Yahoo Tuning Groups Ultimate Backup tuning ETHNO EXTRAS: Zalzalian 12 (Pt. 1) Intro, Rotation 0

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Ethno Extras: Zalzalian 12 set
Part 1: Introduction; Rotation 0
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Hello, all.

Please let me open my participation in the "Ethno Extras" project
with an enthusiastic homage to Jacques Dudon's most admirable
version of a Near Eastern mode that has captured both of our
imaginations: s-n-buzurg.scl in the "3 Persia" folder.

Part of the genus of s-n-buzurg scale is that it constructs a
medieval Buzurg mode by combining two gamelan scales of the
septimal slendro type.

Thus my "Zalzalian 12" set, taken from a 24-note rank 3 or planar
temperament of the roughcoated variety known as O3, presents a
complete Buzurg tuning at two locations, plus some slendro and
pelog modes including a complete version at the 1/1 of Erv
Wilson's 1-3-7-9 hexany with its rich septimal slendro material.

Further, the 12-note s-n-buzurg.scl may actually be described as
a decatonic system with pairs of notes a comma apart for two of
the ten basic steps. Similarly, my "Zalzalian 12" from the O3
temperament has two of these "comma pairs" which often allow a
choice of shadings for Near Eastern maqam/dastgah music, and also
open some special possibilities for gamelan!

With great humility, please let me add that my task in this
"Ethno Extra" is much less exacting than that faced by Jacques in
his truly ingenious Buzurg tuning. He combines and integrates two
distinct types of slendro yielding a rich banquet of gamelan
flavors including some intervals around 241 and 257 cents, a
territory not explored in my more constrained tuning. Also, he
provides alternatives such as 14/13 and 13/12 above the same
note, a feature not supported in this variation.

Before offering a Scala file of the "Zalzalian 12" tuning and
giving a quick tour, I should say a word about the larger 24-note
O3 tuning and also explain the Buzurg mode as described by two
theorists from the era of around 1250-1300, Safi al-Din al-Urmawi
and Qutb al-Din al-Shirazi.

------------------------------
1. What is the O3 temperament?
------------------------------

Since this is not only the debut of my "Ethno Extras" but also of
the O3 temperament on the Tuning list, I should briefly explain
what this 24-note tuning system is and how it came out.

The name "O3" is the chemical symbol for ozone, and alludes to an
important event during the Ethno2 contest: the period of "Ozan
depletion" brought about as Ozan Yarman labored to produce his
peerless interpretations of Ottoman music revivifying this
tradition in the cultural and technological world of the 21st
century. Such a labor was necessarily taxing, and resulted in a
depletion of his ability promptly to respond to tuning
discussions on this list.

This momentary crisis of Ozan depletion led me to focus on the
idea of a 24-note tempered system optimizing the large Zalzalian
or neutral third at 26/21 (370 cents) which he mentioned was one
historical flavor for an Ottoman Rast. More generally, it was my
goal to optimize all four of the Zalzalian or middle second steps
discussed by medieval Islamic theorists such as Safi al-Din, and
also by Ozan, the 14:13, 13:12: 12:11, and 11:10.

Thus the name "O3" not only serves as the symbol for ozone, but
stands for Ozan, Ottoman, and Optimize -- this last word carrying
the humble meaning of an always open goal and striving with many
possible solutions, notably including George Secor's HTT-29, to
which this temperament, like the rather similar Peppermint, is
much indebted (and the latter, of course, also to Keenan Pepper
and Erv Wilson for defining the basic regular Wilson/Pepper
tuning!).

To emphasize the humorous aspects of this temperament before
sharing a few technical details for the curious, I should add
that the name "O3" is also a kind of open question for Ozan and
others to answer. Ozone is notably a life-protecting element when
present at its natural location in the upper atmosphere, but a
harmful one when it when makes an unwelcome appearance in the
lower atmosphere as a component of urban smog. Thus the open
question: is O3 a stratospheric flight to a pleasant layer of
intonation for Ottoman music, or a pollution of the pure
Istanbuline airs?

If it were a "smoothcoated" or simple planar (i.e. rank 3)
temperament, O3 could be defined by three simple generators. The
period is the 2:1 octave. The regular fifth generating each of
the two 12-note chains is (84/11)^(1/5), that is, the fifth at
about 703.893 cents (1.938 cents wide) that produces a regular
diatonic semitone or limma at a just 22/21 (80.537 cents). The
third generator, the "artificial diesis" or distance between
the two 12-note (Eb-G#) chains, is equal to a pure 7/4 (968.825
cents) less the regular major sixth of this tuning at about
911.678 cents, or 57.148 cents.

As a roughcoated planar temperament, however, O3 very slightly
nuances this theoretical scheme by mapping to 1024-EDO in a way
so that each 22:21 diatonic semitone is about 0.322 cents wide,
and thus an 11:10 built from two such semitones is narrow by
about 3.286 cents, comparable to the 3.247-cent tolerance
standard of Secor's HTT-29. By comparison, 11:10 is 3.930 cents narrow in a smoothcoated (theoretical planar) version of O3, or
3.466 cents in a 104-EDO version worthy of mention since a
discussion of 104-EDO on this list focused my attention on almost
exactly the right size of fifth for what became the O3 system.

Here is O3 in its roughcoated 1024-EDO version:

! O3-24.scl
!
O3 or "Ozone" (24): just 22/21 limma, 7/4, 11/6 (1024-EDO version)
24
!
57.42188
126.56250
183.98438
207.42188
264.84376
288.28125
345.70313
414.84375
472.26563
495.70312
553.12500
622.26563
679.68751
703.12500
760.54688
830.85937
888.28125
911.71875
969.14063
992.57813
1050.00001
1119.14063
1176.56251
2/1

Having explained O3, with a well-merited bow to Ozan Yarman and
George Secor, I should reassure readers that the 12-note or other
"Ethno Extras" I present should speak for themselves without any
need to understand the basis of this underlaying 24-note system.
Rather, with s-n-buzurg and the other Ethno2 tunings as sterling
examples, each Ethno Extra should be a world within itself.

------------------
2. What is Buzurg?
------------------

While both Jacques and I may speak of a Buzurg "mode," suggesting
some kind of scheme covering the range of an octave or more,
strictly speaking the Buzurg of Safi al-Din and Qutb al-Din is a
division of the 3:2 fifth, with one form being the following.

1/1 14/13 16/13 4/3 56/39 3/2
0 128 359 498 626 702
14:13 8:7 13:12 14:13 117:112
128 231 139 128 76

A related scheme, also suggested in these medieval sources, uses
mostly the same steps (14:13, 13:12, 8:7), but with a different
ordering:

1/1 13/12 26/21 4/3 13/9 3/2
0 139 359 498 637 702
13:12 8:7 14:13 13:12 27:26
139 231 128 128 65

As it happens, while O3 as a whole supports both types, the
Zalzalian 12 set supports only the first variety with a lower
tetrachrod of 1/1-14/13-16/13-4/3.

If we wish to expand the Buzurg 3:2 division to a mode in the
sense of an octave division, one simple approach is to add a
second tetrachord at the 3/2 symmetrical with that at the 1/1.
Here we follow the first type of Buzurg, where the tetrachord is
14:13-8:7-13:12 or 128-231-139 cents:

|----------------------| |-------------------|
1/1 14/13 16/13 4/3 56/39 3/2 21/13 24/13 2/1
0 128 359 498 626 702 830 1061 1200
14:13 8:7 13:12 14:13 117:112 14:13 8:7 13:12
128 231 139 128 76 128 231 139

As we shall see, some other types of upper tetrachords also seem
congenial to Buzurg, and really "making a maqam out of it" calls
for a melodic path or procedure often involving inflections or
modulations. However, this concept of a "Buzurg mode" is one
starting point.

In the Zalzalian 12 set, as it happens, such a Buzurg mode does
not appear on the 1/1 (as it does in s-n-buzurg.scl), but rather
on the steps at 346 cents (11/9 or 39/32) and 843 cents (13/8).

Thus before getting to our first Buzurg mode, we'll encounter
some other Near Eastern and gamelan modes; but I should assure
Buzurg lovers that we will get there!

------------------------------------
3. Ethno Extras: The Zalzalian 12 set
-------------------------------------

Here is the 12-note set as a Scala file:

! O3-zalzalian12_D.scl
!
Sampling of Zalzalian maqam/dastgah modes, slendro/pelog modes
12
!
138.28125
207.42187
264.84375
345.70312
472.26563
680.85937
704.29687
842.57813
969.14063
1050.00000
1176.56249
2/1

Note the presence of two 23-cent commas, interestingly involving
the fifth and octave above the 1/1. In the overall context of O3,
this might be interpreted as 78/77, for example, so that one JI
interpretation of this set is

1/1 13/8 44/39 7/6 11/9 21/16 77/52 3/2 13/8 7/4 11/6 77/39 2/1
0 139 207 267 347 472 680 702 841 969 1049 1178 1200

As with s-n-buzurg.scl, the commas make possible lots of nuances
and choices -- and also, here, an MOS septimal slendro mode
possibly a bit outside the parameters of Jacques' famous article
in 1/1. For those in suspense, this comes up in the last rotation.

Also, a disclaimer. I am used to playing this subset as a portion
of the 24-note O3 keyboard layout with two 12-note manuals, and
am not sure what the most intuitive arrangement would be on a
single 12-note keyboard, for which it is definitely intended!
Advice from Jacques and others would be warmly welcome.

To get a quick preview of our tour, we can look at a Scala matrix
of the rotations, which I'm reformatting a bit to reduce the line
length and also to identify the number of each rotation:

Rotation 0: 1/1
0 138.3 207.4 264.8 345.7 472.3 680.9 704.3 842.6 969.1 1050.0 1176.6 2/1

Rotation 1: 138.3 (~13/12)
0 69.1 126.6 207.4 334.0 542.6 566.0 704.3 830.9 911.7 1038.3 1061.7 2/1

Rotation 2: 207.4 (~9/8 or ~44/39)
0 57.4 138.3 264.8 473.4 496.9 635.2 761.7 842.6 969.1 992.6 1130.9 2/1

Rotation 3: 264.8 (~7/6)
0 80.9 207.4 416.0 439.5 577.7 704.3 785.2 911.7 935.2 1073.4 1142.6 2/1

Rotation 4: 345.7 (~11/9)
0 126.6 335.2 358.6 496.9 623.4 704.3 830.9 854.3 992.6 1061.7 1119.1 2/1

Rotation 5: 472.3 (~21/16)
0 208.6 232.0 370.3 496.9 577.7 704.3 727.7 866.0 935.2 992.6 1073.4 2/1

Rotation 6: 680.9 (~77/52)
0 23.4 161.7 288.3 369.1 495.7 519.1 657.4 726.6 784.0 864.8 991.4 2/1

Rotation 7: 704.3 (~3/2)
0 138.3 264.8 345.7 472.3 495.7 634.0 703.1 760.5 841.4 968.0 1176.6 2/1

Rotation 8: 842.6 (~13/8)
0 126.6 207.4 334.0 357.4 495.7 564.8 622.3 703.1 829.7 1038.3 1061.7 2/1

Rotation 9: 969.1 (~7/4)
0 80.9 207.4 230.9 369.1 438.3 495.7 576.6 703.1 911.7 935.2 1073.4 2/1

Rotation 10: 1050.0 (~11/6)
0 126.6 150.0 288.3 357.4 414.8 495.7 622.3 830.9 854.3 992.6 1119.1 2/1

Rotation 11: 1176.6 (~77/39)
0 23.4 161.7 230.9 288.3 369.1 495.7 704.3 727.7 866.0 992.6 1073.4 2/1

From this "itinerary," some readers may draw a few conclusions.
Thus Rotations 4 (~11/9) and 8 (~13/8) include Buzurg modes,
while Rotations 5 (~21/16) and 9 (~7/4) look like good places for
Rast, and Rotation 7 (~3/2) likewise for Shur.

We'll encounter these and more, and I warmly invite readers to
celebrate other modes, gamelan or Near Eastern or other, that
I've missed.

-------------------------------------------------------------
Rotation 0 (1/1): Slendro, pelog, and Wilson's 1-3-7-9 hexany
-------------------------------------------------------------

0 138.3 207.4 264.8 345.7 472.3 680.9 704.3 842.6 969.1 1050.0 1176.6 2/1

Starting on the 1/1 or Scala step 0 of the Zalzalian 12 set, we
find the slendro and pelog modes that originally served to define
the 10-note nucleus of the tuning. The original 5-note slendro
mode was this:

0 265 472 704 969 1200
1/1 7/6 21/16 3/2 7/4 2/1
265 207 232 265 231

This includes the beautiful 16:21:24:28 sonority which according
to Kyle Gann was used by LaMonte Young at least as early as the
1960's, and has since been discussed by Keenan Pepper (from whom
I learned about it) and others. In the wider context of our
12-note set, this sonority has a striking resolution to a fifth
featuring Zalzalian or neutral second steps around 13:12 and
14:13.

969 843
704 843
265 138
0 138

Keeping our focus on septimal slendro, this rotation offers a
complete tempered version of Erv Wilson's 1-3-7-9 hexany:

0 207 265 472 704 969 1200
1/1 9/8 7/6 21/16 3/2 7/4 2/1
207 57 207 232 265 231

In addition to the slendro mode above with an opening 7:6 step,
we have a mode with an opening 9:8.

0 207 472 704 969 1200
1/1 9/8 21/16 3/2 7/4 2/1
207 265 232 265 231

This second type with steps of 9:8-7:6-8:7-7:6-8:7 is a rotation
of Jacques' N or "Natural" variety of septimal slendro, while the
first type with 7:6-9:8-8:7:7:6-8:7 is a rotation of his M or
"Mirror image" mode in relation to N.

Both N and M modes have three step sizes: 7:6, 8:7, and 9:8. We
will also encounter M and N in their original rotations as we
move through the Zalzalian 12 set -- but not other, more complex
septimal slendro patterns present in s-n-buzurg.scl.

Another basic component of the Zalzalian 12 set is a basic pelog
mode using a narrow fifth at 681 cents, and optionally a narrow
octave at 1177 cents also! Here I use a vertical bar | to
indicate two versions of the "same step," which might well
both be used at different points in a performance.

0 138 346 681 843 1177|1200
1/ 1 13/12 11/9 77/52 13/8 77/39| 2/1
138 207 335 162 334|357

While this was the pelog that first caught my attention, another
form also seems attractive to me, with the first three notes
suggesting to me a septimal Shur Dastgah but also not too far
from reported averages for one typical variety of pelog mode.

0 138 265 681 843 1177|1200
1/1 13/12 7/6 77/52 13/8 77/39| 2/1
138 127 415 162 334/357

If we willing to explore "altered" forms of Near Eastern modes
with a 21/16 substituted for the usual 4/3, then two other modes
stand out to me. Some modern Arab theory speaks of tetrachords
which at times may be narrowed by a comma, while Nelly Caron and
Dariouche Safvate write that a fourth of around 484 cents was
common in traditional Persian tuning, notably appearing in an
older version of the Avaz-e Bayat-e Tork (to be included in Ethno
Extras).

One possibility is a version of Ibn Sina's 11th-century tuning
with Shur-like qualities where the narrow 21/16 serves for Ibn
Sina's original 4/3:

0 138 265 472 704 843 969 1200
1/1 13/12 7/6 21/16 3/2 13/8 7/4 2/1
138 127 207 232 138 127 231

Some exploration at the keyboard shows me that this is a fine
Shur from a melodic point of view, and offers some beautiful
polyphonic cadences if one wishes to develop dastgah-based
counterpoint. The 21/16 step plays a premier role in making some
of these progressions and shadings possible, for example in this
cadence featuring a small Zalzalian or neutral third at 334 cents
which expands to a fifth:

843 (13/8) 969 (7/4) 1200 (2/1)
472 (21/16) 704 (3/2)
138 (13/12) 0 (1/1)

Here the opening sonority of 0-334-704 might represent 14:17:21,
with the highest voice then moving up by a 127-cent step so that
the sonority becomes 0-334-831, with 52:63:84 as one JI reading
suggested by the near-pure 21:13 small neutral sixth not far from
the intriguing ratio of Phi (833.090 cents). Then, the small
neutral neutral third and sixth expand to fifth and octave in a
manner recalling the classic European polyphony practiced in the
era of Safi al-Din and Qutb al-Din -- or more precisely as it
might have been practiced if the Zalzalian intervals of these and
other Islamic theorists had been part of its vocabulary!

Another possibility is a variation on Jacques Dudon's beautiful
Ibina, 1/1-13/12-11/9-4/3-3/2-13/8-16/9-2/1. The lower tetrachord
is of the Mohajira type with Z-T-Z where "Z" is a Zalzalian or
neutral second and "T" and regular major second or tone, while
the upper tetrachord on the 3/2 is a form of Shur, Turkish
Ushshaq, or Arab Bayyati, with Z-Z-T, two Zalzalian steps
followed by a tone. Here both the 4/3 fourth and 16/9 minor
seventh are lowered by a comma to 21/16 and 7/4.

"Narrow Moha" Shur/Bayyati
|----------------| |----------------|
0 138 346 472 704 843 969 1200
1/1 13/12 11/9 21/16 3/2 13/8 7/4 2/1
138 207 127 232 138 127 231

Here, in a curious way, the lower Mohajira ("Moha" for short)
variant tetrachord introduces two of the steps of Buzurg: a lower
138-cent step representing 13:12, and an upper 127-cent step
representing 14:13. The middle step, however, is a comma narrower
than Buzurg's usual 8:7 (231 cents), at 207 cents or a near-9:8
(also a near-44:39), so that the fourth is compressed from a
usual rounded 496 or 497 cents in this temperament to 472 cents,
or in JI terms from 4/3 to 21/16.

While I am not aware of any discussion of these specific altered
modes in medieval or modern Near Eastern theory, I mention them
in keeping with the adventurous xenharmonic spirit of Ethno, and
also the wise adage that one should not spurn what the equations
or tuning parameters generously cast at one's feet. In fact, as I
relate above, the Shur with 21/16 in place of 4/3 proves both
melodically apt and contrapuntally delightful when considered as
a mode in its own right, as well as resembling the kind of
pattern I often fall into when improvising in a septimal Shur or
Arab Bayyati where a usual 4/3 step is the norm but the
progression of the _sayr_ or development may lead at some points
to the lowering of this step by a comma. Likewise, the Ibina-like
mode with lowered steps at 21/16 and 7/4, although not following
the original scheme of differential coherence (-c), nevertheless
presents fruitful possibilities as a septimal variation on the
Mohajira/Ibina theme.

(Conclusion of Part 1)

Best,

Margo Schulter
mschulter@...

🔗Jacques Dudon <fotosonix@...>

Hi Margo,
I started to reply to your post :
ETHNO EXTRAS: Zalzalian 12 (Pt. 1) Intro, Rotation 0
when I noticed you already gave many advised comments on our differents versions of possible Buzurg temperaments, a subject which inspired both of us apparently at the very same moment !
I should be also working on my next concert, so my excuses if I am only doing very fast - my excuses also to Andy who sent many answers to our previous exchanges that interests me a lot, but to which I could not find the time to reply.
My reflexions arrive to the same conclusions as yours, basically that the two propositions may look different, but are in fact only half-different.
To show this let me start from your precious scales citations from Safi-Al-Din and Qutb al-Din :

> While both Jacques and I may speak of a Buzurg "mode," suggesting
> some kind of scheme covering the range of an octave or more,
> strictly speaking the Buzurg of Safi al-Din and Qutb al-Din is a
> division of the 3:2 fifth, with one form being the following.
>
> 1/1 14/13 16/13 4/3 56/39 3/2
> 0 128 359 498 626 702
> 14:13 8:7 13:12 14:13 117:112
> 128 231 139 128 76
>
> A related scheme, also suggested in these medieval sources, uses
> mostly the same steps (14:13, 13:12, 8:7), but with a different
> ordering:
>
> 1/1 13/12 26/21 4/3 13/9 3/2
> 0 139 359 498 637 702
> 13:12 8:7 14:13 13:12 27:26
> 139 231 128 128 65

Here we find two versions for a neutral third over 1/1 : 16/13 and 26/21.
Without knowing it, a "noble mediant" of those two intervals is very much what I did between those two, when considering they belong to the same series :
21 : 26 : 32...
And tempering the difference between 16/13 and 26/21, over-present in Buzurg JI scales, or 169/168, was very precisely from where my idea came.
Therefore it was very logical to complete the series to :
17 : 21 : 26 : 32 : 39 : 48 : 59 : 73 : 90 ...
where 90 - 73 = 17 gives the key of the recurrence.
And where again the difference between 21/17 and 32/26, or 273/272 can be tempered as well, etc.
Then Safi-Al-Din gives a very interesting clue with that strange interval after 4/3, 56/39 :
I note that 56/39 and 23/16 (in between the two versions) only differ by 897/896 : another one I tempered.
(we also find it between 16/13 and 69/56, that you mention)
And when you divide 23/1 in 15 steps, you find again the same generator - this means that the path to that precise note
(56/39) contains the whole scale :
= 0, 7, 1, 8, 15 of those generators giving the first pentachord, also defining the fifth symmetrically, by -8 generators.

Now correct Buzurg-tempered zalzals can define a wide variety of fifths, and why not one slightly extended one as you suggested, that's why I would say our two ideas have no contradiction.
In fact, the recurrent sequence 4x^4 = x + 8 I gave in my list as a central one, generates very precisely such a fifth, with 703.837171 c.
Inversely, to find exactly your fifth of 703.893 c. a generator of 1,232577031 would be needed, that would find many good approximations in the series of that fractal (one is 53/43 with 1,23255814...).
Here is one that starts by this 53/43 interval :
516 : 636 : 784 : 966 : 1191 : 1468 : >3619 > 8919 > 2749 >27107 ...
where 8*516/2749 = 1.501637 = 703.843277 c.

Then all your following remarks are very right too !
many thanks,
- - - - - - - -
Jacques

> (Jacques) :
> > 6) More surprising, I found some holes in the linear
> > temperament list, at places where musical systems, even
> > used in traditional music, have galaxies of fractal
> > solutions : the "Buzurg" zone is one of these, that would
> > generate very musical scales : at least Margo Schulter will
> > not contradict me on that point (Margo, I have not read
> > your last article on Buzurg yet : will see if we find some
> > concordances on the subject !).
>
> Dear Jacques,
>
> Please let me agree that the Buzurg zone is a wonderful place for
> fractal solutions -- and also for the kinds of regular or planar
> temperaments that I often use. Of course, I will be very
> interested to read any comments you have on my Buzurg article,
> which is proving far longer than I planned on, for better or
> worse, maybe because the "Zalzalian 12" set has caused me to
> focus on a variety of modes in the different rotations.
>
> In fact, your discussion below of a Buzurg generator gave me an
> idea for an experiment to show that -c tunings and regular or
> planar temperaments can often lead to musically congenial,
> although distinct, results, with both approaches lending
> themselves to maqam/dastgah music. One of the goals of my "Ethno
> Extras" is indeed to seek out such concordances.
>
> And here I would add that a -c tuning like your Aulos/Soria seems
> to me closer to the spirit of an irregular Persian tar fretting,
> for example, than a regular or even planar temperament.
>
> > The only reason I see for that omission in the temperament list
> > is that the Buzurg generator before anything else conciliates 7
> > and 13, and will not come to harmonics 3, 5 and 11 before
> > longer cycles, therefore it is not on a list that privilegiates
> > temperaments with full 3, 5, 7 solutions and after.
>
> Curiously, the situation with the Buzurg generator may be like
> that with my regular "e-based" temperament (704.607c), or my
> Peppermint planar temperament based on the regular Wilson/Pepper
> noble fifth temperament (704.096c) with a distance between the
> 12-note chains or "ribbons" of 58.680c. These systems, like your
> Buzurg, support harmonics 7 and 13 -- and also here 3 and 11 --
> but not 5, at least within the intended size of 24 notes. We
> might indeed say that such temperaments, like your Buzurg,
> neither privilege nor are privileged by the usual "regular
> mapping" approach.
>
> > Here is a 23-limit mapping, showing main MOS at 10, 43 , 53,
> > that would be resolved by a "Buzurg" neutral third of 16
> > unequal steps of 53 steps in one octave (around 362 cents) :
> > <0, -8, 11, 6, 28, -1, -3, 24, 15] (note that the 23rd
> > harmonic, one of the best centered, would be reached precisely
> > by 15 generators, suggesting a useful and efficient target
> > generator with 1.2324856 or 361.884956 c.) note also that a
> > pure harmonic 3 will be attained with a generator of
> > 362.255625c.
>
> Your generators syggested an experiment: I used Scala to define a
> regular temperament with 361.884956c as the diminished fourth
> (e.g. G#-C) from eight fifths down or fourths up. Of course, this
> method is very different from using this large neutral third of
> Buzurg as itself the generator, and different again from
> a -c system using a series including a 69/56 third (361.402c),
> for example, maybe somewhat in the manner of the Ibina tuning
> (or the very slightly larger 53/43 you mention below)!
>
> The fifth is 704.76438 cents, almost identical to 63-EDO, and
> actually a bit closer to the point where the apotome is equal to
> precisely half of 7/6, which thus is virtually pure.
>
> Your generator, interestingly, produces a fifth (from 8
> generators down) of 704.920 cents, with 16 in a 24-note tuning.
> And we get lots of hemifourths at 247.540 cents not present in my
> regular temperament! And you have 8 locations with symmetrical
> Buzurg tetrachords, (0-133-362-495-705-838-1066-1200). one of
> which also includes a 23/16 step (56/39 or 13/9 in medieval JI
> versions).
>
> Here is a Buzurg mode in the regular 704.764c temperament with
> the upper tetrachord like the lower:
>
> ! rbuzurg-buzurg8_Cup.scl
> !
> Buzurg pentachord plus 133-229-133 tetrachord at ~3/2
> 8
> !
> 133.35066
> 361.88496
> 495.23562
> 628.58628
> 704.76438
> 838.11504
> 1066.64934
> 2/1
>
>
> and here is Qutb al-Din al-Shirazi's Buzurg-Hijaz combination:
>
> ! rbuzurg-buzurg_hijaz_Cup.scl
> !
> Qutb al-Din al-Shirazi's Buzurg plus upper Hijaz (JI 12:11-7:6-22:21)
> 8
> !
> 133.35066
> 361.88496
> 495.23562
> 628.58628
> 704.76438
> 857.12058
> 1123.82190
> 2/1
>
>
> As you remark, in this temperament as in your "buzurg" mapping,
> we get a ~23/16 step as a variation on the 56/39 of Safi al-Din
> al-Urmawi and Qutb al-Din.
>
> Of course, we could also explore this territory with a -c tuning
> maybe something like Soria 17 + 2 in the A version with the
> larger comma, where Buzurg or Buzurg-Rast modes turn up at a
> couple of locations.
>
> > Many practical fractals would qualify as Buzurgs,
> > such as :
>
> > 7x^2 = 7x + 2 > 1,23192505471 > 361,09738964 c.
> > 4x^7 = 16 + x > 1,2320003029 > 361,2031329 c.
> > 4x^2 = 11 - 4x > 1,2320508076 > 361,2741 c.
> > x^8 = x^7 + 1 > 1,2320546314 > 361,2794748 c.
> > x^2 = 20 - 15x > 1,2321245983 > 361,37778668556 c.
> > 3x^2 = 11x - 9 > 1,2324081208 > 361,77611271646 c.
> > 4x^4 = 8 + x > 1.23258192464 > 362,020247741 c.
> > 2x^5 = 8 - x^4 > 1,2326439928 > 362,107458 c.
> > 8x^5 = 24 - x > 1,2326632514 > 362,1344722332 c.
> > 2x^8 = 15 - x^7 > 1,2328237225 > 362,359833742 c.
> > x^2 = 28x - 33 > 1,2328546652 > 362,403288 c.
>
> > The simplest series are generated by x^8 = x^7 + 1, such as :
> > 17 21 26 32 39 48 59 73 90 111 137 169 208 256 315 388 478...
> > (differentials 4 5 6 7 9 11 14 17 21 26 32 39 48 59 73 90...)
> > 4x^4 = 8 + x converges to a generator by coincidence also
> > approximated by the main MOS ratio : 53/43...
>
> Indeed this series includes many of the intervals based on
> harmonics 3-7-11-13 that I seek out in regular or planar
> temperaments, and I think would be a "charmed attractor" to
> anyone with a passion for these intervals. You may recall
> explaining to me, when I proposed a sequence for "Mohajira,"
> that what I was seeking was actually this "Buzurg 8" series.
>
> </tuning/topicId_89500.html#89511>
>
> A curious question is whether 69/56, like 53/43, might make an
> interesting generator.
>
> > One last thought : 43 + 53 = 96 steps/octave, a division I
> > know to be dear to Shaahin Mohajeri, features of course also
> > a very good Buzurg third of 13 + 16 = 29 steps.
>
> Shaahin's creative use of 96-EDO, and your comment, make me take
> note now that indeed this equal temperament has lots of support
> for some traditional Persian modes. For example, symmetrical
> Buzurg:
>
> 0 137.5 362.5 500.0 625.0 700.0 837.5 1062.5 1200
>
> And Qutb al-Din's Buzurg-Hijaz:
>
> 0 137.5 362.5 500.0 625.0 700.0 850.0 1112.5 1200
>
> So with your -c tunings or a mapping like buzurg, or Shaahin's
> 96-EDO, or my regular and planar temperaments, what we seem to
> be looking for in common is "modal goodness to fit," intervals
> which will form pleasant maqamat or dastgah-ha, etc. And so we
> may find some notable concordances as well as differences.
>
> With many thanks,
>
> Margo Schulter

🔗Margo Schulter <mschulter@...>

> Hi Margo,

> I started to reply to your post : ETHNO EXTRAS: Zalzalian 12
> (Pt. 1) Intro, Rotation 0 when I noticed you already gave many
> advised comments on our differents versions of possible Buzurg
> temperaments, a subject which inspired both of us apparently at the
> very same moment !

Dear Jacques,

Thank you for your most generous comment at a time when you are
preparing for a concert. Please read this at your convenience, and
with my wishes for a fine and happy performance!

> I should be also working on my next concert, so my excuses if I am
> only doing very fast - my excuses also to Andy who sent many
> answers to our previous exchanges that interests me a lot, but to
> which I could not find the time to reply. My reflexions arrive to
> the same conclusions as yours, basically that the two propositions
> may look different, but are in fact only half-different.

This is certainly a mutually agreeable conclusion, and I would be
delighted if we can explore the aspects of how these different
approaches to intonational systems may often produce congenial
results, different but with a clear musical affinity.

One delightful thing I noted about your Soria 17 + 2 (Version B with
the smaller comma) is that there are many neutral sevenths around the
size of your Awj (or Tribonacci), 1055 cents or very slightly
smaller.

As part of my Ethno Extras, I will be offering (Inshallah) a variation
or adaptation of Soria to the O3 temperament, where the closest
approximation is 1050 or 1062 cents -- basically 11/6 or 24/13. While
both 17 + 2 tunings should be attractive for Persian music, and there
are some interesting parallels, yet that Awj or Tribonacci interval is
a special feature of your original Soria but not my analogue.

> To show this let me start from your precious scales citations from
> Safi-Al-Din and Qutb al-Din :

[First classic form of Buzurg]

1/1 14/13 16/13 4/3 13/9 3/2
0 128 359 498 626 702
14:13 8:7 13:12 14:13 117:112
139 231 139 128 76

[Alternative classic form of Buzurg]

1/1 13/12 26/21 4/3 13/9 3/2
0 139 370 498 637 702
13:12 8:7 14:13 13:12 27:26
139 231 128 139 65

> Here we find two versions for a neutral third over 1/1 : > 16/13 and 26/21.

Yes, with s-n-buzurg.scl of Ethno2 as a fine example of a system
which, unlike O3 for example, sometimes permits the use of either
neutral third over the same step, for example the 1/1.

> Without knowing it, a "noble mediant" of those two intervals is
> very much what I did between those two, when considering they
> belong to the same series :
> 21 : 26 : 32...

> And tempering the difference between 16/13 and 26/21, over-present
> in Buzurg JI scales, or 169/168, was very precisely from where my
> idea came.

In the related world of regular or planar temperaments which I often
favor for maqam/dastgah music, likewise, a regular or rank 2
temperament (e.g. the e-based system, which I might also name Euler)
generally tempers out the 169/168, while a planar or rank 3
temperament like Peppermint or O3 observes it (like s-n-buzurg.scl).

> Therefore it was very logical to complete the series to :
> 17 : 21 : 26 : 32 : 39 : 48 : 59 : 73 : 90 ...
> where 90 - 73 = 17 gives the key of the recurrence.

Interestingly, 90:73 is around 362.434 cents. And for a least squares
regular or rank 2 temperament optimizing 2-3-7-11-13-23 (with a 2/1
octave), Scala gives a generator of 495.318 cents (or 704.682 cents),
with a Buzurg neutral third of 362.547 cents!

And this agrees with your conclusion below that the methods are only
"half-different."

> And where again the difference between 21/17 and 32/26, or 273/272
> can be tempered as well, etc.

Yes, with a just 90:73, or an irrational size like 362.547 cents,
(leastsquare rank 2 for 3-7-11-13-23), or 363.145 in e-based/Euler as
examples. And Ozan might have me mention the Turkish or Syrian
interval of 16 commas (e.g. 16/53 octave) at 362.264 cents, or the
almost identical 24 yarmans in the 79/80-MOS of 159-EDO (actually with
minute variations in step sizes from 159-EDO in some versions).

In contrast, Peppermint (rank 3) has 367.235 cents, either 21/17 or
26/21 (tempering 442/441); and 357.703, not too far from 16/13 but
actually closer to 59/48, which also appears in your series and is, of
course, part of the famous Mohajira variety with 48:52:59:64.

> Then Safi-Al-Din gives a very interesting clue with that strange
> interval after 4/3, 56/39 : I note that 56/39 and 23/16 (in between
> the two versions) only differ by 897/896 : another one I tempered.
> (we also find it between 16/13 and 69/56, that you mention)

Yes, when it comes to these commas, we seem to be speaking the same
basic language. What I noticed in e-based/Euler is that the best
approximation of the medieval 56/39 (14/13 plus 4/3) was 627.641
cents, or 0.633 cents narrow of 23/16.

> And when you divide 23/1 in 15 steps, you find again the same
> generator - this means that the path to that precise note (56/39)
> contains the whole scale :

> = 0, 7, 1, 8, 15 of those generators giving the first pentachord,
> also defining the fifth symmetrically, by -8 generators.

> Now correct Buzurg-tempered zalzals can define a wide variety of
> fifths, and why not one slightly extended one as you suggested,
> that's why I would say our two ideas have no contradiction.

Yes, we agree that these are two roads to the same musical region.

> In fact, the recurrent sequence 4x^4 = x + 8 I gave in my list as a
> central one, generates very precisely such a fifth, with 703.837171 c.

> Inversely, to find exactly your fifth of 703.893 c. a generator of
> 1,232577031 would be needed, that would find many good
> approximations in the series of that fractal (one is 53/43 with
> 1,23255814...).

In a curious way, either of these fifths might be relevant to the O3
temperament, which although in theory a planar or "rank 3" temperament
actually uses on my 1024-EDO synthesizer two different sizes of fifths
at 600 tuning units or 703.125 cents, and 601 units of 704.297 cents.
There are 7 larger fifths and 4 smaller ones in each 12-note chain,
placed so that the usual minor second or limma is always 80.859 cents,
very slightly wider than the theoretically just 22/21.

This means that each diminished third or large neutral second within a
single chain of fifths, at 161.719 cents, will be only about 3.286
cents narrow of 11/10, a step size often favored in some of the
maqamat as performed in the Ottoman tradition. This 161.719-cent step
would result from regular fifths at 703.828 cents, very close to your
703.837171 cents!

The average fifth shown by Scala for my 1024-EDO version is 703.871
cents, quite close to our 703.893 cents, the regular fifth producing a
just 22/21 limma.

Here is one that starts by this 53/43 interval :
516 : 636 : 784 : 966 : 1191 : 1468 : >3619 > 8919 > 2749 >27107 ...
where 8*516/2749 = 1.501637 = 703.843277 c.

This agreement between our approaches to Buzurg is inspiring, and I
appreciate your generosity in pointing out these concordances even
while preparing for a concert.

> - - - - - - - -
> Jacques

Merci beaucoup,

Margo

🔗Jacques Dudon <fotosonix@...>

🔗Margo Schulter <mschulter@...>

Dear Jacques,

Please let me first correct a mistake in my previous post, which
is fairly obvious but would be good to note for anyone who may
read this, and then consider your beautiful tuning making use of
169/168.

> [First classic form of Buzurg]
>
> 1/1 14/13 16/13 4/3 13/9 3/2
> 0 128 359 498 626 702
> 14:13 8:7 13:12 14:13 117:112
> 139 231 139 128 76

Here, of course, the step immediately below 3/2 should be 56/39,
not 13/9! Here's the corrected version.

> [First classic form of Buzurg]
>
> 1/1 14/13 16/13 4/3 56/39 3/2
> 0 128 359 498 626 702
> 14:13 8:7 13:12 14:13 117:112
> 139 231 139 128 76

> You are welcome and these reunions with Buzurg inspired me to
> use for my concert one of my earliest photosonic disks, an
> heptatonic scale from which I rediscovered the mode of F : -c
> Buzurg 39 (= original tonic) - disk#523, 1997

It is a great pleasure to learn that these discussions about
Buzurg helped to set the tone for your concert.

> 104 : 117 : 126 : 143 : 144 : 156 : 168 : 169 : 192 : 207 : 208
> (with 507 = 13*39 later on)

A very small point: 143:104 is listed below as 11/6, where 11/8
was evidently intended.

> F-mode :
> 1/1
> 9/8
> 63/52
> 39/32
> 11/6
> 18/13
> 3/2
> 21/13
> 13/8
> 24/13
> 207/104
> 2/1

> (I note 23/16 was already there on a coherent way,
> with 207 - 144 = 63, or 23 - 16 = 7...)

> That's were the commas would be most useful indeed, and I
> wonder if JI versions are not the best!

This is a good question. And happily, we can have both -c versions
and tempered versions, as with Mohajira.

> But still it is tempting to have a Buzurg-based temperament
> that conciliates 3, 5 , 7, 13, 23 and more.

Yes, that is a worthy as well as ambitious project, and something
far beyond my experience. The structure is quite different from
that of temperaments which I am familiar, and so your own musical
judgment, plus your experience with -c, might make you indeed the
ideal judge of how such a temperament might best be fine-tuned.

What I notice is that around or just below 362 cents, we get not
only 3, 5, 7, 13, 23 -- but also 11! Something close to your
generator for a just 23/16 is also close to (384/11)^(1/17). or
361.802180 cents. It's interesting that here I was seeking to
optimize 12/11 rather than 11/8, maybe showing a tendency often to
think of superparticular melodic steps as well as harmonic primes.

Of course, this is in part a matter of taste where Middle Eastern
musicians and theorists have cultivated a variety of flavors for
over a millennium!

Thus while 12/11 is an excellent step, how about 59/54 or 128/117?
We would get 154 cents with a 362-cent generator. Actually I
suspect that something around 361.9 cents might be close to
optimal, a zone certainly including your idea of 23^(1/15), but
the melodic nuances do leave room for a range of solutions.

> I tried to see also if my "Buzurg comma" of 10 zalzal
> generators could be reduced to 169/168 ... this is done with
> 1.231875282 or 361.027442 c., but it leads to a fifth of
> 711.780467 c. - it would mean that pure fifhs would be
> attained via one more cycle with -18 , another story.

Now I see that it is the departure from 360 cents or 3/10 octave
which creates the comma!

> At this point I think a "slightly under 362 c.", leading to
> slightly extended fifths, or a near 362,25 c., leading to pure
> fifths, would be the best options for a Buzurg-zalal generator.
> I have no precise idea at this moment of what would be the
> optimal "slightly under 362 c." version, and as you have been
> working a lot with near 704 c. fifths in relation to
> Middle-East tunings I think you would know better.

The beginning of wisdom for me may be to confess that a system
such as that with the Buzurg generator is quite new to me! I did
find a that a range around 361.940-361.960 cents looks
interesting, but that is only a first impression. And a bit
lower, around 361.910 cents, also looks attractive at first
glance. [I wasn't focusing here on your 23^(1/15) at 361.884956
cents, just a bit lower yet and with its own advantages!]

What I noticed is that the patterns I'm familiar with using
extended fifth generators do not necessarily hold! Suppose, to
make the mathematics simpler, we take a generator of 362 cents,
which produces a fifth of 704 cents. With a rank 2 temperament at
704 cents, we have an apotome at 128 cents, and thus an interval
from 14 fifths up at twice this, or 256 cents -- a fine
hemifourth, but not so close to 7/6.

With the 362-cent Buzurg generator, however, we a have fifth at
704 cents plus a near-7/6 at 268 cents, a near 9/7 at 436 cents,
and a near 7/4 at 972 cents! This is like a rank 2 temperament
with a generator around 704.8 cents, a bit wider than 37/63
octave, as far as the septimal approximations.

What looking at a 48-note version of the Buzurg generator shows is
that there are lots of modes present, certainly including Buzurg,
Rast, and Shur!

And speaking of s-n-buzurg.scl, I notice that there's good
coverage of slendro_mat.scl, with the most notable difference
being a virtually just 26/15 in place of 256/147 (and likewise
15/13 in place of 147/128). Here I speak of the 48-note version.

Of course, there's the question of the best tuning size or sizes,
possibly based on MOS sets.

Thus I'd see this as a generator that derives from a Near Eastern
mode (medieval Buzurg, or one flavor of Avaz-e Bayat-e Esfahan),
and produces a system supporting that mode as well as many
others. It may be fun to see how accurately I can emulate some of
those modes using a rank 2 or rank 3 temperament with extended
fifths.

> - - - - - - - -
> Jacques

Best,

Margo

🔗Ozan Yarman <ozanyarman@...>

Dear Margo,

In the midst of the Islamic holy month of Ramadan as the moon slowly
turns to full in the night sky, when the debilitating heat and humidiy
(for the first time over 40 degrees Celsius and %90 moisture) wafting
over Istanbul has abated a little and fasting for the greater glory ofRahman and Rahim Allah is not anymore a burden on the persevering
spirit as much as aforetimes, I find this oppurtunity to concentrate
on your humourous e-mails promoting the "O3 Temperament" from three
weeks ago.

First of all, a big thank you for your kind words and praises. How
flattering to receive such attention and encouragement from you!

You will surely remember from our past correspondences, that I had
remarked positively on the approach of using a chain of fifths a tad
larger than pure - and even went so far as to formulate middle-
resolution tuning schemes of my own in the same vein to incorporate
maqam flavours in as comprehensive a manner as possible. This path
promises to yield favourable results not much tried in Turkish Maqam
music (where the "3-limit mainstream theory market" still dominates
the notion of "natural pitches" despite my "sinister presence" in
cyber music circles. Hah hah!)

A particular thought has occured to me while trying to follow your
latest exposition of maqams such as Buzurg, Rast-Najid, Segah, etc in
O3... I have found out that my memory is lately chuck full of useless
everyday political dilly-dallying and I cannot recollect which maqam
was transformed how in what tuning. It would be prudent, I believe,
for you to categorize the maqams we have elaborated so far in one
concise master article, comprising your theoretical constructs
(including some of my interpretations and commentary maybe?) in theirrespective tunings and how they evolved thus in succinct steps (using
cent values with dot zero decimals for quick SCALA access too).

The lengthy exegesis of makamlar in your messages requires much deeper
deliberation that I can reflect to my response here. Nevertheless, let
me say that Rotation 1 (13/12) Maqam Segah hits the spot very well. I
also like the Rast flavour with 8/7 as perde dugah instead of the
equivalent or approximation of 9/8. Yet, I feel Penchgah-i Hagar (with
so low a segah and hijaz) has left the realm of Penchgah and entered
that of Nihavend. Maybe one could rename it "Penchgah fi Nihavend-i
Hagar" (Penchgah within Nihavend of Hagar). More fittingly so, since
Nihavend exhibits more the Hijaz upper tetrachord you seek compared to
Penchgah, which almost never shows it.

Shur and Najdi are hard to come by in Turkish circles to my knowledge,
so I make no further commentary on those.

And at long last, Buzurg once more. Just a minor interjection on my
part: It is my impression, based on no solid evidence except erudite
conjecture, that Buzurg is supposed to be an ascending/descending:

14/13
16/13
56/39
3/2

In one thematic version and

14/13
16/13
4/3
56/39

diminished pentachord in another ascending/descending cadential
version. I don't remember if I had mentioned this, but there it is.
The latter is akin to what I dub the "Ferahnak pentachord". This construct is amiss in theoretical and historical explanations of
makamlar, but chanced - even if rarely - in performances if my
scrutiny is to be trusted. Ah, but I see that the intiguing descending
Segah upper region in your third e-mail features this very Ferahnak
pentachord as well as the already-known diminished Ferahnak pentachord
mixed!

About the upper "Buzurg tetrachord", I imagine it would be judicious
to say Hijaz-i Buzurg to punctuate the Hijaz sphere of influence here.
We see such denominations as Hijaz-i Muhalif, Hijaz-i Turki, etc... to
categorize maqam savours centering on Hijaz in historical sources, so,
why not scale structures themselves?

So far, I liked the Buzurg variants you delineated. Good show! The
possibilities of fine intonation with the O3 type tuning demonstrates clearly how our cliché notions of trying to keep segah close to 5/4 is
much misguided. It has been lately my inclination to focus on 370
cents or so as the nominal spot for perde segah in most (and perhaps
all) instances in keeping with historicity of maqam theory.

Most cordially,
Oz.

✩ ✩ ✩
www.ozanyarman.com

On Aug 3, 2010, at 10:43 AM, Margo Schulter wrote:

> ----------------------------------
> Ethno Extras: Zalzalian 12 set
> Part 1: Introduction; Rotation 0
> ----------------------------------
>
> [To preserve formatting as much as possible, please try the Use
> Fixed Font Width option if viewing on the Yahoo site.]
>
> Hello, all.
>
> Please let me open my participation in the "Ethno Extras" project
> with an enthusiastic homage to Jacques Dudon's most admirable
> version of a Near Eastern mode that has captured both of our
> imaginations: s-n-buzurg.scl in the "3 Persia" folder.
>
> Part of the genus of s-n-buzurg scale is that it constructs a
> medieval Buzurg mode by combining two gamelan scales of the
> septimal slendro type.
>
> Thus my "Zalzalian 12" set, taken from a 24-note rank 3 or planar
> temperament of the roughcoated variety known as O3, presents a
> complete Buzurg tuning at two locations, plus some slendro and
> pelog modes including a complete version at the 1/1 of Erv
> Wilson's 1-3-7-9 hexany with its rich septimal slendro material.
>
> Further, the 12-note s-n-buzurg.scl may actually be described as
> a decatonic system with pairs of notes a comma apart for two of
> the ten basic steps. Similarly, my "Zalzalian 12" from the O3
> temperament has two of these "comma pairs" which often allow a
> choice of shadings for Near Eastern maqam/dastgah music, and also
> open some special possibilities for gamelan!
>
> With great humility, please let me add that my task in this
> "Ethno Extra" is much less exacting than that faced by Jacques in
> his truly ingenious Buzurg tuning. He combines and integrates two
> distinct types of slendro yielding a rich banquet of gamelan
> flavors including some intervals around 241 and 257 cents, a
> territory not explored in my more constrained tuning. Also, he
> provides alternatives such as 14/13 and 13/12 above the same
> note, a feature not supported in this variation.
>
> Before offering a Scala file of the "Zalzalian 12" tuning and
> giving a quick tour, I should say a word about the larger 24-note
> O3 tuning and also explain the Buzurg mode as described by two
> theorists from the era of around 1250-1300, Safi al-Din al-Urmawi
> and Qutb al-Din al-Shirazi.
>
>
> ------------------------------
> 1. What is the O3 temperament?
> ------------------------------
>
> Since this is not only the debut of my "Ethno Extras" but also of
> the O3 temperament on the Tuning list, I should briefly explain
> what this 24-note tuning system is and how it came out.
>
> The name "O3" is the chemical symbol for ozone, and alludes to an
> important event during the Ethno2 contest: the period of "Ozan
> depletion" brought about as Ozan Yarman labored to produce his
> peerless interpretations of Ottoman music revivifying this
> tradition in the cultural and technological world of the 21st
> century. Such a labor was necessarily taxing, and resulted in a
> depletion of his ability promptly to respond to tuning
> discussions on this list.
>
> This momentary crisis of Ozan depletion led me to focus on the
> idea of a 24-note tempered system optimizing the large Zalzalian
> or neutral third at 26/21 (370 cents) which he mentioned was one
> historical flavor for an Ottoman Rast. More generally, it was my
> goal to optimize all four of the Zalzalian or middle second steps
> discussed by medieval Islamic theorists such as Safi al-Din, and
> also by Ozan, the 14:13, 13:12: 12:11, and 11:10.
>
> Thus the name "O3" not only serves as the symbol for ozone, but
> stands for Ozan, Ottoman, and Optimize -- this last word carrying
> the humble meaning of an always open goal and striving with many
> possible solutions, notably including George Secor's HTT-29, to
> which this temperament, like the rather similar Peppermint, is
> much indebted (and the latter, of course, also to Keenan Pepper
> and Erv Wilson for defining the basic regular Wilson/Pepper
> tuning!).
>
> To emphasize the humorous aspects of this temperament before
> sharing a few technical details for the curious, I should add
> that the name "O3" is also a kind of open question for Ozan and
> others to answer. Ozone is notably a life-protecting element when
> present at its natural location in the upper atmosphere, but a
> harmful one when it when makes an unwelcome appearance in the
> lower atmosphere as a component of urban smog. Thus the open
> question: is O3 a stratospheric flight to a pleasant layer of
> intonation for Ottoman music, or a pollution of the pure
> Istanbuline airs?
>
> If it were a "smoothcoated" or simple planar (i.e. rank 3)
> temperament, O3 could be defined by three simple generators. The
> period is the 2:1 octave. The regular fifth generating each of
> the two 12-note chains is (84/11)^(1/5), that is, the fifth at
> about 703.893 cents (1.938 cents wide) that produces a regular
> diatonic semitone or limma at a just 22/21 (80.537 cents). The
> third generator, the "artificial diesis" or distance between
> the two 12-note (Eb-G#) chains, is equal to a pure 7/4 (968.825
> cents) less the regular major sixth of this tuning at about
> 911.678 cents, or 57.148 cents.
>
> As a roughcoated planar temperament, however, O3 very slightly
> nuances this theoretical scheme by mapping to 1024-EDO in a way
> so that each 22:21 diatonic semitone is about 0.322 cents wide,
> and thus an 11:10 built from two such semitones is narrow by
> about 3.286 cents, comparable to the 3.247-cent tolerance
> standard of Secor's HTT-29. By comparison, 11:10 is 3.930 cents
> narrow in a smoothcoated (theoretical planar) version of O3, or
> 3.466 cents in a 104-EDO version worthy of mention since a
> discussion of 104-EDO on this list focused my attention on almost
> exactly the right size of fifth for what became the O3 system.
>
> Here is O3 in its roughcoated 1024-EDO version:
>
>
> ! O3-24.scl
> !
> O3 or "Ozone" (24): just 22/21 limma, 7/4, 11/6 (1024-EDO version)
> 24
> !
> 57.42188
> 126.56250
> 183.98438
> 207.42188
> 264.84376
> 288.28125
> 345.70313
> 414.84375
> 472.26563
> 495.70312
> 553.12500
> 622.26563
> 679.68751
> 703.12500
> 760.54688
> 830.85937
> 888.28125
> 911.71875
> 969.14063
> 992.57813
> 1050.00001
> 1119.14063
> 1176.56251
> 2/1
>
>
> Having explained O3, with a well-merited bow to Ozan Yarman and
> George Secor, I should reassure readers that the 12-note or other
> "Ethno Extras" I present should speak for themselves without any
> need to understand the basis of this underlaying 24-note system.
> Rather, with s-n-buzurg and the other Ethno2 tunings as sterling
> examples, each Ethno Extra should be a world within itself.
>
>
> ------------------
> 2. What is Buzurg?
> ------------------
>
> While both Jacques and I may speak of a Buzurg "mode," suggesting
> some kind of scheme covering the range of an octave or more,
> strictly speaking the Buzurg of Safi al-Din and Qutb al-Din is a
> division of the 3:2 fifth, with one form being the following.
>
> 1/1 14/13 16/13 4/3 56/39 3/2
> 0 128 359 498 626 702
> 14:13 8:7 13:12 14:13 117:112
> 128 231 139 128 76
>
> A related scheme, also suggested in these medieval sources, uses
> mostly the same steps (14:13, 13:12, 8:7), but with a different
> ordering:
>
> 1/1 13/12 26/21 4/3 13/9 3/2
> 0 139 359 498 637 702
> 13:12 8:7 14:13 13:12 27:26
> 139 231 128 128 65
>
> As it happens, while O3 as a whole supports both types, the
> Zalzalian 12 set supports only the first variety with a lower
> tetrachrod of 1/1-14/13-16/13-4/3.
>
> If we wish to expand the Buzurg 3:2 division to a mode in the
> sense of an octave division, one simple approach is to add a
> second tetrachord at the 3/2 symmetrical with that at the 1/1.
> Here we follow the first type of Buzurg, where the tetrachord is
> 14:13-8:7-13:12 or 128-231-139 cents:
>
> |----------------------| |-------------------|
> 1/1 14/13 16/13 4/3 56/39 3/2 21/13 24/13 2/1
> 0 128 359 498 626 702 830 1061 1200
> 14:13 8:7 13:12 14:13 117:112 14:13 8:7 13:12
> 128 231 139 128 76 128 231 139
>
> As we shall see, some other types of upper tetrachords also seem
> congenial to Buzurg, and really "making a maqam out of it" calls
> for a melodic path or procedure often involving inflections or
> modulations. However, this concept of a "Buzurg mode" is one
> starting point.
>
> In the Zalzalian 12 set, as it happens, such a Buzurg mode does
> not appear on the 1/1 (as it does in s-n-buzurg.scl), but rather
> on the steps at 346 cents (11/9 or 39/32) and 843 cents (13/8).
>
> Thus before getting to our first Buzurg mode, we'll encounter
> some other Near Eastern and gamelan modes; but I should assure
> Buzurg lovers that we will get there!
>
> ------------------------------------
> 3. Ethno Extras: The Zalzalian 12 set
> -------------------------------------
>
> Here is the 12-note set as a Scala file:
>
> ! O3-zalzalian12_D.scl
> !
> Sampling of Zalzalian maqam/dastgah modes, slendro/pelog modes
> 12
> !
> 138.28125
> 207.42187
> 264.84375
> 345.70312
> 472.26563
> 680.85937
> 704.29687
> 842.57813
> 969.14063
> 1050.00000
> 1176.56249
> 2/1
>
> Note the presence of two 23-cent commas, interestingly involving
> the fifth and octave above the 1/1. In the overall context of O3,
> this might be interpreted as 78/77, for example, so that one JI
> interpretation of this set is
>
> 1/1 13/8 44/39 7/6 11/9 21/16 77/52 3/2 13/8 7/4 11/6 77/39 2/1
> 0 139 207 267 347 472 680 702 841 969 1049 1178 1200
>
> As with s-n-buzurg.scl, the commas make possible lots of nuances
> and choices -- and also, here, an MOS septimal slendro mode
> possibly a bit outside the parameters of Jacques' famous article
> in 1/1. For those in suspense, this comes up in the last rotation.
>
> Also, a disclaimer. I am used to playing this subset as a portion
> of the 24-note O3 keyboard layout with two 12-note manuals, and
> am not sure what the most intuitive arrangement would be on a
> single 12-note keyboard, for which it is definitely intended!
> Advice from Jacques and others would be warmly welcome.
>
> To get a quick preview of our tour, we can look at a Scala matrix
> of the rotations, which I'm reformatting a bit to reduce the line
> length and also to identify the number of each rotation:
>
> Rotation 0: 1/1
> 0 138.3 207.4 264.8 345.7 472.3 680.9 704.3 842.6 969.1 1050.0
> 1176.6 2/1
>
> Rotation 1: 138.3 (~13/12)
> 0 69.1 126.6 207.4 334.0 542.6 566.0 704.3 830.9 911.7 1038.3
> 1061.7 2/1
>
> Rotation 2: 207.4 (~9/8 or ~44/39)
> 0 57.4 138.3 264.8 473.4 496.9 635.2 761.7 842.6 969.1 992.6
> 1130.9 2/1
>
> Rotation 3: 264.8 (~7/6)
> 0 80.9 207.4 416.0 439.5 577.7 704.3 785.2 911.7 935.2 1073.4
> 1142.6 2/1
>
> Rotation 4: 345.7 (~11/9)
> 0 126.6 335.2 358.6 496.9 623.4 704.3 830.9 854.3 992.6 1061.7
> 1119.1 2/1
>
> Rotation 5: 472.3 (~21/16)
> 0 208.6 232.0 370.3 496.9 577.7 704.3 727.7 866.0 935.2 992.6
> 1073.4 2/1
>
> Rotation 6: 680.9 (~77/52)
> 0 23.4 161.7 288.3 369.1 495.7 519.1 657.4 726.6 784.0 864.8
> 991.4 2/1
>
> Rotation 7: 704.3 (~3/2)
> 0 138.3 264.8 345.7 472.3 495.7 634.0 703.1 760.5 841.4 968.0
> 1176.6 2/1
>
> Rotation 8: 842.6 (~13/8)
> 0 126.6 207.4 334.0 357.4 495.7 564.8 622.3 703.1 829.7 1038.3
> 1061.7 2/1
>
> Rotation 9: 969.1 (~7/4)
> 0 80.9 207.4 230.9 369.1 438.3 495.7 576.6 703.1 911.7 935.2
> 1073.4 2/1
>
> Rotation 10: 1050.0 (~11/6)
> 0 126.6 150.0 288.3 357.4 414.8 495.7 622.3 830.9 854.3 992.6
> 1119.1 2/1
>
> Rotation 11: 1176.6 (~77/39)
> 0 23.4 161.7 230.9 288.3 369.1 495.7 704.3 727.7 866.0 992.6
> 1073.4 2/1
>
> From this "itinerary," some readers may draw a few conclusions.
> Thus Rotations 4 (~11/9) and 8 (~13/8) include Buzurg modes,
> while Rotations 5 (~21/16) and 9 (~7/4) look like good places for
> Rast, and Rotation 7 (~3/2) likewise for Shur.
>
> We'll encounter these and more, and I warmly invite readers to
> celebrate other modes, gamelan or Near Eastern or other, that
> I've missed.
>
>
> -------------------------------------------------------------
> Rotation 0 (1/1): Slendro, pelog, and Wilson's 1-3-7-9 hexany
> -------------------------------------------------------------
>
> 0 138.3 207.4 264.8 345.7 472.3 680.9 704.3 842.6 969.1 1050.0
> 1176.6 2/1
>
> Starting on the 1/1 or Scala step 0 of the Zalzalian 12 set, we
> find the slendro and pelog modes that originally served to define
> the 10-note nucleus of the tuning. The original 5-note slendro
> mode was this:
>
> 0 265 472 704 969 1200
> 1/1 7/6 21/16 3/2 7/4 2/1
> 265 207 232 265 231
>
> This includes the beautiful 16:21:24:28 sonority which according
> to Kyle Gann was used by LaMonte Young at least as early as the
> 1960's, and has since been discussed by Keenan Pepper (from whom
> I learned about it) and others. In the wider context of our
> 12-note set, this sonority has a striking resolution to a fifth
> featuring Zalzalian or neutral second steps around 13:12 and
> 14:13.
>
> 969 843
> 704 843
> 265 138
> 0 138
>
> Keeping our focus on septimal slendro, this rotation offers a
> complete tempered version of Erv Wilson's 1-3-7-9 hexany:
>
> 0 207 265 472 704 969 1200
> 1/1 9/8 7/6 21/16 3/2 7/4 2/1
> 207 57 207 232 265 231
>
> In addition to the slendro mode above with an opening 7:6 step,
> we have a mode with an opening 9:8.
>
> 0 207 472 704 969 1200
> 1/1 9/8 21/16 3/2 7/4 2/1
> 207 265 232 265 231
>
> This second type with steps of 9:8-7:6-8:7-7:6-8:7 is a rotation
> of Jacques' N or "Natural" variety of septimal slendro, while the
> first type with 7:6-9:8-8:7:7:6-8:7 is a rotation of his M or
> "Mirror image" mode in relation to N.
>
> Both N and M modes have three step sizes: 7:6, 8:7, and 9:8. We
> will also encounter M and N in their original rotations as we
> move through the Zalzalian 12 set -- but not other, more complex
> septimal slendro patterns present in s-n-buzurg.scl.
>
> Another basic component of the Zalzalian 12 set is a basic pelog
> mode using a narrow fifth at 681 cents, and optionally a narrow
> octave at 1177 cents also! Here I use a vertical bar | to
> indicate two versions of the "same step," which might well
> both be used at different points in a performance.
>
> 0 138 346 681 843 1177|1200
> 1/ 1 13/12 11/9 77/52 13/8 77/39| 2/1
> 138 207 335 162 334|357
>
> While this was the pelog that first caught my attention, another
> form also seems attractive to me, with the first three notes
> suggesting to me a septimal Shur Dastgah but also not too far
> from reported averages for one typical variety of pelog mode.
>
> 0 138 265 681 843 1177|1200
> 1/1 13/12 7/6 77/52 13/8 77/39| 2/1
> 138 127 415 162 334/357
>
> If we willing to explore "altered" forms of Near Eastern modes
> with a 21/16 substituted for the usual 4/3, then two other modes
> stand out to me. Some modern Arab theory speaks of tetrachords
> which at times may be narrowed by a comma, while Nelly Caron and
> Dariouche Safvate write that a fourth of around 484 cents was
> common in traditional Persian tuning, notably appearing in an
> older version of the Avaz-e Bayat-e Tork (to be included in Ethno
> Extras).
>
> One possibility is a version of Ibn Sina's 11th-century tuning
> with Shur-like qualities where the narrow 21/16 serves for Ibn
> Sina's original 4/3:
>
> 0 138 265 472 704 843 969 1200
> 1/1 13/12 7/6 21/16 3/2 13/8 7/4 2/1
> 138 127 207 232 138 127 231
>
> Some exploration at the keyboard shows me that this is a fine
> Shur from a melodic point of view, and offers some beautiful
> polyphonic cadences if one wishes to develop dastgah-based
> counterpoint. The 21/16 step plays a premier role in making some
> of these progressions and shadings possible, for example in this
> cadence featuring a small Zalzalian or neutral third at 334 cents
> which expands to a fifth:
>
> 843 (13/8) 969 (7/4) 1200 (2/1)
> 472 (21/16) 704 (3/2)
> 138 (13/12) 0 (1/1)
>
> Here the opening sonority of 0-334-704 might represent 14:17:21,
> with the highest voice then moving up by a 127-cent step so that
> the sonority becomes 0-334-831, with 52:63:84 as one JI reading
> suggested by the near-pure 21:13 small neutral sixth not far from
> the intriguing ratio of Phi (833.090 cents). Then, the small
> neutral neutral third and sixth expand to fifth and octave in a
> manner recalling the classic European polyphony practiced in the
> era of Safi al-Din and Qutb al-Din -- or more precisely as it
> might have been practiced if the Zalzalian intervals of these and
> other Islamic theorists had been part of its vocabulary!
>
> Another possibility is a variation on Jacques Dudon's beautiful
> Ibina, 1/1-13/12-11/9-4/3-3/2-13/8-16/9-2/1. The lower tetrachord
> is of the Mohajira type with Z-T-Z where "Z" is a Zalzalian or
> neutral second and "T" and regular major second or tone, while
> the upper tetrachord on the 3/2 is a form of Shur, Turkish
> Ushshaq, or Arab Bayyati, with Z-Z-T, two Zalzalian steps
> followed by a tone. Here both the 4/3 fourth and 16/9 minor
> seventh are lowered by a comma to 21/16 and 7/4.
>
> "Narrow Moha" Shur/Bayyati
> |----------------| |----------------|
> 0 138 346 472 704 843 969 1200
> 1/1 13/12 11/9 21/16 3/2 13/8 7/4 2/1
> 138 207 127 232 138 127 231
>
> Here, in a curious way, the lower Mohajira ("Moha" for short)
> variant tetrachord introduces two of the steps of Buzurg: a lower
> 138-cent step representing 13:12, and an upper 127-cent step
> representing 14:13. The middle step, however, is a comma narrower
> than Buzurg's usual 8:7 (231 cents), at 207 cents or a near-9:8
> (also a near-44:39), so that the fourth is compressed from a
> usual rounded 496 or 497 cents in this temperament to 472 cents,
> or in JI terms from 4/3 to 21/16.
>
> While I am not aware of any discussion of these specific altered
> modes in medieval or modern Near Eastern theory, I mention them
> in keeping with the adventurous xenharmonic spirit of Ethno, and
> also the wise adage that one should not spurn what the equations
> or tuning parameters generously cast at one's feet. In fact, as I
> relate above, the Shur with 21/16 in place of 4/3 proves both
> melodically apt and contrapuntally delightful when considered as
> a mode in its own right, as well as resembling the kind of
> pattern I often fall into when improvising in a septimal Shur or
> Arab Bayyati where a usual 4/3 step is the norm but the
> progression of the _sayr_ or development may lead at some points
> to the lowering of this step by a comma. Likewise, the Ibina-like
> mode with lowered steps at 21/16 and 7/4, although not following
> the original scheme of differential coherence (-c), nevertheless
> presents fruitful possibilities as a septimal variation on the
> Mohajira/Ibina theme.
>
> (Conclusion of Part 1)
>
> Best,
>
> Margo Schulter
> mschulter@calweb.com
>
>
> ------------------------------------
>
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>

🔗Margo Schulter <mschulter@...>

> Dear Margo,

> In the midst of the Islamic holy month of Ramadan as the moon
> slowly turns to full in the night sky, when the debilitating
> heat and humidiy (for the first time over 40 degrees Celsius
> and %90 moisture) wafting over Istanbul has abated a little and
> fasting for the greater glory of Rahman and Rahim Allah is not
> anymore a burden on the persevering spirit as much as
> aforetimes, I find this oppurtunity to concentrate on your
> humourous e-mails promoting the "O3 Temperament" from three
> weeks ago.

Dear Ozan,

Please let me wish you a happy Ramadan, and express my pleasure
that the weather in Istanbul, at least at the time you were
writing, had become more merciful.

> First of all, a big thank you for your kind words and
> praises. How flattering to receive such attention and
> encouragement from you!

What I cannot overemphasize are the benefits of reading your
thesis which you have so generously made available. The
translations of Turkish documents and accounts of the controversy
over Alla Franca and Alla Turca into English, including the
question of maqam intonation and "quartertones," are at once
illuminating, entertaining, and at another level tragic when we
remember the promising musical careers ruined. You guide the
reader through an appreciation of all these levels of Turkish
music theory and criticism in the 20th century.

And for me, seeing that explanation of a performer's measured
intonation in Maqam Ushshaq was a wonderful moment (pp. 27-29),
as if to confirm the validity of the quest for a more accurate
and more diverse intonation of middle or Zalzalian intervals, a
quest reflected in sometimes similar and sometimes different ways
in systems such as Yarman-79/80-MOS, Yarman-24, and O3.

You have indeed been my mentor, for it was a desire to enjoy a
small part of the richness of the 79/80-MOS, and especially the
diversity of superparticular middle second steps, that led early
this summer to the O3 temperament.

> You will surely remember from our past correspondences, that I
> had remarked positively on the approach of using a chain of
> fifths a tad larger than pure - and even went so far as to
> formulate middle- resolution tuning schemes of my own in the
> same vein to incorporate maqam flavours in as comprehensive a
> manner as possible. This path promises to yield favourable
> results not much tried in Turkish Maqam music (where the
> "3-limit mainstream theory market" still dominates the notion
> of "natural pitches" despite my "sinister presence" in cyber
> music circles. Hah hah!)

A curious point here is that O3, from one point of view, uses "a
chain of fifths a tad larger than pure" in order to achieve a
tuning not too far from that likely for a 12-note Halberstadt
keyboard in 14th-century Europe in a Pythagorean Eb-G# (more on
that tuning, about which you asked, in another post), while
stretching the fifths just enough to get an apotome near 14:13
and a diminished third near 11:10. A look at Maqam Rast on B, and
Maqam Huseyni on C#, may be instructive:

Rast Rast
|-------------------|.......|--------------------|
rast dugah segah chargah neva huseyni evdj gerdaniye
B C# Eb E F# G# Bb B
0.0 207.4 369.1 495.7 703.1 911.7 1073.4 1200.0 ~ 1/1 44/39 26/21 4/3 3/2 22/13 13/7 2/1

In this ascending form of Rast, we have two Rast tetrachords at
207.4-161.7-126.6 cents and 208.6-161.7-126.6 cents. This is near
Safi al-Din al-Urmavi's 9:8-11:10-320:297 or 203.9-165.0-129.1
cents (1/1-9/8-99/80-4/3). This appears on p. 10 of Dr. Fazli
Arslan's most admirable publication, where this tetrachord is
termed "Medium disjunct." And "disjunct" here, as Arslan
explains, refers not to an arrangement of two tetrachords, but to
the "skipping" within the tetrachord from 9:8 to 11:10, omitting
the intervening superparticular ratio of 10:9.

<http://www.muslimheritage.com/uploads/The__Theory_of_Music.pdf>

Maqam Huseyni uses another permutation of this same tetrachord of
some interest for recent Turkish music theory and its political
vicissitudes:

Rast Rast
|--------------------|......|----------------------|
dugah segah chargah neva huseyni evdj gerdaniye muhayyer
C# Eb E F# G# Bb B C#
0.0 161.7 288.3 495.7 704.3 866.0 992.6 1200.0
~ 1/1 56/51 13/11 4/3 3/2 33/20 39/22 2/1

Here the tetrachords of 161.7-288.3-495.7 cents are close to the
Huseyni genus of 11:10-320:297-9:8 (165.0-129.1-203.9 cents) or
1/1-11/10-32/27-4/3 suggested by Suphi Ezgi in 1933. As very
aptly put in the article of you and your colleagues on "Theory
vs. Practice" in Turkish intonation, Ezgi later "back-pedalled"
and settled on the orthodox Arel-Ezgi-Uzdilek (AEU) ratio of a
Pythagorean diminished third at 65536:59049 or 180.45 cents (see page 50, the sixth page of the PDF version):

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

Since calling 161.7 cents a close representation of 11/10 when it
is about 3.3 cents narrow might literally be a bit of a stretch,
as you are often wont to say, I have styled it a 56/51 (161.9
cents); but I would say it is not unreasonably far from 11/10,
and apt as a dugah-segah step in either Rast or Huseyni.

For both Rast and Huseyni, of course, perde ajem at A is very
handy as the minor seventh of Acemli Rast (992.6 cents) or the
minor sixth often used in Huseyni (784.0 cents), for example; but
my purpose here is simply to illustrate how the moderate
tempering of the fifth brings about a tetrachord like that of
Safi al-Din or Ezgi in his original 1933 version of Huseyni.

> A particular thought has occured to me while trying to follow
> your latest exposition of maqams such as Buzurg, Rast-Najid,
> Segah, etc in O3... I have found out that my memory is lately
> chuck full of useless everyday political dilly-dallying and I
> cannot recollect which maqam was transformed how in what
> tuning. It would be prudent, I believe, for you to categorize
> the maqams we have elaborated so far in one concise master
> article, comprising your theoretical constructs (including some
> of my interpretations and commentary maybe?) in their
> respective tunings and how they evolved thus in succinct steps
> (using cent values with dot zero decimals for quick SCALA
> access too).

This is an excellent proposal! Indeed, Inshallah, it should be my
next step after finishing my Zalzalian 12 articles. I realize, in
fact, that the kind of concise guide to some main maqamat that
you describe could be a helpful guide to the Zalzalian 12
articles. And the discussion of Yarman-79/80 tunings for some of
the principal maqamat in your thesis is one fine model for such
an article regarding O3.

Another complication of something like the Zalzalian 12 articles
is that such a 12-note set may invite one to come up with
"variations" on maqamat where one or more usual steps are missing
or out of place by a comma, say. This can be a creative process,
but perhaps easier to follow if the reader were first familiar
with the usual forms of such maqamat. Thus it becomes especially
helpful to know "which maqam was transformed how," as you put it.

The more I think about it, the more attractive a model the
presentation in your thesis becomes.

Since this may be our first discussion of O3, maybe I should try
my hand at a draft of the article we are discussing, share it
with you by private e-mail, and then add any commentary you might
offer for the version for this list, as well as any relevant
interpretations or commentary from earlier discussions you might
suggest.

And your idea, when using rounded cents, to give dot zero
decimals for Scala access is an excellent one I will follow!

> The lengthy exegesis of makamlar in your messages requires much
> deeper deliberation that I can reflect to my response
> here. Nevertheless, let me say that Rotation 1 (13/12) Maqam
> Segah hits the spot very well. I also like the Rast flavour
> with 8/7 as perde dugah instead of the equivalent or
> approximation of 9/8. Yet, I feel Penchgah-i Hagar (with so low
> a segah and hijaz) has left the realm of Penchgah and entered
> that of Nihavend. Maybe one could rename it "Penchgah fi
> Nihavend-i Hagar" (Penchgah within Nihavend of Hagar). More
> fittingly so, since Nihavend exhibits more the Hijaz upper
> tetrachord you seek compared to Penchgah, which almost never
> shows it.

As to Penchgah fi Nihavend-i Hagar, I absolutely agree that this
is quite different from Penchgah, and belongs to a different
realm. And if your ear deems it to fit the name of Nihavend, I
will gladly accept your judgment. As I realized when seeking for
a name, "Penchgah" in this context means simply "with a step at
around a 9:8 above perde segah." Your name ingeniously expresses
the situation very nicely! May I add that the realm of Penchgah
with segah at 26/21 is most delightful, with the simple form
available on a single 12-note keyboard:

Penchgah Rast
|---------------------------|-------------------|
rast dugah segah hijaz neva huseyni evdj gerdaniye
B C# Eb F F# G# Bb B
0 207.4 369.1 576.6 703.1 911.7 1073.4 1200.0
~ 1/1 44/39 26/21 88/63 3/2 22/13 13/7 2/1

And I must agree, even as a newcomer not acquainted with the
nuances of the seyir for Penchgah and its common modulations,
that I would not think of an upper Hijaz -- quite unlike Penchgah
fi Nihavend-i Hagar, where it is a usual part of the seyir.
And it might be said that while the steps or perde-s form the
frame or skeleton of a maqam, the seyir is the flesh and blood.

> Shur and Najdi are hard to come by in Turkish circles to my
> knowledge, so I make no further commentary on those.

With Shur, it is interesting that Turkish performers sometimes
play a very low or septimal Ushshaq, if we may take as an example
the performance of "a venerable Turkish Neyzen" or _Niyazi
Sayin_. as you explain in your thesis at pp. 27-29. Here I quote
your measured steps for this __Niyazi Sayin Ushshak Ney_ Taksim
and JI values, plus an approximation in O3 (full 24 notes):

Niyazi Sayin Ushshak Ney Taksim: 123.47 137.13 227.87

JI: 128.30 138.57 231.17
14:13 13:12 8:7

O3: 126.56 138.28 230.86

However, while either this low flavor of Ushshaq or a similar
flavor of Shur might suggest a medieval 28:26:24:21, Ibn Sina's
famous tetrachord or a permutation of it (if 12:13:14:16 is his
actual form), the seyir of Ushshaq would, of course, differ from
that of Shur Dastgah.

And I am not sure if Najdi is very common in the Arab world,
although it is mentioned by theorists such as Amine Beyhom. One
might actually think of it as two conjunct Rast tetrachords plus
a _lower_ tone. In a typical Arab intonation as realized in O3,
perde segah (or, in Arabic, sikah) might be at 357.4 or 358.6
cents, close to Jacques Dudon's 59/48 or the 16/13 of Yarman-24.
To play Nadji with segah at around 26/21 is really taking an Arab
maqam and applying an Ottoman intonation, I would guess.

> And at long last, Buzurg once more. Just a minor interjection
> on my part: It is my impression, based on no solid evidence
> except erudite conjecture, that Buzurg is supposed to be an
> ascending/descending:

> 14/13
> 16/13
> 56/39
> 3/2

An interesting point is the steps of 14:13-8:7-7:6-117:112
(128.3-231.2-266.9-75.6 cents). The adjacent 8:7 and 7:6 steps in
the middle lead me to ask if these steps occur together, thus in
effect dividing 4:3 into a trichord of 8:7:6, in other maqamat.
I need to try playing this and seeing where it takes me, but your
erudite intuition is indeed to be carefully considered.

> In one thematic version and

> 14/13
> 16/13
> 4/3
> 56/39

> diminished pentachord in another ascending/descending cadential
> version. I don't remember if I had mentioned this, but there it
> is. The latter is akin to what I dub the "Ferahnak
> pentachord".

Looking at a few page on the web about Makam Ferahnak, I see some
parallels, and some with a maqam we were previously discussing
(see below). It is curious that I found a descending seyir with
this pentachord through an analogy with Shur Dastgah, where the
fifth is often lowered by a koron, or often about 1/3 tone, in
descending.

You should indeed educate me more on Ferahnak. and how you
interpret the intonation and the seyir. What I will quickly
mention here is a version on the web from Ezgi where, if I take
the signs of S and K (lesser and greater mujannab) as around
14/13 and 11/10, the maqam seems very similar to our Penchgah fi
Nihavend-i Hagar. Here I will use O3 pitches:

Ferahnak Hijaz
|--------------------------|-----------------|
Eb E F# G# Bb B D Eb
0 126.6 334.0 542.6 704.3 830.8 1119.1 1200.0
S T T K S A B
126.6 207.4 208.6 161.7 126.6 288.3 81.9

And what I take to be a descending form, reminding me of your
suggestion for Nihavend that the descending seventh degree should
form a perfect fifth with the third step of the lower tetrachord,
here C#-G#:

Ferahnak Segah
|--------------------------|-----------------|
Eb E F# G# Bb B C# Eb
0 126.6 334.0 542.6 704.3 830.8 1038.3 1200.0
S T T K S T K
126.6 207.4 208.6 161.7 126.6 207.4 161.7

> This construct is amiss in theoretical and historical
> explanations of makamlar, but chanced - even if rarely - in
> performances if my scrutiny is to be trusted. Ah, but I see
> that the intiguing descending Segah upper region in your third
> e-mail features this very Ferahnak pentachord as well as the
> already-known diminished Ferahnak pentachord mixed!

It is curious that I looked up Ferahnak on Google, recognized the
similarity with a variation on Penchgah fi Nihavend-i Hagar, and
then came to your similar recognition in the next paragraph! (I
read this paragraph earlier, but had yet checked my earlier post
to see exactly which ajnas (genera) you were referring to here,
evidently the Segah variations at the end of my Part 3 on the
Zalzalian 12 set.

One thing I did not have available in the Zalzalian 12 set,
although it is available on a single 12-note keyboard, is a
seventh at 20/11 or 51/28, here more the latter at 1038.3 cents,
in that rotation. And I might say that the lower pentachord
found in both of Ezgi's forms of Ferahnak, and also Penchgah fi
Nihavend-i Hagar, is related to a 1/1-14/13-40/33-4/3 flavor of
Segah or the like rather as Makam Penchgah is to Rast (with segah
at around 26/21).

Returning to Buzurg, the difference I'd see is that the latter
has a semitone below the fifth, or acting as a kind of lowered
fifth, at around 56/39; while in Ferahnak we have a step maybe
not too much higher than 15/11, here 542.6 cents. But I agree
it's intriguing how the descending Segah region in Part 3 of my
Zalzalian 12 series of articles brings into play the 56/39 also
found in Buzurg, and thus the Ferahnak ajnas you are discussing.

> About the upper "Buzurg tetrachord", I imagine it would be
> judicious to say Hijaz-i Buzurg to punctuate the Hijaz sphere
> of influence here. We see such denominations as Hijaz-i
> Muhalif, Hijaz-i Turki, etc... to categorize maqam savours
> centering on Hijaz in historical sources, so, why not scale
> structures themselves?

Certainly an upper tetrachord of 1/1-14/13-16/13-4/3, or in the
example from O3, 0.0-126.6-357.4-495.7 cents, could fit with one
flavor of Turkish Hijaz: Hijaz-i Buzurg might be exactly right!
And in the world of Iranian music, one might call this Avaz-e
Bayat-e Esfahan-e Buzurg (if so many possessives are admissible),
or simply Esfahan-e Buzurg, to distinguish it from various other
flavors of Esfahan. Farhat gives Esfahan, if one applies his tar
tuning to his notation, as

D Ep F> G
0.0 135.0 360.0 495.0
135.0 225.0 135.0

By the way, Hijaz-e Muhalif reminds me of the Persian Mokhalef,
another topic (and rather like one flavor of Esfahan)! I'd love
to learn more about Hijaz-i Muhalif.

> So far, I liked the Buzurg variants you delineated. Good show!
> The possibilities of fine intonation with the O3 type tuning
> demonstrates clearly how our clich?? notions of trying to keep
> segah close to 5/4 is much misguided. It has been lately my
> inclination to focus on 370 cents or so as the nominal spot for
> perde segah in most (and perhaps all) instances in keeping with
> historicity of maqam theory.

Indeed O3 is designed to place perde segah at around 370 cents in
order to optimize the kind of historical Ottoman flavor we are
discussing. And it's fascinating how Safi al-Din al-Urmavi's
"Medium disjunct" tetrachord of 9:8-11:10-320:297, or Ezgi's
rotation of this for Huseyni in 1933, so nicely fits with this
placement of rast-segah at around 26/21.

> Most cordially,
> Oz.

Best, with warmest thanks to Dr. Arslan also,

Margo

🔗Margo Schulter <mschulter@...>

🔗Ozan Yarman <ozanyarman@...>

A belated reply to Margo:

✩ ✩ ✩
www.ozanyarman.com

On Aug 24, 2010, at 7:55 AM, Margo Schulter wrote:

>> Dear Margo,
>
>> In the midst of the Islamic holy month of Ramadan as the moon
>> slowly turns to full in the night sky, when the debilitating
>> heat and humidiy (for the first time over 40 degrees Celsius
>> and %90 moisture) wafting over Istanbul has abated a little and
>> fasting for the greater glory of Rahman and Rahim Allah is not
>> anymore a burden on the persevering spirit as much as
>> aforetimes, I find this oppurtunity to concentrate on your
>> humourous e-mails promoting the "O3 Temperament" from three
>> weeks ago.
>
> Dear Ozan,
>
> Please let me wish you a happy Ramadan, and express my pleasure
> that the weather in Istanbul, at least at the time you were
> writing, had become more merciful.

You are very kind.

>
>> First of all, a big thank you for your kind words and
>> praises. How flattering to receive such attention and
>> encouragement from you!
>
> What I cannot overemphasize are the benefits of reading your
> thesis which you have so generously made available. The
> translations of Turkish documents and accounts of the controversy
> over Alla Franca and Alla Turca into English, including the
> question of maqam intonation and "quartertones," are at once
> illuminating, entertaining, and at another level tragic when we
> remember the promising musical careers ruined. You guide the
> reader through an appreciation of all these levels of Turkish
> music theory and criticism in the 20th century.
>

Splendid.

> And for me, seeing that explanation of a performer's measured
> intonation in Maqam Ushshaq was a wonderful moment (pp. 27-29),
> as if to confirm the validity of the quest for a more accurate
> and more diverse intonation of middle or Zalzalian intervals, a
> quest reflected in sometimes similar and sometimes different ways
> in systems such as Yarman-79/80-MOS, Yarman-24, and O3.
>

Indeed.

> You have indeed been my mentor, for it was a desire to enjoy a
> small part of the richness of the 79/80-MOS, and especially the
> diversity of superparticular middle second steps, that led early
> this summer to the O3 temperament.
>

And so have I - at the risk of running into repetition, let me say
once more - benefitted so very much from our correspondences.

>> You will surely remember from our past correspondences, that I
>> had remarked positively on the approach of using a chain of
>> fifths a tad larger than pure - and even went so far as to
>> formulate middle- resolution tuning schemes of my own in the
>> same vein to incorporate maqam flavours in as comprehensive a
>> manner as possible. This path promises to yield favourable
>> results not much tried in Turkish Maqam music (where the
>> "3-limit mainstream theory market" still dominates the notion
>> of "natural pitches" despite my "sinister presence" in cyber
>> music circles. Hah hah!)
>
> A curious point here is that O3, from one point of view, uses "a
> chain of fifths a tad larger than pure" in order to achieve a
> tuning not too far from that likely for a 12-note Halberstadt
> keyboard in 14th-century Europe in a Pythagorean Eb-G# (more on
> that tuning, about which you asked, in another post), while
> stretching the fifths just enough to get an apotome near 14:13
> and a diminished third near 11:10. A look at Maqam Rast on B, and
> Maqam Huseyni on C#, may be instructive:
>
> Rast Rast
> |-------------------|.......|--------------------|
> rast dugah segah chargah neva huseyni evdj gerdaniye
> B C# Eb E F# G# Bb B
> 0.0 207.4 369.1 495.7 703.1 911.7 1073.4 1200.0
> ~ 1/1 44/39 26/21 4/3 3/2 22/13 13/7 2/1
>

A wonderfully designed scale of rightful pitches supporting not only
maqams Rast and Huseyni, but also Segah.

> In this ascending form of Rast, we have two Rast tetrachords at
> 207.4-161.7-126.6 cents and 208.6-161.7-126.6 cents. This is near
> Safi al-Din al-Urmavi's 9:8-11:10-320:297 or 203.9-165.0-129.1
> cents (1/1-9/8-99/80-4/3). This appears on p. 10 of Dr. Fazli
> Arslan's most admirable publication, where this tetrachord is
> termed "Medium disjunct." And "disjunct" here, as Arslan
> explains, refers not to an arrangement of two tetrachords, but to
> the "skipping" within the tetrachord from 9:8 to 11:10, omitting
> the intervening superparticular ratio of 10:9.
>
> <http://www.muslimheritage.com/uploads/The__Theory_of_Music.pdf>
>

Frankly, I do not think Fazli chose the best English wording here for
the Arabic originals. Rauf Yekta had suggested as early as 1922 the
correct wordings in French of those terms adopted by early Islamic
theorists from Hellenistic literature. Let me recapitulate them here.

According to Safi al-din Urmavi in his "Risalat al-Sharafiyyah", if
the largest of three melodic intervals within a tetrachord is greater
in size than the sum of the other two, the genus is called "Leyyin" -
if not, "Qawi". Monz would surely recognize with satisfaction that one
proper translation of the former term is his proposed adjective
"relaxed". Indeed, "Leyyin" is Arabic for "soft, softened, light,
gentle, easy-going, mild, mellow, smooth, creamy, etc..." and is
obviously the chosen equivalent of the Greek word "Malakon". Likewise,
"Qawi" means "sturdy, rigid, firm, tenacious, resistant, strong,
powerful, safe, secure, trustworthy, well-supplied, propertied etc..."
some of which correspond justly to the Greek word
"Syntonon" (strained). I feel Monz' proposed "tense" might not be the
best translation for the Arabic term compared to "firm" here.

In the same "esprit", Rauf Yekta translates Leyyin as "mou" (soft) and
Qawi as "fort" (strong) in the section devoted to his monograph in
Encyclopédie de la musique et dictionnaire du Conservatoire (p. 2990):

-------------------------------------------------

L'ensemble de trois intervalles ordonnés dans une
quarte s'appelle « genre » (j-i»-. Une quarte con-
tient donc trois intervalles qui réalisent quatre sons ;
de là lui vient son nom qui signifie : « intervalle sur
lequel on construit une modulation de quatre sons. »
Il y a différents genres. Si l'un des trois intervalles
d'un genre est d'un rapport plus grand que la somme
des deux autres, le genre est mou (j^) ; s'il n'en est
pas ainsi, il est fort (i^y).

Le genre mou se divise en trois parties princi-
pales :

1° Le genre normal (RASIM).
2° Le genre chromatique (LEVNI).
3° Le genre ordonnateur (NAZIM).

-----------------------------------------------------

Urmevi goes on to permute the intervals he categorized under these two
general types of tetrachord (Leyyin & Qawi) so that he positions the
largest interval either on the left, on the right, or in the middle
(for he accepts no more than 3 interval ratios per tetrachord). He
eventually comes up with 6 classes per tetrachord type, 2 of which
become "gayr-i muntazam" (disorderly) for having the largest in the
middle, the other 2 of which become "muntazam mutetali" (sequentially
ordered) for intervals sizes arranged from high to low (or low to
high), and the last two of which become "muntazam gayr-i
mutetali" (non-sequentially ordered).

Those tetrachords that employ 5:4 as the largest interval among three
are called RASIM,
Those tetrachords that employ 6:5 as the largest interval among three
are called LEVNI,
Those tetrachords that employ 7:6 as the largest interval among three
are called NAZIM.

Yekta has translated RASIM (that which draws or flows through) as
normal, LEVNI (that which cascades in colours) as chromatic, and NAZIM
(arranging one after the other) as organizing.

These translations do fairness to the Arabic originals, which insooth
stand for the famous "Diatonic", "Chromatic" and "Enharmonic" genera
respectively.

Following table after table of permutations, Urmevi shows a new
method, where he uses the same interval ratio twice in a tetrachord. A
pair of 8/7s makes the tetrachord "qawi zu al-taz'eef fi al-
awwal" (the first paired of the FIRM genus); a pair of 9/8s makes the
tetrachord "zu al-taz'eef fi al-thani" (the second paired); a pair of
10/9s makes the tetrachord "zu al-taz'eef fi al-thalith" (the third
paired).

Yet another operation for finding new tetrachords for Urmavi is taking
a pair of sequential superparticular ratios. Safi al-din pairs a 8/7
and 9/8 to arrive at "Muttasil al-Awwal" (the first conjoined); a 9/8
and 10/9 to arrive at "Muttasil al-Awsat" (the middle conjoined); a
10/9 and 11/10 to arrive at "Muttasil al-Thalith" (the third conjoined).

The same operation where one diminishing superparticular ratio is
skipped yields "qawi munfasil" (Firm, sundered) for 8/7 and 10/9;
"mutadil munfasil" (Moderate, sundered) for 9/8 and 11/10; and "Shedd
munfasil" (Tightened, sundered) for 10/9 and 12/11.

One can see similar explanations in Rauf Yekta, shedding (excuse the
pun) much light into the confusion of the tetrachordal genera of the
Ancient world.

The tetrachord in question in your response is "mutadil munfasil",
which is better translated as "Moderate, sundered" - to avoid
confusion with the wholetone disjunction between tetrachords making an
octave.

> Maqam Huseyni uses another permutation of this same tetrachord of
> some interest for recent Turkish music theory and its political
> vicissitudes:
>
> Rast Rast
> |--------------------|......|----------------------|
> dugah segah chargah neva huseyni evdj gerdaniye muhayyer
> C# Eb E F# G# Bb B C#
> 0.0 161.7 288.3 495.7 704.3 866.0 992.6 1200.0
> ~ 1/1 56/51 13/11 4/3 3/2 33/20 39/22 2/1
>
> Here the tetrachords of 161.7-288.3-495.7 cents are close to the
> Huseyni genus of 11:10-320:297-9:8 (165.0-129.1-203.9 cents) or
> 1/1-11/10-32/27-4/3 suggested by Suphi Ezgi in 1933. As very
> aptly put in the article of you and your colleagues on "Theory
> vs. Practice" in Turkish intonation, Ezgi later "back-pedalled"
> and settled on the orthodox Arel-Ezgi-Uzdilek (AEU) ratio of a
> Pythagorean diminished third at 65536:59049 or 180.45 cents
> (see page 50, the sixth page of the PDF version):
>
> <http://www.ozanyarman.com/files/theoryVSpractice.pdf>
>

So very observant of you! Indeed, that's my synopsis on Ezgi.

> Since calling 161.7 cents a close representation of 11/10 when it
> is about 3.3 cents narrow might literally be a bit of a stretch,
> as you are often wont to say, I have styled it a 56/51 (161.9
> cents); but I would say it is not unreasonably far from 11/10,
> and apt as a dugah-segah step in either Rast or Huseyni.
>

Surely.

> For both Rast and Huseyni, of course, perde ajem at A is very
> handy as the minor seventh of Acemli Rast (992.6 cents) or the
> minor sixth often used in Huseyni (784.0 cents), for example; but
> my purpose here is simply to illustrate how the moderate
> tempering of the fifth brings about a tetrachord like that of
> Safi al-Din or Ezgi in his original 1933 version of Huseyni.
>

An excellent demonstration thereto, if I may add.

>> A particular thought has occured to me while trying to follow
>> your latest exposition of maqams such as Buzurg, Rast-Najid,
>> Segah, etc in O3... I have found out that my memory is lately
>> chuck full of useless everyday political dilly-dallying and I
>> cannot recollect which maqam was transformed how in what
>> tuning. It would be prudent, I believe, for you to categorize
>> the maqams we have elaborated so far in one concise master
>> article, comprising your theoretical constructs (including some
>> of my interpretations and commentary maybe?) in their
>> respective tunings and how they evolved thus in succinct steps
>> (using cent values with dot zero decimals for quick SCALA
>> access too).
>
> This is an excellent proposal! Indeed, Inshallah, it should be my
> next step after finishing my Zalzalian 12 articles. I realize, in
> fact, that the kind of concise guide to some main maqamat that
> you describe could be a helpful guide to the Zalzalian 12
> articles. And the discussion of Yarman-79/80 tunings for some of
> the principal maqamat in your thesis is one fine model for such
> an article regarding O3.
>
> Another complication of something like the Zalzalian 12 articles
> is that such a 12-note set may invite one to come up with
> "variations" on maqamat where one or more usual steps are missing
> or out of place by a comma, say. This can be a creative process,
> but perhaps easier to follow if the reader were first familiar
> with the usual forms of such maqamat. Thus it becomes especially
> helpful to know "which maqam was transformed how," as you put it.
>
> The more I think about it, the more attractive a model the
> presentation in your thesis becomes.
>

One could perhaps organize this article in a database application such
as Excel or Numbers. That would tidy things up a bit with interactive
links for what goes where and which came whence.

> Since this may be our first discussion of O3, maybe I should try
> my hand at a draft of the article we are discussing, share it
> with you by private e-mail, and then add any commentary you might
> offer for the version for this list, as well as any relevant
> interpretations or commentary from earlier discussions you might
> suggest.

That's a notion. In the case of a Spreadsheet, one could variate the
tunings by a drop-down menu to observe the effect instantaneously. Of
course, some good folk from the list - who know Excel or Numbers much better than I - might be willing to assist?

>
> And your idea, when using rounded cents, to give dot zero
> decimals for Scala access is an excellent one I will follow!
>
>> The lengthy exegesis of makamlar in your messages requires much
>> deeper deliberation that I can reflect to my response
>> here. Nevertheless, let me say that Rotation 1 (13/12) Maqam
>> Segah hits the spot very well. I also like the Rast flavour
>> with 8/7 as perde dugah instead of the equivalent or
>> approximation of 9/8. Yet, I feel Penchgah-i Hagar (with so low
>> a segah and hijaz) has left the realm of Penchgah and entered
>> that of Nihavend. Maybe one could rename it "Penchgah fi
>> Nihavend-i Hagar" (Penchgah within Nihavend of Hagar). More
>> fittingly so, since Nihavend exhibits more the Hijaz upper
>> tetrachord you seek compared to Penchgah, which almost never
>> shows it.
>
> As to Penchgah fi Nihavend-i Hagar, I absolutely agree that this
> is quite different from Penchgah, and belongs to a different
> realm. And if your ear deems it to fit the name of Nihavend, I
> will gladly accept your judgment. As I realized when seeking for
> a name, "Penchgah" in this context means simply "with a step at
> around a 9:8 above perde segah." Your name ingeniously expresses
> the situation very nicely! May I add that the realm of Penchgah
> with segah at 26/21 is most delightful, with the simple form
> available on a single 12-note keyboard:
>
> Penchgah Rast
> |---------------------------|-------------------|
> rast dugah segah hijaz neva huseyni evdj gerdaniye
> B C# Eb F F# G# Bb B
> 0 207.4 369.1 576.6 703.1 911.7 1073.4 1200.0
> ~ 1/1 44/39 26/21 88/63 3/2 22/13 13/7 2/1
>

Yes, this is a very good Penchgah scale. What it needs is the
occasional 4/3, or perde chargah for alterations.

> And I must agree, even as a newcomer not acquainted with the
> nuances of the seyir for Penchgah and its common modulations,
> that I would not think of an upper Hijaz -- quite unlike Penchgah
> fi Nihavend-i Hagar, where it is a usual part of the seyir.
> And it might be said that while the steps or perde-s form the
> frame or skeleton of a maqam, the seyir is the flesh and blood.
>
>> Shur and Najdi are hard to come by in Turkish circles to my
>> knowledge, so I make no further commentary on those.
>
> With Shur, it is interesting that Turkish performers sometimes
> play a very low or septimal Ushshaq, if we may take as an example
> the performance of "a venerable Turkish Neyzen" or _Niyazi
> Sayin_. as you explain in your thesis at pp. 27-29. Here I quote
> your measured steps for this __Niyazi Sayin Ushshak Ney_ Taksim
> and JI values, plus an approximation in O3 (full 24 notes):
>
> Niyazi Sayin Ushshak Ney Taksim: 123.47 137.13 227.87
>
> JI: 128.30 138.57 231.17
> 14:13 13:12 8:7
>
> O3: 126.56 138.28 230.86
>

Good comparisons. The whole point being not only to approximate the
middle seconds anymore of course ... But to supply the listener with
the benefits of enriched harmony through a clever tuning & temperament!

> However, while either this low flavor of Ushshaq or a similar
> flavor of Shur might suggest a medieval 28:26:24:21, Ibn Sina's
> famous tetrachord or a permutation of it (if 12:13:14:16 is his
> actual form), the seyir of Ushshaq would, of course, differ from
> that of Shur Dastgah.
>
> And I am not sure if Najdi is very common in the Arab world,
> although it is mentioned by theorists such as Amine Beyhom. One
> might actually think of it as two conjunct Rast tetrachords plus
> a _lower_ tone. In a typical Arab intonation as realized in O3,
> perde segah (or, in Arabic, sikah) might be at 357.4 or 358.6
> cents, close to Jacques Dudon's 59/48 or the 16/13 of Yarman-24.
> To play Nadji with segah at around 26/21 is really taking an Arab
> maqam and applying an Ottoman intonation, I would guess.
>

One of many possibilities most welcome in the pursuit of refined music-
making no doubt!

>> And at long last, Buzurg once more. Just a minor interjection
>> on my part: It is my impression, based on no solid evidence
>> except erudite conjecture, that Buzurg is supposed to be an
>> ascending/descending:
>
>> 14/13
>> 16/13
>> 56/39
>> 3/2
>
> An interesting point is the steps of 14:13-8:7-7:6-117:112
> (128.3-231.2-266.9-75.6 cents). The adjacent 8:7 and 7:6 steps in
> the middle lead me to ask if these steps occur together, thus in
> effect dividing 4:3 into a trichord of 8:7:6, in other maqamat.
> I need to try playing this and seeing where it takes me, but your
> erudite intuition is indeed to be carefully considered.
>

Yes, there is 4:3 between the adjacent 8:7 and 7:6. There is no
interruption in ascent or descent of the given scale. But this is a
very peculiar and little-trodden domain! One can seldom see this kind
of thing in a double-Segah instance seperated by a fifth: a "segah-
chargah-segah-kurdi-rast-kurdi-segah" pattern repeated 3:2 above with the addition of perde chargah and neva in ascent up to there. I
noticed the full pentachord more pronounced in the seyir of Ferahnak
than anywhere else; hence the name.

>> In one thematic version and
>
>> 14/13
>> 16/13
>> 4/3
>> 56/39
>
>> diminished pentachord in another ascending/descending cadential
>> version. I don't remember if I had mentioned this, but there it
>> is. The latter is akin to what I dub the "Ferahnak
>> pentachord".
>

Errata: I meant "the former is akin to the Ferahnak Pentachord". Not
the diminished one, which is already defined in theory.

> Looking at a few page on the web about Makam Ferahnak, I see some
> parallels, and some with a maqam we were previously discussing
> (see below). It is curious that I found a descending seyir with
> this pentachord through an analogy with Shur Dastgah, where the
> fifth is often lowered by a koron, or often about 1/3 tone, in
> descending.
>
> You should indeed educate me more on Ferahnak. and how you
> interpret the intonation and the seyir. What I will quickly
> mention here is a version on the web from Ezgi where, if I take
> the signs of S and K (lesser and greater mujannab) as around
> 14/13 and 11/10, the maqam seems very similar to our Penchgah fi
> Nihavend-i Hagar. Here I will use O3 pitches:
>
> Ferahnak Hijaz
> |--------------------------|-----------------|
> Eb E F# G# Bb B D Eb
> 0 126.6 334.0 542.6 704.3 830.8 1119.1 1200.0
> S T T K S A B
> 126.6 207.4 208.6 161.7 126.6 288.3 81.9
>
> And what I take to be a descending form, reminding me of your
> suggestion for Nihavend that the descending seventh degree should
> form a perfect fifth with the third step of the lower tetrachord,
> here C#-G#:
>
> Ferahnak Segah
> |--------------------------|-----------------|
> Eb E F# G# Bb B C# Eb
> 0 126.6 334.0 542.6 704.3 830.8 1038.3 1200.0
> S T T K S T K
> 126.6 207.4 208.6 161.7 126.6 207.4 161.7
>

Very good so far. But always have in spare the diminished Ferahnak
pentachord on the finalis. Without that (and possibly my Ferahnak
pentachord as well) the seyir will be incomplete. Also, preserve the
Eb-Ab perfect fourth, which is a must for the correct tuning.

>> This construct is amiss in theoretical and historical
>> explanations of makamlar, but chanced - even if rarely - in
>> performances if my scrutiny is to be trusted. Ah, but I see
>> that the intiguing descending Segah upper region in your third
>> e-mail features this very Ferahnak pentachord as well as the
>> already-known diminished Ferahnak pentachord mixed!
>
> It is curious that I looked up Ferahnak on Google, recognized the
> similarity with a variation on Penchgah fi Nihavend-i Hagar, and
> then came to your similar recognition in the next paragraph! (I
> read this paragraph earlier, but had yet checked my earlier post
> to see exactly which ajnas (genera) you were referring to here,
> evidently the Segah variations at the end of my Part 3 on the
> Zalzalian 12 set.
>
> One thing I did not have available in the Zalzalian 12 set,
> although it is available on a single 12-note keyboard, is a
> seventh at 20/11 or 51/28, here more the latter at 1038.3 cents,
> in that rotation. And I might say that the lower pentachord
> found in both of Ezgi's forms of Ferahnak, and also Penchgah fi
> Nihavend-i Hagar, is related to a 1/1-14/13-40/33-4/3 flavor of
> Segah or the like rather as Makam Penchgah is to Rast (with segah
> at around 26/21).

So you have discovered once more the subtleties of the nuances of
pitch that differentiate maqams seperated only by the berth of an
acoustical blot!

>
> Returning to Buzurg, the difference I'd see is that the latter
> has a semitone below the fifth, or acting as a kind of lowered
> fifth, at around 56/39; while in Ferahnak we have a step maybe
> not too much higher than 15/11, here 542.6 cents. But I agree
> it's intriguing how the descending Segah region in Part 3 of my
> Zalzalian 12 series of articles brings into play the 56/39 also
> found in Buzurg, and thus the Ferahnak ajnas you are discussing.
>

543 cents cannot be allowed for maqam Ferahnak, the perfect fourth
must be present at all times.

>> About the upper "Buzurg tetrachord", I imagine it would be
>> judicious to say Hijaz-i Buzurg to punctuate the Hijaz sphere
>> of influence here. We see such denominations as Hijaz-i
>> Muhalif, Hijaz-i Turki, etc... to categorize maqam savours
>> centering on Hijaz in historical sources, so, why not scale
>> structures themselves?
>
> Certainly an upper tetrachord of 1/1-14/13-16/13-4/3, or in the
> example from O3, 0.0-126.6-357.4-495.7 cents, could fit with one
> flavor of Turkish Hijaz: Hijaz-i Buzurg might be exactly right!
> And in the world of Iranian music, one might call this Avaz-e
> Bayat-e Esfahan-e Buzurg (if so many possessives are admissible),
> or simply Esfahan-e Buzurg, to distinguish it from various other
> flavors of Esfahan. Farhat gives Esfahan, if one applies his tar
> tuning to his notation, as
>
> D Ep F> G
> 0.0 135.0 360.0 495.0
> 135.0 225.0 135.0
>
> By the way, Hijaz-e Muhalif reminds me of the Persian Mokhalef,
> another topic (and rather like one flavor of Esfahan)! I'd love
> to learn more about Hijaz-i Muhalif.

I recall it was mentioned by Nasir Dede, but I have to check that
later when an oppurtune moment arrives.

>
>> So far, I liked the Buzurg variants you delineated. Good show!
>> The possibilities of fine intonation with the O3 type tuning
>> demonstrates clearly how our clich?? notions of trying to keep
>> segah close to 5/4 is much misguided. It has been lately my
>> inclination to focus on 370 cents or so as the nominal spot for
>> perde segah in most (and perhaps all) instances in keeping with
>> historicity of maqam theory.
>
> Indeed O3 is designed to place perde segah at around 370 cents in
> order to optimize the kind of historical Ottoman flavor we are
> discussing. And it's fascinating how Safi al-Din al-Urmavi's
> "Medium disjunct"

Moderate, sundered. :)

> tetrachord of 9:8-11:10-320:297, or Ezgi's
> rotation of this for Huseyni in 1933, so nicely fits with this
> placement of rast-segah at around 26/21.
>
>> Most cordially,
>> Oz.
>
> Best, with warmest thanks to Dr. Arslan also,
>
> Margo
>
>

I'm forwarding this to him as BCC. I'm sure he'll be delighted to know
an erudite Renaissance music theorist is so deeply interested in the
theory of makamlar!

Cordially,
Oz.

🔗Margo Schulter <mschulter@...>

> You are very kind.

> First of all, a big thank you for your kind words and
> praises. How flattering to receive such attention and
> encouragement from you!

Dear Ozan,

Please let me say that as someone so intimately familiar with Ottoman
music and ready to share this information with others, you are more
than worthy of attention and encouragement.

Here, asking your permission, I will take the liberty of snipping a
lot of my own quoted portion of your post, knowing that nevertheless
this reply figures to be long enough. What I will say generally to
cover many of these instances is that for me as a student, it is most
pleasant when we seem happily agreed. And while I have trimmed a bit
your very helpful explanation of Safi al-Din al-Urmavi and his theory
of tetrachords, I would very much recommend your full presentation for
careful reading! It is fascinating not only for clarifying his thought
and its connection to the Greek tradition, but for its instruction in
how interval or ratio space may be classified or divided in many
different ways -- the "pitch universe" of your new book in Turkish.

>> Rast Rast
>> |-------------------|.......|--------------------|
>> rast dugah segah chargah neva huseyni evdj gerdaniye
>> B C# Eb E F# G# Bb B
>> 0.0 207.4 369.1 495.7 703.1 911.7 1073.4 1200.0
>> ~ 1/1 44/39 26/21 4/3 3/2 22/13 13/7 2/1

> A wonderfully designed scale of rightful pitches supporting not only
> maqams Rast and Huseyni, but also Segah.

This is what I was hoping for: to have somethine like 14:13-9:8-11:10
or 128-204-165 cents, or here about 127-207-162 cents, serve as a good
Segah, based on the tetrachord of Safi al-Din al-Urmavi which I shall
follow you in calling "moderate, sundered."

Here I should quickly caution that since there is no true Ab in this
tuning system with its two 12-note chains of Eb-G#, one would need to
select Bb on the lower or upper chain as perde segah rather than Eb in
order to have an accurate 4/3. And from your comment below that Maqam
Ferahnak also must "at all times" have a perfect fourth, I might
conclude that this Maqam also must have its final or tonic on Bb
rather than Eb, as discussed below.

<http://www.muslimheritage.com/uploads/The__Theory_of_Music.pdf>

> Frankly, I do not think Fazli chose the best English wording here
> for the Arabic originals. Rauf Yekta had suggested as early as 1922
> the correct wordings in French of those terms adopted by early
> Islamic theorists from Hellenistic literature. Let me recapitulate
> them here.

It is fascinating to get the benefit of Yekta's translations into the
language which humorously reminds me of the term Alla Franca, although
his purpose was, of course, Alla Turca! And I wonder if he had in mind
Qutb al-Din al-Shirazi when he made the comment you quote at p. 152 of
your thesis and n. iii about Turkish music using intervals such 7:6,
12:11, and 22:21, since they occur in Qutb al-Din's classic Hijaz:
12:11-7:6-22:21, indeed a permutation of Ptolemy's firm chromatic.

> According to Safi al-din Urmavi in his "Risalat al-Sharafiyyah", if
> the largest of three melodic intervals within a tetrachord is
> greater in size than the sum of the other two, the genus is called
> "Leyyin" - if not, "Qawi". Monz would surely recognize with
> satisfaction that one proper translation of the former term is his
> proposed adjective "relaxed".

This would suggest that Leyyin or "relaxed" would apply to a
tetrachord with a largest interval somewhere near 7:6 or greater, with
a hemifourth around 15:13 or so on the border between Leyyin and Qawi.

> Indeed, "Leyyin" is Arabic for "soft, softened, light, gentle,
> easy-going, mild, mellow, smooth, creamy, etc..." and is obviously
> the chosen equivalent of the Greek word "Malakon". Likewise, "Qawi"
> means "sturdy, rigid, firm, tenacious, resistant, strong, powerful,
> safe, secure, trustworthy, well-supplied, propertied etc..." some
> of which correspond justly to the Greek word "Syntonon"
> (strained). I feel Monz' proposed "tense" might not be the best
> translation for the Arabic term compared to "firm" here.

Possibly there is a certain analogy here with the Latin terms _molle_
for Bb and _durum_ for B-natural, which could be translated as "soft"
and "hard" or "strong." Your "soft" and "firm" seem agreeable to me.

> In the same "esprit", Rauf Yekta translates Leyyin as "mou" (soft)
> and Qawi as "fort" (strong) in the section devoted to his monograph
> in Encyclop??die de la musique et dictionnaire du Conservatoire
> (p. 2990):
-------------------------------------------------
> L'ensemble de trois intervalles ordonn??s dans une quarte s'appelle
> ?? genre ?? (j-i??-. Une quarte con- tient donc trois intervalles
> qui r??alisent quatre sons ; de l? lui vient son nom qui signifie :
> ?? intervalle sur lequel on construit une modulation de quatre
> sons. ?? Il y a diff??rents genres. Si l'un des trois intervalles
> d'un genre est d'un rapport plus grand que la somme des deux
> autres, le genre est mou (j^) ; s'il n'en est pas ainsi, il est
> fort (i^y).

> Le genre mou se divise en trois parties princi-
> pales :
> 1?? Le genre normal (RASIM).
> 2?? Le genre chromatique (LEVNI).
> 3?? Le genre ordonnateur (NAZIM).
-----------------------------------------------------

[... other interesting material ]

> Those tetrachords that employ 5:4 as the largest interval among
> three are called RASIM,

> Those tetrachords that employ 6:5 as the largest interval among
> three are called LEVNI,

> Those tetrachords that employ 7:6 as the largest interval among
> three are called NAZIM.

> Yekta has translated RASIM (that which draws or flows through) as
> normal, LEVNI (that which cascades in colours) as chromatic, and
> NAZIM (arranging one after the other) as organizing. These
> translations do fairness to the Arabic originals, which insooth
> stand for the famous "Diatonic", "Chromatic" and "Enharmonic"
> genera respectively.

A curious thing is that I might have guessed that a largest interval
of 5:4 would be enharmonic or Nazim; and a largest interval of 6:5 or
7:6 would be chromatic or Levni, as with Qutb al-Din's Hijaz; while a
largest interval or around 15:13 or smaller (e.g. 8:7 or 9:8) would be
diatonic Rasim.

An especially interesting point is that 6:5 and 7:6 are in different
categories, a distinction which might fit with that in modern Ottoman
theory between Nihavend (e.g. 9-5-8 commas) and Buselik (e.g. 9-3-10
commas in a septimal flavor). From a Greek perspective, I might guess
that both could be regarded as characteristic of a chromatic genus
with a semiditone or minor third and two semitone steps, as with
Ptolemy's Soft Chromatic at 1/1-28/27-10/9-4/3 or 28:27-15:14-6:5, and
his Firm Chromatic at 1/1-22/21-8/7-4/3 or 22:21-12:11-7:6.

> Following table after table of permutations, Urmevi shows a new
> method, where he uses the same interval ratio twice in a
> tetrachord. A pair of 8/7s makes the tetrachord "qawi zu al-taz'eef
> fi al-awwal" (the first paired of the FIRM genus); a pair of 9/8s
> makes the tetrachord "zu al-taz'eef fi al-thani" (the second
> paired); a pair of 10/9s makes the tetrachord "zu al-taz'eef fi
> al-thalith" (the third paired).

In passing I might mention that Curt Sachs documented a medieval
European source mentioning the 8:7-8:7-49:48 tetrachord.

> Yet another operation for finding new tetrachords for Urmavi is
> taking a pair of sequential superparticular ratios. Safi al-din
> pairs a 8/7 and 9/8 to arrive at "Muttasil al-Awwal" (the first
> conjoined); a 9/8 and 10/9 to arrive at "Muttasil al-Awsat" (the
> middle conjoined); a 10/9 and 11/10 to arrive at "Muttasil
> al-Thalith" (the third conjoined). The same operation where one
> diminishing superparticular ratio is skipped yields "qawi munfasil"
> (Firm, sundered) for 8/7 and 10/9; "mutadil munfasil" (Moderate,
> sundered) for 9/8 and 11/10; and "Shedd munfasil" (Tightened,
> sundered) for 10/9 and 12/11.

Here I notice that all the ratios in question are 8/7 or smaller,
which would fit with my usual concept of a "diatonic" genus.

> One can see similar explanations in Rauf Yekta, shedding (excuse
> the pun) much light into the confusion of the tetrachordal genera
> of the Ancient world.

While I have not quoted every line of your post, I would emphasize
that every line is well worth study!

> The tetrachord in question in your response is "mutadil munfasil",
> which is better translated as "Moderate, sundered" - to avoid
> confusion with the wholetone disjunction between tetrachords making
> an octave.

Yes, I agree that this is a fitting English translation!

[On coming article outlining some basic maqamat and O3 tunings]

> One could perhaps organize this article in a database application
> such as Excel or Numbers. That would tidy things up a bit with
> interactive links for what goes where and which came whence.

This sounds like a fine idea, although I am quite ignorant of such
programs.

> That's a notion. In the case of a Spreadsheet, one could variate
> the tunings by a drop-down menu to observe the effect
> instantaneously. Of course, some good folk from the list - who know
> Excel or Numbers much better than I - might be willing to assist?

Such assistance could be very helpful. I do know that spreadsheets are
often used in presenting tuning systems, and that you refer to such
files in your thesis.

> Penchgah Rast
> |---------------------------|-------------------|
> rast dugah segah hijaz neva huseyni evdj gerdaniye
> B C# Eb F F# G# Bb B
> 0 207.4 369.1 576.6 703.1 911.7 1073.4 1200.0
> ~ 1/1 44/39 26/21 88/63 3/2 22/13 13/7 2/1

> Yes, this is a very good Penchgah scale. What it needs is the
> occasional 4/3, or perde chargah for alterations.

Intuitively I suspected that a 4/3 at perde chargah might occur, in
part on the basis of looking at a few pieces in Penchgah available on
the web. However, I must admit that when I start polyphonizing in
Penchgah, the results are influenced mainly by 14th-century European
patterns, which this maqam seems to fit so nicely in a Zalzalian
variation, as it were! Understanding the typical Ottoman seyir might
give me a fuller perspective.

> With Shur, it is interesting that Turkish performers sometimes
> play a very low or septimal Ushshaq, if we may take as an example
> the performance of "a venerable Turkish Neyzen" or _Niyazi
> Sayin_. as you explain in your thesis at pp. 27-29. Here I quote
> your measured steps for this __Niyazi Sayin Ushshak Ney_ Taksim
> and JI values, plus an approximation in O3 (full 24 notes):
> Niyazi Sayin Ushshak Ney Taksim: 123.47 137.13 227.87
> JI: 128.30 138.57 231.17
> 14:13 13:12 8:7
> O3: 126.56 138.28 230.86

> Good comparisons. The whole point being not only to approximate the
> middle seconds anymore of course ... But to supply the listener
> with the benefits of enriched harmony through a clever tuning &
> temperament!

I much agree. What George Secor and I found is that harmonic or
polyphonic progressions involving middle second steps can have a
special beauty.

[On Buzurg]

>> An interesting point is the steps of 14:13-8:7-7:6-117:112
>> (128.3-231.2-266.9-75.6 cents). The adjacent 8:7 and 7:6 steps in
>> the middle lead me to ask if these steps occur together, thus in
>> effect dividing 4:3 into a trichord of 8:7:6, in other maqamat. I
>> need to try playing this and seeing where it takes me, but your
>> erudite intuition is indeed to be carefully considered.

> Yes, there is 4:3 between the adjacent 8:7 and 7:6. There is no
> interruption in ascent or descent of the given scale. But this is
> a very peculiar and little-trodden domain! One can seldom see this
> kind of thing in a double-Segah instance seperated by a fifth: a
> "segah-chargah-segah-kurdi-rast-kurdi-segah" pattern repeated 3:2
> above with the addition of perde chargah and neva in ascent up to
> there. I noticed the full pentachord more pronounced in the seyir
> of Ferahnak than anywhere else; hence the name.

Certainly this interpretation of Buzurg as 1/1-14/13-16/13-56/39-3/2
seems "very peculiar and little trodden" to me also! But as to the
double Segah instance, I am trying to understand this as possibly
something like the following, where I have indicated the pitches in
cents with respect both to rast, the first cardinal point as it were
on the compass of the maqamat, and also segah:

segah chargah segah kurdi rast kurdi segah chargah neva rast: 370 497 370 289 0 289 370 497 704
Bb B Bb A F# A Bb B C#
segah: 0 127 0 1119 830 1119 0 127 334

evjd gerdaniye evjd ajem neva ajem evdj rast: 1073 1200 1073 993 704 993 1073
F F# F E C# E F
segah: 703 830 703 622 334 622 703

In Maqam Segah, I would take rast-kurdi-segah as what the Arabs call a
_dint_ or semitone, here kurdi-segah, leading up to an important step
of a maqam such here the final or tonic; and I have read of this in
Signell's _Makam_. Thus perde dugah, the usual step below segah, is
altered to kurdi, and from there a semitone up to segah.

And I see how, from this "double Segah," we can get a pentachord
0-127-334-622-703, rather like your 0-128-359-622-702 as one
interpretation of Buzurg.

But reading again your comments, I must ask: is this "double segah" a
form of Maqam Segah, or Maqam Ferahnak?

> In one thematic version and
> 14/13
> 16/13
> 4/3
> 56/39
> diminished pentachord in another ascending/descending cadential
> version. I don't remember if I had mentioned this, but there it
> is. The latter is akin to what I dub the "Ferahnak
> pentachord".

> Errata: I meant "the former is akin to the Ferahnak
> Pentachord". Not the diminished one, which is already defined in
> theory.

This correction I will note!

Now comes our discussion of Ferahnak, which raises a problem which I
can solve in O3, but imperfectly! To solve it more convincingly, I
would need chains of fifths at least 12 fifths long, as would happen
in a system based on two 17-MOS chains. Let us see my dilemma,
starting with my quotation of Ferahnak according to Suphi Ezgi, and
taking his two versions to be the ascending and descending forms:

Ferahnak Hijaz
|--------------------------|-----------------|
Eb E F# G# Bb B D Eb
0 126.6 334.0 542.6 704.3 830.8 1119.1 1200.0
S T T K S A B
126.6 207.4 208.6 161.7 126.6 288.3 81.9

Ferahnak Segah
|--------------------------|-----------------|
Eb E F# G# Bb B C# Eb
0 126.6 334.0 542.6 704.3 830.8 1038.3 1200.0
S T T K S T K
126.6 207.4 208.6 161.7 126.6 207.4 161.7

> Very good so far. But always have in spare the diminished Ferahnak
> pentachord on the finalis. Without that (and possibly my Ferahnak
> pentachord as well) the seyir will be incomplete. Also, preserve
> the Eb-Ab perfect fourth, which is a must for the correct tuning.

This advice points to a glaring flaw in the O3 system, if we wish to
have available both Ezgi's pentachord of S-T-T-K at Eb-E-F#-G#-Bb. and
a 4/3 step: the absence of a true Ab for a 4/3 step above Eb on either
12-note keyboard, which has a chain of only 11 fifths, Eb-G#!

And I should note a question that comes up later in this reply: is a
step at 543 cents permissible at any point in the seyir of Maqam
Ferahnak, or must the fourth step always remain within about a comma
of 4/3, as it woold with Ezgi's S-T-T-K at 5-9-9=8 commas in AEU, but
not in O3? If in fact the O3 version of S-T-T-K does not fit Ferahnak,
then the following tuning set would nicely provide all of the other
ajnas you describe, including the "double segah," if I am correct. The diagram shows rast-evdj on the first line, with evdj-tiz segah on
the second line:

rast: 0 209 289 370 496 704 866 993 1073 segah: -370 -162 -81 0 127 334 496 622 704
F#* G#* A* Bb* B* C#* Eb* E* F*
rast dugah kurdi segah chargah neva hisar ajem evdj

rast: 1073 1200 1409 1489 1570 segah: 704 830 1038 1119 1200
F* F#* G#* A* Bb*
evdj gerdaniye muhayyer sunbule tiz segah

To get Ezgi's version of a Ferahnak pentachord, S-T-T-K, we must start
at Eb on either keyboard, permitting Eb-E-F#-G#-Bb, with Eb-G# at
around 543 cents from 11 fifths up. To get the closest equivalent to a
step at 4/3, we must place the final of Ferahnak at Eb* on the upper
keyboard.

rast: 0 207 288 369 496 703 854 912 993 1073 segah: -369 -162 -81 0 127 334 485 543 623 704
B* C#* D* Eb* E* F#* G# G#* A* Bb*
rast dugah kurdi segah chargah neva nerm huseyni ajem evdj
hisar

rast: 1073 1200 1407 369 496 segah: 704 831 1038 1119 127
Bb* B* C#* D* Eb*
evdj gerdaniye muhayyer sunbule tiz segah

Here Ezgi's version of Ferahnak is available without problem, as is
the "double segah" you described above, and your Ferahnak pentachord
resembling your first interpretation of Buzurg with an ajem-evdj step:

0 127 334 623 704
Eb* E* F#* A* Bb*
segah chargah neva ajem evdj

The diminished Ferahnak pentachord, however, must use Eb*-G# at about
485 cents, or 13 cents narrow of 4/3, as the closest equivalent for a
perfect fourth:

0 127 334 485 623
Eb* E* F#* G# A*
segah chargah neva nerm ajem
hisar

This tuning might in fact be closer to a Syrian version of Maqam Iraq,
which may favor a fourth step around 21 commas or 21/16, with a school
of Aleppo specifying 6-9|6-7-9|9-7 commas, than a diminished Ferahnak
pentachord.

However, from a further comment you make, this compromise may be not
only unnecessary but beside the point, since the purpose is also to
have available a step at 543 cents (Eb*-G#* or segah-huseyni), which
in fact may be impermissible for Maqam Ferahnak.

> 543 cents cannot be allowed for maqam Ferahnak, the perfect fourth
> must be present at all times.

The statement "at all times" -- rather that in certain portions of the
seyir such as the diminished Ferahnak pentachord -- suggests to me
that Ezgi's S-T-T-K might be admissible in AEU, but not in O3.

In AEU, Ezgi's lower Ferahnak tetrachord S-T-T-K would be, as Signell
notes, 5-9-9-8 commas or 0-114-318-522-702 cents, with 23 commas or
522 cents curiously fitting the observed peak at 523 cents in Maqam
Segah reported in theoryVSpractice (pp. 64 and 66).

In O3, S-T-T-K or Eb-E-F#-G#-Bb is 0-127-334-543-704 cents, with Eb-G#
at 543 cents resulting, like the 23-comma step in AEU, from 11 fifths
up. If 543 cents "cannot be allowed" at any point in the seyir,
although the 522 cents of AEU is sometimes permissible, could this be
because the fourth step may be up to about a comma wide, but not wider
to the point where it it is no longer recognizable as any kind of
"perfect fourth," but becomes a Zalzalian interval more like 11/8?

If so, a lesson would be that a given jins often, but not always, will
translate successfully from AEU to the "moderate, sundered" style of
intonation in O3, based on rast-segah at around 26/21, with S-T-T-K of
Maqam Ferahnak as an example correct in AEU but not O3. One should
instead use S-T-K (usual Segah genus at 127-207-162 cents), S-T-K-S
(diminished Ferahnak pentachord at 127-207-162-127 cents), or your
striking Ferahnak pentachord of S-T-A-B (127-207-288-81 cents). All
of these ajnas except S-T-T-K are available with the final of Ferahnak
at Bb or Bb*, where a regular 4/3 at 496 cents is available without
any problem! And at Bb or Bb* we also have the "double Segah" pattern
your have pointed out.

>> By the way, Hijaz-e Muhalif reminds me of the Persian Mokhalef,
>> another topic (and rather like one flavor of Esfahan)! I'd love to
>> learn more about Hijaz-i Muhalif.

> I recall it was mentioned by Nasir Dede, but I have to check that
> later when an oppurtune moment arrives.

This I would be very curious to learn about when you do check it.

>> Indeed O3 is designed to place perde segah at around 370 cents in
>> order to optimize the kind of historical Ottoman flavor we are
>> discussing. And it's fascinating how Safi al-Din al-Urmavi's
>> "Medium disjunct"

> Moderate, sundered. :)

I definitely agree, and will prefer this English translation.

> Best, with warmest thanks to Dr. Arslan also,
> Margo

> I'm forwarding this to him as BCC. I'm sure he'll be delighted to
> know an erudite Renaissance music theorist is so deeply interested
> in the theory of makamlar!

One fine point about the term "Renaissance," which I find correct,
although some conventional historians of European music might be
surprised.

In fact, the Mutazilah Era in the Islamic world coincides with a
series of "Renaissance" movements in Europe, starting around 800-900
with the Carolingian Renaissance, and reaching a height with what is
often called the "12th-century Renaissance" continuing through the
13th century, or the age of Safi al-Din and Qutb al-DIn. The 12th-14th
centuries especially influence my approach to Zalzalian polyphony.

In conventional European history, the term "Renaissance" often means
the 15th and 16th centuries, marked in musical terms, for example, by
the rise of meantone temperament. Indeed this period also fascinates
me, but I would say that my approach to maqam/dastgah polyphony draws
much more on the earlier Mutazilah Era, which of course had a vast
influence on European philosophy, music, and other aspects of culture!
While European history often simply terms this era "medieval," it
could equally well be described as "Renaissance."

> Cordially,
> Oz.

With many thanks,

Margo

🔗monz <joemonz@...>

🔗Ozan Yarman <ozanyarman@...>

🔗monz <joemonz@...>

🔗Ozan Yarman <ozanyarman@...>

Dear Margo,

At long last a reply...

Do forgive my inattentiveness to the matter at hand on how the O3
tuning can be utilized to house Turkish/Arabic/Persian maqams. Having
found a much amiss peace-space in the tuning list (which has been
vandalized to the point of utter uselessness in my view as you can
glean from my latest criticisms), I wish to concentrate a final time
to respond to you before engaging those urgently pressing academic
tasks that await my attention here for the following two months or so.

Before all else, let me iterate that my comments on the correct tuning
of maqam scales are my own opinions and must be taken with a grain of
salt! More so, since I have lost track of many particulars of the
maqam traditions in my gross (and sadly, obsessive) involvement for
the past weeks with a shaky software overhaul operation in my Macbook
Pro that still tugs at a corner of my mind.

Bear in mind also, that the devastating penetration of the 12-equal
parlance and acclimatization into our native music culture has
resulted in so many pitch distortions that it has become very hard to
chance upon a truly authentic performance nowadays! I cannot shy away
from admitting that getting drawn into the daily video and music links
filling my mailbox and newsfeed network has somewhat disrupted my
purist enjoyment of authentic Maqam traditions. There is also the
socio-political air of human corruption that eats away at our very
souls and moral beliefs in this day and age. I undertake to write to
you at a period of intense weariness (plus some health issues it
appears) and ask pardon if I miss any pertinent points you made.

Aside from nodding my head as I skim through your comments on the
largest intervals in Rasim, Levni and Nazim types of tetrachords, I am
intrigued by the European source that is reported as mentioning the
"paired tetrachord" involving two 8:7s.

This brings to mind once again possibilities on the direct connection
between the Islamic world (the "Mutazilah Era" as you pleasingly
state) and Christendom during the "Middle Ages"; especially given the
much overlooked contributions and scientific innovations of such
towering Muslim intellects as Abu'l Hasan a.k.a. "Ziryab", al-Kindi,
al-Farabi, Ibn Sina, Ibn al-Haytham, Jabir bin Hayyan, al-Biruni, Omar
Khayyam, al-Khwarizmi, Nasraddin al-Tusi, Qutbaddin Shirazi, ibn
Rushd... From what I know, the Carolingian Era was set in motion with
the Andalusian and Moroccan Muslim culture, arts and sciences seeping
into Europe over the Baghdadi Darulhikmah centre > Egyptian Al-Azhar
mosque > Tunisian Zeytune mosque > Moroccan Qarawiyin mosque > Cordoba.

I noticed with dismay that many "tunaniks" (as Charles Lucy puts it)
have preferred to pursue inane arguments of no consequence so far
instead of offering to assist you toward the more constructive
endeavour of preparing an MS Excel document that would demonstrate the
myriad maqam tunings you have formulated up to now. There is still a
chance they will remember their roots and make themselves more useful
than nowadays perhaps!

Once again I nod as I read your interpretation of what I termed the
"double Segah" phenomenon. The cent values seem quite right for the purpose. To make the transition from Segah on segah to Segah on evdj,
one needs a perde huseyni at about 27/16 between the two seyirs you
notated. And indeed, there it is: the Ferahnak pentachord of mine (not
Buzurg) when you climb segah+chargah+neva+ajem+evdj (0-128-359-622-702
cents).

Yes, you rightfully ask me whether this is a feature of Segah or
Ferahnak. More that of Segah I must say! But there is already one
tetrachord and a whole PLUS a diminished pentachord ascribed to Segah
already; none of which is the pentachord we seek. Though surely a rare
thing to chance in Ferahnak, 0-128-359-622-702 serves our purposes and
helps us avoid some confusion when we call it the "Ferahnak pentachord".

A step of 543 cents in

126.6 334.0 542.6 704.3 830.8 1119.1 1200.0

could of course be admissable if you allow room for flexibility of
intonation without any qualms about offending indoctrinated old school
people out there. In fact, it could be neatly camouflaged to give the
impression of a perfect fourth if you compose to avoid direct fourth
jumps in the melody line. But we are not just talking monophony, are
we? So, the desired Zalzalian effect requires at least a comma
deviation from the pure fourth up, which will surely be needed in
another F#-G-A-B-C# AEU Ferahnak pentachord shade (however rare) even
in monophony. (This also answers your inquiry about how that pure fourth above the tonic F# in the preceding example can turn a comma
higher than advertised: C# in the whole AEU Ferahnak pentachord pulls
it up.)

Note elsewhere, that you cannot ordinarily have kurdi -81 cents from
perde segah. If I must name it, that pitch would serve better as perde
nihavend, which is about a comma higher than kurdi.

I'd suggest taking care when manipulating to install a maqam setting
at a particular key and forgetting about how the rest will fall in
place in the same Ahenk. One must remember that setting Ferahnak's
finalis on Eb means Segah's is at Ab, Rast's at E, Huseyni's at F#,
etc... This is one of the most troublesome features of Maqam music,
which was one chief reason that lead me to design the 79-tone qanun.

I checked Nasir Dede on Hijaz-i Muhalif, which is nothing other than
Hijaz-Ashiran. You start with Hijaz and conclude with Ashiran (just
Huseyni transposed to perde ashiran, a fourth below dugah). It seems
to have nothing to do with the Persian Mukhalif.

I have read the rest on the Zalzalian rotations and have no more to
comment on them, except pronounce my thanks for mentioning my name in
such positive and encouraging light!

And Margo, I believe you must always endeavour to produce more
glorified musical examples and pieces in the Mutazili, Zalzalian
polyphonic manner! :)

Cordially,
Oz.

✩ ✩ ✩
www.ozanyarman.com

On Sep 7, 2010, at 9:37 PM, Margo Schulter wrote:

>> You are very kind.
>
>> First of all, a big thank you for your kind words and
>> praises. How flattering to receive such attention and
>> encouragement from you!
>
> Dear Ozan,
>
> Please let me say that as someone so intimately familiar with Ottoman
> music and ready to share this information with others, you are more
> than worthy of attention and encouragement.
>
> Here, asking your permission, I will take the liberty of snipping a
> lot of my own quoted portion of your post, knowing that nevertheless
> this reply figures to be long enough. What I will say generally to
> cover many of these instances is that for me as a student, it is most
> pleasant when we seem happily agreed. And while I have trimmed a bit
> your very helpful explanation of Safi al-Din al-Urmavi and his theory
> of tetrachords, I would very much recommend your full presentation for
> careful reading! It is fascinating not only for clarifying his thought
> and its connection to the Greek tradition, but for its instruction in
> how interval or ratio space may be classified or divided in many
> different ways -- the "pitch universe" of your new book in Turkish.
>
>>> Rast Rast
>>> |-------------------|.......|--------------------|
>>> rast dugah segah chargah neva huseyni evdj gerdaniye
>>> B C# Eb E F# G# Bb B
>>> 0.0 207.4 369.1 495.7 703.1 911.7 1073.4 1200.0
>>> ~ 1/1 44/39 26/21 4/3 3/2 22/13 13/7 2/1
>
>> A wonderfully designed scale of rightful pitches supporting not only
>> maqams Rast and Huseyni, but also Segah.
>
> This is what I was hoping for: to have somethine like 14:13-9:8-11:10
> or 128-204-165 cents, or here about 127-207-162 cents, serve as a good
> Segah, based on the tetrachord of Safi al-Din al-Urmavi which I shall
> follow you in calling "moderate, sundered."
>
> Here I should quickly caution that since there is no true Ab in this
> tuning system with its two 12-note chains of Eb-G#, one would need to
> select Bb on the lower or upper chain as perde segah rather than Eb in
> order to have an accurate 4/3. And from your comment below that Maqam
> Ferahnak also must "at all times" have a perfect fourth, I might
> conclude that this Maqam also must have its final or tonic on Bb
> rather than Eb, as discussed below.
>
> <http://www.muslimheritage.com/uploads/The__Theory_of_Music.pdf>
>
>> Frankly, I do not think Fazli chose the best English wording here
>> for the Arabic originals. Rauf Yekta had suggested as early as 1922
>> the correct wordings in French of those terms adopted by early
>> Islamic theorists from Hellenistic literature. Let me recapitulate
>> them here.
>
> It is fascinating to get the benefit of Yekta's translations into the
> language which humorously reminds me of the term Alla Franca, although
> his purpose was, of course, Alla Turca! And I wonder if he had in mind
> Qutb al-Din al-Shirazi when he made the comment you quote at p. 152 of
> your thesis and n. iii about Turkish music using intervals such 7:6,
> 12:11, and 22:21, since they occur in Qutb al-Din's classic Hijaz:
> 12:11-7:6-22:21, indeed a permutation of Ptolemy's firm chromatic.
>
>> According to Safi al-din Urmavi in his "Risalat al-Sharafiyyah", if
>> the largest of three melodic intervals within a tetrachord is
>> greater in size than the sum of the other two, the genus is called
>> "Leyyin" - if not, "Qawi". Monz would surely recognize with
>> satisfaction that one proper translation of the former term is his
>> proposed adjective "relaxed".
>
> This would suggest that Leyyin or "relaxed" would apply to a
> tetrachord with a largest interval somewhere near 7:6 or greater, with
> a hemifourth around 15:13 or so on the border between Leyyin and Qawi.
>
>> Indeed, "Leyyin" is Arabic for "soft, softened, light, gentle,
>> easy-going, mild, mellow, smooth, creamy, etc..." and is obviously
>> the chosen equivalent of the Greek word "Malakon". Likewise, "Qawi"
>> means "sturdy, rigid, firm, tenacious, resistant, strong, powerful,
>> safe, secure, trustworthy, well-supplied, propertied etc..." some
>> of which correspond justly to the Greek word "Syntonon"
>> (strained). I feel Monz' proposed "tense" might not be the best
>> translation for the Arabic term compared to "firm" here.
>
> Possibly there is a certain analogy here with the Latin terms _molle_
> for Bb and _durum_ for B-natural, which could be translated as "soft"
> and "hard" or "strong." Your "soft" and "firm" seem agreeable to me.
>
>> In the same "esprit", Rauf Yekta translates Leyyin as "mou" (soft)
>> and Qawi as "fort" (strong) in the section devoted to his monograph
>> in Encyclop??die de la musique et dictionnaire du Conservatoire
>> (p. 2990):
> -------------------------------------------------
>> L'ensemble de trois intervalles ordonn??s dans une quarte s'appelle
>> ?? genre ?? (j-i??-. Une quarte con- tient donc trois intervalles
>> qui r??alisent quatre sons ; de l? lui vient son nom qui signifie :
>> ?? intervalle sur lequel on construit une modulation de quatre
>> sons. ?? Il y a diff??rents genres. Si l'un des trois intervalles
>> d'un genre est d'un rapport plus grand que la somme des deux
>> autres, le genre est mou (j^) ; s'il n'en est pas ainsi, il est
>> fort (i^y).
>
>> Le genre mou se divise en trois parties princi-
>> pales :
>> 1?? Le genre normal (RASIM).
>> 2?? Le genre chromatique (LEVNI).
>> 3?? Le genre ordonnateur (NAZIM).
> -----------------------------------------------------
>
> [... other interesting material ]
>
>> Those tetrachords that employ 5:4 as the largest interval among
>> three are called RASIM,
>
>> Those tetrachords that employ 6:5 as the largest interval among
>> three are called LEVNI,
>
>> Those tetrachords that employ 7:6 as the largest interval among
>> three are called NAZIM.
>
>> Yekta has translated RASIM (that which draws or flows through) as
>> normal, LEVNI (that which cascades in colours) as chromatic, and
>> NAZIM (arranging one after the other) as organizing. These
>> translations do fairness to the Arabic originals, which insooth
>> stand for the famous "Diatonic", "Chromatic" and "Enharmonic"
>> genera respectively.
>
> A curious thing is that I might have guessed that a largest interval
> of 5:4 would be enharmonic or Nazim; and a largest interval of 6:5 or
> 7:6 would be chromatic or Levni, as with Qutb al-Din's Hijaz; while a
> largest interval or around 15:13 or smaller (e.g. 8:7 or 9:8) would be
> diatonic Rasim.
>
> An especially interesting point is that 6:5 and 7:6 are in different
> categories, a distinction which might fit with that in modern Ottoman
> theory between Nihavend (e.g. 9-5-8 commas) and Buselik (e.g. 9-3-10
> commas in a septimal flavor). From a Greek perspective, I might guess
> that both could be regarded as characteristic of a chromatic genus
> with a semiditone or minor third and two semitone steps, as with
> Ptolemy's Soft Chromatic at 1/1-28/27-10/9-4/3 or 28:27-15:14-6:5, and
> his Firm Chromatic at 1/1-22/21-8/7-4/3 or 22:21-12:11-7:6.
>
>> Following table after table of permutations, Urmevi shows a new
>> method, where he uses the same interval ratio twice in a
>> tetrachord. A pair of 8/7s makes the tetrachord "qawi zu al-taz'eef
>> fi al-awwal" (the first paired of the FIRM genus); a pair of 9/8s
>> makes the tetrachord "zu al-taz'eef fi al-thani" (the second
>> paired); a pair of 10/9s makes the tetrachord "zu al-taz'eef fi
>> al-thalith" (the third paired).
>
> In passing I might mention that Curt Sachs documented a medieval
> European source mentioning the 8:7-8:7-49:48 tetrachord.
>
>> Yet another operation for finding new tetrachords for Urmavi is
>> taking a pair of sequential superparticular ratios. Safi al-din
>> pairs a 8/7 and 9/8 to arrive at "Muttasil al-Awwal" (the first
>> conjoined); a 9/8 and 10/9 to arrive at "Muttasil al-Awsat" (the
>> middle conjoined); a 10/9 and 11/10 to arrive at "Muttasil
>> al-Thalith" (the third conjoined). The same operation where one
>> diminishing superparticular ratio is skipped yields "qawi munfasil"
>> (Firm, sundered) for 8/7 and 10/9; "mutadil munfasil" (Moderate,
>> sundered) for 9/8 and 11/10; and "Shedd munfasil" (Tightened,
>> sundered) for 10/9 and 12/11.
>
> Here I notice that all the ratios in question are 8/7 or smaller,
> which would fit with my usual concept of a "diatonic" genus.
>
>> One can see similar explanations in Rauf Yekta, shedding (excuse
>> the pun) much light into the confusion of the tetrachordal genera
>> of the Ancient world.
>
> While I have not quoted every line of your post, I would emphasize
> that every line is well worth study!
>
>> The tetrachord in question in your response is "mutadil munfasil",
>> which is better translated as "Moderate, sundered" - to avoid
>> confusion with the wholetone disjunction between tetrachords making
>> an octave.
>
> Yes, I agree that this is a fitting English translation!
>
> [On coming article outlining some basic maqamat and O3 tunings]
>
>> One could perhaps organize this article in a database application
>> such as Excel or Numbers. That would tidy things up a bit with
>> interactive links for what goes where and which came whence.
>
> This sounds like a fine idea, although I am quite ignorant of such
> programs.
>
>> That's a notion. In the case of a Spreadsheet, one could variate
>> the tunings by a drop-down menu to observe the effect
>> instantaneously. Of course, some good folk from the list - who know
>> Excel or Numbers much better than I - might be willing to assist?
>
> Such assistance could be very helpful. I do know that spreadsheets are
> often used in presenting tuning systems, and that you refer to such
> files in your thesis.
>
>> Penchgah Rast
>> |---------------------------|-------------------|
>> rast dugah segah hijaz neva huseyni evdj gerdaniye
>> B C# Eb F F# G# Bb B
>> 0 207.4 369.1 576.6 703.1 911.7 1073.4 1200.0
>> ~ 1/1 44/39 26/21 88/63 3/2 22/13 13/7 2/1
>
>> Yes, this is a very good Penchgah scale. What it needs is the
>> occasional 4/3, or perde chargah for alterations.
>
> Intuitively I suspected that a 4/3 at perde chargah might occur, in
> part on the basis of looking at a few pieces in Penchgah available on
> the web. However, I must admit that when I start polyphonizing in
> Penchgah, the results are influenced mainly by 14th-century European
> patterns, which this maqam seems to fit so nicely in a Zalzalian
> variation, as it were! Understanding the typical Ottoman seyir might
> give me a fuller perspective.
>
>> With Shur, it is interesting that Turkish performers sometimes
>> play a very low or septimal Ushshaq, if we may take as an example
>> the performance of "a venerable Turkish Neyzen" or _Niyazi
>> Sayin_. as you explain in your thesis at pp. 27-29. Here I quote
>> your measured steps for this __Niyazi Sayin Ushshak Ney_ Taksim
>> and JI values, plus an approximation in O3 (full 24 notes):
>> Niyazi Sayin Ushshak Ney Taksim: 123.47 137.13 227.87
>> JI: 128.30 138.57 231.17
>> 14:13 13:12 8:7
>> O3: 126.56 138.28 230.86
>
>> Good comparisons. The whole point being not only to approximate the
>> middle seconds anymore of course ... But to supply the listener
>> with the benefits of enriched harmony through a clever tuning &
>> temperament!
>
> I much agree. What George Secor and I found is that harmonic or
> polyphonic progressions involving middle second steps can have a
> special beauty.
>
> [On Buzurg]
>
>>> An interesting point is the steps of 14:13-8:7-7:6-117:112
>>> (128.3-231.2-266.9-75.6 cents). The adjacent 8:7 and 7:6 steps in
>>> the middle lead me to ask if these steps occur together, thus in
>>> effect dividing 4:3 into a trichord of 8:7:6, in other maqamat. I
>>> need to try playing this and seeing where it takes me, but your
>>> erudite intuition is indeed to be carefully considered.
>
>> Yes, there is 4:3 between the adjacent 8:7 and 7:6. There is no
>> interruption in ascent or descent of the given scale. But this is
>> a very peculiar and little-trodden domain! One can seldom see this
>> kind of thing in a double-Segah instance seperated by a fifth: a
>> "segah-chargah-segah-kurdi-rast-kurdi-segah" pattern repeated 3:2
>> above with the addition of perde chargah and neva in ascent up to
>> there. I noticed the full pentachord more pronounced in the seyir
>> of Ferahnak than anywhere else; hence the name.
>
> Certainly this interpretation of Buzurg as 1/1-14/13-16/13-56/39-3/2
> seems "very peculiar and little trodden" to me also! But as to the
> double Segah instance, I am trying to understand this as possibly
> something like the following, where I have indicated the pitches in
> cents with respect both to rast, the first cardinal point as it were
> on the compass of the maqamat, and also segah:
>
> segah chargah segah kurdi rast kurdi segah chargah neva
> rast: 370 497 370 289 0 289 370 497 704
> Bb B Bb A F# A Bb B C#
> segah: 0 127 0 1119 830 1119 0 127 334
>
> evjd gerdaniye evjd ajem neva ajem evdj
> rast: 1073 1200 1073 993 704 993 1073
> F F# F E C# E F
> segah: 703 830 703 622 334 622 703
>
> In Maqam Segah, I would take rast-kurdi-segah as what the Arabs call a
> _dint_ or semitone, here kurdi-segah, leading up to an important step
> of a maqam such here the final or tonic; and I have read of this in
> Signell's _Makam_. Thus perde dugah, the usual step below segah, is
> altered to kurdi, and from there a semitone up to segah.
>
> And I see how, from this "double Segah," we can get a pentachord
> 0-127-334-622-703, rather like your 0-128-359-622-702 as one
> interpretation of Buzurg.
>
> But reading again your comments, I must ask: is this "double segah" a
> form of Maqam Segah, or Maqam Ferahnak?
>
>> In one thematic version and
>> 14/13
>> 16/13
>> 4/3
>> 56/39
>> diminished pentachord in another ascending/descending cadential
>> version. I don't remember if I had mentioned this, but there it
>> is. The latter is akin to what I dub the "Ferahnak
>> pentachord".
>
>> Errata: I meant "the former is akin to the Ferahnak
>> Pentachord". Not the diminished one, which is already defined in
>> theory.
>
> This correction I will note!
>
> Now comes our discussion of Ferahnak, which raises a problem which I
> can solve in O3, but imperfectly! To solve it more convincingly, I
> would need chains of fifths at least 12 fifths long, as would happen
> in a system based on two 17-MOS chains. Let us see my dilemma,
> starting with my quotation of Ferahnak according to Suphi Ezgi, and
> taking his two versions to be the ascending and descending forms:
>
> Ferahnak Hijaz
> |--------------------------|-----------------|
> Eb E F# G# Bb B D Eb
> 0 126.6 334.0 542.6 704.3 830.8 1119.1 1200.0
> S T T K S A B
> 126.6 207.4 208.6 161.7 126.6 288.3 81.9
>
>
> Ferahnak Segah
> |--------------------------|-----------------|
> Eb E F# G# Bb B C# Eb
> 0 126.6 334.0 542.6 704.3 830.8 1038.3 1200.0
> S T T K S T K
> 126.6 207.4 208.6 161.7 126.6 207.4 161.7
>
>> Very good so far. But always have in spare the diminished Ferahnak
>> pentachord on the finalis. Without that (and possibly my Ferahnak
>> pentachord as well) the seyir will be incomplete. Also, preserve
>> the Eb-Ab perfect fourth, which is a must for the correct tuning.
>
> This advice points to a glaring flaw in the O3 system, if we wish to
> have available both Ezgi's pentachord of S-T-T-K at Eb-E-F#-G#-Bb. and
> a 4/3 step: the absence of a true Ab for a 4/3 step above Eb on either
> 12-note keyboard, which has a chain of only 11 fifths, Eb-G#!
>
> And I should note a question that comes up later in this reply: is a
> step at 543 cents permissible at any point in the seyir of Maqam
> Ferahnak, or must the fourth step always remain within about a comma
> of 4/3, as it woold with Ezgi's S-T-T-K at 5-9-9=8 commas in AEU, but
> not in O3? If in fact the O3 version of S-T-T-K does not fit Ferahnak,
> then the following tuning set would nicely provide all of the other
> ajnas you describe, including the "double segah," if I am correct.
> The diagram shows rast-evdj on the first line, with evdj-tiz segah on
> the second line:
>
> rast: 0 209 289 370 496 704 866 993 1073
> segah: -370 -162 -81 0 127 334 496 622 704
> F#* G#* A* Bb* B* C#* Eb* E* F*
> rast dugah kurdi segah chargah neva hisar ajem evdj
>
> rast: 1073 1200 1409 1489 1570
> segah: 704 830 1038 1119 1200
> F* F#* G#* A* Bb*
> evdj gerdaniye muhayyer sunbule tiz segah
>
> To get Ezgi's version of a Ferahnak pentachord, S-T-T-K, we must start
> at Eb on either keyboard, permitting Eb-E-F#-G#-Bb, with Eb-G# at
> around 543 cents from 11 fifths up. To get the closest equivalent to a
> step at 4/3, we must place the final of Ferahnak at Eb* on the upper
> keyboard.
>
> rast: 0 207 288 369 496 703 854 912 993 1073
> segah: -369 -162 -81 0 127 334 485 543 623 704
> B* C#* D* Eb* E* F#* G# G#* A* Bb*
> rast dugah kurdi segah chargah neva nerm huseyni ajem evdj
> hisar
>
> rast: 1073 1200 1407 369 496
> segah: 704 831 1038 1119 127
> Bb* B* C#* D* Eb*
> evdj gerdaniye muhayyer sunbule tiz segah
>
> Here Ezgi's version of Ferahnak is available without problem, as is
> the "double segah" you described above, and your Ferahnak pentachord
> resembling your first interpretation of Buzurg with an ajem-evdj step:
>
> 0 127 334 623 704
> Eb* E* F#* A* Bb*
> segah chargah neva ajem evdj
>
> The diminished Ferahnak pentachord, however, must use Eb*-G# at about
> 485 cents, or 13 cents narrow of 4/3, as the closest equivalent for a
> perfect fourth:
>
> 0 127 334 485 623
> Eb* E* F#* G# A*
> segah chargah neva nerm ajem
> hisar
>
> This tuning might in fact be closer to a Syrian version of Maqam Iraq,
> which may favor a fourth step around 21 commas or 21/16, with a school
> of Aleppo specifying 6-9|6-7-9|9-7 commas, than a diminished Ferahnak
> pentachord.
>
> However, from a further comment you make, this compromise may be not
> only unnecessary but beside the point, since the purpose is also to
> have available a step at 543 cents (Eb*-G#* or segah-huseyni), which
> in fact may be impermissible for Maqam Ferahnak.
>
>> 543 cents cannot be allowed for maqam Ferahnak, the perfect fourth
>> must be present at all times.
>
> The statement "at all times" -- rather that in certain portions of the
> seyir such as the diminished Ferahnak pentachord -- suggests to me
> that Ezgi's S-T-T-K might be admissible in AEU, but not in O3.
>
> In AEU, Ezgi's lower Ferahnak tetrachord S-T-T-K would be, as Signell
> notes, 5-9-9-8 commas or 0-114-318-522-702 cents, with 23 commas or
> 522 cents curiously fitting the observed peak at 523 cents in Maqam
> Segah reported in theoryVSpractice (pp. 64 and 66).
>
> In O3, S-T-T-K or Eb-E-F#-G#-Bb is 0-127-334-543-704 cents, with Eb-G#
> at 543 cents resulting, like the 23-comma step in AEU, from 11 fifths
> up. If 543 cents "cannot be allowed" at any point in the seyir,
> although the 522 cents of AEU is sometimes permissible, could this be
> because the fourth step may be up to about a comma wide, but not wider
> to the point where it it is no longer recognizable as any kind of
> "perfect fourth," but becomes a Zalzalian interval more like 11/8?
>
> If so, a lesson would be that a given jins often, but not always, will
> translate successfully from AEU to the "moderate, sundered" style of
> intonation in O3, based on rast-segah at around 26/21, with S-T-T-K of
> Maqam Ferahnak as an example correct in AEU but not O3. One should
> instead use S-T-K (usual Segah genus at 127-207-162 cents), S-T-K-S
> (diminished Ferahnak pentachord at 127-207-162-127 cents), or your
> striking Ferahnak pentachord of S-T-A-B (127-207-288-81 cents). All
> of these ajnas except S-T-T-K are available with the final of Ferahnak
> at Bb or Bb*, where a regular 4/3 at 496 cents is available without
> any problem! And at Bb or Bb* we also have the "double Segah" pattern
> your have pointed out.
>
>>> By the way, Hijaz-e Muhalif reminds me of the Persian Mokhalef,
>>> another topic (and rather like one flavor of Esfahan)! I'd love to
>>> learn more about Hijaz-i Muhalif.
>
>> I recall it was mentioned by Nasir Dede, but I have to check that
>> later when an oppurtune moment arrives.
>
> This I would be very curious to learn about when you do check it.
>
>>> Indeed O3 is designed to place perde segah at around 370 cents in
>>> order to optimize the kind of historical Ottoman flavor we are
>>> discussing. And it's fascinating how Safi al-Din al-Urmavi's
>>> "Medium disjunct"
>
>> Moderate, sundered. :)
>
> I definitely agree, and will prefer this English translation.
>
>> Best, with warmest thanks to Dr. Arslan also,
>> Margo
>
>> I'm forwarding this to him as BCC. I'm sure he'll be delighted to
>> know an erudite Renaissance music theorist is so deeply interested
>> in the theory of makamlar!
>
> One fine point about the term "Renaissance," which I find correct,
> although some conventional historians of European music might be
> surprised.
>
> In fact, the Mutazilah Era in the Islamic world coincides with a
> series of "Renaissance" movements in Europe, starting around 800-900
> with the Carolingian Renaissance, and reaching a height with what is
> often called the "12th-century Renaissance" continuing through the
> 13th century, or the age of Safi al-Din and Qutb al-DIn. The 12th-14th
> centuries especially influence my approach to Zalzalian polyphony.
>
> In conventional European history, the term "Renaissance" often means
> the 15th and 16th centuries, marked in musical terms, for example, by
> the rise of meantone temperament. Indeed this period also fascinates
> me, but I would say that my approach to maqam/dastgah polyphony draws
> much more on the earlier Mutazilah Era, which of course had a vast
> influence on European philosophy, music, and other aspects of culture!
> While European history often simply terms this era "medieval," it
> could equally well be described as "Renaissance."
>
>> Cordially,
>> Oz.
>
> With many thanks,
>
> Margo
>
>
>
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