Yahoo Tuning Groups Ultimate Backup tuning Maqam tuning as a reasoned practice (was: Dissonance...)

Dear Ozan, Carl, Cameron, Michael, and all,

Ozan: Please let me begin by saying that even if the whole rest of the
world were otherwise, I would be delighted to reside in your house
when it comes to the value of making fine distinctions in the tuning
of the maqamat, even if you might add that I am actually somewhere out
on your porch with some of my curious tunings, rather than closer to
your sofa as you play your qanun!

Carl: As to the Turkish tuning of Rast, p. 57 of the "theory vs.
practice" paper has some vital fine print. The third step of Rast is
often tuned either around 16/13 (359 cents) or around 5/4 (386 cents),
Thus Turkish Rast often has a middle third at around 16/13, or a bit
higher (e.g. 21/17 or 26/21), although at times this step approaches
the region of 5/4. The 5/4-ish flavor is described by Safi al-Din
al-Urmawi (later 13th century) and Qutb al-Din al-Shirazi (around
1300), while Safi al-Din's "medium sundered" tetrachord
(1/1-9/8-99/80-4/3 or 0-204-369-498 cents) nicely fits a "largish
neutral third" version.

More specifically, 350 cents would evidently be too low for a stylish
Turkish Rast, where a "low" but acceptable third might be around
16/13; a common historical choice, 26/21 or so (which I often favor);
and a "high" placement somewhere approaching 5/4, maybe 380 cents or
so, or comparable to the near-5/4 of 19-EDO or 22-EDO.

The 53-comma model popular in Turkey and Syria would sum up this
situation by saying that a Rast tetrachord may be 9 7 6 or 9 8 5.
The Syrian theorist al-Sabbagh favors the first form, while the
"theoryVSpractice" study has shown that Turkish musicians may lean
toward 9 7 6 commas (e.g. 1/1-9/8-16/13-4/3 or 1/1-9/8-21/17-4/3) or
the 5-limit-like 9-8-5 commas (e.g. 1/1-9/8-5/4-4/3).

When people are measured with 21st-century technology playing on the
Turkish ney, for example, genera or ajnas much like those described by
Safi al-Din and Qutb al-Din seven centuries ago, or Ibn Sina a
millennium ago, and distinct from 24-EDO, I tend to take these
theorists quite seriously.

Compare, for example, the measured intervals in Niyazi's Sayin's
Ushshak Ney Taksim (Ozan's thesis, p. 29) with either the original
form or a permutation of a tuning by Ibn Sina in the early 11th
century at 28:26:24:21 or 1/1-14/13-7/6-4/3:

Measured: 123.47 137.13 227.87

Ibn Sina: 14:13 13:12 8:7
128.30 138.57 231.17

Cameron: In approaching Maqam `Iraq, my first general impression is
that we'll start with a lower Sikah trichord having a smallish
neutral second and third, maybe 1/1-13/12-11/9 in a "moderate"
interpretation or 1/1-14/13-40/33 in a "low" one. I'd expect the first
interval to be substantially lower than 12/11 or 150 cents, although
the third might be around 11/9, and thus not too far from 350 cents.

Here are a "low" and "moderate" version of Maqam `Iraq, the former
using a nuance favored by at least one Syrian source where the fourth
is about a comma narrow, with the tempered O3 tuning in cents, and
then a JI interpretation:

Low `Iraq (ascending)

Sikah Bayyati Rast
|-------------|----------------------|-----------------|
0 127 334 472 623 831 1038 1200
1/1 14/13 40/33 21/16 56/39 21/13 51/28 2/1
0 128 333 471 626 830 1038 1200

Moderate `Iraq (ascending)

Sikah Bayyati Rast
|-------------|----------------------|-----------------|
0 138 346 497 635 843 1050 1200
1/1 13/12 11/9 4/3 13/9 13/8 11/6 2/1
0 139 347 497 637 841 1049 1200

A subtle point of the Syrian tuning with its near-21/16 step (at 21
commas) is that in this way we can get a more idiomatic Bayyati
tetrachord with the smaller middle or neutral second first. In Syrian
theory, this would be 6 7 9 commas (about 136-158-204 cents), while
here it is 138-150-208 cents or so, close to 1/1-13/12-13/11-4/3). The
second version, while not wrong, gives a less "stylish" Bayyati
tetrachord at 1/1-12/11-13/11-4/3, a common flavor of Turkish Ushshaq,
for example (around 7 6 9 commas), but the reverse of the usual
pattern for Arab Bayyati. Scott Marcus, reporting on the practice of
traditional Egyptian musicians, notes a preference for tuning the
first interval of Maqam Bayyati somewhere around 135-145 cents, but in
any event as the smaller of the two middle or neutral seconds.

More exactly, the Syrian model is 6-9|6-7-9|9-7 commas or, in 53-EDO,
0-136-340-475-634-838-1042-1200 cents, or 136-204|136-158-204|204-158
cents. This may be compared with the tempered versions above, with
the understanding that the 53-EDO values are a general guide rather than
a precise specification for Syrian musicians of this tradition.

Michael: As Hormoz Farhat discusses, Persian music often distinguishes
between small neutral steps around 125-140 cents (say from around
14/13 to 13/12) and large ones around 150-165 cents (say from 12/11 to
11/10 or so). While in Zalzal's tuning as described by al-Farabi this
contrast is quite subtle, with steps of 151 cents (12/11) or 143 cents
(88/81), the later interpretation of Ibn Sina with steps at 13/12 (139
cents) or 128/117 (155 cents) could fit much modern Persian practice
rather well. In 53-EDO, 6 and 7 commas (136 and 158 cents) can
represent these smaller and larger neutral seconds. Of course, as Ozan
often points out, there are infinitely fine shadings. Note that the
main focus of these traditions is on melody, although the polyphonic
use of various neutral intervals is certainly possible.

Most appreciatively,

Margo Schulter
mschulter@...

🔗Ozan Yarman <ozanyarman@...>

🔗c_ml_forster <cris.forster@...>

For those interested in doing their own research,
Al-Farabi never described a mode with interval
ratios 12/11 and 88/81 as belonging to Zalzal. I
gave Al-Farabi's mode the name `Mode of Zalzal' in
my book "Musical Mathematics: On the Art and
Science of Acoustic Instruments" p. 645.

Also, Ibn Sina's tetrachord, which he called
Diatonic Genus 7, consists of ascending interval
ratios 9/8, 13/12, and 128/117. See "Musical
Mathematics," p. 677.

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

>While in Zalzal's tuning as described by al-Farabi
>this contrast is quite subtle, with steps of 151
>cents (12/11) or 143 cents (88/81), the later
>interpretation of Ibn Sina with steps at 13/12 (139
>cents) or 128/117 (155 cents) could fit much
>modern Persian practice rather well.

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

Farhat approximates the "small neutral second" (n)
at 135 cents; and he approximates the "large
neutral step" (N) at 160 cents. Farhat does not give
rational interval ratios. See "Musical Mathematics,"
p. 686.

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

>As Hormoz Farhat discusses, Persian music often
>distinguishes between small neutral steps around
>125-140 cents (say from around 14/13 to 13/12)
>and large ones around 150-165 cents (say from
>12/11 to 11/10 or so).

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

Finally, to understand why Ibn Sina's tuning
"could fit much modern Persian practice rather
well" refer to "Musical Mathematics," pp. 688-689,
and pp. 692-696.

It took me two years to research, translate, compile,
illustrate, and write the materials in Musical
Mathematics, Chapter 11, Part IV, called "Arabian,
Persian, and Turkish Music."

--- In tuning@yahoogroups.com, Margo Schulter <mschulter@...> wrote:
>
> Dear Ozan, Carl, Cameron, Michael, and all,
>
> Ozan: Please let me begin by saying that even if the whole rest of the
> world were otherwise, I would be delighted to reside in your house
> when it comes to the value of making fine distinctions in the tuning
> of the maqamat, even if you might add that I am actually somewhere out
> on your porch with some of my curious tunings, rather than closer to
> your sofa as you play your qanun!
>
> Carl: As to the Turkish tuning of Rast, p. 57 of the "theory vs.
> practice" paper has some vital fine print. The third step of Rast is
> often tuned either around 16/13 (359 cents) or around 5/4 (386 cents),
> Thus Turkish Rast often has a middle third at around 16/13, or a bit
> higher (e.g. 21/17 or 26/21), although at times this step approaches
> the region of 5/4. The 5/4-ish flavor is described by Safi al-Din
> al-Urmawi (later 13th century) and Qutb al-Din al-Shirazi (around
> 1300), while Safi al-Din's "medium sundered" tetrachord
> (1/1-9/8-99/80-4/3 or 0-204-369-498 cents) nicely fits a "largish
> neutral third" version.
>
> More specifically, 350 cents would evidently be too low for a stylish
> Turkish Rast, where a "low" but acceptable third might be around
> 16/13; a common historical choice, 26/21 or so (which I often favor);
> and a "high" placement somewhere approaching 5/4, maybe 380 cents or
> so, or comparable to the near-5/4 of 19-EDO or 22-EDO.
>
> The 53-comma model popular in Turkey and Syria would sum up this
> situation by saying that a Rast tetrachord may be 9 7 6 or 9 8 5.
> The Syrian theorist al-Sabbagh favors the first form, while the
> "theoryVSpractice" study has shown that Turkish musicians may lean
> toward 9 7 6 commas (e.g. 1/1-9/8-16/13-4/3 or 1/1-9/8-21/17-4/3) or
> the 5-limit-like 9-8-5 commas (e.g. 1/1-9/8-5/4-4/3).
>
> When people are measured with 21st-century technology playing on the
> Turkish ney, for example, genera or ajnas much like those described by
> Safi al-Din and Qutb al-Din seven centuries ago, or Ibn Sina a
> millennium ago, and distinct from 24-EDO, I tend to take these
> theorists quite seriously.
>
> Compare, for example, the measured intervals in Niyazi's Sayin's
> Ushshak Ney Taksim (Ozan's thesis, p. 29) with either the original
> form or a permutation of a tuning by Ibn Sina in the early 11th
> century at 28:26:24:21 or 1/1-14/13-7/6-4/3:
>
> Measured: 123.47 137.13 227.87
>
> Ibn Sina: 14:13 13:12 8:7
> 128.30 138.57 231.17
>
> Cameron: In approaching Maqam `Iraq, my first general impression is
> that we'll start with a lower Sikah trichord having a smallish
> neutral second and third, maybe 1/1-13/12-11/9 in a "moderate"
> interpretation or 1/1-14/13-40/33 in a "low" one. I'd expect the first
> interval to be substantially lower than 12/11 or 150 cents, although
> the third might be around 11/9, and thus not too far from 350 cents.
>
> Here are a "low" and "moderate" version of Maqam `Iraq, the former
> using a nuance favored by at least one Syrian source where the fourth
> is about a comma narrow, with the tempered O3 tuning in cents, and
> then a JI interpretation:
>
> Low `Iraq (ascending)
>
> Sikah Bayyati Rast
> |-------------|----------------------|-----------------|
> 0 127 334 472 623 831 1038 1200
> 1/1 14/13 40/33 21/16 56/39 21/13 51/28 2/1
> 0 128 333 471 626 830 1038 1200
>
>
> Moderate `Iraq (ascending)
>
> Sikah Bayyati Rast
> |-------------|----------------------|-----------------|
> 0 138 346 497 635 843 1050 1200
> 1/1 13/12 11/9 4/3 13/9 13/8 11/6 2/1
> 0 139 347 497 637 841 1049 1200
>
> A subtle point of the Syrian tuning with its near-21/16 step (at 21
> commas) is that in this way we can get a more idiomatic Bayyati
> tetrachord with the smaller middle or neutral second first. In Syrian
> theory, this would be 6 7 9 commas (about 136-158-204 cents), while
> here it is 138-150-208 cents or so, close to 1/1-13/12-13/11-4/3). The
> second version, while not wrong, gives a less "stylish" Bayyati
> tetrachord at 1/1-12/11-13/11-4/3, a common flavor of Turkish Ushshaq,
> for example (around 7 6 9 commas), but the reverse of the usual
> pattern for Arab Bayyati. Scott Marcus, reporting on the practice of
> traditional Egyptian musicians, notes a preference for tuning the
> first interval of Maqam Bayyati somewhere around 135-145 cents, but in
> any event as the smaller of the two middle or neutral seconds.
>
> More exactly, the Syrian model is 6-9|6-7-9|9-7 commas or, in 53-EDO,
> 0-136-340-475-634-838-1042-1200 cents, or 136-204|136-158-204|204-158
> cents. This may be compared with the tempered versions above, with
> the understanding that the 53-EDO values are a general guide rather than
> a precise specification for Syrian musicians of this tradition.
>
> Michael: As Hormoz Farhat discusses, Persian music often distinguishes
> between small neutral steps around 125-140 cents (say from around
> 14/13 to 13/12) and large ones around 150-165 cents (say from 12/11 to
> 11/10 or so). While in Zalzal's tuning as described by al-Farabi this
> contrast is quite subtle, with steps of 151 cents (12/11) or 143 cents
> (88/81), the later interpretation of Ibn Sina with steps at 13/12 (139
> cents) or 128/117 (155 cents) could fit much modern Persian practice
> rather well. In 53-EDO, 6 and 7 commas (136 and 158 cents) can
> represent these smaller and larger neutral seconds. Of course, as Ozan
> often points out, there are infinitely fine shadings. Note that the
> main focus of these traditions is on melody, although the polyphonic
> use of various neutral intervals is certainly possible.
>
> Most appreciatively,
>
> Margo Schulter
> mschulter@...
>

🔗Margo Schulter <mschulter@...>

Cris Forster wrote:

> For those interested in doing their own research, Al-Farabi
> never described a mode with interval ratios 12/11 and 88/81 as
> belonging to Zalzal. I gave Al-Farabi's mode the name `Mode of
> Zalzal' in my book "Musical Mathematics: On the Art and Science
> of Acoustic Instruments" p. 645.

Hello, Cris, and please let me begin by congratulating you on the
publication of your book, a really monumental achievement. A
friend read to me some of your insights about tuning and timbre
on acoustical instruments, and commented (based on very extensive
experience with both acoustical and digital instruments) on how
well your remarks expressed his experiences also.

Thank you both for your new information in response to my post,
and for giving me an opportunity to clarify some of my points, as
well as correct my statement of the ranges given by Hormoz Farhat
for the smaller and larger neutral seconds.

As to Zalzal and al-Farabi, I must admit that my knowledge has
always been based on secondary sources, although I would love to
see d'Erlanger's versions of al-Farabi and Ibn Sina. What these
two theorists say about Zalzal and his _wusta_ or neutral third
finger, and how they introduce their tetrachords we associate with
different placements of that _wusta_, would be of great interest.

> Also, Ibn Sina's tetrachord, which he called
> Diatonic Genus 7, consists of ascending interval
> ratios 9/8, 13/12, and 128/117. See "Musical
> Mathematics," p. 677.

Yes, and on this list I have referred to this tetrachord and the
octave species based on two such conjunct tetrachords plus an
upper 9/8 tone as Mustaqim, which I understand to be Ibn Sina's
own name. More generally, I use "Mustaqim" to refer to a genre
with a tone, smaller neutral second, and larger neutral second,
in contrast to Rast, which has tone, larger neutral second, and
smaller neutral second.

It is curious that Ibn Sina uses the Arabic name Mustaqim for his
arrangement, still I would say influential at least indirectly in
Persian music; while Arab and Turkish musicians use the Persian
term Rast for the converse arrangement with the larger neutral
second coming before the smaller after the initial step of a
tone. Either Mustaqim or Rast, as I understand, can mean the
"right, correct, or usual" tuning.

In the 53-comma model, Rast is often expressed as 9 7 6; one
modern Arab theorist speaks of "Rast Jadid" or "New Rast"
as 9 6 7 or (in 53-EDO) 204-136-158 cents, which is not far from
Ibn Sina's Mustaqim at 204-139-155 cents.

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

>> While in Zalzal's tuning as described by al-Farabi this
>> contrast is quite subtle, with steps of 151 cents (12/11) or
>> 143 cents (88/81), the later interpretation of Ibn Sina with
>> steps at 13/12 (139 cents) or 128/117 (155 cents) could fit
>> much modern Persian practice rather well.

> ******************************

> Farhat approximates the "small neutral second" (n) at 135
> cents; and he approximates the "large neutral step" (N) at 160
> cents. Farhat does not give rational interval ratios. See
> "Musical Mathematics," p. 686.

Those are indeed his suggested average values, Hormoz Farhat,
_The Dastgah Concept in Persian Music_ (Cambridge University
Press, 1st paperback ed. 2004), p. 16.

He also describes the ranges in terms that call for correction of
my not-so-accurate paraphrase that you quote below. I should also
thank you for your important point that indeed Farhat does not
use JI ratios in explaining his suggested tunings, interval
categories, and ranges in cents; these ratios belonged to my
commentary, not his text!

After noting that neutral steps larger than a semitone but
smaller than a tone are "very flexible," he adds:

"Two separate neutral intervals can, however, be
identified. A smaller neutral tone can fluctuate
between 125 and 145 cents, the mean for which can
be taken as 135 cents. A larger neutral tone
fluctuates between 150 and 170 cents, the mean
being 160 cents." (Ibid. p. 16)

> ******************************

>> As Hormoz Farhat discusses, Persian music often
>> distinguishes between small neutral steps around
>> 125-140 cents (say from around 14/13 to 13/12)
>> and large ones around 150-165 cents (say from
>> 12/11 to 11/10 or so).

Again, thank you for your welcome query giving my the opportunity
to correct these ranges to 125-145 and 150-170 cents in line with
the quote above, and to emphasize that the JI ratios mentioned
above are mine, not Farhat's.

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

> Finally, to understand why Ibn Sina's tuning "could fit much
> modern Persian practice rather well" refer to "Musical
> Mathematics," pp. 688-689, and pp. 692-696.

I look forward to reading your conclusions. In the meantime, I
certainly agree with your statement in an article on this list
(#66928 from 13 June 2006) that "the works of Ibn Sina have
everything to do with Persian music." And I happily agree with
your comment in that post on the special importance of "the
strategic implementation of prime number 13."

My own tentative observation would be that the tetrachord
structure of Ibn Sina's Mustaqim, 9:8-13:12-128:117, or more
generically in a 53-comma notation something like 9 6 7 (not a
precise specification, but a guide to the placement of smaller
and larger neutral seconds which could vary in size, as Farhat
notes) can explain the structure of some of the dastgah-ha. (And
I should add that Farhat himself doesn't apply the 53-comma
system, but makes similar distinctions between smaller and larger
neutral intervals which the 53-comma system expresses in a
Turkish or Syrian context).

For example, many of the notes of some main gushe-ha of Shur
Dastgah can be derived by combining conjunct and disjunct forms
of Mustaqim and starting on the second step of the main
tetrachord above the final; and likewise with Segah Dastgah if we
start on the third step (as Segah, the "third" step, implies).
However, this is only my own impression, and I haven't so far
encountered any similar analysis from an Iranian source. I'll
develop this possible line of analysis in another post.

Also, Ibn Sina's diatonic with tetrachords sometimes given in the
secondary sources I've had access to as either 12:13:14:16 or
28:26:24:21 (I'm not sure which ordering of the 13:12 and 14:13
steps is his original version, and which a permutation), could
fit some septimal or near-septimal flavors of modern Shur which
Farhat doesn't address, but are described, for example, by
Dariouche Safvate.

And in the 13th century, Safi al-Din's Buzurg, given with some
variations also by Qutb al-Din around 1300, for example
14:13-8:7-13:12 (another permutation of Ibn Sina's septimal
tetrachord above), seems similar to a flavor of Avaz-e Bayat-e
Esfahan that Farhat specifies if we apply his notation (p. 76)
using his suggested tar tuning (p. 17) in _The Dastgah Concept in
Persian Music_. Following that notation and tuning, we get for
the tetrachord leading up to the final of Esfahan:

D Ep F> G
0 135 360 495
135 225 135

Interestingly, while Farhat discusses and catalogues some
categories and sizes of melodic steps, he doesn't mention the
central step at around 225 cents, although he does discuss the
"plus-tone" at around 270 cents typical of Chahargah Dastgah, for
example (the modern Persian counterpart of Arab or Turkish
Hijaz). A medieval Buzurg such as 1/1-14/13-16/13-4/3 or
0-128-359-496 cents or 128-231-139 cents seems not too far from
this, although I'd emphasize that both this possible connection
and the just ratios are my editorial comment, not Farhat's!

And I should also add that Farhat's own interval category
notation for this tetrachord below the final of Bayat-e Esfahan
shows "n M N," which would imply something like 135-205-160
cents, with a small neutral second, tone, and large neutral
second. This is available with his tar tuning if we move things
up a fourth:

G Ap Bp C
0 135 340 500
135 205 160
n M N

This form, sometimes known in modern theory as the "Old Esfahan,"
might be derived from a permutation of a Mustaqim tetrachord,
here 205-135-160 or 0-205-340-500 cents, not too far from Ibn
Sina's 1/1-9/8-39/32-4/3 or 0-204-342-498 cents (204-139-155
cents).

> It took me two years to research, translate, compile,
> illustrate, and write the materials in Musical Mathematics,
> Chapter 11, Part IV, called "Arabian, Persian, and Turkish
> Music."

This does not surprise me, given the vastness of the field over
the last millennium and more!

Best, with warmest congratulations on your book and many thanks
for the helpful queries and corrections,

Margo
mschulter@...

🔗robert <robertthomasmartin@...>

Baron Rodolphe D'erlanger:
http://wn.com/baron_rodolphe_d'erlanger
Includes a slide-show of the 1932 Congress as well as some presumably related music tracks which might be of interest.

--- In tuning@yahoogroups.com, Margo Schulter <mschulter@...> wrote:
>
> Cris Forster wrote:
>
> > For those interested in doing their own research, Al-Farabi
> > never described a mode with interval ratios 12/11 and 88/81 as
> > belonging to Zalzal. I gave Al-Farabi's mode the name `Mode of
> > Zalzal' in my book "Musical Mathematics: On the Art and Science
> > of Acoustic Instruments" p. 645.
>
> Hello, Cris, and please let me begin by congratulating you on the
> publication of your book, a really monumental achievement. A
> friend read to me some of your insights about tuning and timbre
> on acoustical instruments, and commented (based on very extensive
> experience with both acoustical and digital instruments) on how
> well your remarks expressed his experiences also.
>
> Thank you both for your new information in response to my post,
> and for giving me an opportunity to clarify some of my points, as
> well as correct my statement of the ranges given by Hormoz Farhat
> for the smaller and larger neutral seconds.
>
> As to Zalzal and al-Farabi, I must admit that my knowledge has
> always been based on secondary sources, although I would love to
> see d'Erlanger's versions of al-Farabi and Ibn Sina. What these
> two theorists say about Zalzal and his _wusta_ or neutral third
> finger, and how they introduce their tetrachords we associate with
> different placements of that _wusta_, would be of great interest.
>
> > Also, Ibn Sina's tetrachord, which he called
> > Diatonic Genus 7, consists of ascending interval
> > ratios 9/8, 13/12, and 128/117. See "Musical
> > Mathematics," p. 677.
>
> Yes, and on this list I have referred to this tetrachord and the
> octave species based on two such conjunct tetrachords plus an
> upper 9/8 tone as Mustaqim, which I understand to be Ibn Sina's
> own name. More generally, I use "Mustaqim" to refer to a genre
> with a tone, smaller neutral second, and larger neutral second,
> in contrast to Rast, which has tone, larger neutral second, and
> smaller neutral second.
>
> It is curious that Ibn Sina uses the Arabic name Mustaqim for his
> arrangement, still I would say influential at least indirectly in
> Persian music; while Arab and Turkish musicians use the Persian
> term Rast for the converse arrangement with the larger neutral
> second coming before the smaller after the initial step of a
> tone. Either Mustaqim or Rast, as I understand, can mean the
> "right, correct, or usual" tuning.
>
> In the 53-comma model, Rast is often expressed as 9 7 6; one
> modern Arab theorist speaks of "Rast Jadid" or "New Rast"
> as 9 6 7 or (in 53-EDO) 204-136-158 cents, which is not far from
> Ibn Sina's Mustaqim at 204-139-155 cents.
>
>
> ******************************
>
> >> While in Zalzal's tuning as described by al-Farabi this
> >> contrast is quite subtle, with steps of 151 cents (12/11) or
> >> 143 cents (88/81), the later interpretation of Ibn Sina with
> >> steps at 13/12 (139 cents) or 128/117 (155 cents) could fit
> >> much modern Persian practice rather well.
>
> > ******************************
>
> > Farhat approximates the "small neutral second" (n) at 135
> > cents; and he approximates the "large neutral step" (N) at 160
> > cents. Farhat does not give rational interval ratios. See
> > "Musical Mathematics," p. 686.
>
> Those are indeed his suggested average values, Hormoz Farhat,
> _The Dastgah Concept in Persian Music_ (Cambridge University
> Press, 1st paperback ed. 2004), p. 16.
>
> He also describes the ranges in terms that call for correction of
> my not-so-accurate paraphrase that you quote below. I should also
> thank you for your important point that indeed Farhat does not
> use JI ratios in explaining his suggested tunings, interval
> categories, and ranges in cents; these ratios belonged to my
> commentary, not his text!
>
> After noting that neutral steps larger than a semitone but
> smaller than a tone are "very flexible," he adds:
>
> "Two separate neutral intervals can, however, be
> identified. A smaller neutral tone can fluctuate
> between 125 and 145 cents, the mean for which can
> be taken as 135 cents. A larger neutral tone
> fluctuates between 150 and 170 cents, the mean
> being 160 cents." (Ibid. p. 16)
>
> > ******************************
>
> >> As Hormoz Farhat discusses, Persian music often
> >> distinguishes between small neutral steps around
> >> 125-140 cents (say from around 14/13 to 13/12)
> >> and large ones around 150-165 cents (say from
> >> 12/11 to 11/10 or so).
>
> Again, thank you for your welcome query giving my the opportunity
> to correct these ranges to 125-145 and 150-170 cents in line with
> the quote above, and to emphasize that the JI ratios mentioned
> above are mine, not Farhat's.
>
>
> ******************************
>
> > Finally, to understand why Ibn Sina's tuning "could fit much
> > modern Persian practice rather well" refer to "Musical
> > Mathematics," pp. 688-689, and pp. 692-696.
>
> I look forward to reading your conclusions. In the meantime, I
> certainly agree with your statement in an article on this list
> (#66928 from 13 June 2006) that "the works of Ibn Sina have
> everything to do with Persian music." And I happily agree with
> your comment in that post on the special importance of "the
> strategic implementation of prime number 13."
>
> My own tentative observation would be that the tetrachord
> structure of Ibn Sina's Mustaqim, 9:8-13:12-128:117, or more
> generically in a 53-comma notation something like 9 6 7 (not a
> precise specification, but a guide to the placement of smaller
> and larger neutral seconds which could vary in size, as Farhat
> notes) can explain the structure of some of the dastgah-ha. (And
> I should add that Farhat himself doesn't apply the 53-comma
> system, but makes similar distinctions between smaller and larger
> neutral intervals which the 53-comma system expresses in a
> Turkish or Syrian context).
>
> For example, many of the notes of some main gushe-ha of Shur
> Dastgah can be derived by combining conjunct and disjunct forms
> of Mustaqim and starting on the second step of the main
> tetrachord above the final; and likewise with Segah Dastgah if we
> start on the third step (as Segah, the "third" step, implies).
> However, this is only my own impression, and I haven't so far
> encountered any similar analysis from an Iranian source. I'll
> develop this possible line of analysis in another post.
>
> Also, Ibn Sina's diatonic with tetrachords sometimes given in the
> secondary sources I've had access to as either 12:13:14:16 or
> 28:26:24:21 (I'm not sure which ordering of the 13:12 and 14:13
> steps is his original version, and which a permutation), could
> fit some septimal or near-septimal flavors of modern Shur which
> Farhat doesn't address, but are described, for example, by
> Dariouche Safvate.
>
> And in the 13th century, Safi al-Din's Buzurg, given with some
> variations also by Qutb al-Din around 1300, for example
> 14:13-8:7-13:12 (another permutation of Ibn Sina's septimal
> tetrachord above), seems similar to a flavor of Avaz-e Bayat-e
> Esfahan that Farhat specifies if we apply his notation (p. 76)
> using his suggested tar tuning (p. 17) in _The Dastgah Concept in
> Persian Music_. Following that notation and tuning, we get for
> the tetrachord leading up to the final of Esfahan:
>
> D Ep F> G
> 0 135 360 495
> 135 225 135
>
> Interestingly, while Farhat discusses and catalogues some
> categories and sizes of melodic steps, he doesn't mention the
> central step at around 225 cents, although he does discuss the
> "plus-tone" at around 270 cents typical of Chahargah Dastgah, for
> example (the modern Persian counterpart of Arab or Turkish
> Hijaz). A medieval Buzurg such as 1/1-14/13-16/13-4/3 or
> 0-128-359-496 cents or 128-231-139 cents seems not too far from
> this, although I'd emphasize that both this possible connection
> and the just ratios are my editorial comment, not Farhat's!
>
> And I should also add that Farhat's own interval category
> notation for this tetrachord below the final of Bayat-e Esfahan
> shows "n M N," which would imply something like 135-205-160
> cents, with a small neutral second, tone, and large neutral
> second. This is available with his tar tuning if we move things
> up a fourth:
>
> G Ap Bp C
> 0 135 340 500
> 135 205 160
> n M N
>
> This form, sometimes known in modern theory as the "Old Esfahan,"
> might be derived from a permutation of a Mustaqim tetrachord,
> here 205-135-160 or 0-205-340-500 cents, not too far from Ibn
> Sina's 1/1-9/8-39/32-4/3 or 0-204-342-498 cents (204-139-155
> cents).
>
> > It took me two years to research, translate, compile,
> > illustrate, and write the materials in Musical Mathematics,
> > Chapter 11, Part IV, called "Arabian, Persian, and Turkish
> > Music."
>
> This does not surprise me, given the vastness of the field over
> the last millennium and more!
>
> Best, with warmest congratulations on your book and many thanks
> for the helpful queries and corrections,
>
> Margo
> mschulter@...
>

🔗c_ml_forster <cris.forster@...>

Margo,

In Farhat's book "The Dastgah Concept of Persian
Music," pp. 15-16 and 25-26, he describes in cents not
only two intervals, but a grand total of nine
constituent intervals of modern Persian music. If
your claim hold true that Ibn Sina's tuning "could
fit much modern Persian practice rather well" then
the question arises: does Ibn Sina's `ud tuning
include accurate representations of all nine
constituent intervals? Even so, a further question
arises: given the interval patterns of Farhat's 12
modern Persian dastgaha, do the distributions of
these intervals on Ibn Sina's `ud facilitate playing
these dastgaha as notated? For example, on Ibn
Sina's `ud, can one play these dastgaha directly, or
are transpositions necessary?

Since Farhat only gives intervals in cents, and
since Ibn Sina only gives intervals as rational ratios,
I wonder how were you able to conclude that Ibn
Sina's tuning "could fit much modern Persian
practice rather well"? How were you able to reason
"reasoned practice"?

Cris

🔗Carl Lumma <carl@...>

🔗Margo Schulter <mschulter@...>

Cris wrote:

> Margo,

> In Farhat's book "The Dastgah Concept of Persian
> Music," pp. 15-16 and 25-26, he describes in cents not
> only two intervals, but a grand total of nine
> constituent intervals of modern Persian music.

Hello, Cris, and thank you for raising some important and often
not so clearly articulated points.

Of course, if we're talking here about the basic categories of
melodic steps, there are a lot more than two, and from my reading
of other sources such as Dariouche Safvate, Jean During, and
Dariush Tala`i, I'd say that Farhat's catalogue of five basic
categories as I read it is illustrative but by no means
exhaustive.

We can get into all that, whether we end up with five categories
or nine or some other number, but I think some of the questions
you are raising may be much simpler than this.

> If your claim hold true that Ibn Sina's tuning "could fit much
> modern Persian practice rather well" then the question arises:
> does Ibn Sina's `ud tuning include accurate representations of
> all nine constituent intervals?

Certainly that's not what I meant to say, and in fact I was
thinking simply in terms of how well some of his genera seem to
fit current practice, whether or not he combined the relevant
ones or even used them at all in any instrumental tuning. What
I'm looking at are simply some of his genera -- _ajnas_ in Arabic
(the plural of _jins_ or genus), or, as suggested by Tala`i,
_dang_-s in Farsi (I'm tempted to say dang-ha, but would want to
be sure that that plural is correct; his text has the Englished
form of the plural, "dang-s").

Similarly, if I say, "Safi al-Din al-Urmawi's Medium Sundered
tetrachord makes a wonderful Turkish Rast!" (9:8-11:10-320:297),
that observation doesn't depend on (at least for me) whether he
ever used it for the `oud or some other suggested instrumental
tuning.

Of course, I'm looking at this from the perspective of playing a
digital archicembalo or arciorgano of sorts with 24 notes per
octave using a synthesizer tuning table, something radically
different than building and playing actual acoustical instruments
modelled on those medieval Near Eastern practice. Your project is
in many ways more demanding, and likely more rewarding, than my
curious high-tech neomedieval excursion.

From your message #66928, I know part of your answer to one
question you raise: "All the intervals described by Hormoz Farhat
on the modern tar and setar can be played on Ibn Sina's ud. This
also applies to many modern dastgah."

And what I'd expect over a millennium of time is not a perfect
match, but simply some correspondences in genera that suggest
similar patterns: Near Eastern music is a living and changing
art, with the modern dastgah system arising from the earlier
maqam system maybe sometime around the 17th or 18th century.

However, my analysis is often cruder, even touristic in a sense:
"Wow, what a beautiful tetrachord, and how interesting that it
seems quite close to that performance measured by Can Akkoc or
Amine Beyhom!"

> Even so, a further question arises: given the interval
> patterns of Farhat's 12 modern Persian dastgaha, do the
> distributions of these intervals on Ibn Sina's `ud facilitate
> playing these dastgaha as notated? For example, on Ibn Sina's
> `ud, can one play these dastgaha directly, or are
> transpositions necessary?

An interesting question! How many notes per octave did his `oud
tuning have? For modern dastgah music, I tend to think of about
17 as standard; on my 24-note arrangement using two 12-note
keyboards, I still get into curious transpositions at times, much
to the amusement, I suspect, of someone like Ozan Yarman who
developed his 79-tone qanun to minimize such complications.

> Since Farhat only gives intervals in cents, and since Ibn Sina
> only gives intervals as rational ratios, I wonder how were you
> able to conclude that Ibn Sina's tuning "could fit much modern
> Persian practice rather well"? How were you able to reason
> "reasoned practice"?

Honestly, translating from ratios to cents is something that I
take for granted every day, as well as tempered "near-just"
intervals. My "reasoned" approach is that there are many degrees
of almost exact equivalence, approximate equivalence, "in the
same general ballpark," and "quite distinct from."

Near one end of this spectrum, I'd say that a tempered
126.6-138.3-230.9 cents in 1024-EDO is a "near-just" rendition of
Ibn Sina's 14:13-13:12-8:7 (128.30-138.57-231.17 cents).

How about 132.25-132.25-230.90? It's still rather closely related,
I would say, but different not only in that 14:13 and 13:12 are
each a lot less accurate, but more fundamentally in that they're
both represented by the same tempered interval. That is to me a
rather more significant compromise of Ibn Sina's superparticular
concept.

And what about Nelly Caron and Dariouche Safvate and their
reported lower Shur tetrachord at 136-140-224 cents? We have the
general idea of "two smallish neutral seconds plus a large tone
approaching 8:7," but not quite Ibn Sina's septimal tuning.

Let's compare Ibn Sina's Mustaqim tetrachord we've both been
discussing at 9:8-13:12-128:117 or 204-139-155 cents (actually
128:117 is slightly closer to 156 cents, but I'm rounding down in
order to have the fourth and upper minor third come out at 204
and 294 cents), with Farhat's lower tetrachord for Avaz-e Afshari
at 205-135-160 cents -- or, as a Turkish or Syrian theorist might
say, 9-6-7 commas. Here I'd say that we're dealing with
variations in tuning the same basic "type" of tetrachord --
although in fact there's an important difference that the ratios,
cents, or commas don't reveal!

That difference is that a modern Afshari, at least as described
by Farhat and exemplified by some of the pieces I've seen, tends
to place much less emphasis on the second note of the tetrachord
or the interval of a usual ~9:8 tone leading up to it than I
might guess could occur in Ibn Sina's Mustaqim. In this context
in the modern dastgah system, the descending small neutral third
Ep-C (following Farhat's examples with Shur on D) may act more
like a simple rather than composite melodic interval, so that we
could include it as a category in its own right, although Farhat
(p. 26) discusses it as a composite. Some of the gushe-ha of
Dastgah-e Mahur do shift from a major to a small neutral third
above C with all steps of the tetrachord C-D-Ep-F (~0-205-340-500
cents) in use and lots of conjunct motion, so that might be a
closer parallel to a possible melodic procedure for the medieval
Mustaqim.

So I may be sort of weird in focusing on superparticular or other
rational ratios and at the same time seeing things as a continuum
amenable to measurement in cents, commas, or what have you. If I
play the tetrachord above the final of Shur or Arab Bayyati as
138.3-150.0-207.4 cents, I tend to think of this as "a near-just
52:48:44:39" or 13:12-12:11-44:39 (138.6-150.6-208.8 cents),
although it's only an approximation. And if I encountered this
tetrachord in some medieval Near Eastern source (or secondary
source), I'd be jumping up and down with joy, at least
metaphorically speaking, and celebrating on the Tuning list.

Of course, there are caveats, including that fact that I'm not
aware of any medieval source describing or advocating the
practice of tempering fifths and fourths very slightly wider and
narrower respectively than pure.

And while duly noting that Safi al-Din's arithmetic division of
64:59:54:48 or 64:59-59:54-9:8 at 140-154-204 cents is different
from my tempered 138.3-150.0-207.4 cents or for that matter a
pure 52:48:44:39 (most notably, the minor third at 32/27 or 294
cents in Safi al-Din is narrowed to 13/11 or 289.2 cents in my JI
tuning, and yet a bit more to 288.3 cents in my tempered
version). However, I'd consider them all in the same ballpark,
with the first neutral step notably smaller than the following
one, the minor third in the region of 13/11 or 32/27 (rather than
7/6, say), and the upper step not too far from 9:8; and any of
them might go over well in Cairo or Tehran, although some
empirical tests of that proposition might be prudent!

As Ozan might say, we have infinite flavors and shadings. I find
it possible to embrace the continuum while noting similarities
and differences in a reasoned way, although this is by nature
indeed an inexact art.

> Cris

With many thanks,

Margo
mschulter@...

🔗c_ml_forster <cris.forster@...>

Margo,

A retreat into skepticism more often than not leads
to cynicism.

When I experience a work of art, a painting for
example, the subject of "infinite flavors and
shadings" does not flood my mind. Since all works
of art are by definition finite, contemplating the
infinite in the presence of a work of art would, by
definition, be tantamount to contemplating what
does not exist in that work of art. In my opinion,
contemplating what's not there, or worse, could
have been there, would constitute a denigration of
the artist and the work of art.

I am interested in what's there. This is the lot of
acoustic musicians everywhere. We don't have the
"infinite" at our fingertips. For us, contemplating the
infinite (after an instrument is tuned) comes through
years and years of practicing how to play that
instrument: we practice seemingly infinite forms of
expression, such as touch, articulation, intonation
(on non-fixed pitch instruments), tempo, dynamic
range, etc.

Perhaps we could continue this discussion
sometime in the future when you have answered

>An interesting question! How many notes per
>octave did his [Ibn Sina's] `oud tuning have?

Cris

P.S.

Regarding your statement:

>Honestly, translating from ratios to cents is
>something that I take for granted every day, as
>well as tempered "near-just" intervals.

you completely missed my point. The requirement
here is to translate from Farhat's cents to ratios, not
only with respect to Ibn Sina's `ud tuning, but also
regarding the tunings of Farhat's three setars and
two tars. Apparently, Farhat also took a great
interest in the premise (i.e., in the logic) of how
musicians tune their instruments, and how such
tunings reflect the music (i.e., the modes) they play.

--- In tuning@yahoogroups.com, Margo Schulter <mschulter@...> wrote:
>
> Cris wrote:
>
> > Margo,
>
> > In Farhat's book "The Dastgah Concept of Persian
> > Music," pp. 15-16 and 25-26, he describes in cents not
> > only two intervals, but a grand total of nine
> > constituent intervals of modern Persian music.
>
> Hello, Cris, and thank you for raising some important and often
> not so clearly articulated points.
>
> Of course, if we're talking here about the basic categories of
> melodic steps, there are a lot more than two, and from my reading
> of other sources such as Dariouche Safvate, Jean During, and
> Dariush Tala`i, I'd say that Farhat's catalogue of five basic
> categories as I read it is illustrative but by no means
> exhaustive.
>
> We can get into all that, whether we end up with five categories
> or nine or some other number, but I think some of the questions
> you are raising may be much simpler than this.
>
> > If your claim hold true that Ibn Sina's tuning "could fit much
> > modern Persian practice rather well" then the question arises:
> > does Ibn Sina's `ud tuning include accurate representations of
> > all nine constituent intervals?
>
> Certainly that's not what I meant to say, and in fact I was
> thinking simply in terms of how well some of his genera seem to
> fit current practice, whether or not he combined the relevant
> ones or even used them at all in any instrumental tuning. What
> I'm looking at are simply some of his genera -- _ajnas_ in Arabic
> (the plural of _jins_ or genus), or, as suggested by Tala`i,
> _dang_-s in Farsi (I'm tempted to say dang-ha, but would want to
> be sure that that plural is correct; his text has the Englished
> form of the plural, "dang-s").
>
> Similarly, if I say, "Safi al-Din al-Urmawi's Medium Sundered
> tetrachord makes a wonderful Turkish Rast!" (9:8-11:10-320:297),
> that observation doesn't depend on (at least for me) whether he
> ever used it for the `oud or some other suggested instrumental
> tuning.
>
> Of course, I'm looking at this from the perspective of playing a
> digital archicembalo or arciorgano of sorts with 24 notes per
> octave using a synthesizer tuning table, something radically
> different than building and playing actual acoustical instruments
> modelled on those medieval Near Eastern practice. Your project is
> in many ways more demanding, and likely more rewarding, than my
> curious high-tech neomedieval excursion.
>
> From your message #66928, I know part of your answer to one
> question you raise: "All the intervals described by Hormoz Farhat
> on the modern tar and setar can be played on Ibn Sina's ud. This
> also applies to many modern dastgah."
>
> And what I'd expect over a millennium of time is not a perfect
> match, but simply some correspondences in genera that suggest
> similar patterns: Near Eastern music is a living and changing
> art, with the modern dastgah system arising from the earlier
> maqam system maybe sometime around the 17th or 18th century.
>
> However, my analysis is often cruder, even touristic in a sense:
> "Wow, what a beautiful tetrachord, and how interesting that it
> seems quite close to that performance measured by Can Akkoc or
> Amine Beyhom!"
>
> > Even so, a further question arises: given the interval
> > patterns of Farhat's 12 modern Persian dastgaha, do the
> > distributions of these intervals on Ibn Sina's `ud facilitate
> > playing these dastgaha as notated? For example, on Ibn Sina's
> > `ud, can one play these dastgaha directly, or are
> > transpositions necessary?
>
> An interesting question! How many notes per octave did his `oud
> tuning have? For modern dastgah music, I tend to think of about
> 17 as standard; on my 24-note arrangement using two 12-note
> keyboards, I still get into curious transpositions at times, much
> to the amusement, I suspect, of someone like Ozan Yarman who
> developed his 79-tone qanun to minimize such complications.
>
> > Since Farhat only gives intervals in cents, and since Ibn Sina
> > only gives intervals as rational ratios, I wonder how were you
> > able to conclude that Ibn Sina's tuning "could fit much modern
> > Persian practice rather well"? How were you able to reason
> > "reasoned practice"?
>
> Honestly, translating from ratios to cents is something that I
> take for granted every day, as well as tempered "near-just"
> intervals. My "reasoned" approach is that there are many degrees
> of almost exact equivalence, approximate equivalence, "in the
> same general ballpark," and "quite distinct from."
>
> Near one end of this spectrum, I'd say that a tempered
> 126.6-138.3-230.9 cents in 1024-EDO is a "near-just" rendition of
> Ibn Sina's 14:13-13:12-8:7 (128.30-138.57-231.17 cents).
>
> How about 132.25-132.25-230.90? It's still rather closely related,
> I would say, but different not only in that 14:13 and 13:12 are
> each a lot less accurate, but more fundamentally in that they're
> both represented by the same tempered interval. That is to me a
> rather more significant compromise of Ibn Sina's superparticular
> concept.
>
> And what about Nelly Caron and Dariouche Safvate and their
> reported lower Shur tetrachord at 136-140-224 cents? We have the
> general idea of "two smallish neutral seconds plus a large tone
> approaching 8:7," but not quite Ibn Sina's septimal tuning.
>
> Let's compare Ibn Sina's Mustaqim tetrachord we've both been
> discussing at 9:8-13:12-128:117 or 204-139-155 cents (actually
> 128:117 is slightly closer to 156 cents, but I'm rounding down in
> order to have the fourth and upper minor third come out at 204
> and 294 cents), with Farhat's lower tetrachord for Avaz-e Afshari
> at 205-135-160 cents -- or, as a Turkish or Syrian theorist might
> say, 9-6-7 commas. Here I'd say that we're dealing with
> variations in tuning the same basic "type" of tetrachord --
> although in fact there's an important difference that the ratios,
> cents, or commas don't reveal!
>
> That difference is that a modern Afshari, at least as described
> by Farhat and exemplified by some of the pieces I've seen, tends
> to place much less emphasis on the second note of the tetrachord
> or the interval of a usual ~9:8 tone leading up to it than I
> might guess could occur in Ibn Sina's Mustaqim. In this context
> in the modern dastgah system, the descending small neutral third
> Ep-C (following Farhat's examples with Shur on D) may act more
> like a simple rather than composite melodic interval, so that we
> could include it as a category in its own right, although Farhat
> (p. 26) discusses it as a composite. Some of the gushe-ha of
> Dastgah-e Mahur do shift from a major to a small neutral third
> above C with all steps of the tetrachord C-D-Ep-F (~0-205-340-500
> cents) in use and lots of conjunct motion, so that might be a
> closer parallel to a possible melodic procedure for the medieval
> Mustaqim.
>
> So I may be sort of weird in focusing on superparticular or other
> rational ratios and at the same time seeing things as a continuum
> amenable to measurement in cents, commas, or what have you. If I
> play the tetrachord above the final of Shur or Arab Bayyati as
> 138.3-150.0-207.4 cents, I tend to think of this as "a near-just
> 52:48:44:39" or 13:12-12:11-44:39 (138.6-150.6-208.8 cents),
> although it's only an approximation. And if I encountered this
> tetrachord in some medieval Near Eastern source (or secondary
> source), I'd be jumping up and down with joy, at least
> metaphorically speaking, and celebrating on the Tuning list.
>
> Of course, there are caveats, including that fact that I'm not
> aware of any medieval source describing or advocating the
> practice of tempering fifths and fourths very slightly wider and
> narrower respectively than pure.
>
> And while duly noting that Safi al-Din's arithmetic division of
> 64:59:54:48 or 64:59-59:54-9:8 at 140-154-204 cents is different
> from my tempered 138.3-150.0-207.4 cents or for that matter a
> pure 52:48:44:39 (most notably, the minor third at 32/27 or 294
> cents in Safi al-Din is narrowed to 13/11 or 289.2 cents in my JI
> tuning, and yet a bit more to 288.3 cents in my tempered
> version). However, I'd consider them all in the same ballpark,
> with the first neutral step notably smaller than the following
> one, the minor third in the region of 13/11 or 32/27 (rather than
> 7/6, say), and the upper step not too far from 9:8; and any of
> them might go over well in Cairo or Tehran, although some
> empirical tests of that proposition might be prudent!
>
> As Ozan might say, we have infinite flavors and shadings. I find
> it possible to embrace the continuum while noting similarities
> and differences in a reasoned way, although this is by nature
> indeed an inexact art.
>
> > Cris
>
> With many thanks,
>
> Margo
> mschulter@...
>

🔗Margo Schulter <mschulter@...>

Carl wrote:

> Margo wrote:

>> Thus Turkish Rast often has a middle third at around 16/13,
>> or a bit higher (e.g. 21/17 or 26/21),

> My problem with the use of such ratios is that they imply a kind of
> accuracy that isn't there. These intervals are not perceptibly more
> consonant than their (irrational) neighbors, like the intervals 5/4,
> 7/6, 7/5 et al are. Therefore maqam musicians would not intone them
> unless they deliberately tried to do so. For instance, one would
> need bearing plans to tune them on, e.g. qawanin in advance. Is
> there evidence such bearing plans are used? It seems that if they
> were, the encroachment of 12-ET music would be not so much a
> threat...

Hi, Carl.

First, please let me acknowledge some things you've explained by
confirming my understanding that you're speaking not as a musician
specifically focusing on maqam music, but as a performer and student
of intonation bringing your own experience to bear on statements that
you feel merit a query. And that's a fair invitation to dialogue, in
which people may learn from each other.

In part, this may be a matter of general outlook and philosophy, which
I'll briefly consider before getting to the practical issues you
raise, with the very major caution, in the spirit of your own
disclaimers, that someone who actually tunes and plays Near Eastern
instruments might have a lot more to contribute than I do on questions
of how these instruments are tuned!

Philosophically, I do tend to envision interval space as a continuum
with rational ratios, small and large, as delightful landmarks. Much
of the medieval Islamic theory involves quite complex ratios, and
there's always the argument that in practice things are a lot less
precise. Often when I speak of "16/13" or "21/17" or "26/21" I'm
thinking of a general region, or maybe even of overlapping regions,
and I suspect that Ozan (although he must speak for himself!) might be
taking a somewhat similar outlook when he lists the steps of his
79-tone qanun, for example, and suggests some possible just
interpretations.

Let me confirm that what I take to be an important point you raise,
that certain JI distinctions are much smaller than the variations we
expect in performance, certainly is valid! For example, in a
synthesizer tuning, I happen to have large neutral thirds at around
369.1 cents and 370.3 cents. Rather humorously, I might say that this
temperament "distinguishes 99/80 from 26/21" -- both of which are
rations coming up in medieval Near Eastern tunings --but it's
obviously an academic point if we're talking about likely ensemble
performances.

However, there are distinctions that I hear as significant, and
suspect that a seasoned Near Eastern musician growing up with maqam or
dastgah music may hear yet better and more significantly. Thus the
region around 357-359 cents feels to me a bit different than 369-370
cents, with the latter having a "submajor" quality. And distinctions
of around a comma are in my view certainly significant. Others whom I
respect, from the Near East and elsewhere, find such distinctions
significant also.

Amine Beyhom, in a portion of his thesis available on the Web,
discusses a survey to see how listeners would place the second note of
Maqam Bayyati. He found that people liking a "learned" or "academic"
style placed it at around 155 cents above the final or resting note of
the maqam. People attuned to a "popular" interpretation, however,
placed it at around 130 cents. That's a difference of a full comma. We might or might not wish to associate the first, higher, placement
with something like "128/117" and the second with "14/13" or the like;
I tend to do that because I consider the contemplation of such ratios
ennobling in itself, but Beyhom himself simply gives the values in
cents, and those are sufficient to suggest that, allowing for
variations of +-5 cents or the like, comma differences are real and
significant.

In Egypt, Scott Marcus found that traditional musicians understood,
similarly, that the note sikah (an Arabic form of Persian or Turkish
segah) must be tuned lower for Maqam Bayyati than for Maqam Rast, at
about 135-145 cents above the step dukah. Note that is a bit higher
than the 130 cents favored in the "popular" Lebanese tuning of
Bayyati.

Why don't I explain a bit about the "sikah is lower in Bayyati"
concept. Let's suppose we're tuning an Egyptian Rast. Unfortunately,
Marcus, doesn't give values in cents (or ratios, for that matter).
However, he does comment that the tuning of fretted instruments using
many pure fifths or fourths does tend to favor a Pythagorean or
similar intonation of lots of regular intervals such as minor thirds.
If major second are around 204 cents, and minor thirds around 294
cents, then the following tuning of Rast would be interestingly close
to that of al-Farabi:

0 204 354 498
rast dukah sikah jaharkah
204 150 144

Here I picked an even 150 cents for the sake of simplicity; 12/11, of
course, would be 150.637 cents, and I warmly agree with you that an
"11-limit" concept is really likely irrelevant here in a monophonic or
heterophonic context -- and also, I'd add, in the kind of polyphonic
texture I do enjoy composing or improvising which might have lots of
"ratios of 2-3-7-11-13," many of them quite complex, but very rarely
something like 4-6-7-9-11, which even then wouldn't fit the "11-limit"
concept of something like 4-5-6-7-9-11. That's an aside, just to
acknowledge that either maqam music or my typical polyphonic style in
this kind of context is part of a "non-Partchian" universe so that the
"limit" concept may more confuse than illuminate.

Anyway, the significant thing here is that traditional Egyptian
musicians feel that in tuning Bayyati, sikah needs to be somewhat
lower, at around 135-145 cents above dukah. Here I'll show the lower
tetrachord of Bayyati, along with the step rast below it:

dukah: 0 140 294 498 rast: 0 204 344 498 702
rast dukah sikah jaharkah nawa
204 140 154 204

Here I'm taking 140 cents as a "middle of the road" value for Marcus's
suggestion of 135-145 cents, and I'll restrain myself from the fun of
suggesting kindred just ratios. The basic perspective shared by many
traditional musicians can be stated as holding either that sikah needs
to be lower (here about 10 cents) in Bayyati than in Rast, with the
other "Pythagorean" steps remaining more stable (basically, in terms
of rast, 1/1-9/8-4/3-3/2, or rast-dukah-jaharkah-nawa); or that, in
Bayyati, the first ascending neutral second should be smaller than the
second.

And there's another point noted by Marcus: many traditional performers
have an additional understanding that while the neutral second step of
Bayyati should be smallish, maybe 135-145 cents, a step occurred at a
neutral third below the final, and sometimes a neutral sixth above,
should be considerably _higher_. Marcus doesn't give values in cents,
but if the neutral second is at 140 cents and the neutral sixth at
around 855-860 cents -- or the neutral third below at about 340-345
cents from the final -- then we'd have a narrow fourth from the third
below to the neutral second above at around 480-485 cents or so, and
likewise a wide fifth from the neutral second to the neutral sixth
above at around 715-720 cents. Thus there's an element of deliberate
asymmetry involved.

These are, of course, precisely the kind of nuances which can be lost
to incursions of 12-EDO/24-EDO. According to Ali Jihad Racy in his
book _Making Music in the Arab World: The Culture and Artistry of
Tarab_, the problem is that current qanuns often lack sufficient
levers to make fine microtonal distinctions; and also that, rather
than being set by an informed musician to fit the nature of a given
maqam, they are often tuned to match keyboard instruments in 24-EDO.

>> More specifically, 350 cents would evidently be too low for a
>> stylish Turkish Rast, where a "low" but acceptable third might be
>> around 16/13; a common historical choice

> 16/13 is only 9 cents different from 350 cents, in the middle of
> nowhere (no nearby consonance minima). Intoned on instruments
> routinely employing vibrato and other effects ranging from 20 cents
> to several semitones. Forgive me if I am dubious. Even the best
> barbershop quartets, with the pull of strong consonances to guide
> them, and a vibratoless style, seldom do better than 5 cents
> accuracy, as I know from carrying out painstaking spectral analysis
> of barbershop recordings, as well as having been a barbershop singer
> myself.

Here I suspect that we may be talking in good part abuut the
perception of fine differences in interval sizes, but not necessarily
miniscule ones, e.g. 135 cents vs. 155 cents or the like.

I must admit that "the middle of nowhere" isn't exactly my concept of
the region around 16/13: I visualize al-Farabi's 27/22 (355 cents),
Jacques Dudon's 59/48 (357 cents), 16/13 itself, 69/56 (361 cents),
121/98 (365 cents), 21/17 (366 cents), 99/80 (369 cents), and 26/21
(370 cents). Then again, for the past decade, I've been tending to
hang out with my synthesizer on "plateaus" like this, often descending
to the valleys of 1/1, 4/3, 3/2, and 2/1, and also having a weakness
for 7/6 and 7/4. Of course, when I play in a 16th-century style
in meantone, that is often what could be called a "5-limit" context --
but otherwise, limits may be pretty much inapplicable.

I do consider it worthwhile to say that however debatable my
invocation of ratios may be, I've resolved to avoid the "limit"
concept where it may simply not apply, which in this kind of Near
Eastern concept could be just about everywhere. And I'm not familiar
with any discussion of "limit" by Safi al-Din al-Urmawi, for example,
unless we want to speak of a "3-limit" concept of the main concords
(much like the Greek or medieval European concept of _symphoniae_).
And, in my neomedieval polyphony (drawing on European or Near Eastern
materials), that concept does generally have operational meaning, with
conclusive cadences resolving to "3-limit" sonorities (just or
tempered).

This is purely a guess, but I might hypothesize that performers in a
monophonic or heterophonic context might focus keenly on small
distinctions in melodic interval sizes, say on the order of a comma,
or possibly of a yarman (2/159 octave or so, about 15 cents). Of
course, that fact that I do it on a synthesizer keyboard with some
comma distinctions available doesn't tell us if or how Near Eastern
performances are doing it; but some of them tell us that such
distinctions are practice, worthwhile, and important.

In a polyphonic context, I've found that 13/8 can sound simple and
notably resonant in comparison to 21/13, which is more complex and
active, although in my stylistic context both seek resolution in much
the same general types of progressions (e.g. expansion to an octave);
or, more specifically, tempered forms at around 829.7 or 830.9 cents
in comparison to 841.4 or 842.6 cents.

[from another message, which I'm responding to in this single reply,
since the discussion seems closely related]

>> [snip] while the
>> "theoryVSpractice" study has shown that Turkish musicians
>> may lean toward 9 7 6 commas [snip]

> Which study are you referring to?

That's a fair question:

<http://www.ozanyarman.com/files/theoryVSpractice.pdf>

"Weighing diverse theoretical models..." -- evidentally the same one
you've been looking at also. One lesson is that if I had cited the
title as well as a rather cryptic fragment of the file name, I might
have been clearer!

>> When people are measured with 21st-century technology playing on
>> the Turkish ney, for example, genera or ajnas much like those
>> described by Safi al-Din and Qutb al-Din seven centuries ago, or
>> Ibn Sina a millennium ago, and distinct from 24-EDO, I tend to take
>> these theorists quite seriously.

> Again, which study(ies) are you referring to?

That's another very fair question. One example is the one from Ozan's
thesis on which you quote me below. The other is a study by Amine
Beyhom which should be available on the Web, "Des criteres
d'authenticite dans les musiques metisses et de leur validation:
exemple de la musique arabe":

<http://www.beyhom.com/download/articles/Beyhom_2007_%20Des_criteres_d_authenticite_filigrane_n5.pdf>

Beyhom records an improvisation by the Turkish performer Kudsi Erguner
on the ney in Maqam Hijaz with the sequence 0-131-368-501 cents, or
131-237-133 cents. This seems to me quite similar to a medieval Buzurg
genre, for example 1/1-14/13-16/13-4/3 or 1/1-13/12-26/21-4/3 -- or,
more precisely, the lower fourth of Buzurg, which is a 3:2 division.
Even Beyhom's brief excerpt is a lot more complicated than this, but a
"Buzurg" type of structure, at least at times, is an interesting
reading.

>> Compare, for example, the measured intervals in Niyazi's
>> Sayin's Ushshak Ney Taksim (Ozan's thesis, p. 29) with either
>> the original form or a permutation of a tuning by Ibn Sina in
>> the early 11th century at 28:26:24:21 or 1/1-14/13-7/6-4/3:
>>
>> Measured: 123.47 137.13 227.87
>>
>> Ibn Sina: 14:13 13:12 8:7
>> 128.30 138.57 231.17

> On pg. 25 it is stated,
> "This research confirmed suspicions that the 'melodic intervals'
> most haracteristic of the genre are expressible by such epimoric
> ratios"

> Cited are the paper "Non-deterministic Scales..." by Can Akkoc,
> which most certainly does NOT conclude anything of the kind, and a
> paper and website in Turkish by one M.K. Karaosmanoglu (who is
> Ozan's coauthor on the more recent "Weighing Diverse..." already
> mentioned). Here's the website:

> http://www.musiki.org/mkk_vekom_2004_sunum.htm

> I see nothing here establishing this claim either, even with
> the help of Google Translate. At any rate "Weighing Diverse"
> is more recent and in English and I will come back to it in
> a subsequent post (time permitting).

"Weighing diverse theoretical models" is the document with which I'm
familiar so far. I'll see if I can look into this other.

> On pg.28 we see that the data are in fact being fitted to the
> ratios used. But why are ratios appropriate?

Well, while I'd want to be careful that ratio characterizations don't
overshadow the actual values in cents or fractional commas, ratios can
serve as useful signposts for certain regions, e.g. 16/13 or 26/21.
A caution is that, especially with aggregate data, performers might be
closely approximating a variety of ratios, which may "average out" to
a value which happens to coincide also with some ratio, but not
necessarily the most influential one. This caution, of course, also
applies to averaging values in cents. Thus if a neutral sixth from a
given location of interest on a number of Persian tar or setar tunings
averages out at around 835 cents, that might leave open the
possibility that some performances like a 21/13 flavor and others a
13/8 flavor; that many of them are actually seeking a size right
around 835 cents (say 34/21, or maybe Phi as a point of maximum
complexity), etc.

Intuitively, I'd say that Ozan's example in his thesis from a
performance of Maqam Ushshaq on ney, 123.5-137.1-227.9 cents, is close
enough to 14:13-13:12-8:7 to be worth noting the parallel. Of course,
if it happened in a context with a drone, then 260.6 cents might be
close enough to the "7/6 valley" to be vertically notable also.
However, I think of the resemblance to Ibn Sina's tuning (or a
permutation thereof), as well as the variations (e.g. the narrow
fourth by comparison to 4/3), as something inherently fascinating.

But I'd add that aggregate data in cents or fractional 53-EDO commas,
whatever the relevance or otherwise of ratios, can point up some
interesting things. For example, taking things very broadly, I at
least get the idea that the neutral third step (segah) in a Turkish
Rast will be rather higher than a demififth at around 351 cents, maybe
360-370 cents or somewhere around "16 commas" (I'll spare you my
rational glosses, especially since I've already invoked most of them
earlier in this message!), and sometimes around 380 cents, getting
into the region of 5/4, so that we have a small major rather than
large neutral or submajor third.

In contrast, certain melodic themes of gusheh-ha of the Persian
Dastgah-e Mahur use a tetrachord around maybe 0-205-340-495 cents.
Here I think we can recognize the distinction between a neutral third
at around 335-345 cents, say, and 360-370 cents in Turkish Rast -- a
difference of around a comma, as expressed by the Turkish or Syrian
53-comma notations of 9-6-7 or 9-7-6.

We may have a situation a bit like in natural language, where the
"target regions" for two phonemes may overlap, but a large number of
measurements show that they are focused or centered on distinct
regions.

> -Carl

Best,

Margo
mschulter@...

🔗Carl Lumma <carl@...>

Hi Margo,

Thanks for your reply.

> Philosophically, I do tend to envision interval space as a
> continuum with rational ratios, small and large, as delightful
> landmarks. Much of the medieval Islamic theory involves quite
> complex ratios, and there's always the argument that in
> practice things are a lot less precise. Often when I speak of
> "16/13" or "21/17" or "26/21" I'm thinking of a general region,
> or maybe even of overlapping regions,and I suspect that Ozan
> (although he must speak for himself!) might be taking a somewhat
> similar outlook when he lists the steps of his 79-tone qanun,
> for example, and suggests some possible just interpretations.

I suppose it's OK to use the rationals as a ruler, and I
suspect that's what the theorists of antiquity were doing, not
being familiar with logarithms.* The advantage of the latter,
of course, is that they can be easily doled out in perceptually
equal units, as any good ruler contains. If you say you have
two pieces of wood for sale measuring 26/21 and 31/25 relative
to a 12" stick, I'm going to reach for my pocket calculator.
Such systems are cumbersome because each denominator is
effectively an independent system of units. And I definitely
object to calling intervals so measured intervals of just
intonation. The word "just" makes a literal and practical
contribution to the term, and the term has a long history of
meaning 'intervals distinguishable by their concordance'.

> Let me confirm that what I take to be an important point you
> raise, that certain JI distinctions are much smaller than
> the variations we expect in performance, certainly is valid!

I would say, certain RI (rational intonation) distinctions are.

> Thus the region around 357-359 cents feels to me a bit
> different than 369-370 cents, with the latter having a
> "submajor" quality.

Well, sure. Under lab conditions the melodic JND is about
4 cents and the harmonic JND about 1 cent. In musical
performance, they are some function of the average stable
pitch duration (down to the lab-condition levels).

So I would not doubt it if you told me that when Nihavent
vs Hijaz (to pick examples out of thin air) are tuned up or
performed, one consistently winds up with an interval about
10 cents larger than the other. And that is precisely where
I see the subtly of maqam music -- the variety of melodic
structures employed.

What I have never heard is two intervals differing by 10
cents intentionally juxtaposed in a piece. If you know of
a recording of such a thing, please share it.

> I consider the contemplation of such ratios
> ennobling in itself, but Beyhom himself simply gives the values
> in cents, and those are sufficient to suggest that, allowing for
> variations of +-5 cents or the like, comma differences are real
> and significant.

Yes, of this I have no doubt.

> Here I picked an even 150 cents for the sake of simplicity;
> 12/11, of course, would be 150.637 cents, and I warmly agree
> with you that an "11-limit" concept is really likely irrelevant
> here in a monophonic or heterophonic context

Whew. :)

> and also, I'd add, in the kind of polyphonic
> texture I do enjoy composing or improvising which might have
> lots of "ratios of 2-3-7-11-13," many of them quite complex,
> but very rarely something like 4-6-7-9-11, which even then
> wouldn't fit the "11-limit" concept of something like
> 4-5-6-7-9-11.

Yes, there's a bit of a terminology lack here. I don't see
a problem calling the first case 13-limit or the second
11-limit, but as we leave out more identities things get a
bit hairy. Simply giving the identities as you did here may
be best.

> The basic perspective shared by many traditional musicians
> can be stated as holding either that sikah needs to be lower
> (here about 10 cents) in Bayyati than in Rast,

There you see, I should read ahead before replying (busted!).
I wouldn't have had to fabricate an example.

> These are, of course, precisely the kind of nuances which can
> be lost to incursions of 12-EDO/24-EDO.

No doubt. However, I also hear some stuff that for whatever
reason is about as nearly 24-EDO as can be. I still enjoy it
quite a bit, because our world is so starved for variety,
though I wouldn't doubt it has replaced something still more interesting if you told me so.

> I must admit that "the middle of nowhere" isn't exactly my
> concept of the region around 16/13: I visualize al-Farabi's
> 27/22 (355 cents), Jacques Dudon's 59/48 (357 cents),
> 16/13 itself, 69/56 (361 cents), 121/98 (365 cents),
> 21/17 (366 cents), 99/80 (369 cents), and 26/21 (370 cents).
> Then again, for the past decade, I've been tending to hang
> out with my synthesizer on "plateaus" like this [snip] but
> otherwise, limits may be pretty much inapplicable.

(I hope I elided well.) I would say the rationals are pretty
much inapplicable. That these different intervals sound
differently because of their size alone (and/or their proximity
to JI intervals) and could be recognized after a specific
program of arduous training, I would never doubt. (I do doubt
a monochord would be sufficient for such training, however.)

> >> [snip] while the
> >> "theoryVSpractice" study has shown that Turkish musicians
> >> may lean toward 9 7 6 commas [snip]
> >
> > Which study are you referring to?
>
> That's a fair question:
>
> http://www.ozanyarman.com/files/theoryVSpractice.pdf

Ah, that's Weighing diverse.

> The other is a study by Amine Beyhom which should be available
> on the Web, "Des criteres d'authenticite dans les musiques
> metisses et de leur validation: exemple de la musique arabe":

That definitely looks worth reading. Unfortunately it's not
in the one language my American upbringing imbued me with. :(

> > On pg.28 we see that the data are in fact being fitted to
> > the ratios used. But why are ratios appropriate?

My new answer to my own question is that Caliphate theorists
used rationals to measure intervals because that was the
known/approved method, and now modern theorists are fitting
their data to the rationals because it is still (inexplicably)
the known/approved method. Of course practicing maqam
musicians don't use such rations any more today than they
did back then and we sorely need to move to cents.

-Carl

* Logarithms were known of course, but not used widely.