Yahoo Tuning Groups Ultimate Backup tuning traditional persian just intonation scale

hi jeroen,

--- In tuning@yahoogroups.com, "jpthesseling" <contact@j...> wrote:

> hello. years ago i got the following information from
> mark rankin on a traditional persian just intonation scale.
> could anyone perhaps provide me with more information on
> this particular scale?
>
> best regards,
> jeroen thesseling
>
>
> open strings:
> 6 5 4 3 2 1
> c g c1 c2 g1 c2
> 1/1 3/2 2/1 4/1 3/1 4/1
>
> 0. 1/1
> 1. 54/49
> 2. 9/8
> 3. 32/27
> 4. 27/22
> 5. 81/64
> 6. 4/3
> 7. 1024/729
> 8. 216/147
> 9. 3/2
> 10. 128/81
> 11. 18/11
> 12. 27/16
> 13. 16/9
> 14. 4096/2187
> 15. 288/147

note that 216/147 reduces to 72/49
and 288/147 reduces to 96/49.

this is a "no-fives" tuning. i find it unusual
that some notes use 7^-2 but that there are none
which use 7^-1. i could see this as a result
of arithmetic means, where the 49 would be necessary
to interpolate between 48 (i.e., 24 = 12 = 6 = 3)
and 50 (= 25), but there is no 50 because 5 is not
used as a factor. ...?

here is the scale with all pitches octave-reduced,
for the notes on both the 1/1 and 3/2 strings,
with monzos and approximate cents values:

2,3,5,7,11-monzo ratio ~cents

[ 0 0, * 0 0,> 1 / 1 0
[ 1 3, * -2 0,> 54 / 49 168.2131897
[-3 2, * 0 0,> 9 / 8 203.9100017
[ 5 -3, * 0 0,> 32 / 27 294.1349974
[-1 3, * 0 -1,> 27 / 22 354.5470602
[-6 4, * 0 0,> 81 / 64 407.8200035
[ 2 -1, * 0 0,> 4 / 3 498.0449991
[10 -6, * 0 0,> 1024 / 729 588.2699948
[ 3 2, * -2 0,> 72 / 49 666.2581888
[-1 1, * 0 0,> 3 / 2 701.9550009
[ 7 -4, * 0 0,> 128 / 81 792.1799965
[ 1 2, * 0 -1,> 18 / 11 852.5920594
[-4 3, * 0 0,> 27 / 16 905.8650026
[ 4 -2, * 0 0,> 16 / 9 996.0899983
[12 -7, * 0 0,> 4096 / 2187 1086.314994
[ 5 1, * -2 0,> 96 / 49 1164.303188

[-1 1, * 0 0,> 3 / 2 701.9550009
[ 0 4, * -2 0,> 81 / 49 870.1681905
[-4 3, * 0 0,> 27 / 16 905.8650026
[ 4 -2, * 0 0,> 16 / 9 996.0899983
[-2 4, * 0 -1,> 81 / 44 1056.502061
[-7 5, * 0 0,> 243 / 128 1109.775004
[ 0 0, * 0 0,> 1 / 1 0
[ 8 -5, * 0 0,> 256 / 243 90.22499567
[ 1 3, * -2 0,> 54 / 49 168.2131897
[-3 2, * 0 0,> 9 / 8 203.9100017
[ 5 -3, * 0 0,> 32 / 27 294.1349974
[-1 3, * 0 -1,> 27 / 22 354.5470602
[-6 4, * 0 0,> 81 / 64 407.8200035
[ 2 -1, * 0 0,> 4 / 3 498.0449991
[10 -6, * 0 0,> 1024 / 729 588.2699948
[ 3 2, * -2 0,> 72 / 49 666.2581888

-monz

🔗Daniel A. Wier <dawiertx@sbcglobal.net>

From: "jpthesseling":

> hello. years ago i got the following information from mark rankin on
> a traditional persian just intonation scale. could anyone perhaps
> provide me with more information on this particular scale?

> open strings:
> 6 5 4 3 2 1
> c g c1 c2 g1 c2
> 1/1 3/2 2/1 4/1 3/1 4/1

That looks like the tuning of a tar. But I'm not really sure, I should check on that. (Tars have three courses of strings, setars have two.)

I'm adding Persian note names to your list: "p" is the symbol for koron, a vague quarter-tone flat; ">" is sori, about quarter-tone sharp. I corrected a few errors in the list (just an omitted note and an unreduced ratio) and extended it beyond an octave.

First tetrachord
1/1 [C]
256/243 [Db]
54/49 [Dp]
9/8 [D]
32/27 [Eb]
27/22 [Ep]
81/64 [E]
Second tetrachord
4/3 [F]
1024/729 [Gb]
72/49 [Gp]
3/2 [G]
128/81 [Ab]
18/11 [Ap]
27/16 [A]
Third tetrachord
16/9 [Bb]
4096/2187 [B> or Cb]
96/49 [Cp]
2/1 [C]
512/243 [Db]
24/11 [Dp]
9/4 [D]
Fourth tetrachord
64/27 [Eb]
etc.

That would be a form of a traditional scale used throughout the Middle East, using Pythagorean ratios (256/243 can also be added) with quarter-tones added in the 8th century by Zalzal. The derivation of 54/49 (which some may substitute for 12/11) is based on the arithmetic mean of the string lengths of an open string and a string fretted at 27/22: (1/1 + 22/27)/2 = (54/54 + 44/54)/2 = 49/54. The pitch, of course, is the reciprocal of the string length.

Every 4/3, the pattern is repeated, so the scale is fourth-based, not octave-based.

Joe Monzo has an article on oud (Arabic-Turkish-Armenian fretless lute, which I actually play myself): http://sonic-arts.org/monzo/arablute/arablute.htm. The oud is called barbat in Iran and is only a minor instrument there, but the tuning of the individual notes is similar.

And another article on Persian music in general: http://www.internetserver.com/~beigi/music/iranclas.html. Note that the dastgah system is similar, but not identical to, Arabic and Turkish maqam. The names and notes are different.

🔗monz <monz@tonalsoft.com>

hi Danny,

--- In tuning@yahoogroups.com, "Daniel A. Wier" <dawiertx@s...> wrote:

> From: "jpthesseling":
>
> > hello. years ago i got the following information from
> > mark rankin on a traditional persian just intonation scale.
> > could anyone perhaps provide me with more information on
> > this particular scale?
>
> > open strings:
> > 6 5 4 3 2 1
> > c g c1 c2 g1 c2
> > 1/1 3/2 2/1 4/1 3/1 4/1
>
> That looks like the tuning of a tar. But I'm not really
> sure, I should check on that. (Tars have three courses
> of strings, setars have two.)
>
> I'm adding Persian note names to your list: "p" is the
> symbol for koron, a vague quarter-tone flat; ">" is sori,
> about quarter-tone sharp. I corrected a few errors in
> the list (just an omitted note and an unreduced ratio)
> and extended it beyond an octave.
>
> First tetrachord
> 1/1 [C]
> 256/243 [Db]
> 54/49 [Dp]
> 9/8 [D]
> 32/27 [Eb]
> 27/22 [Ep]
> 81/64 [E]
> Second tetrachord
> 4/3 [F]
> 1024/729 [Gb]
> 72/49 [Gp]
> 3/2 [G]
> 128/81 [Ab]
> 18/11 [Ap]
> 27/16 [A]
> Third tetrachord
> 16/9 [Bb]
> 4096/2187 [B> or Cb]
> 96/49 [Cp]
> 2/1 [C]
> 512/243 [Db]
> 24/11 [Dp]
> 9/4 [D]
> Fourth tetrachord
> 64/27 [Eb]
> etc.
>
> That would be a form of a traditional scale used throughout
> the Middle East, using Pythagorean ratios (256/243 can also
> be added) with quarter-tones added in the 8th century by
> Zalzal. The derivation of 54/49 (which some may substitute
> for 12/11) is based on the arithmetic mean of the string
> lengths of an open string and a string fretted at 27/22:
> (1/1 + 22/27)/2 = (54/54 + 44/54)/2 = 49/54. The pitch,
> of course, is the reciprocal of the string length.
>
> Every 4/3, the pattern is repeated, so the scale is
> fourth-based, not octave-based.

i just posted my analysis of this scale yesterday:

/tuning/topicId_57586.html#57590

but i did give it in octave-reduced form, which is the
wrong interpretation. it's very interesting to me to
see you say that the traditional conception of this
scale is based on a series of all *conjunct* tetrachords!

i've done some research on the medieval Frankish treatise
_musica enchiriadis_, and am convinced that the scale
given in the unique "daseian" notation is based on
all-conjunct tetrachords, which is *not* the accepted
interpretation. see my page about it, especially the
part at the bottom:

http://tonalsoft.com/enc/daseian.htm

i've long thought that the Franks got some of their
music theory ideas from the Byzantine Empire and its
Muslim neighbors. hmm ...

> Joe Monzo has an article on oud (Arabic-Turkish-Armenian
> fretless lute, which I actually play myself):
> http://sonic-arts.org/monzo/arablute/arablute.htm.

but my article is on the *fretting* of the Arab Lute,
and you say that what i wrote about is fretless? ... ?

-monz

🔗jpthesseling <contact@jeroenthesseling.com>

dear monz, daniel, gene,

thank you for your very helpful information! i will surely consider
to tie frets of the traditional intervals on one of my fretless six-
string basses.

best regards,
jeroen

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:

hi Danny,

--- In tuning@yahoogroups.com, "Daniel A. Wier" <dawiertx@s...> wrote:

From: "jpthesseling":

hello. years ago i got the following information from
mark rankin on a traditional persian just intonation scale.
could anyone perhaps provide me with more information on
this particular scale?

open strings:
6 5 4 3 2 1
c g c1 c2 g1 c2
1/1 3/2 2/1 4/1 3/1 4/1

That looks like the tuning of a tar. But I'm not really
sure, I should check on that. (Tars have three courses
of strings, setars have two.)

I'm adding Persian note names to your list: "p" is the
symbol for koron, a vague quarter-tone flat; ">" is sori,
about quarter-tone sharp. I corrected a few errors in
the list (just an omitted note and an unreduced ratio)
and extended it beyond an octave.

That would be a form of a traditional scale used throughout
the Middle East, using Pythagorean ratios (256/243 can also
be added) with quarter-tones added in the 8th century by
Zalzal. The derivation of 54/49 (which some may substitute
for 12/11) is based on the arithmetic mean of the string
lengths of an open string and a string fretted at 27/22:
(1/1 + 22/27)/2 = (54/54 + 44/54)/2 = 49/54. The pitch,
of course, is the reciprocal of the string length.

Every 4/3, the pattern is repeated, so the scale is
fourth-based, not octave-based.

i just posted my analysis of this scale yesterday:

/tuning/topicId_57586.html#57590

http://tonalsoft.com/enc/daseian.htm

i've long thought that the Franks got some of their
music theory ideas from the Byzantine Empire and its
Muslim neighbors. hmm ...

Joe Monzo has an article on oud (Arabic-Turkish-Armenian
fretless lute, which I actually play myself):
http://sonic-arts.org/monzo/arablute/arablute.htm.

but my article is on the *fretting* of the Arab Lute,
and you say that what i wrote about is fretless? ... ?

-monz

🔗Daniel A. Wier <dawiertx@sbcglobal.net>

From: "monz":

> i just posted my analysis of this scale yesterday:
>
> /tuning/topicId_57586.html#57590
>
> but i did give it in octave-reduced form, which is the
> wrong interpretation. it's very interesting to me to
> see you say that the traditional conception of this
> scale is based on a series of all *conjunct* tetrachords!

I think that applies mostly for Persian music, as octave-based scales are the norm in Arab countries and Turkey (Sabï¿½ is a rare exception which contains a diminished octave). Dastgï¿½h-e Segï¿½h repeats every fourth: C D Ep F G Ap Bb C Dp Eb etc., and I think Panjgï¿½h (F G A Bb C D Eb F) might as well, or it could merely be what the West calls Mixolydian mode. Chahï¿½rgï¿½h might be a pentachordal or repeating-fifth scale, but I'm not sure.

> i've done some research on the medieval Frankish treatise
> _musica enchiriadis_, and am convinced that the scale
> given in the unique "daseian" notation is based on
> all-conjunct tetrachords, which is *not* the accepted
> interpretation. see my page about it, especially the
> part at the bottom:
>
> http://tonalsoft.com/enc/daseian.htm
>
> i've long thought that the Franks got some of their
> music theory ideas from the Byzantine Empire and its
> Muslim neighbors. hmm ...

I was thinking it might have been because of the Crusades, but the Enchiriadis was written a good two centures before the First Crusade. The Moors were already well-established in Iberia in the mid-9th century, though, so there could have been an exchange of ideas.

> but my article is on the *fretting* of the Arab Lute,
> and you say that what i wrote about is fretless? ... ?

We may be talking about different instruments. The oud is usually fretless (long-necked lutes such as the tanbur, saz, baglama, buzuq, tar and setar have moveable frets); the Europeans added tied frets to their version of the lute. Music theorists might have added frets to the oud for demonstration purposes, but to have frets on and oud or violin during performances is comparable to Lance Armstrong running the Tour de France on a bike with training wheels.

~Danny~

🔗monz <monz@tonalsoft.com>

hi Danny,

--- In tuning@yahoogroups.com, "Daniel A. Wier" <dawiertx@s...> wrote:

> From: "monz":
>
> > i just posted my analysis of this scale yesterday:
> >
> > /tuning/topicId_57586.html#57590
> >
> > but i did give it in octave-reduced form, which is the
> > wrong interpretation. it's very interesting to me to
> > see you say that the traditional conception of this
> > scale is based on a series of all *conjunct* tetrachords!
>
> I think that applies mostly for Persian music, as
> octave-based scales are the norm in Arab countries and
> Turkey (Sabâ is a rare exception which contains a diminished
> octave). Dastgâh-e Segâh repeats every fourth: C D Ep F
> G Ap Bb C Dp Eb etc., and I think Panjgâh (F G A Bb C D Eb F)
> might as well, or it could merely be what the West calls
> Mixolydian mode. Chahârgâh might be a pentachordal or
> repeating-fifth scale, but I'm not sure.
>
> > i've done some research on the medieval Frankish treatise
> > _musica enchiriadis_, and am convinced that the scale
> > given in the unique "daseian" notation is based on
> > all-conjunct tetrachords, which is *not* the accepted
> > interpretation. see my page about it, especially the
> > part at the bottom:
> >
> > http://tonalsoft.com/enc/daseian.htm
> >
> > i've long thought that the Franks got some of their
> > music theory ideas from the Byzantine Empire and its
> > Muslim neighbors. hmm ...
>
> I was thinking it might have been because of the Crusades,
> but the Enchiriadis was written a good two centures before
> the First Crusade. The Moors were already well-established
> in Iberia in the mid-9th century, though, so there could
> have been an exchange of ideas.

that's an intriguing idea, and it may actually have occurred
in popular and folk music of the time.

but politically, the Moors were enemies of the Franks,
so it's doubtful that any of their musical theory or
practice made its way into Charlemagne's court or the
churches and monasteries. but this would be an interesting
question to research.

it's well documented that Charlemagne was on good terms
with the Byzantine Empire, Persia, and the Baghdad Caliphate,
so it's more than likely that some Arab/Persian musical
culture found its way into the Holy Roman Empire via
the Arab scholars Charlemagne hired to teach his young
"leaders of tomorrow".

from some of my own old posts here:

/tuning/topicId_33250.html#33250

"Good stuff, Klaus! I'm interested in this too, especially
the role Charlemagne apparently played in trying to homogenize
the chant as it existed in the Frankish empire. The bits
I've read about the rustic "vulgarities" in the chant in
local Frankish churches during that time are tantalizing.
Based on my studies of the _musica enchiriadis_, I think
that chant may have had a 5-limit basis, perhaps even 7.

It was Charlemagne's goal to eliminate this vagaries, so
I wonder what the rustic chant was really like, and I've
often thought that Byzantine chant probably holds part of
the answer, but I've never looked into it seriously."

/tuning/topicId_30446.html#30507

"as far back as the late 700s, Charlemagne had close diplomatic
ties with the Baghdad Caliphate".

/tuning/topicId_8315.html#8315

"Charlemagne (c 750-800), who had good diplomatic ties with the
Byzantine (i.e., Greek) Empire, Persia, and the Baghdad Caliphate,
and who knew how important education was, began to bring some
of the Greek learning back into Europe - some of it filtered
thru the Arab scholars."

here's a fairly detailed article about the dissemination
of Muslim musical culture into Europe during medieval times:

http://www.muslimheritage.com/topics/default.cfm?ArticleID=404

i can relate an anecdote of interest here: when i was in
Italy in 2001, i attended a concert by a group performing
12th/13th-century troubadour music, on period instruments.
one piece was lute solo from Occitan (southern France)
that sounded *exactly* like a folk piece from Morocco on
a CD i had. the influence was clear. (BTW, this concert took
place in the great hall of a palace built in the 1200s.)

one other thing i should note: most scholars believe
that the _enchiriadis_ treatises were written in the
later 900s, but i feel fairly strongly that they are at
least a century older.

the only cogent argument against my early dating is that
the daseian notation of _enchiriadis_ seems to be a
simplification of the notation system presented by Hucbald,
who lived 840-930, in his treatise _de harmonica institutione_.
apparently this is an early work by him ... list member
Margo Schulter cites it as c.880 here:

http://www.medieval.org/emfaq/harmony/hex1.html

some scholars believe that he also wrote the
_enchiriadis_ treatises, later in life. see:

http://www.newadvent.org/cathen/07510b.htm

in fact, one or both of the _enchiriadis_ treatises were
long attributed to Hucbald, but then he was discredited,
which is how it stood when i did most of my research on
this period in music theory. now apparently he's back in.

anyway, there was a lot more research i wanted to do
on both _enchiriadis_ and Hucbald, but never got around
to it ...

-monz

traditional persian just intonation scale

🔗jpthesseling <contact@jeroenthesseling.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗monz <monz@tonalsoft.com>

🔗Daniel A. Wier <dawiertx@sbcglobal.net>

🔗monz <monz@tonalsoft.com>

🔗jpthesseling <contact@jeroenthesseling.com>

🔗Daniel A. Wier <dawiertx@sbcglobal.net>

🔗monz <monz@tonalsoft.com>

🔗ertugrulinanc <ertugrulinanc@yahoo.com>

🔗Danny Wier <dawiertx@sbcglobal.net>

🔗Ozan Yarman <ozanyarman@superonline.com>