400s. The original full mathematical description
of this is in Plato's _Timaeus_, but the ratios can be
calculated from Philolaus's description c.450 BC, and
that is the earliest description of tuning from any
world culture which has clearly determined mathematics:

http://tonalsoft.com/enc/p/philolaus.aspx

According to Thrasyllus, the chromatic genus could also
be calculated by pythagorean means.

It's only the enharmonic genus which AFAIK was never given
with pythagorean ratios, and the obvious reason for that is
that you'd have to extend the pythagorean system all the
way to 3^24 to find an interval resembling a quarter-tone.

Then again, according to what i seem to be finding with
my examination of Boethius's description of Greek notation,
it's possible that the "diesis" (i.e., "quarter-tone") of
the enharmonic genus might actually have been a type of
comma, either pythagorean or syntonic, and thus really
more like an eighth-tone. I'm still not sure about this,
because of a discrepancy i see in two of the tetrachords,
and i've had to go back and study other descriptions of
the Greek notation; right now i'm working on that of
Aristides Quintilianus.

Anyway, Aristoxenus recognized pretty early on that
musicians were actually using all sorts of tunings for
those two moveable inner notes, and he decided to chuck
the whole idea of using ratios, and instead based his
measurements on logarithmic divisions of a tone, and he
defined "tone" as the difference between a "4th" and "5th",
which he said any musician could clearly hear. His method
was patently empirical, attempting to provide a clear
examination of pitches that were actually used by musicians.

Then many other writers followed Aristoxenus, who still
wanted to use ratios, to reconcile their belief in
pythagoreanism with the incontrovertible evidence which
Aristoxenus provided. There is so much about this that
John Chalmers was able to write an entire book on the subject:
_Divisions of the Tetrachord_, now available complete here:

http://lumma.org/tuning/chalmers/DivisionsOfTheTetrachord.pdf

The only thing i was really emphasizing to Marc was my
surprising find that so many ancient musical cultures
all described the oldest versions of their tunings in
pythagorean terms. The fact that other links exist,
such as shared versions of many various myths, shows
that the Sumerian, Indus, Egyptian, and ancient Greek
cultures did not develop in isolation. I find it interesting
to see these connections in music also.

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

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

----- Original Message -----
From: "hstraub64" <hstraub64@telesonique.net>
To: <tuning@yahoogroups.com>
Sent: 15 Aï¿½ustos 2007 ï¿½arï¿½amba 17:56
Subject: [tuning] Re: Magic[22] as srutis

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > From: "hstraub64" <hstraub64@...>
> > >
> > > The paragraph above does, to me, not appear to describe a
> > > difference between the western and indian paradigm but rather the
> > > notorious "theory lover" vs. "theory hater" debate, which I keep
> > > coming across again and again, inside western music as well.
> > >
> >
> > Believe it or not, that is exactly what transpired in a huge Turkish
> > Music discussion platform I took part in these recent days. You
> > could not guess the animosity certain people harbor against the
> > notion of temperament in the name of preserving tradition.
> >
>
> Oh, I believe it, without hesitation.
>
> To be fair, among the "theory-lovers" (of which I am one), there is
> sometimes a tendency to overestimate the theory. I gotta remind myself
> sometimes that an adequate understanding and application of any theory
> implies knowing where the limits of the theory are...
>

Which are?

> >
> > > I cannot judge the theoretical texts - they may well be as wrong
> > > as you said. However, to me this is not a sign that abstract
> > > intellectual systems do not fit at all but rather that an
> > > appropriate, fitting system has not been found yet.
> > >
> >
> > 79/80 MOS 159-tET: try it, you'll love it.
> >
>
> So 79/80 MOS 159-tET works for indian music, too?
>
> It is on my agenda, in any case. There are just, um, so many notes in
> it... ;-)

That is why it ought to be compatible with many microtonal music cultures.

> --
> Hans Straub
>
>
>

Oz.

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

Fascinating.

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 16 Aï¿½ustos 2007 Perï¿½embe 1:08
Subject: [tuning] pythagorean origins of tuning systems (was: Magic[22] as
srutis)

> Hi Cameron,
>
>
> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
>
> > > [monz:]
> > > Of course we don't know what tuning systems musicians
> > > used before the dawn of writing, other than to examine
> > > the spacing of holes on bone-flutes etc. But from the
> > > earliest written music-theory, we can see that pythagorean
> > > tuning was developed as a standard means of scale-building.
> >
> > I think it's important to remember that the first steps,
> > of tuning up an instrument don't necessarily dictate the
> > final scale, and I see no reason why a character/mood-based
> > tetrachordal approach, like what Ozan calls "maqam" music,
> > isn't downright antedeluvian. Pure fifths do the blocking,
> > the specific flavors are learned by ear, that kind of thing.
>
>
> Yes, again i think you're right on the mark here.
>
>
> The ancient Greek tetrachord theory had the _hestotes_
> (fixed notes) bounding the tetrachords, and these
> were all 4/3 and 9/8 ratios, and there was never any
> question about that. These equate to our modern notes
> A B E a b e in the GPS and A B E a d in the LPS.
>
> http://tonalsoft.com/enc/g/gps.aspx
>
> http://tonalsoft.com/enc/l/lps.aspx
>
>
> Then the two inner notes of the tetrachords were moveable,
> and that's what all of the Greek tuning literature is about.
>
> Originally, the moveable notes were certainly found by
> means of pythagorean tuning, and thus the diatonic genus,
> which later became known as the A-natural-minor scale,
> was tuned in pythagorean form and lasted all the way
> to the 1400s. The original full mathematical description
> of this is in Plato's _Timaeus_, but the ratios can be
> calculated from Philolaus's description c.450 BC, and
> that is the earliest description of tuning from any
> world culture which has clearly determined mathematics:
>
> http://tonalsoft.com/enc/p/philolaus.aspx
>
>
> According to Thrasyllus, the chromatic genus could also
> be calculated by pythagorean means.
>
> It's only the enharmonic genus which AFAIK was never given
> with pythagorean ratios, and the obvious reason for that is
> that you'd have to extend the pythagorean system all the
> way to 3^24 to find an interval resembling a quarter-tone.
>
> Then again, according to what i seem to be finding with
> my examination of Boethius's description of Greek notation,
> it's possible that the "diesis" (i.e., "quarter-tone") of
> the enharmonic genus might actually have been a type of
> comma, either pythagorean or syntonic, and thus really
> more like an eighth-tone. I'm still not sure about this,
> because of a discrepancy i see in two of the tetrachords,
> and i've had to go back and study other descriptions of
> the Greek notation; right now i'm working on that of
> Aristides Quintilianus.
>
> Anyway, Aristoxenus recognized pretty early on that
> musicians were actually using all sorts of tunings for
> those two moveable inner notes, and he decided to chuck
> the whole idea of using ratios, and instead based his
> measurements on logarithmic divisions of a tone, and he
> defined "tone" as the difference between a "4th" and "5th",
> which he said any musician could clearly hear. His method
> was patently empirical, attempting to provide a clear
> examination of pitches that were actually used by musicians.
>
> Then many other writers followed Aristoxenus, who still
> wanted to use ratios, to reconcile their belief in
> pythagoreanism with the incontrovertible evidence which
> Aristoxenus provided. There is so much about this that
> John Chalmers was able to write an entire book on the subject:
> _Divisions of the Tetrachord_, now available complete here:
>
> http://lumma.org/tuning/chalmers/DivisionsOfTheTetrachord.pdf
>
>
> The only thing i was really emphasizing to Marc was my
> surprising find that so many ancient musical cultures
> all described the oldest versions of their tunings in
> pythagorean terms. The fact that other links exist,
> such as shared versions of many various myths, shows
> that the Sumerian, Indus, Egyptian, and ancient Greek
> cultures did not develop in isolation. I find it interesting
> to see these connections in music also.
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
>
>
>
>
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
> Yahoo! Groups Links
>
>
>

🔗Cameron Bobro <misterbobro@yahoo.com>

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Cameron,
>
>
> --- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@>
wrote:
>
> > > [monz:]
> > > Of course we don't know what tuning systems musicians
> > > used before the dawn of writing, other than to examine
> > > the spacing of holes on bone-flutes etc. But from the
> > > earliest written music-theory, we can see that pythagorean
> > > tuning was developed as a standard means of scale-building.
> >
> > I think it's important to remember that the first steps,
> > of tuning up an instrument don't necessarily dictate the
> > final scale, and I see no reason why a character/mood-based
> > tetrachordal approach, like what Ozan calls "maqam" music,
> > isn't downright antedeluvian. Pure fifths do the blocking,
> > the specific flavors are learned by ear, that kind of thing.
>
>
> Yes, again i think you're right on the mark here.
>
>
> The ancient Greek tetrachord theory had the _hestotes_
> (fixed notes) bounding the tetrachords, and these
> were all 4/3 and 9/8 ratios, and there was never any
> question about that. These equate to our modern notes
> A B E a b e in the GPS and A B E a d in the LPS.
>
> http://tonalsoft.com/enc/g/gps.aspx
>
> http://tonalsoft.com/enc/l/lps.aspx
>
>
> Then the two inner notes of the tetrachords were moveable,
> and that's what all of the Greek tuning literature is about.
>
> Originally, the moveable notes were certainly found by
> means of pythagorean tuning, and thus the diatonic genus,
> which later became known as the A-natural-minor scale,
> was tuned in pythagorean form and lasted all the way
> to the 1400s. The original full mathematical description
> of this is in Plato's _Timaeus_, but the ratios can be
> calculated from Philolaus's description c.450 BC, and
> that is the earliest description of tuning from any
> world culture which has clearly determined mathematics:
>
> http://tonalsoft.com/enc/p/philolaus.aspx
>
>
> According to Thrasyllus, the chromatic genus could also
> be calculated by pythagorean means.
>
> It's only the enharmonic genus which AFAIK was never given
> with pythagorean ratios, and the obvious reason for that is
> that you'd have to extend the pythagorean system all the
> way to 3^24 to find an interval resembling a quarter-tone.
>
> Then again, according to what i seem to be finding with
> my examination of Boethius's description of Greek notation,
> it's possible that the "diesis" (i.e., "quarter-tone") of
> the enharmonic genus might actually have been a type of
> comma, either pythagorean or syntonic, and thus really
> more like an eighth-tone. I'm still not sure about this,
> because of a discrepancy i see in two of the tetrachords,
> and i've had to go back and study other descriptions of
> the Greek notation; right now i'm working on that of
> Aristides Quintilianus.
>
> Anyway, Aristoxenus recognized pretty early on that
> musicians were actually using all sorts of tunings for
> those two moveable inner notes, and he decided to chuck
> the whole idea of using ratios, and instead based his
> measurements on logarithmic divisions of a tone, and he
> defined "tone" as the difference between a "4th" and "5th",
> which he said any musician could clearly hear. His method
> was patently empirical, attempting to provide a clear
> examination of pitches that were actually used by musicians.
>
> Then many other writers followed Aristoxenus, who still
> wanted to use ratios, to reconcile their belief in
> pythagoreanism with the incontrovertible evidence which
> Aristoxenus provided. There is so much about this that
> John Chalmers was able to write an entire book on the subject:
> _Divisions of the Tetrachord_, now available complete here:
>
> http://lumma.org/tuning/chalmers/DivisionsOfTheTetrachord.pdf

Yes, this is a great book.
>
>
> The only thing i was really emphasizing to Marc was my
> surprising find that so many ancient musical cultures
> all described the oldest versions of their tunings in
> pythagorean terms. The fact that other links exist,
> such as shared versions of many various myths, shows
> that the Sumerian, Indus, Egyptian, and ancient Greek
> cultures did not develop in isolation. I find it interesting
> to see these connections in music also.

I think Occam's razor favors a dispersionist view, and
also favors the idea that shared ideas are always going
to be preceded by and tempered by shared physical realities,
ie the integer harmonic series (or lack of it in percussion-based
music theory, etc.).

I also find that the ancient approach above is the musically
productive, for me at least, but I picture and practice it
in a certain way, not with chains of fifths or lattices, but
with nestled spheres. The main thing is, there are "fixed" reference
points from the lower harmonic series and expressive tones from
other relationships.

-Cameron Bobro

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

hiandreas
but it is not 53-ADO , it is 256-ADO.

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web site?? ???? ????? ?????? <http://240edo.googlepages.com/>

My farsi page in Harmonytalk ???? ??????? ?? ??????? ??? <http://www.harmonytalk.com/mohajeri>

Shaahin Mohajeri in Wikipedia ????? ?????? ??????? ??????? ???? ???? <http://en.wikipedia.org/wiki/Shaahin_mohajeri>

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Andreas Sparschuh
Sent: Wednesday, August 15, 2007 10:08 PM
To: tuning@yahoogroups.com
Subject: [tuning] 21:19:17:15:13:11:9:7:5:3:1 in an 53-ADO, was: Re: Magic[22] as srutis

--- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com> , Kraig Grady <kraiggrady@...> wrote:
>
> .... even the Greeks thought beyond 5 limit.
>.... we are up to 18-19 and beyond.

Here comes an 53-ADO that contains exactly the harmonic
overtone series:

21 : 19 : 17 : 15 : 13 : 11 : 9 : 7 : 5 : 3 : 1 on the pitches
E/ : D//: Db\: A#/: Ab : F :D\\: A/: D#:G\\: C\\

Legenda of 2 types of accidentials:

1.Commatic:
'/' elevation about an comma sharper up
'\' depression about an comma flattened down

2. Major halftone
'#' ~ ///// ~ 3^7/2^11 = 2187:2048 apotome
'b' ~ \\\\\ ~ 1:# reverse apotome

Additional lower case letters in []s correspond to indian note names.

Pitch-classes as circle of 5ths

abs.name.rel.
256 C\\ _1:1_ middle C\\ unison
284 G\\ _3:2_
288 D\\ _9:8_
432 A\\ 27:16
324 E\\=Fb\ 81:64
486 B\\=Cb\ 243:128
364 Gb\ (729>)728 364 182 91:64
272 Db\ (273>)272 136 68 34 _17:16_
410 Ab\ (51 102 204<)205:128
306 Eb\ (615<)616 308154 77:64
462 Bb\ 231:128
347 F\ (693<)694 347:256
260 C\ (1041>)1040 520 260 130 65:64
390 G\ 195:128
293 D\ (585<)586 293:256
440 A\ (879<)880 440 220 110 55:32 http://en.wikipedia.org/wiki/A440 <http://en.wikipedia.org/wiki/A440>
330 E\=Fb 165:128
495 B\=Cb 495:256
371 Gb (1485>)1484 742 371:256
278 Db (1113>1112 556 278 139:128
416 Ab (417>)416 208 104 52 26 _13:8_
312 Eb 39:32
468 Bb 117:64
352 F (351<)352 176 88 44 22 _11:8_
264 C 33:32
396 G 99:64
297 D 297:256
445 A (891>)890 445:256
334 E (1335<)1336 668 334 167:128
500 B (501>)500 250 125:64 = 5^3:2^8
375 F# 375:256
281 C# (1125>)1124 562 281:256
422 G# (843<)844 422 211:128
317 D# (633<)634 317:256
475 A# (951>)950 475:256
356 F/=E# (1425>)1424 712 356 178 89:64
267 C/=B# 267:256
400 G/ (801>)800 400 200 100 50 25:16
299 D/ (75 150 300>)299:128 [g]
448 A/ (897>)896 448 224 112 56 28 14 _7:4_ [n]
336 E/ _21:16_
504 B/ 63:32
378 F#/ 189:64
284 G#/ (567<)568 284 172 71:64
426 G#/ 213:128
320 D#/ (639>)640 320 160 80 40 20 10 _5:4_ [m]
480 A#/ _15:8_ [s]
360 F//=E#/ 45:32 [p]
270 C//=B#/ 135:128 [r]
405 G// 405:256 [d]
304 D// (1215<)1216 608 304 152 76 38 _19:16_
456 A// 57:32
342 E//=F\\ 171:128
512 B//=C\\ (513>)512 256 128 64 32 16 8 4 2 _1:1_ unison

that's in ascending order:

abs.name.rel.
256 C\\ _1:1_ middle C\\ unison
260 C\ 65:64
264 C 33:32
267 C/ 267:256
270 C// 135:128 [r]
272 Db\ _17:16_
278 Db 139:128
281 C# 281:256
284 C#/ 71:64
288 D\\ _9:8_
293 D\ 293:256
297 D 297:256
299 D/ 299:256 [g]
304 D// _19:16_
308 Eb\ 77:64
312 Eb 39:32
317 D# 317:256
320 D#/ _5:4_ [m]
324 E\\ 81:64
330 E\ 165:128
334 E 167:128
336 E/ _21:16_
342 E// 171:128
347 F\ 347:256
352 F _11:8_
356 F/ 89:64
360 F// 45:32 [p]
364 Gb\ 91:64
371 Gb 371:256
375 F# 375:256
378 F#/ 189:128
384 G\\ _3:2_
390 G\ 195:128
396 G 99:64
400 G\ 25:16
405 G// 405:256 [d]
410 Ab\ 205:128
416 Ab _13:8_
422 G# 211:128
426 G#/ 213:128
432 A\\ 27:16
440 A\ 55:32 http://en.wikipedia.org/wiki/A440 <http://en.wikipedia.org/wiki/A440>
445 A 445:256
448 A/ _7:4_ [n]
456 A// 57:32
462 Bb\ 231:128
468 Bb 117:64
475 A# 475:256
480 A#/ _15:8_ [s]
486 B\\ 243:128
495 B\ 495:256
500 B 126:64
504 B/ 63:32
512 B//=C// 2:1

Indian music uses today 22-28 shruthis
http://forums.chandrakantha.com/viewtopic.php?t=1681&start=15&sid=4b177186546a592d78f549d61b3e4ce1 <http://forums.chandrakantha.com/viewtopic.php?t=1681&start=15&sid=4b177186546a592d78f549d61b3e4ce1>
"explore all the posibilities for intonation for each of the notes,
you'll find the missing sruti-s. i'm reluctant to write it out because
it would take a while. there are actually 28 differnt pitches you can
get overtonally staying true to only one version of sa, shuddh ma, and
pa. then, because of the 3 overtones that we're using (from the
harmonics of sa-pa and ga and their recipricols), we get 3 options for
both re-s, komal ga, tivra ma, both dha-s and both ni-s. that adds up
to 28. now some of those are weird intervals, so the asthetics of
hindustani music says that 5 of those aren't used. leaving you the
magic number of 22"
.....
"Frightening though it may be, the 53 tone scale is very nearly
"pythagorean" - meaning the tones are almost completely symetrical
according to "just temperament" - what we use in Indian music."

Back to the original ancient sources:
Who in that group knows more about the historically vague
http://en.wikipedia.org/wiki/Bharata_Muni <http://en.wikipedia.org/wiki/Bharata_Muni>
's alleged experimental discovery of 53?
http://www.exoticindiaart.com/book/details/IDG155/ <http://www.exoticindiaart.com/book/details/IDG155/>
Is the corresponding chapter there understandable in that way?

But back from Newton's 53 to the indian nomenclature:
Attend the absolute shruti to Hz conversion of
south-indian pitches by P.Sambamoorthy's (1954 Madras)
http://anaphoria.com/sruti.PDF <http://anaphoria.com/sruti.PDF>
on p.18 "114, TABLE X: Sankarabharana Just-Intonation"

240 [s] A#/
270 [r] C//
300 [g] D/ 299
320 [m] D#/
360 [p] F//
405 [d] G//
450 [n] A/
480 [s]'A#'

Have a lot of fun
in identifying the others 15=22-7 missing srutis.

A.S.

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

and you will see this cultural overlap by musical instrument.

http://acousticsoftombak.googlepages.com/gobletdrumsthroughhistory

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web site?? ???? ????? ?????? <http://240edo.googlepages.com/>

My farsi page in Harmonytalk ???? ??????? ?? ??????? ??? <http://www.harmonytalk.com/mohajeri>

Shaahin Mohajeri in Wikipedia ????? ?????? ??????? ??????? ???? ???? <http://en.wikipedia.org/wiki/Shaahin_mohajeri>

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of monz
Sent: Thursday, August 16, 2007 1:39 AM
To: tuning@yahoogroups.com
Subject: [tuning] pythagorean origins of tuning systems (was: Magic[22] as srutis)

Hi Cameron,

--- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com> , "Cameron Bobro" <misterbobro@...> wrote:

Yes, again i think you're right on the mark here.

http://tonalsoft.com/enc/g/gps.aspx <http://tonalsoft.com/enc/g/gps.aspx>

http://tonalsoft.com/enc/l/lps.aspx <http://tonalsoft.com/enc/l/lps.aspx>

Then the two inner notes of the tetrachords were moveable,
and that's what all of the Greek tuning literature is about.

http://tonalsoft.com/enc/p/philolaus.aspx <http://tonalsoft.com/enc/p/philolaus.aspx>

According to Thrasyllus, the chromatic genus could also
be calculated by pythagorean means.

http://lumma.org/tuning/chalmers/DivisionsOfTheTetrachord.pdf <http://lumma.org/tuning/chalmers/DivisionsOfTheTetrachord.pdf>

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

🔗Cameron Bobro <misterbobro@yahoo.com>

🔗hstraub64 <hstraub64@telesonique.net>

🔗Andreas Sparschuh <a_sparschuh@yahoo.com>

--- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@...> wrote:
>
> hiandreas
> but it is not 53-ADO , it is 256-ADO.
>
http://240edo.googlepages.com/arithmeticrationaldivisionsofoctave
suggests for "256-ADO" the harmonic series from the 256th to 512th
harmonic partials consisting in 256 individual pitch classes:

512:511:510:509:... : : : ...:258:257:256

but i intended in
/tuning/topicId_63593.html#72755
to select from that only a subset
that amounts barely in 53 tones out of 256-ADO:

512:504:500:495:485:485:480:475:... ::: ...:270:267:260:256

click on: 'meassage-options', than 'Use Fixed Widh Font'

!53out_of256ADO.scl
!
53-tones out of the harmonic partials 256...512Hz absolute
53
!
! 1/1 ! 00; 256 C\\ middle C\\ unison root
65/64 ! 01; 260 C\ mediant of the 13th partial
33/32 ! 02; 264 C dominant of the 11th partial
267/256 ! 03; 267 C/
270/256 ! 04; 270 C// [r]
17/16 ! 05; 272 Db\ 17th partial
139/128 ! 06; 278 Db
281/256 ! 07; 281 C#
71/64 ! 08; 284 C#/
9/8 ! 09; 288 D\\ 9th partial
293/256 ! 10; 293 D\
297/256 ! 11; 297 D
299/256 ! 12; 299 D/ [g=300]
19/16 ! 13; 304 D// 19th partial
77/64 ! 14; 308 Eb\ harmonic 7th of the 11th partial
39/32 ! 15; 312 Eb dominant of the 13th partial
317/256 ! 16; 317 D#
5/4 ! 17; 329 D#/ 5th partial [m]
81/64 ! 18; 324 E\\ ditone
165/128 ! 19; 330 E\ dominantic mediant of the 11th partial
167/128 ! 20; 334 E
21/16 ! 21; 336 E/ 21th partial=dominant of the 7th partial
171/128 ! 22; 342 E// double-dominant of the 19th partial
347/256 ! 23; 347 F\
11/8 ! 24; 352 F 11th partial
89/64 ! 25; 356 F/
45/32 ! 26; 360 F// double-dominantic mediant [p]
91/64 ! 27; 364 Gb\
371/256 ! 28; 371 Gb
375/256 ! 29; 375 F# domiantic triple mediant
189/128 ! 30; 378 F#/
3/2 ! 31; 384 G\\ 3rd partial = domiant
195/128 ! 32; 390 G\ mediant of the 19th partial
99/64 ! 33; 396 G double-domiant of the 11th partial
25/16 ! 34; 400 G\ double-mediant
405/256 ! 35; 405 G// mediant of the ditone [d]
205/128 ! 36; 410 Ab\ mediant of the 41th partial
13/8 ! 37; 416 Ab 13th partial
211/128 ! 38; 422 G#
213/128 ! 39; 426 G#/
27/16 ! 40; 432 A\\ triple-dominant
55/32 ! 41; 440 A\ http://en.wikipedia.org/wiki/A440
445/256 ! 42; 445 A
7/4 ! 43; 448 A/ 7th partial [n]
57/32 ! 44; 456 A// dominant of the 19th partial
231/128 ! 45; 462 Bb\
117/64 ! 46; 468 Bb double-dominant of the 13th partial
475/256 ! 47; 475 A# double-mediant of the 19th partial
15/8 ! 48; 480 A#/ 15th partial = domiantic mediant [s]
243/128 ! 49; 486 B\\ 3^5/2^7
495/256 ! 50; 495 B\ double-dominant mediant of the 11th partial
125/64 ! 51; 500 B triple mediant
63/32 ! 52; 508 B/ double-dominant of the 7th partial
2/1 ! 53; 512 B//=C//' octave

compared to the famous
http://en.wikipedia.org/wiki/Harry_Partch's_43-tone_scale
that 5th-generated gamut contains by definition
in all denominators alone powers of 2 exclusively.

Hence all resulting pitch-frequency values consist in:
http://en.wikipedia.org/wiki/Dyadic_fraction
s for exact representation in dual floating-point arithmetic,
without any objectonable rounding errors as in
the problematic
http://en.wikipedia.org/wiki/53_equal_temperament
that fails to match partials 21:19:17:15:13:9:7:5:3:1 precisely.

Classical literature:
http://diapason.xentonic.org/ttl/ttl04.html

Keyboard:
http://tardis.dl.ac.uk/FreeReed/English/organ_book/node17.html
"The Enharmonic Harmonium of Bosanquet was another experiment, which
now belongs to the Science Museum, South Kensington, London. It was
built in 1872-3 and has 53 differently pitched notes per octave..."

Pics:
http://tardis.dl.ac.uk/FreeReed/English/organ_book/pictures/10213657.jpg
http://tardis.dl.ac.uk/FreeReed/English/organ_book/pictures/rfg-0101.jpg
http://tardis.dl.ac.uk/FreeReed/English/organ_book/bosanquet_saltaire.html
http://www.freewebs.com/mireut/hrmonium.htm

Sincerly
A.S.

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

----- Original Message -----
From: "hstraub64" <hstraub64@telesonique.net>
To: <tuning@yahoogroups.com>
Sent: 17 Aï¿½ustos 2007 Cuma 18:41
Subject: [tuning] Re: Magic[22] as srutis

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> >
> > ----- Original Message -----
> > From: "hstraub64" <hstraub64@...>
> > >
> > > To be fair, among the "theory-lovers" (of which I am one), there
> > > is sometimes a tendency to overestimate the theory. I gotta remind
> > > myself sometimes that an adequate understanding and application of
> > > any theory implies knowing where the limits of the theory are...
> > >
> >
> > Which are?
> >
>
> Well, I have nothing specific in mind right now - it is more a matter
> of philosophy. It's just good to keep in mind that music is indeed
> more than "applying abstract intellectual systems". Which holds for
> any music, including western music.
>

But without theory of some kind, there surely can be no music?

> > >
> > > So 79/80 MOS 159-tET works for indian music, too?
> > >
> > > It is on my agenda, in any case. There are just, um, so many notes
> > > in
> > > it... ;-)
> >
> > That is why it ought to be compatible with many microtonal music
> > cultures.
> >
>
> Only because of that (the number of notes)?
> That would be a kind of a trivial statement, and then I could take
> 79TET or 87TET or 120TET or whatever, too...
>
> But you sure chose 79MOS 159-tET because it has, besides the number of
> notes, a number of specific properties that make it especially
> suitable for maqam music. (I do not know the details yet - not yet
> having studied your dissertation, which I will, however.) I would be
> interested to know whether these properties would qualify 79MOS
> 159-tET for indian music, too?

You are right, 79/80 MOS 159-tET has properties that make it a viable
candidate as master tuning of Maqam Music. Let's just say it has so many
"right" notes.

> --
> Hans Straub
>
>
>

Oz.

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

hi dear andreas
now , i am agree with 53 out_of 256-ADO.scl

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web site?? ???? ????? ?????? <http://240edo.googlepages.com/>

My farsi page in Harmonytalk ???? ??????? ?? ??????? ??? <http://www.harmonytalk.com/mohajeri>

Shaahin Mohajeri in Wikipedia ????? ?????? ??????? ??????? ???? ???? <http://en.wikipedia.org/wiki/Shaahin_mohajeri>

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Andreas Sparschuh
Sent: Friday, August 17, 2007 7:44 PM
To: tuning@yahoogroups.com
Subject: [tuning] 21:19:17:15:13:11:9:7:5:3:1 in an 53-ADO, was: Re: Magic[22] as srutis

--- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com> , "Mohajeri Shahin" <shahinm@...> wrote:
>
> hiandreas
> but it is not 53-ADO , it is 256-ADO.
>
http://240edo.googlepages.com/arithmeticrationaldivisionsofoctave <http://240edo.googlepages.com/arithmeticrationaldivisionsofoctave>
suggests for "256-ADO" the harmonic series from the 256th to 512th
harmonic partials consisting in 256 individual pitch classes:

512:511:510:509:... : : : ...:258:257:256

but i intended in
/tuning/topicId_63593.html#72755 </tuning/topicId_63593.html#72755>
to select from that only a subset
that amounts barely in 53 tones out of 256-ADO:

512:504:500:495:485:485:480:475:... ::: ...:270:267:260:256

click on: 'meassage-options', than 'Use Fixed Widh Font'

!53out_of256ADO.scl
!
53-tones out of the harmonic partials 256...512Hz absolute
53
!
! 1/1 ! 00; 256 C\\ middle C\\ unison root
65/64 ! 01; 260 C\ mediant of the 13th partial
33/32 ! 02; 264 C dominant of the 11th partial
267/256 ! 03; 267 C/
270/256 ! 04; 270 C// [r]
17/16 ! 05; 272 Db\ 17th partial
139/128 ! 06; 278 Db
281/256 ! 07; 281 C#
71/64 ! 08; 284 C#/
9/8 ! 09; 288 D\\ 9th partial
293/256 ! 10; 293 D\
297/256 ! 11; 297 D
299/256 ! 12; 299 D/ [g=300]
19/16 ! 13; 304 D// 19th partial
77/64 ! 14; 308 Eb\ harmonic 7th of the 11th partial
39/32 ! 15; 312 Eb dominant of the 13th partial
317/256 ! 16; 317 D#
5/4 ! 17; 329 D#/ 5th partial [m]
81/64 ! 18; 324 E\\ ditone
165/128 ! 19; 330 E\ dominantic mediant of the 11th partial
167/128 ! 20; 334 E
21/16 ! 21; 336 E/ 21th partial=dominant of the 7th partial
171/128 ! 22; 342 E// double-dominant of the 19th partial
347/256 ! 23; 347 F\
11/8 ! 24; 352 F 11th partial
89/64 ! 25; 356 F/
45/32 ! 26; 360 F// double-dominantic mediant [p]
91/64 ! 27; 364 Gb\
371/256 ! 28; 371 Gb
375/256 ! 29; 375 F# domiantic triple mediant
189/128 ! 30; 378 F#/
3/2 ! 31; 384 G\\ 3rd partial = domiant
195/128 ! 32; 390 G\ mediant of the 19th partial
99/64 ! 33; 396 G double-domiant of the 11th partial
25/16 ! 34; 400 G\ double-mediant
405/256 ! 35; 405 G// mediant of the ditone [d]
205/128 ! 36; 410 Ab\ mediant of the 41th partial
13/8 ! 37; 416 Ab 13th partial
211/128 ! 38; 422 G#
213/128 ! 39; 426 G#/
27/16 ! 40; 432 A\\ triple-dominant
55/32 ! 41; 440 A\ http://en.wikipedia.org/wiki/A440 <http://en.wikipedia.org/wiki/A440>
445/256 ! 42; 445 A
7/4 ! 43; 448 A/ 7th partial [n]
57/32 ! 44; 456 A// dominant of the 19th partial
231/128 ! 45; 462 Bb\
117/64 ! 46; 468 Bb double-dominant of the 13th partial
475/256 ! 47; 475 A# double-mediant of the 19th partial
15/8 ! 48; 480 A#/ 15th partial = domiantic mediant [s]
243/128 ! 49; 486 B\\ 3^5/2^7
495/256 ! 50; 495 B\ double-dominant mediant of the 11th partial
125/64 ! 51; 500 B triple mediant
63/32 ! 52; 508 B/ double-dominant of the 7th partial
2/1 ! 53; 512 B//=C//' octave

compared to the famous
http://en.wikipedia.org/wiki/Harry_Partch <http://en.wikipedia.org/wiki/Harry_Partch> 's_43-tone_scale
that 5th-generated gamut contains by definition
in all denominators alone powers of 2 exclusively.

Hence all resulting pitch-frequency values consist in:
http://en.wikipedia.org/wiki/Dyadic_fraction <http://en.wikipedia.org/wiki/Dyadic_fraction>
s for exact representation in dual floating-point arithmetic,
without any objectonable rounding errors as in
the problematic
http://en.wikipedia.org/wiki/53_equal_temperament <http://en.wikipedia.org/wiki/53_equal_temperament>
that fails to match partials 21:19:17:15:13:9:7:5:3:1 precisely.

Classical literature:
http://diapason.xentonic.org/ttl/ttl04.html <http://diapason.xentonic.org/ttl/ttl04.html>

Keyboard:
http://tardis.dl.ac.uk/FreeReed/English/organ_book/node17.html <http://tardis.dl.ac.uk/FreeReed/English/organ_book/node17.html>
"The Enharmonic Harmonium of Bosanquet was another experiment, which
now belongs to the Science Museum, South Kensington, London. It was
built in 1872-3 and has 53 differently pitched notes per octave..."

Pics:
http://tardis.dl.ac.uk/FreeReed/English/organ_book/pictures/10213657.jpg <http://tardis.dl.ac.uk/FreeReed/English/organ_book/pictures/10213657.jpg>
http://tardis.dl.ac.uk/FreeReed/English/organ_book/pictures/rfg-0101.jpg <http://tardis.dl.ac.uk/FreeReed/English/organ_book/pictures/rfg-0101.jpg>
http://tardis.dl.ac.uk/FreeReed/English/organ_book/bosanquet_saltaire.html <http://tardis.dl.ac.uk/FreeReed/English/organ_book/bosanquet_saltaire.html>
http://www.freewebs.com/mireut/hrmonium.htm <http://www.freewebs.com/mireut/hrmonium.htm>

Sincerly
A.S.

🔗hstraub64 <hstraub64@telesonique.net>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

🔗monz <monz@tonalsoft.com>

Hi Hans and Ozan,

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> So, it is safe to say that theory is embedded in music
> is embedded in theory?
>
> I assume, even a primeval music surely had some
> primeval theory to go with it.
>
> Oz.

Sticking a tube in one's mouth and blowing,
while moving the fingers to cover and uncover
holes drilled in the side of the tube,
is not what most would call a "natural act".

So apart from solo and small-ensemble singing
(duet, trio, quartet), which *is* a natural
extension of speaking (and in fact, some scholars
believe that singing predated speaking), making music
always involves some kind of abstraction regarding
various measurements of pitch and time, and various
techniques for producing and modifying the sound
-- those would fall under "theory".

I've seen it pointed out in this thread that
the theory describes an idea first, and the music
follows as an embodiment of that theory:
"proscriptive" theory.

This is true for some music-and-theory relationships,
but not all. I would venture to say that most of
the time, the theories come *after* the rule-breaking
inventive music: "descriptive" theory.

At any rate, this is approximately how things went:

c.50,000 BC - human acquisition of spoken language.
This is the approximate date of the big migration
of "Cro-Magnon" _homo sapiens_ out of Africa, and
the sudden increased sophistication of stone tool design
(and thus the beginning of what we now call the
"Upper Paleolithic" period). Because spoken language
is ubiquitous today among human cultures in every
corner of the world, most scholars believe that it
must have originated in Africa before the migration.
There's still debate on which came first, speaking
or singing, but in any case one could surely say that
they had emerged approximately in parallel by this time.

c.3000 BC - recognition by the Sumerians of music
and singing as art forms. The Sumerians probably
began writing down music-theory not long after this,
but the oldest music-theory cuneiform tablets which
we know about so far are Babylonian, from c.1600 BC.
However, the roots of the Akkadian words on these
tablets are Sumerian logograms which embrace the
essential concepts, thus arguing in favor of an
older Sumerian origin of the ideas.

However accurate or approximate one wishes to pin
down those dates, that's quite a long time-span
in which music-theory certainly existed but was
not written down.

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

🔗Klaus Schmirler <KSchmir@online.de>

Ozan Yarman schrieb:
> So, it is safe to say that theory is embedded in music is embedded in
> theory?
> > I assume, even a primeval music surely had some primeval theory to go with
> it.

I guess the listener's needs are the first "theory" (and the musician is the first listener). Do we want to get into a state? Do we want to imitate something? Are we - but this already needs set states and an educated audience to built upon - playing with emotions or expectations?

Then other cultural considerations come in. In our case, it's the idea that things are measurable, so they get measured (Is there a rhythm and timing group on the internet?). Conflict with the first ideas ensues - music changes and becomes rationalized into a new theory.

klaus

> > Oz.
> > ----- Original Message -----
> From: "hstraub64" <hstraub64@telesonique.net>
> To: <tuning@yahoogroups.com>
> Sent: 21 Aï¿½ustos 2007 Salï¿½ 12:27
> Subject: [tuning] Re: Magic[22] as srutis
> > >> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>>> But without theory of some kind, there surely can be no music?
>>>
>> Hmm, that may be one fo the key questions... I imagine there *can* be
>> music without theory (there must have been in the beginning) - just,
>> in practice, nowadays there is none. I am quite sure that in all music
>> cultures, there has been theory (of some kind) around for thousands of
>> years - western, arabic and indian for sure, in any case. You can
>> become a good musician without formal theory training - but in any
>> case, every musician's musical intuition is shaped on existing music
>> first, which, in its turn, inevitably is shaped by theory of some kind.
>> --
>> Hans Straub
>>
>>
>>
> > > > You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> > Yahoo! Groups Links
> > >

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

I opt for proscriptive theory.

Oz.

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 24 Aï¿½ustos 2007 Cuma 1:58
Subject: [tuning] ancient origins of music-theory (was: Magic[22] as srutis)

> Hi Hans and Ozan,
>
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > So, it is safe to say that theory is embedded in music
> > is embedded in theory?
> >
> > I assume, even a primeval music surely had some
> > primeval theory to go with it.
> >
> > Oz.
>
>
> Sticking a tube in one's mouth and blowing,
> while moving the fingers to cover and uncover
> holes drilled in the side of the tube,
> is not what most would call a "natural act".
>
> So apart from solo and small-ensemble singing
> (duet, trio, quartet), which *is* a natural
> extension of speaking (and in fact, some scholars
> believe that singing predated speaking), making music
> always involves some kind of abstraction regarding
> various measurements of pitch and time, and various
> techniques for producing and modifying the sound
> -- those would fall under "theory".
>
>
> I've seen it pointed out in this thread that
> the theory describes an idea first, and the music
> follows as an embodiment of that theory:
> "proscriptive" theory.
>
> This is true for some music-and-theory relationships,
> but not all. I would venture to say that most of
> the time, the theories come *after* the rule-breaking
> inventive music: "descriptive" theory.
>
>
> At any rate, this is approximately how things went:
>
> c.50,000 BC - human acquisition of spoken language.
> This is the approximate date of the big migration
> of "Cro-Magnon" _homo sapiens_ out of Africa, and
> the sudden increased sophistication of stone tool design
> (and thus the beginning of what we now call the
> "Upper Paleolithic" period). Because spoken language
> is ubiquitous today among human cultures in every
> corner of the world, most scholars believe that it
> must have originated in Africa before the migration.
> There's still debate on which came first, speaking
> or singing, but in any case one could surely say that
> they had emerged approximately in parallel by this time.
>
> c.3000 BC - recognition by the Sumerians of music
> and singing as art forms. The Sumerians probably
> began writing down music-theory not long after this,
> but the oldest music-theory cuneiform tablets which
> we know about so far are Babylonian, from c.1600 BC.
> However, the roots of the Akkadian words on these
> tablets are Sumerian logograms which embrace the
> essential concepts, thus arguing in favor of an
> older Sumerian origin of the ideas.
>
> However accurate or approximate one wishes to pin
> down those dates, that's quite a long time-span
> in which music-theory certainly existed but was
> not written down.
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
>

🔗J.A.Martin Salinas <tony@tonysalinas.com>

Hi there,

I have uploaded at

http://xenharmonic.wikispaces.com/

A demonstration

the demo of the Conic Bellophone which took
place at the UK Microfest last 3rd of March (2007)
showing a full range of dynamics with different
mallets and brushes hitting in different places.
Bowing sounds, and friction sounds with a tibetan
bowl stick. Chromatic glissandi at different speeds
and with different patterns, dumping in different ways,
tremolo, rolls, cross glissandi (which produces
a chromatic glissando in equal temperaments
included in the 96edo), mouth vibrato.

10 minutes edited to cover a full range of dynamics.
Soon the video version will also be available.

Coming next:

Study No.1 (for one tone range to be played in any
of the 6 rows of 16 notes)

Also a reminder that 2 order have been placed and
for this first series the charge will only be for:

1) Materials
2) Person spinning the steel in China
3) Delivery from China (the cheapest Graham could find)

No profit for me at this point since having different sets
produced in different tunings enriches the results of my
PhD in music technology to be presented next year.

Tunings up to a few hundred divisions of the octave are
practicle. Anything above has to be played by a mechanical
device.

Layouts have been thought of from 5edo up to 240edo but
it would be easy to work out the rest.

If interested to get in to compose for the instrument, the only one
available is right now in Germany with Lee Ferguson who would
be very happy to try out, and I can always send sample files to use
with the computer.

Tony Salinas
tony@tonysalinas.com

Magic[22] as srutis

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗hstraub64 <hstraub64@telesonique.net>

🔗monz <monz@tonalsoft.com>

🔗hstraub64 <hstraub64@telesonique.net>

🔗ma1973 <marcsavage73@mchsi.com>

🔗monz <monz@tonalsoft.com>

🔗ma1973 <marcsavage73@mchsi.com>

🔗Mark Rankin <markrankin95511@yahoo.com>

🔗monz <monz@tonalsoft.com>

🔗monz <monz@tonalsoft.com>

🔗ma1973 <marcsavage73@mchsi.com>

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗ma1973 <marcsavage73@mchsi.com>

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗ma1973 <marcsavage73@mchsi.com>

🔗monz <monz@tonalsoft.com>

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗ma1973 <marcsavage73@mchsi.com>

🔗ma1973 <marcsavage73@mchsi.com>

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗ma1973 <marcsavage73@mchsi.com>

🔗ma1973 <marcsavage73@mchsi.com>

🔗ma1973 <marcsavage73@mchsi.com>

🔗monz <monz@tonalsoft.com>

🔗ma1973 <marcsavage73@mchsi.com>

🔗monz <monz@tonalsoft.com>

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

🔗Cameron Bobro <misterbobro@yahoo.com>

🔗Cameron Bobro <misterbobro@yahoo.com>

🔗monz <monz@tonalsoft.com>

🔗Aaron K. Johnson <aaron@akjmusic.com>

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗Cameron Bobro <misterbobro@yahoo.com>

🔗hstraub64 <hstraub64@telesonique.net>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

🔗hstraub64 <hstraub64@telesonique.net>

🔗Klaus Schmirler <KSchmir@online.de>

🔗Andreas Sparschuh <a_sparschuh@yahoo.com>

🔗monz <monz@tonalsoft.com>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

🔗Cameron Bobro <misterbobro@yahoo.com>

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

🔗Cameron Bobro <misterbobro@yahoo.com>

🔗hstraub64 <hstraub64@telesonique.net>

🔗Andreas Sparschuh <a_sparschuh@yahoo.com>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

🔗hstraub64 <hstraub64@telesonique.net>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

🔗monz <monz@tonalsoft.com>

🔗Klaus Schmirler <KSchmir@online.de>

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

🔗J.A.Martin Salinas <tony@tonysalinas.com>

🔗J.A.Martin Salinas <tony@tonysalinas.com>