Traditional Tunbur Tunings and Spirals of Fifths

Dear Mr. Lumma,

Let's start from the beginning, as obnoxious and stupefying as it
is. And in the future, if there is a future, please try to remember
that I am a trained historian who reads original sources, and who
has a passion for footnotes. Without historical context and
meaning, all numbers are meaningless.

Here is Mr. Yarman's diatribe before he disappeared to wherever:

>Hah! Hark at the one who presumes he has monopoly over
>interpreting Maqam Music theory. Hark at those who assume
>that JI intervals used by Maqam Music can be correctly
>represented both in pitch and notation by a pure cycle of fifths.
>Even a simple scrutiny of the link to a taksim recording on the
>bottom of that >same page would confirm the usage of intervals
>around 12/11 and 13/12. Of course some people do not concern
>themselves at all whether the frets give these interval or not.

Here is my COMPLETE non-edited response:

>From my manuscript Musical Mathematics: A Practice in the
>Mathematics of Tuning Instruments and Analyzing Scales
>
>******************************
>
>"A numerical analysis reveals that Al-Farabi's length ratios
>include six prime factors: 2, 3, 7, 11, 17, 149, and Ibn Sina's,
>only four prime factors: 2, 3, 7, 13."
>
>******************************
>
>Obviously, the moveable frets on uds and tunburs do not exclude
>any prime factors.
>
>For that reason, equally obvious is the fact that within a given
>civilization, theorists and theories may differ and coexist, but not
>at the expense of myopic and historical denial.

I chose to respond with a prime factor analysis because Mr.
Yarman thinks that because he heard "intervals around 12/11 and
13/12," he therefore has license to dismiss "pure cycle of fifths" as
a basic tuning theory of the modern Turkish tunbur. To read my
text on the modern Turkish Tunbur, please visit:

http://www.Chrysalis-Foundation.org/Modern_Turkish_Tunbur_&_53_TET.pdf

Now, had you read this PDF (Tuning Message #59094), you
would have immediately noticed my references to:

Signell, K.L. (1986). Makam: Modal Practice in Turkish Art Music.
Da Capo Press, New York, New York.

an extremely informative published Ph.D. dissertation.

Also, had you read this PDF, you would also have immediately
noticed my historical allusions to Al-Farabi's tunbur tuning in the
first paragraph, and to Al-Farabi's and Safi Al-Din's tunings in
Figure 81.

In Figure 81, it should be clear to you that nothing about my
studies, writings, and comprehensions is haphazard.
Figure 81 clearly illustrates a tuning principle first described by Al-
Farabi more than a thousand years ago: two spirals of fifths, one
ascending 12 fifths, the other descending 12 fifths.

Of course, if you want "natural laws" based on Mr. Yarman
questionably perceived "intervals around 12/11 and 13/12," you'll
have to ask him. I take no responsibility for the ludicrous
assumption that on the tunbur there exists a historic systematic13-limit
tuning.

However, on the ancient uds and on modern tunburs the frets are
moveable, not just with respect to tunings, transpositions, etc., but
for MUSICALLY EXPRESSIVE PURPOSES. You're numbers
ain't gonna help you here!

To begin reading about the tunings of the ancient Arabian masters from
original sources, please visit:

http://www.Chrysalis-Foundation.org/Manuscript.htm

Yes, I am upset that an argument of Destructive Criticism -- based
on the "perceived" existence of 'a 13-limit fly in the 2/1 ointment' --
should be used by someone who is absolutely ignorant of how
tunburs have been traditionally tuned for more than a thousand
years.

Of course, unless you read Arabic or French, you will need my
Musical Mathematics to cross-examine my historical analysis of
systematic tunbur tunings. Should I hand you this tool for
potentially Destructive Criticism?

Cris Forster, Music Director
www.Chrysalis-Foundation.org

>The assumption behind at least one brand of music theory, Mr.
>Forster, is that those who move frets do not do so haphazardly,
>but unknowingly follow (to some degree of approximation)
>natural laws. An effort to discover such laws does not necessarily
>seek to upset people such as yourself, though if you like being
>upset it's fine I suppose.
>-Carl

Chris,

> Here is Mr. Yarman's diatribe before he disappeared to wherever:
>
> >Hah! Hark at the one who presumes he has monopoly over
> >interpreting Maqam Music theory. Hark at those who assume
> >that JI intervals used by Maqam Music can be correctly
> >represented both in pitch and notation by a pure cycle of
> >fifths. Even a simple scrutiny of the link to a taksim
> >recording on the bottom of that same page would confirm
> >the usage of intervals around 12/11 and 13/12. Of course
> >some people do not concern themselves at all whether the
> >frets give these interval or not.
>
> Here is my COMPLETE non-edited response:
>
> >From my manuscript Musical Mathematics: A Practice in the
> >Mathematics of Tuning Instruments and Analyzing Scales
> >
> >******************************
> >
> >"A numerical analysis reveals that Al-Farabi's length ratios
> >include six prime factors: 2, 3, 7, 11, 17, 149, and Ibn
> >Sina's, only four prime factors: 2, 3, 7, 13."
> >
> >******************************
> >
> >Obviously, the moveable frets on uds and tunburs do not exclude
> >any prime factors.
> >
> >For that reason, equally obvious is the fact that within a given
> >civilization, theorists and theories may differ and coexist, but
> >not at the expense of myopic and historical denial.
>
> I chose to respond with a prime factor analysis because Mr.
> Yarman thinks that because he heard "intervals around 12/11 and
> 13/12," he therefore has license to dismiss "pure cycle of
> fifths" as a basic tuning theory of the modern Turkish tunbur.

One way to read my reply...
"""
The assumption behind at least one brand of music theory,
Mr. Forster, is that those who move frets do not do so
haphazardly, but unknowingly follow (to some degree of
approximation) natural laws."""

...is that it is possible that moveable frets exclude
prime factors (though I'm not claming they do).

I wasn't making a reference to Ozan's comments at all, nor do I
know what you meant by "myopic and historical denial".

> To read my text on the modern Turkish Tunbur, please visit:
>
> http://www.Chrysalis-
> Foundation.org/Modern_Turkish_Tunbur_&_53_TET.pdf
>
> Now, had you read this PDF (Tuning Message #59094), you
> would have immediately noticed my references to:
>
> Signell, K.L. (1986). Makam: Modal Practice in Turkish Art Music.
> Da Capo Press, New York, New York.
>
> an extremely informative published Ph.D. dissertation.
>
> Also, had you read this PDF, you would also have immediately
> noticed my historical allusions to Al-Farabi's tunbur tuning in
> the first paragraph, and to Al-Farabi's and Safi Al-Din's
> tunings in Figure 81.

I don't believe I denied such references or allusions.

> In Figure 81, it should be clear to you that nothing about my
> studies, writings, and comprehensions is haphazard.

I did not call your studies haphazard. I said some believe that
the placement of moveable frets is not haphazard.

> However, on the ancient uds and on modern tunburs the frets are
> moveable, not just with respect to tunings, transpositions, etc.,
> but for MUSICALLY EXPRESSIVE PURPOSES. You're numbers
> ain't gonna help you here!

Why is musical expression beyond numbers?

> To begin reading about the tunings of the ancient Arabian
> masters from original sources, please visit:
>
> http://www.Chrysalis-Foundation.org/Manuscript.htm

Ok, I'll check it out.

-Carl

How do the systematist fit into this question since they used 11 and 13 limit intervals?
i thought i had this paper up, but it seems not to be.

> From: Cris Forster <76153.763@compuserve.com>
>Subject: Traditional Tunbur Tunings and Spirals of Fifths
>
> >
>
>Of course, if you want "natural laws" based on Mr. Yarman >questionably perceived "intervals around 12/11 and 13/12," you'll >have to ask him. I take no responsibility for the ludicrous >assumption that on the tunbur there exists a historic systematic13-limit >tuning. >
> >
>
> >

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

Hi Kraig,

Your question goes to the heart and plumbs the depth of the
phenomenal achievements of the theorists of the Arabian
Renaissance.

Before I attempt to answer your question, I would like to apologize
to you and other members of the Tuning Group for my less than
rational responses to Destructive Criticisms. I take full
responsibility for my cantankerous choice of words, and will
attempt to change my ways.

First, I would like to state that I do not use terms
like "systematist,"
"microtonalist," or "temperamentist," because more is lost than
gained by such categorizations.

Second, due to serious email font issues, and the lack of a Yahoo
graphics page (where Tuning Group Members can upload figures,
tables, equations, etc.), I cannot respond to your question without
posting yet another page from my Musical Mathematics at
www.Chrysalis-Foundation.org.

Third, in general, but not without significant exceptions, one must
carefully distinguish between the mathematics of tuning uds and
the mathematics of tuning tunburs.

In my manuscript Musical Mathematics, I devote 248 pages to
Chapter 11, Part IV, entitled -- A Collection of World Tunings:
Arabian, Persian, and Turkish Music. Since I cannot attempt to
answer your question by posting all the required pages from this
work, I have chosen the following page that may help --

http://www.Chrysalis-Foundation.org/Al-Farabi's_Distinctions.pdf

******************************

This page CANNOT be accessed by clicking on a button at the
www.Chrysalis-Foundation.org website.

******************************

Due to extremely long ratios generated by long spirals of fifths, I
invented a new notation that SYMBOLICALLY works very much
like the sharps and flats of Western music, and the korons and
soris of modern Persian music.

A schisma comma is the difference between the comma of
Pythagoras (531441/524288) and the comma of Didymus (81/80),
and, therefore, equals ratio: 32805/32768 = 1.95 ¢.

For more information on the schisma comma, please visit --

http://www.Chrysalis-Foundation.org/Al-Din_&_Ramis.htm

Starting on C, if we descend 8 fifths we get Fb, or ratio
8192/6561 = 384 ¢. Now, if we reduce 5-limit E, ratio 5/4 = 386 ¢,
by the schisma comma, we also get 8192/6561 = 384 ¢. Since
the human ear cannot distinguish between two pitches that are
less than 2 ¢ apart, 5/4 and 8192/6561 are for all practical musical
purposes identical.

In the above-mentioned PDF file, I use a "down arrow" with an "S"
on top to indicate a 5-limit ratio reduced by a schisma comma,
which, equivalently, represents the exact ratio in the descending
spiral of fifths.

In the above-mentioned PDF file, I also use the koron sign, which I
describe on the following page --

http://www.Chrysalis-Foundation.org/Al-Farabi's_'Uds.htm

Here you can examine the ud tuning tradition, which, unlike the
tunbur tuning tradition, is NOT based on spirals of fifths.

To access the Turkish tunbur page, please visit --

http://www.Chrysalis-
Foundation.org/Modern_Turkish_Tunbur_&_53_TET.pdf

Hope this helps a little.

Sincerely,

Cris Forster, Music Director
www.Chrysalis-Foundation.org

>How do the systematist fit into this question since they used 11
>and 13 limit intervals?
>i thought i had this paper up, but it seems not to be.

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
> How do the systematist fit into this question since they used 11
and 13
> limit intervals?
> i thought i had this paper up, but it seems not to be.
>
> > From: Cris Forster <76153.763@c...>
> >Subject: Traditional Tunbur Tunings and Spirals of Fifths
> >
> >
> >
> >
> >Of course, if you want "natural laws" based on Mr. Yarman
> >questionably perceived "intervals around 12/11 and 13/12," you'll
> >have to ask him. I take no responsibility for the ludicrous
> >assumption that on the tunbur there exists a historic
systematic13-limit
> >tuning.
> >
> >
> >
> >
> >
> >
>
> --
> Kraig Grady
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
> The Wandering Medicine Show
> KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

--- In tuning@yahoogroups.com, "c_ml_forster" <76153.763@c...> wrote:

> http://www.Chrysalis-Foundation.org/Al-Farabi's_Distinctions.pdf
>
> ******************************
>
> This page CANNOT be accessed by clicking on a button at the
> www.Chrysalis-Foundation.org website.

It doesn't seem it can be accessed using this url either.

> Starting on C, if we descend 8 fifths we get Fb, or ratio
> 8192/6561 = 384 ¢. Now, if we reduce 5-limit E, ratio 5/4 = 386 ¢,
> by the schisma comma, we also get 8192/6561 = 384 ¢. Since
> the human ear cannot distinguish between two pitches that are
> less than 2 ¢ apart, 5/4 and 8192/6561 are for all practical musical
> purposes identical.

If they are identical, why do you want to distinguish them? Could you
not simply use the 53-et that some Turkish theorists use?

> In the above-mentioned PDF file, I use a "down arrow" with an "S"
> on top to indicate a 5-limit ratio reduced by a schisma comma,
> which, equivalently, represents the exact ratio in the descending
> spiral of fifths.

You might find Keenan and Secor's sagittal notation interesting. I
think anyway there is no point in introducing yet another special
symbol for the schisma.

> In the above-mentioned PDF file, I also use the koron sign, which I
> describe on the following page --
>
> http://www.Chrysalis-Foundation.org/Al-Farabi's_'Uds.htm

There are a lot of Al-Farabi scales in the Scala archives, but I
didn't find the 9 and 22 note scales on this page there. I give them
below, and suggest they be added.

One thing to note about these scales is that 159-et does an excellent
job of representing them.

! farabi9.scl
Al-Farabi 9 note ud scale
9
!
9/8
27/22
81/64
4/3
3/2
18/11
27/16
16/9
2

! farabi22ud.scl
Al-Farabi 22 note ud scale
22
!
256/243
18/17
12/11
9/8
32/27
27/22
8192/6561
81/64
4/3
1024/729
24/17
16/11
3/2
128/81
18/11
32768/19683
27/16
16/9
4096/2187
32/17
64/33
2

In 159 equal, these scales are

0, 27, 47, 54, 66, 93, 113, 120, 132

and

0, 12, 13, 20, 27, 39, 47, 51, 54, 66, 78, 79, 86, 93, 105, 113,
117, 120, 132, 144, 145, 152

In terms of the 2deg159 MOS, they are

-66, -56, -33, -23, 0, 27, 33, 60, 66

and

-73, -66, -60, -56, -54, -40, -33, -27, -23, -21, -7, 0, 6, 10, 27,
33, 39, 43, 60, 66, 72, 76

In other words, 159-et represents them very well, but the 79 note
2deg159 MOS is useless. Other temperaments do better--for instance
"guiron", the 118&159 temperament, which is 31deg159.

Sorry about that. Anyway, I'm leaving for a long vacation. All my
best.

Cris Forster

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning@yahoogroups.com, "c_ml_forster" <76153.763@c...>
wrote:
>
> > http://www.Chrysalis-Foundation.org/Al-Farabi's_Distinctions.pdf
> >
> > ******************************
> >
> > This page CANNOT be accessed by clicking on a button at the
> > www.Chrysalis-Foundation.org website.
>
> It doesn't seem it can be accessed using this url either.
>
> > Starting on C, if we descend 8 fifths we get Fb, or ratio
> > 8192/6561 = 384 ¢. Now, if we reduce 5-limit E, ratio 5/4 = 386
¢,
> > by the schisma comma, we also get 8192/6561 = 384 ¢. Since
> > the human ear cannot distinguish between two pitches that are
> > less than 2 ¢ apart, 5/4 and 8192/6561 are for all practical
musical
> > purposes identical.
>
> If they are identical, why do you want to distinguish them? Could
you
> not simply use the 53-et that some Turkish theorists use?
>
> > In the above-mentioned PDF file, I use a "down arrow" with
an "S"
> > on top to indicate a 5-limit ratio reduced by a schisma comma,
> > which, equivalently, represents the exact ratio in the
descending
> > spiral of fifths.
>
> You might find Keenan and Secor's sagittal notation interesting. I
> think anyway there is no point in introducing yet another special
> symbol for the schisma.
>
> > In the above-mentioned PDF file, I also use the koron sign,
which I
> > describe on the following page --
> >
> > http://www.Chrysalis-Foundation.org/Al-Farabi's_'Uds.htm
>
> There are a lot of Al-Farabi scales in the Scala archives, but I
> didn't find the 9 and 22 note scales on this page there. I give
them
> below, and suggest they be added.
>
> One thing to note about these scales is that 159-et does an
excellent
> job of representing them.
>
> ! farabi9.scl
> Al-Farabi 9 note ud scale
> 9
> !
> 9/8
> 27/22
> 81/64
> 4/3
> 3/2
> 18/11
> 27/16
> 16/9
> 2
>
> ! farabi22ud.scl
> Al-Farabi 22 note ud scale
> 22
> !
> 256/243
> 18/17
> 12/11
> 9/8
> 32/27
> 27/22
> 8192/6561
> 81/64
> 4/3
> 1024/729
> 24/17
> 16/11
> 3/2
> 128/81
> 18/11
> 32768/19683
> 27/16
> 16/9
> 4096/2187
> 32/17
> 64/33
> 2
>
> In 159 equal, these scales are
>
> 0, 27, 47, 54, 66, 93, 113, 120, 132
>
> and
>
> 0, 12, 13, 20, 27, 39, 47, 51, 54, 66, 78, 79, 86, 93, 105, 113,
> 117, 120, 132, 144, 145, 152
>
> In terms of the 2deg159 MOS, they are
>
> -66, -56, -33, -23, 0, 27, 33, 60, 66
>
> and
>
> -73, -66, -60, -56, -54, -40, -33, -27, -23, -21, -7, 0, 6, 10, 27,
> 33, 39, 43, 60, 66, 72, 76
>
> In other words, 159-et represents them very well, but the 79 note
> 2deg159 MOS is useless. Other temperaments do better--for instance
> "guiron", the 118&159 temperament, which is 31deg159.