Tuning of Bayyati, Ushshak, and Shur

Dear Marcel and Hans,

Here I will address the tuning of Arab Bayyati and related modal
types such as Turkish Ushshak and Persian Shur, but without
expressing any views as to harmonizations in a European triadic
style. Certain some 20th-21st century Near Eastern musicians have
done or advocated such harmonizations, but my own approach to
maqam-based or dastgah-based polyphony is different. And, above
all, I would emphasize that this is mainly monophonic music with
an emphasis on pure melody, although drones and devices such as
parallel fourths or fifths do occur in traditional performances.

A very widespread pattern for these modes is a small neutral
second maybe at around 13/12 (139 cents), followed by a larger
neutral second maybe at around 12/11 (151 cents) or 128/117 (155
cents), followed by a whole tone at 9/8 (204 cents) or sometimes
a bit larger.

Marcel, the Pythagorean comma or 53-EDO notation of 6-7-9 commas
very nicely expresses this, and a Pythagorean tuning of
137-157-204 cents would be fine for the kind of Egyptian Bayyati
that Scott Marcus describes with the lower step at around 135-145
cents, as well as for a Syrian school which simply defines the
Bayyati tetrachord as 6-7-9 commas.

For Persian Shur, Hormoz Farhat suggests something like
135-155-205 cents, interestingly very close to a permutation of
one of Ibn Sina's favorite tetrachords from the early 11th
century, which gives 13:12-128:117-9:8 or 139-155-204 cents.

In JI, an attractive form of Bayyati, Ushshak, or Shur has a
13:12:11 division, i.e. 52:48:44:39 or 13:12-12:11-44:39
(139-151-209 cents).

In 20th-century Turkish theory, which often prefers to avoid
neutral intervals, an alternative form of Ushshak (a name from
Arabic ushshaq, "the lovers," for a Turkish maqam generally
corresponding to Arab Bayyati) is 8-5-9 commas, or essentially
10:9-16:15-9:8. Note that in this 5-limit interpretation, the
larger or diminished third step comes first. However, even while
this kind of theory was the norm in Turkey, traditional
performers would use an "unofficial" step sometimes called
ushshak, which Karl Signell measured at around 140 cents --
pretty much agreeing with Marcus, Farhat, and the 6-7-9 comma
concept of Syria.

However, some Near Eastern performers prefer other intonations.
Especially for players of fixed-pitch instruments in the Arab
world where Rast is "the mother of all maqamat," with a lower
tetrachord at around 9-7-6 commas (e.g. 200-155-145 cents in
Lebanon, according to Amine Beyhom), there is a tendency to leave
the neutral third step of Rast, called sikah (or segah in Persian
and Turkish), unchanged for Bayyati, which becomes 7-6-9 commas,
something like 157-137-204 cents in theory and not too far from
this in practice.

In part this may be inertia, or the difficulty of retuning sikah
from its Rast position to a lower Bayyati position, but as
fastidious a musician as Tawfiq al-Sabbagh of Syria, much
interested in comma nuances that can make different maqamat more
beautiful, takes 7-6-9 commas as a correct Bayyati. So it would
seem that either 6-7-9 commas or 7-6-9 commas has its place.

Indeed Beyhom reports that a "classical" Lebanese practice
prefers the first neutral step of Bayyati at around 155 cents
(suggesting 7-6-9 commas or similar approach), but in a "popular"
or "folk" style it is much lower, at 130 cents or so, a
difference of 25 cents.

There is also the question of whether the minor third should be a
full Pythagorean 32/27 or 13 commas (294 cents), as the formula
of 6-7-9 or 7-6-9 commas would suggest, or somewhat smaller.
Marcus suggests that in Egypt, 32/27 may be about right -- a bit
smaller, in practice, than the 300 cents of 24-equal theory. In
other places, however, the third may be slightly or considerably
narrower. Ali Jihad Racy of Lebanon notes that the third of
Bayyati is smaller than the 32/27 from three pure fourths,
although he does not specify how much smaller -- in Arab thought,
a "comma" can be any small interval, not necessarily any specific
ratio such as 64:63 in this connection, for example (which would
yield a 7/6 third).

In 1966, Nelly Caron and Dariush Safvate reported a Persian
tuning of Shur, generally analogous to Arab Bayyati, at
136-140-224 cents -- the 276-cent third being about 9 cents wide
of a pure 7/6. More recently, Dariush Tala`i has recommended a
Shur tuning of 140-140-220 cents, for which 17-EDO offers a
reasonable approximation at 141-141-212 cents. Thus equal or
near-equal neutral steps are not necessarily wrong, although
Farhat and the 6-7-9 comma model reflect a widespread preference
that the first step be markedly smaller than the second.

There are also JI or near-JI models based on ratios involving
prime 13, whose use as an important factor in Near Eastern
tunings goes back to Ibn Sina. Thus a 6-7-9 comma model
(137-157-204 cents) is more or less synonymous with the 13:12:11
division of 52:48:44:39 or 139-151-209 cents. For the kind of
division described by al-Sabbagh at 7-6-9 commas, a division of
33:36:39:44 or 11:12:13 (151-139-209 cents) is synonymous. One
can also use a septimal tuning of 12:13:14:16 (139-128-231 cents)
or 28:26:24:21 (128-139-231 cents) with a 7/6 third.

Tunings of Shur like those of Dariush Safvate or Dariush Tala`i,
with the third at around 275-280 cents, suggest another JI or
near-JI variation, although with more unequal neutral steps than
the Iranian examples of 136-140-224 cents or an equal 140-140-220
cents. This variation would be 14:13-12:11-143:126 (128-151-219
cents) or the like, with a third at around 168:143 or 279 cents,
a size typical of Iranian music.

Here's a tempered tuning of Shur approximating this just division
by steps of 125.4-150.0-220.3 cents. I should add that while Arab
Bayyati, Turkish Ushshak, and Persian Shur share similar lower
tetrachords and some other traits (like a typical minor sixth
degree above the final, but a neutral third below it, a fine
example of octave nonequivalence), each modal form has its own
special characteristics. For example, Persian Shur often replaces
the 3/2 fifth with a lowered or koron step about a thirdtone flat
of this, with 13/9 as one classic ratio, as occurs in this piece.

<http://www.bestII.com/~mschulter/Homage_to_Dariush_Safvate.mp3>

Also, a quick note on the Arab and Turkish maqamat. Arab Bayyati
and Turkish Ushshaq are similar. Each has a variation where the
second tetrachord on the 4/3 step, usually Nahawand (9-4-9
commas) or Rast (9-7-6 commas), is replaced by a form of Hijaz.
I often play it at around 4-12-6 commas, although practices can
vary greatly. But the main point here is that in this offshoot
of Bayyati or Ushshak, this Hijaz tetrachord above 4/3 introduces
a smallish tritone somewhere around 1024/729 (588 cents) or maybe
88/63 (578 cents), for example. This note, which would be at some
kind of minor sixth above the step rast (since Bayyati starts on
the 9/8 of Rast, called step dukah in Arabic or dugah in Persian
and Turkish), is called shuri in Arab theory, but beyati in
Turkish theory.

Thus the Arabs have Maqam Bayyati, with Shuri as the variation
with Hijaz on 4/3, while the Turks have Makam Ushshak with Beyati
as the variation. It can be helpful to remember that Turkish
Beyati corresponds most directly to Arab Shuri, rather than to
Arab Bayyati (the counterpart of Turkish Ushshaq). Persian Shur
is a bit different, and uses a lowered fifth degree -- but not
generally in the context of a Hijaz tetrachord (or Chahargah, as
a similar tetrachord is called in the Persian system, for example
something like 6-12-4 commas or 135-275-85 cents).

Also, Scott Marcus makes a point that applies to some tendencies
in Turkish as well as Arab intonation: while the neutral second
step of Bayyati or Ushshaq often tends to be small (say 125-145
cents), the neutral sixth, when it's used, tends to be higher,
say 855-870 cents. This fits with the fact that while a Bayyati
tetrachords is often 6-7-9 commas, the neutral sixth step tends
to occur as part of Rast tetrachord on the 4/3 step, which is
9-7-6 commas or the like. Here's a tempered tuning with support
the three most common forms of upper tetrachords: Nahawand, Rast,
or Hijaz (the last in the Shuri variation):

! met24-bayyati9_fsharp.scl
!
Set for Maqam Bayyati and Maqam Shuri
9
!
139.45312
289.45312
496.87500
577.73437
704.29687
785.15624
867.18750
992.57812
2/1

For Nahawand on 4/3, we have 497-704-785-993 cents, or
207.4-80.9-207.4 cents, with a minor sixth near 11/7 (or 52/33).
For Rast on 4/3, we have 497-704-867-993 cents, or
207.4-162.9-125.4 cents, with a neutral sixth near 104/63, and at
around a large 32/21 fifth rather than 3/2 from the second degree
of Bayyati at 139 cents, near 13/12. And for Maqam Shuri, with
Hijaz on 4/3, we have 497-578-867-993 cents, or 80.9-289.5-125.4
cents (roughly 21:22:26:28), again using the high neutral sixth
step. A Rast tetrachord with the third at 370 cents or so is
common in some Syrian styles, for example in Aleppo, although
other regions might place this step at 355-360 cents.

To sum all this up: I would say a model of 6-7-9 commas for
Bayyati, Ushshaq, or Shur is a good place to start, allowing for
a range of fine tunings, and also noting that 7-6-9 commas often
occurs in Arab practice, and is favored by some theorists such as
al-Sabbagh. Some Arab, Turkish, and Persian musicians lean toward
a minor third rather smaller than 32/27, with something subtly
narrower like 13/11 or 33/28 appearing common in Persian
practice, along with some reported or recommended tunings like
276 cents which are closer to 7/6. And I find 12:13:14 or
14:13:12 a very pleasant division, recognized in medieval theory,
which may occur now and then in modern Near Eastern practice.

With many thanks,

Margo Schulter
mschulter@...

Dear Margo,

Thank you soo much for this wealth of information!
Will keep this around for reference!

> Marcel, the Pythagorean comma or 53-EDO notation of 6-7-9 commas
> very nicely expresses this, and a Pythagorean tuning of
> 137-157-204 cents would be fine for the kind of Egyptian Bayyati
> that Scott Marcus describes with the lower step at around 135-145
> cents, as well as for a Syrian school which simply defines the
> Bayyati tetrachord as 6-7-9 commas.
>

Yes that's the one I'm going with for now. In enharmonic notation on D: D - Cx# - F - G

>
> For Persian Shur, Hormoz Farhat suggests something like
> 135-155-205 cents, interestingly very close to a permutation of
> one of Ibn Sina's favorite tetrachords from the early 11th
> century, which gives 13:12-128:117-9:8 or 139-155-204 cents.
>
> In JI, an attractive form of Bayyati, Ushshak, or Shur has a
> 13:12:11 division, i.e. 52:48:44:39 or 13:12-12:11-44:39
> (139-151-209 cents).
>

All seem like the same thing to me, so close to each other I can't see them expressing a different note.

> In 20th-century Turkish theory, which often prefers to avoid
> neutral intervals, an alternative form of Ushshak (a name from
> Arabic ushshaq, "the lovers," for a Turkish maqam generally
> corresponding to Arab Bayyati) is 8-5-9 commas, or essentially
> 10:9-16:15-9:8. Note that in this 5-limit interpretation, the
> larger or diminished third step comes first. However, even while
> this kind of theory was the norm in Turkey, traditional
> performers would use an "unofficial" step sometimes called
> ushshak, which Karl Signell measured at around 140 cents --
> pretty much agreeing with Marcus, Farhat, and the 6-7-9 comma
> concept of Syria.
>

Aah ok interesting, that would correspond to D-Fb-F-G and not to D-D#-F-G as I thought the Turkish interpretation was like.

> However, some Near Eastern performers prefer other intonations.
> Especially for players of fixed-pitch instruments in the Arab
> world where Rast is "the mother of all maqamat," with a lower
> tetrachord at around 9-7-6 commas (e.g. 200-155-145 cents in
> Lebanon, according to Amine Beyhom), there is a tendency to leave
> the neutral third step of Rast, called sikah (or segah in Persian
> and Turkish), unchanged for Bayyati, which becomes 7-6-9 commas,
> something like 157-137-204 cents in theory and not too far from
> this in practice.
>

Ahaa, I would translate this to D-Gbbb-F-G.
Indeed 157-137-204 in Pythagorean.

> There is also the question of whether the minor third should be a
> full Pythagorean 32/27 or 13 commas (294 cents), as the formula
> of 6-7-9 or 7-6-9 commas would suggest, or somewhat smaller.
> Marcus suggests that in Egypt, 32/27 may be about right -- a bit
> smaller, in practice, than the 300 cents of 24-equal theory. In
> other places, however, the third may be slightly or considerably
> narrower. Ali Jihad Racy of Lebanon notes that the third of
> Bayyati is smaller than the 32/27 from three pure fourths,
> although he does not specify how much smaller -- in Arab thought,
> a "comma" can be any small interval, not necessarily any specific
> ratio such as 64:63 in this connection, for example (which would
> yield a 7/6 third).
>
> In 1966, Nelly Caron and Dariush Safvate reported a Persian
> tuning of Shur, generally analogous to Arab Bayyati, at
> 136-140-224 cents -- the 276-cent third being about 9 cents wide
> of a pure 7/6. More recently, Dariush Tala`i has recommended a
> Shur tuning of 140-140-220 cents, for which 17-EDO offers a
> reasonable approximation at 141-141-212 cents. Thus equal or
> near-equal neutral steps are not necessarily wrong, although
> Farhat and the 6-7-9 comma model reflect a widespread preference
> that the first step be markedly smaller than the second.
>

Ok interesting again. First I heard about the minor third being smaller sometimes.
For me in Pythagorean there's a double diminished fourth at 271 cents.

> To sum all this up: I would say a model of 6-7-9 commas for
> Bayyati, Ushshaq, or Shur is a good place to start, allowing for
> a range of fine tunings, and also noting that 7-6-9 commas often
> occurs in Arab practice, and is favored by some theorists such as
> al-Sabbagh. Some Arab, Turkish, and Persian musicians lean toward
> a minor third rather smaller than 32/27, with something subtly
> narrower like 13/11 or 33/28 appearing common in Persian
> practice, along with some reported or recommended tunings like
> 276 cents which are closer to 7/6. And I find 12:13:14 or
> 14:13:12 a very pleasant division, recognized in medieval theory,
> which may occur now and then in modern Near Eastern practice.
>
> With many thanks,
>
> Margo Schulter
> mschulter@...
>
> Thank you again Margo!
I will explore the variations you've given me.

Kind regards,
Marcel de Velde

Hi Margo,

I join Marcel in thanking you for this very informative post! I was a little
surprised to read that even near-eastern performers sometimes play Bayati with
the larger neutral second first - this vast variety in tuning practices, not
just between regions but sometimes even between individual musicians, can really
be a source for despair... I will stay with 17edo for now, but I am thinking of
trying 53edo or 46edo one day. I prefer equal systems over non-equal
well-temperaments since I like free transposability and modulation capability -
and more ease for harmonization - with not too many notes (still enough,
however...). As for 29edo, I think the Rast scale in it comes out with a third
close to 5/4, so I would say it is suited for turkish Rast but less so for
arabic Rast, correct?

Here is now my harmonization of the Bayati phrase by Najat Aatabou, in 17edo. It
is not triadic but only two voices, and you will hear that I avoid the decision
whether the base note of Bayati is to be harmonized as minor or major. As my
previous examples, I consider it a success insofar as it sounds pleasing (well,
to me, at least) but maybe rather a failure insofar as the original character
rof the maqam tends to be altered substantially, if not destroyed. Possibly this
is the fate of any tentative to introduce polyphony in maqam music - but let's
see what the future holds!

https://www.dropbox.com/s/a1da0e9asgzvcjp/BayatiCounterpoint17edoTest2.mp3

--

Hans Straub

--- In tuning@yahoogroups.com, <marcel@...> wrote:

Dear Margo,

Thank you soo much for this wealth of information!
Will keep this around for reference!

> Marcel, the Pythagorean comma or 53-EDO notation of 6-7-9 commas
very nicely expresses this, and a Pythagorean tuning of
137-157-204 cents would be fine for the kind of Egyptian Bayyati
that Scott Marcus describes with the lower step at around 135-145
cents, as well as for a Syrian school which simply defines the
Bayyati tetrachord as 6-7-9 commas.

Yes that's the one I'm going with for now. In enharmonic notation on D: D - Cx#
- F - G

>
For Persian Shur, Hormoz Farhat suggests something like
135-155-205 cents, interestingly very close to a permutation of
one of Ibn Sina's favorite tetrachords from the early 11th
century, which gives 13:12-128:117-9:8 or 139-155-204 cents.

In JI, an attractive form of Bayyati, Ushshak, or Shur has a
13:12:11 division, i.e. 52:48:44:39 or 13:12-12:11-44:39
(139-151-209 cents).

All seem like the same thing to me, so close to each other I can't see them
expressing a different note.

> In 20th-century Turkish theory, which often prefers to avoid
neutral intervals, an alternative form of Ushshak (a name from
Arabic ushshaq, "the lovers," for a Turkish maqam generally
corresponding to Arab Bayyati) is 8-5-9 commas, or essentially
10:9-16:15-9:8. Note that in this 5-limit interpretation, the
larger or diminished third step comes first. However, even while
this kind of theory was the norm in Turkey, traditional
performers would use an "unofficial" step sometimes called
ushshak, which Karl Signell measured at around 140 cents --
pretty much agreeing with Marcus, Farhat, and the 6-7-9 comma
concept of Syria.

Aah ok interesting, that would correspond to D-Fb-F-G and not to D-D#-F-G as I
thought the Turkish interpretation was like.

> However, some Near Eastern performers prefer other intonations.
Especially for players of fixed-pitch instruments in the Arab
world where Rast is "the mother of all maqamat," with a lower
tetrachord at around 9-7-6 commas (e.g. 200-155-145 cents in
Lebanon, according to Amine Beyhom), there is a tendency to leave
the neutral third step of Rast, called sikah (or segah in Persian
and Turkish), unchanged for Bayyati, which becomes 7-6-9 commas,
something like 157-137-204 cents in theory and not too far from
this in practice.

Ahaa, I would translate this to D-Gbbb-F-G.
Indeed 157-137-204 in Pythagorean.

> There is also the question of whether the minor third should be a
full Pythagorean 32/27 or 13 commas (294 cents), as the formula
of 6-7-9 or 7-6-9 commas would suggest, or somewhat smaller.
Marcus suggests that in Egypt, 32/27 may be about right -- a bit
smaller, in practice, than the 300 cents of 24-equal theory. In
other places, however, the third may be slightly or considerably
narrower. Ali Jihad Racy of Lebanon notes that the third of
Bayyati is smaller than the 32/27 from three pure fourths,
although he does not specify how much smaller -- in Arab thought,
a "comma" can be any small interval, not necessarily any specific
ratio such as 64:63 in this connection, for example (which would
yield a 7/6 third).

In 1966, Nelly Caron and Dariush Safvate reported a Persian
tuning of Shur, generally analogous to Arab Bayyati, at
136-140-224 cents -- the 276-cent third being about 9 cents wide
of a pure 7/6. More recently, Dariush Tala`i has recommended a
Shur tuning of 140-140-220 cents, for which 17-EDO offers a
reasonable approximation at 141-141-212 cents. Thus equal or
near-equal neutral steps are not necessarily wrong, although
Farhat and the 6-7-9 comma model reflect a widespread preference
that the first step be markedly smaller than the second.

Ok interesting again. First I heard about the minor third being smaller
sometimes.
For me in Pythagorean there's a double diminished fourth at 271 cents.

> To sum all this up: I would say a model of 6-7-9 commas for
Bayyati, Ushshaq, or Shur is a good place to start, allowing for
a range of fine tunings, and also noting that 7-6-9 commas often
occurs in Arab practice, and is favored by some theorists such as
al-Sabbagh. Some Arab, Turkish, and Persian musicians lean toward
a minor third rather smaller than 32/27, with something subtly
narrower like 13/11 or 33/28 appearing common in Persian
practice, along with some reported or recommended tunings like
276 cents which are closer to 7/6. And I find 12:13:14 or
14:13:12 a very pleasant division, recognized in medieval theory,
which may occur now and then in modern Near Eastern practice.

With many thanks,

Margo Schulter
mschulter@... [mschulter@...]

Thank you again Margo!
I will explore the variations you've given me.

Kind regards,
Marcel de Velde