Yahoo Tuning Groups Ultimate Backup tuning Jacques Dudon, 1/1-7/6-11/8-13/8, and maqam music (I)

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Hello, all.

Recently I checked the archives on the Tuning List and was
delighted to read a number of posts by Jacques Dudon, who I knew
mainly through some beautiful gamelan, Near Eastern, and other
tunings in the scale archive of Scala.

Encountering these posts inviting creative dialogue and
exploration in many directions, I will here begin with a thread
on the 75/64 in which Jacques Dudon proposed the following chord,
and asked if it might be used in maqam music:

1/1 75/64 11/8 13/8
0 275 551 841
75:64 88:75 13:11
275 277 289

This idea led me to focus on a somewhat related sonority that I
could approximate with some accuracy in my regular 24-note
temperament with fifths at 704.607 cents, with 7/6 used in place
of the more complex 75/64:

1/1 7/6 11/8 13/8
0 267 551 841
7:6 33:28 13:11
267 284 289

As it happens, this chord has a ratio which may be expressed
using relatively small integers, 24:28:33:39. The smaller 33:28
(284.45 cents) and larger 13:11 (289.21 cents) differ by the
364:363 kleisma at 4.76 cents.

In my 24-note regular tuning, placed on two 12-note keyboards at
a diesis of about 55.28 cents apart, shown in the following
notation by an asterisk (*) for notes on the higher keyboard,
we get this approximation, here with A as the 1/1:

A B* D* F*
0 264 551 837
264 286 286

Here, the 7/6 is slightly narrow at 264.50 cents, while either
33:28 or 13:11 is represented by a regular minor third at 286.18
cents. The smaller Zalzalian or neutral sixth at 837 cents is
about 3.67 cents narrow of 13:8, and curiously almost the same
amount wide of the transcendent Phi (833.09 cents), that epitome
of complex assonance. Possibly "a tempered 13:8 with a touch of
complexity" is one description.

For a Scala file of the 24-note regular temperament, see
<http://www.bestII.com/~mschulter/eb24.scl>

----------------------------
1. Journey to "Sazkar Jadid"
----------------------------

Now for the main question: how might the steps of this intriguing
structure be used in maqam music? The solution that occurred to
me is a variation on Maqam Sazkar. The ascending form of the basic
maqam is as follows:

Sazkar Jadid tone Bayyati
|-------------------|......|-----------------|
A B* C* D E F* F#* A
cents 0 264 341 495 705 837 969 1200 JI approx 1/1 7/6 39/32 4/3 3/2 13/8 7/4 2/1
264 77 154 209 132 132 231
7:6 117:112 128:117 9:8 13:12 14:13 8:7

This form draws on two beautiful JI tunings of the renowned
11th-century philosopher and music theorist Ibn Sina. His noble
tuning known as Mustaqim (which in Arabic, like Rast in Persian,
means "right, correct, standard") features a tetrachord of
1/1-9/8-39/32-4/3 or 0-204-342-498 cents (204-139-155 cents).
Here there is a tone or major second, followed by two Zalazalian
or neutral second steps, with the first (13:12, 139 cents)
smaller than the second (128:117, 155 cents). In the Arab world
today, this pattern is sometimes as "Rast Jadid" or "New Rast,"
in contrast to a more usual Rast where the larger Zalzalian
second precedes the smaller.

In Sazkar, the first interval of a Rast tetrachord at a major
second is replaced by the striking leap of a minor third -- here
the 7:6. Thus we have 0-264-341-495 cents, or 264-77-154 cents.
The small middle interval is here our regular minor second or
limma at 77 cents -- but with the quite extraordinary effect this
step has in the context of Sazkar, or Sazkar Jadid as I term this
variation.

The upper tetrachord (E-A) features another of Ibn Sina's
tunings, in a just form a tetrachord sometimes read as either
28:26;24:21 or 1/1-14/13-7/6-4/3 (0-128-267-498 cents), with 7:6
divided arithmetically into 14:13:12; or 12:13:14:16,
1/1-13/12-7/6-4/3 (0-139-267-498 cents), with 7:6 divided
harmonically into 12:13:14. Either form is represented by a
tempered 0-132-264-495 cents (132-132-231 cents),

While I find this approximation satisfactory, it illustrates a
form of "intonational color-blindness" to which this temperament
is subject, losing the fine distinction between 14:13 and 13:12.

The descending form brings into play the 11/8, and also a
cadential step a larger neutral second below the final:

G* A B* C* D* E F* F#* A
cents -154 0 264 341 551 705 837 969 1200 JI approx 11/12 1/1 7/6 39/32 11/8 3/2 13/8 7/4 2/1
154 267 77 209 154 132 132 231
12:11 7:6 117:112 44:39 12:11 13:12 14:13 8:7

The D* or virtually just 11/8 is to me a kind of "mirror
reflection" of the koron or lowered version of the fifth often used in Shur Dastgah when one descends toward the final:
here, instead, the fourth is raised, so that in a Persian manner we might term D* a sori, or D>.

Somehow the contour of the ascending tetrachord A-B*-C*-D, or
the descending pentachord leading to the final, E-D*-C*-B*-A,
seems "jazzy" or "Bluesy" to me, possibly because of the
junxtaposition of a septimal minor third and Zalzalian or neutral
third above the final. How it would sound to a Near Eastern
musician familiar with Sazkar, I am not sure.

If one wishes to develop this maqam while keeping within its
basic structure, one possibility would be to focus on a third
tetrachord revealed if we move from a septimal minor seventh at
969 cents (F#*) to a regular minor seventh at 991 cents (G):

Sazkar Jadid tone Bayyati
|-------------------|......|-----------------|
Mustaqim
|------------------|
A B* C* D E F* G A
cents 0 264 341 495 705 837 991 1200 17-steps 0 4- 5s 7 10 12s 14 17
JI approx 1/1 7/6 39/32 4/3 3/2 13/8 39:22 2/1
267 77 154 209 132 154 209
4- 1 2L 3 2s 2L 3
7:6 117:112 128:117 9:8 13:12 12:11 44:39

Here we can follow our ascending Sazkar (or Sazkar Jadid) with a
conjunct tetrachord of Ibn Sina's Mustaqim at a tempered
0-209-341-495 cents or 209-132-154 cents. Note that our upper
Bayyati tetrachord, which might be close to some Arab
(e.g. popular Lebanese) practice and also to a typical Persian
intonation for a Shur tetrachord, 0-132-286-495 cents
(132-154-209 cents), remains idiomatic while presenting a subtle
contrast to Ibn Sina's septimal form approximated in our earlier
ascending form.

From here, one could move the striking minor third B* of Sazkar
to its usual location for Mustaqim or Rast Jadid at B, arriving
at a tempering of Ibn Sina's original maqam, with many
possibilities for further development:

Mustaqim tone Bayyati
|-------------------|......|------------------|
Mustaqim
|-------------------|
A B C* D E F* G A
cents 0 209 341 495 705 837 991 1200 17-steps 0 4- 5s 7 10 12s 14 17
JI approx 1/1 9/8 39/32 4/3 3/2 13/8 16/9 2/1
267 77 154 209 132 154 209
4- 1 2L 3 2s 2L 3
7:6 9:8 128:117 9:8 13:12 128:117 9:8

--------------------------------------------------------
2. Analysis and modulation: Enter Qutb al-Din al-Shirazi
--------------------------------------------------------

While Sazkar Jadid was taking shape for me in its ascending and
descending forms, I realized that the Sazkar Jadid tetrachord
could lead to an interesting analysis if viewed in JI terms as
follows:

A B* C* D
tempered: 0 264 341 495
264 77 154

JI: 1/1 7/6 11/9 4/3
0 267 347 498
7:6 22:21 12:11
267 81 151

While a reader might rightly call attention to the rather
inaccurate representation of 11:9 in this temperament, which
indeed is much closer to 28:23 or 39:32, our main interest here
is in the adjacent intervals of 7:6, 22:21, and 12:11 (at
267-81-151 cents).

These are, of course, the steps of Ptolemy's Intense Chromatic
(22:21-12:11-7:6), famously permuted around 1300 by Qutb al-Din
al-Shirazi in a classic form of Hijaz, which John Chalmers has
temred "neo-chromatic" because of the placement of the large step
in the middle:

1/1 12/11 14/11 4/3
0 151 418 498
12:11 7:6 22:21
151 267 81

G* A B* C*
0 154 418 495
154 264 77

Thus my discovery or rediscovery of "Sazkar Jadid" could be taken
as a demonstrating a permutation of Qutb al-Din's Hijaz -- in
turn, a permutation of Ptolemy's Intense Diatonic!

In fact, as shown by my tempered example for Qutb al-Din's
tetrachord, this theoretical model leads to an interesting
modulation, moving from my descending form of Sazkar Jadid to a
usual Hijaz on G*:

Hijaz
|------------------|
G* A B* C* D* E F* F#* A
cents -154 0 264 341 551 705 837 969 1200 JI approx 11/12 1/1 7/6 39/32 11/8 3/2 13/8 7/4 2/1
154 267 77 209 154 132 132 231
2L 4- 1 3 2L 2s 2s 3+
12:11 7:6 117:112 44:39 12:11 13:12 14:13 8:7

Once we establish a focus on this Hijaz tetrachord (G*-C*), the
maqam we have shifted into might take shape like this:

Hijaz Rast tone
|------------------|------------------|......|
G* A B* C* D* E F* G*
Huseyni
|-------------------|
cents 0 154 418 495 705 859 991 1200 JI approx 1/1 12/11 14/11 4/3 3/2 64/39 39/22 2/1
154 264 77 209 154 132 209
12:11 7:6 22:21 9:8 128:117 13:12 44:39

In its ascending form, this usual version of Maqam Hijaz (usual
to me in this temperament, that is) has conjunct Hijaz and Rast
tetrachords, the latter in one shading of the usual Arab pattern
with the larger neutral second preceding the smaller (here
0-209-363-495 cents or 209-154-132 cents). In descending, the
larger Zalzalian sixth at 859 cents (near 23/14 or 64/39), found
at E*, might be inflected to a minor sixth at Eb or 782 cents,
very close to a just 11/7. Some styles might favor one version or
the other of this sixth degree, with others fluidly alternating
between them.

The version with the Zalzalian sixth also has an upper tetrachord
D*-E-F*-G* at 0-154-286-495 cents or 154-132-209 cents which I
here call Huseyni, since the order of the larger Zalzalian second
followed by the smaller is more typical of Maqam Huseyni than of
Maqam Bayyati, in this tuning often 132-154-209 cents. However,
the term "Bayyati" is often applied in Arab theory to either
arrangement, the general concept being simply two Zalzalian
seconds followed by a tone (or 3-3-4 in a usual 24-step
notation).

From this Maqam Hijaz on G* we might easily proceed to related
destinations such as, in my style, Rast and related forms on G*.

-----------------------------------------------------------
3. The 1/1-7/6-11/8-13/8 chord: resolutions and modulations -----------------------------------------------------------

While the Sazkar Jadid introduces the notes of the chord, how
might it be resolved in the context of what I shall term
Zalzalian polyphony, or the application of polyphonic techniques
to music drawing on the maqam and dastgah traditions, however
closely or loosely.

In such a polytphonic style, a given vertical progression may
serve either to realize the qualities of a given maqam or gusheh
(i.e. a melodic theme or mode within the larger modal family of a
dastgah), or to move from one such maqam or gusheh to another,
possibly as part of a more or less standard modulatory scheme.
Two possible modulations using 1/1-7/6-11/8-13/8 occurred to me.

The first is as follows, with the tempered chord at 0-264-551-705
cents, and the expanding resolution arriving at a tempered 2:3:4.

F* +154 G
D* -55 D
B* +231 D
A -209 G

Here the expansions of the lower ~7:6 minor third to a fifth, and
of the outer ~13:8 Zalzalian sixth to an octave, are quite
routine in this type of neomedieval style (the "neomedieval"
referring both to the Near Eastern tunings and 13th-14th century
European polyphonic techniques which here have a "fusion" in the
setting of a 21st-century temperament). The ~33:28 minor third
between the two middle voices likewise has a usual resolution
contracting to a unison, with melodic steps of 231 and 55 cents
that might represent the 8:7 and 28:27 steps of the Archytas
Diatonic. Stated more generically as 3-1 or 3-5 and 6-8, these
basic patterns for resolutions can apply to major, minor, or
Zalzalian (neutral) intervals alike.

Other resolutions here are a bit less "classical," for example
the stepwise expansion of the upper ~13:11 minor third to a
fourth (D*-F* to D-G), but the total effect is a progression
"taking us somewhere" in a maqam performance, here to G. One
colorful possibility for a new maqam on G is a form of Najdi or
`Ajam Murassa:

Najdi Mustaqim
|---------------------------|--------------------|
G A B C* D E F* G
Mustaqim
|--------------------|
cents 0 209 418 551 705 914 1046 1200 JI approx 1/1 44/39 14/11 11/8 3/2 56/33 11/6 2/1
209 209 132 154 209 132 154
44:39 182:121 121:112 12:11 128:117 121:112 12:11

One way that has been suggested to view this fascinating maqam is
as two conjunct tetrachords of Rast (or here Mustaqim or Rast
Jadid) with a tone added below to fill out the octave, and with
this added step now felt as the final. The affinity to the
descending form of Sazkar Jadid, with its 11/8 step above the
final, may have drawn me to this maqam as a companion for use in
an improvisation.

Of course, one could follow the vertical resolution of our
1/1-7/6-11/8-13/8 sonority to G with many maqamat, but this
choice is to me engaging.

Another resolution leads in another direction:

F* -77 E*
D* +209 E*
B* -209 A*
A +55 A*

This resolution treats the outer small Zalzalian sixth at 837
cents as a diminished seventh (which it is, being formed from
three minor thirds) contracting to a fifth: the lowest voice
ascends A-A* by a diesis or minimal semitone of 55 cents, while
the highest voice descends F*-E* by a regular 77-cent limma.
The two lower voices have a classic 3-1 resolution, one moving by
a regular 209-cent tone and the other by a 55-cent semitone,
which here may be said to represent 28:27 (63 cents). The middle
pair of voices expand from regular minor third to fifth (3-5),
and the highest pair from a like minor third to a unison (3-1),
these progressions involving steps of a regular tone or semitone
(209 or 77 cents).[1]

While this journey up a diesis or small semitone to A* could lead
into many maqamat, one choice I like is a usual Huseyni, as if to
offset the more "exotic" qualities of Sazkar Jadid:

Huseyni tone Huseyni
|--------------------|.......|--------------------|
A* B C* D* E* F# G* A* cents 0 154 286 495 705 859 991 1200 JI approx 1/1 12/11 13/11 4/3 3/2 64/39 16/9 2/1
154 132 209 209 154 132 209
12:11 13:12 44:39 9:8 128:117 13:12 9:8

In Part II, I will present another maqam that later occurred to
me as including 1/1-7/6-11/8-13/8 in a structure I would freely
use either ascending or descending, with another possible
resolution of this sonority, this time suggesting a modulation
which offers an opportunity to touch on a topic which I hope will
receive much fuller discussion: Jacques Dudon's "Soria" algorithm
for a 17-note rational tuning, and some versions of 12-note
subsets he has posted.

----
Note
----

1. From the viewpoint of polyphonic technique, these two
resolutions of A-B*-D*-F*, showing how a Zalzalian sixth can
either expand to an octave, or less "classically" contract to a
fifth, might recall the discussion by Marchettus of Padua (1317)
about how a major sixth typically expands to an octave, but
through a "feigned" inflection or cadence can also contract to a
fifth! In a 17-note system, or a larger system like this
featuring most similar types of intervals, a Zalzalian seventh
similarly may contract "classically" to a fifth (7-5), or
strikingly expand to an octave, with George Secor educating me on
the latter choice in the setting of his 17-tone well-temperament
(17-WT). To take simple two-voice example, the small Zalzalian
seventh or augmented sixth Eb-C# at 1046 cents or ~11:6 might
resolve either by contracting to E-B (7-5) or expanding to the
octave D-D. In a Near Eastern context, the first resolution can
come up routinely in a polyphonic setting of Maqam Sikah on Eb,
for example, while the second seems more likely to signal a
dramatic and not unlikely surprising shift of focus.

Most appreciatively,

Margo Schulter
mschulter@...

🔗Marcel de Velde <m.develde@...>

🔗Margo Schulter <mschulter@...>

> From: Marcel de Velde <m.develde@...>
> Hi Margo,

Hello, Marcel and thank you for an interesting reply.

> I find 75/64 to be a more simple interval than 7/6 in a way.
> It occurs between 8/5 and 15/8.

> Your 1/1 7/6 11/8 13/8 tetrad could be approximated in 5-limit JI in
> the following ways: > 1/1 75/64 25/18 25/16 (8/5 15/8 9/4 5/2, > a sometimes used chord in common practice music) or > 1/1 32/27 36/25 8/5 (9/8 4/3 8/5 9/5, > also sometimes used in common practice music)
> Though they don't come very close on some tones.

Here I would certainly agree that 75/64 and 7/6 are in a similar
category as small minor thirds, while 36/25 in fact has been
mentioned by Dariush Anooshfar, a Persian musician, as a fine tuning for a fifth lowered by a koron, often roughly a third-tone
of about 70 cents.

As you may be suggesting when you note that your ratios "don't
come very close on some tones," we need some intervals with a
neutral quality, or what I often call a "Zalzalian" quality after
the great 8th-century 'oudist (or lutenist, to cite this instrument's
European form) Mansur Zalzal.

It is easily done, as Anooshfar and others have demonstrated. For
example, 36/25 plus a 9:8 tone gives us a neutral sixth at 81/50 or about 835 cents. Using some of your ratios above, and proceeding in
this way, we can obtain, for example, a 9-note version of the Persian
Shur Dastgah, to which Anooshfar's persian.scl in the Scala archives
might be compared (revealing my indebtedness to you both!):

|
9-note Shur, ratios of 2-3-5: Includes 36/25 koron, minor and neutral 6ths
0: 1/1 0.000 unison, perfect prime
1: 27/25 133.238 large limma, BP small semitone
2: 75/64 274.582 classic augmented second
3: 4/3 498.045 perfect fourth
4: 36/25 631.283 classic diminished fifth
5: 3/2 701.955 perfect fifth
6: 25/16 772.627 classic augmented fifth
7: 81/50 835.193 acute minor sixth
8: 225/128 976.537 augmented sixth
9: 2/1 1200.000 octave

The seven-note "textbook" form of Shur -- actually a family of
melodic themes or related modes -- uses steps 0-1-2-3-5-6-8-9.
Additionally, step 4, the fifth lowered by a koron, often occurs
in descending passages, and additionally is used in some of the
gushehs (melodic themes) of Shur to create a transposed form of
the lower tetrachord (0-133-275-498 cents) on the 4/3. The neutral
sixth, step 7, most commonly occurs an octave lower as the third
below the final (50/81 in JI terms), but can also arise as the
sixth above it in certain gushehs.

> In 7-limit there are many many possibilities, several of which come
> very close.

> A simple one would be 1/1 7/6 7/5 8/5.

> Which could be used in for instance > 1/1 21/20 7/6 4/3 7/5 3/2 8/5 7/4 28/15 2/1 > (7/6 *6/5 on 1/1, 6/5 *7/6 on 4/3, 7/6 * 6/5 on 3/2)

> I'm thinking arabic music is 7-limit myself, 11 and 13 limit
> intervals are much more complex and don't work very well in musical
> structures I think.

What I'd say we need for lots of the Near Eastern modes and styles --
not all, as Ozan Yarman would rightly have me emphasize! -- is some
way of obtaining neutral intervals. However, 81/50 might be just as
stylish as 13/8, in the same way that Joe Monzo for his piece tried
out a range of minor thirds including 7/6 by ear and hit on a size of
279 cents, with 75/64 as the ideal just ratio for his purposes.

> Marcel

With many thanks,

Margo

🔗Jacques Dudon <fotosonix@...>

🔗Margo Schulter <mschulter@...>

> #88705 From: Jacques Dudon
> Dear Margo,

> Thank you so much for this super-documented essay on this
> passionating subject !

Thank you for your delightful reply, and also for having the patience
to read through the first part of my article. Indeed this is an art
filled with passion and excitement: first learning of a tuning or
getting an idea for one, and then actually making music in it and
possibly getting new ideas.

> Your message gives me the occasion to say how much I enjoy reading
> your articles, even if I am lacking of musicological bases, and how
> much I am willing, now that I can use Scala, to learn from the
> numerous models of scales we can find in illustration of your works
> in the Scala archive, 1/1 and other publications.

Please let me say in return that while I have focused on medieval
European music and more recently have been learning about Near Eastern
styles, your tunings have a wonderful scope and perspective, often
drawing connections between different cultures and traditions that I
might not otherwise appreciate.

> Thanks for your encouraging words about my humble works, that come
> rather from intuitive tuning and hearing than from real
> musicological knowledge !

Often performing or listening to some music in a given tuning or
tradition can be worth many volumes of theory. And your combination of
musical intuition and sensitivity with ingenious scale design, as with
Airos/Soria, is a very special gift.

> I will greatly appreciate any critic or comment on any of the tuning
> models I proposed in the Ethno2 collection, which I suppose you
> found in the Tuning list files.

In fact I learned about the Ethno2 collection from reading two posts
where you shared the older and then the new versions of 12-note soria
(soria.scl and soria12.scl), but didn't realize that the collection
was available for downloading! Now I have it, and eagerly look foward
to enjoying Ethno2 and sharing any comments. Already, your Mohajira
scales in the Scala archives have given me some ideas for an article
raising some possibilities we might explore on this list.

> Surprisingly enough, I found the scale based on the
> "differentially-coherent" recurrent sequence you mention :

> 64 : 75 : 88 : 104 : 128 : 192

> placed in the African scales folder (isrep.scl) of my Ethno
> collection, while I was pretty sure I placed it in the Persian
> section !

Here I'll have to learn about the "differentially-coherent" concept,
which you discuss in your message #85245 on this pentatonic scale.
The differences of 11:13:16:24:64 fit intervals like the melodic steps
in this pentatonic of 13:11 and 16:13, maybe one of the properties of
this kind of fractal technique, which is very new to me.

> I supposed it landed here because I had no serious clue of possible
> relation with Middle-East musical culture, before I read your study.

You did exactly the right thing by discussing the scale and asking an
open question -- and so inviting me to get a new perspective on Maqam
Sazkar and related forms.

> Perhaps also because in its summary pentatonic structure it was
> missing the more "oriental" double tetrachordal or heptatonic
> genus, or may be it reminded me of some african mode, I don't know
> (good subject of experiences then for users of Ethno2 !).

Indeed sometimes I'm not sure if certain tunings are closer to a Near
Eastern outlook, or some kind of African or possibly Southeast Asian
style. In my article on "Mohajira" variations I want to tell a
humorous story about how I arrived at a scale very close to
dudon_a.scl, as I learned using the Scala COMPARE command.

> Anyway you gave me good reasons to extend it to seven tones now and
> the "Sazkar Jadid" Maqam seems like a very good proposition, both
> 39/32 and 7/4 being related by fifths to the defective mode.

Thank you for your feedback on this as the person who proposed the
scale in its pentatonic version.

> Note that those two additional notes have a special property for
> me, since the difference tone of 39/32, is precisely,
> octaves-reduced, 7/4 :

> 39 - 32 = 7

Yes! This is something I hadn't recognized.

> and that's a very Persian consonance to me, that I've been using
> also in "s-n-buzurg.scl", formed by a h.13-related superposition of
> two slendros S & N (which I over-used for cheap flights travels
> between Indonesia and Iran...), and that makes also a good use of
> the 13/12 and 14/13 neutral seconds you very well mentionned in Ibn
> Sina tetrachords.

Buzurg is one of my favorites! I tend to use the term generally not
only for the full pentachord 1/1-14/13-16/13-4/3-56/39-3/2, but for
the lower tetrachord, a tuning I love for Dastgah-e Bayat-e Esfahan.
Indeed this is a beautiful permutation on Ibn Sina's 14:13-13:12-8:7,
and I wonder if Safi al-Din or Qutb al-Din conceived it in this way.

Combining two just slendro scales to get this result is ingenious!
While getting the Ethno2 zip, I found a copy of your 1/1 article on
slendro which I must read! And I see you have some intervals at around
943 cents, which reminded me of this little improvisation in a JI
slendro:

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

> I am also very curious to hear your comments on another 7 + 13
> harmonics system, the Soria /Airos algorithm, that I had no
> hesitation on the other hand to relate to Persian music (at least
> for the 2e version, soria12.scl, that I will extend to 17 tones very
> soon).

In the second part of my article on your isrep_75 and my variation of
1/1-7/6-11/8-13/8, I plan to discuss your soria12, which as you
intended is a fine tuning for Shur Dastgah in an Ibn Sina kind of
interpretation. This will just be opening the subject, and I eagerly
await your 17-tone Soria.

One comment for now. In your s-n-buzurg.scl, you show how a Persian
tuning such as Buzurg can be realized in a scale with both septimal
intervals such as 8:7 and 7:4, and in certain positions hemi-fourths
at around 240-260 cents, along with intervals around 940-960 cents.
I'm wondering whether or how, in your Soria-17, you could combine the
features of both soria.scl (with 951 cents above the 1/1) and
soria12.scl (with 974 cents, close to Ibn Sina's 7/4).

Amine Beyhom has measured steps of around 242 cents in a Turkish
version of Hijaz, and the leading Persian performer and scholar
Dariush Tala`i writes that steps of around 240 or 250 cents are usual
for Chargah, the Persian equivalent of Hijaz. The 7:6 step of Qutb
al-Din is also very popular in Persian and Turkish versions. So
there's your musicological justification, if you're inclined to take
Soria-17 in this direction of including some hemi-fourths as well as
septimal intervals.

> There are lots of matters to learn in your article for me and I will
> read it again in detail !...

And likewise I have your 1/1 article on slendro, the Ethno2 tunings,
and some of your articles here we are now discussing to read, enjoy,
and appreciate!

> Thanks for sharing,
> Harmonically,
> - - - - - - - - - - - - -
> Jacques Dudon

Likewise with warmest thanks,

Margo

🔗Margo Schulter <mschulter@...>

🔗Jacques Dudon <fotosonix@...>

On Wed. May 5, 2010, Margo Schulter wrote :

> Here I'll have to learn about the "differentially-coherent" concept,
> which you discuss in your message #85245 on this pentatonic scale.
> The differences of 11:13:16:24:64 fit intervals like the melodic steps
> in this pentatonic of 13:11 and 16:13, maybe one of the properties of
> this kind of fractal technique, which is very new to me.

These frequencies 11:13:16:24:64 are indeed the 1st order difference
tones of the low-minor third intervals of the scale
64 : 75 : 88 : 104 : 128 : 192
And the fact that they belong to the scale (because it also uses the
octave as period),
is what I call a property of "differential coherence" - this concept
has been exposed in detail in 1/1, vol.11, #2 (2003), and I can send
a copy in the Tuning List archives anyway.
Then the "fractality" comes from the fact that the same algorithm of
differential coherence is applied recurrently between the terms of
the sequence :
If I resume the terms 64, 75, 88, 104, 128, 192 to
H(0), H(1), H(2), H(3), H(4), H(5),
we can generalise this property by saying that
8H(n+1) - 8H(n) = H(n+2)
(ex : 8*75 - 8*64 = 88, etc.).
In a even more resumed form (like in these Scala files), I write it
simply :
8x - 8 = x^2
and the general solution of this algorithm, where x = the fractal
ratio of the generator is
4 - 2*sqrt of 2 = 1.1715728752538 or 274.136 c.
You might be interested in another way I have to see this interval,
as a
"C#* : E interval of a Hijaz (in C) whose difference tone would
result in G"...
ex. (C = 208)> : 225 : 264 : 312 (264 - 225 = 39 = G)
We can find many other series using this algorithm, such as
204 : 239 : 280 : 328 : 384 : 448 : 512 (here it ends with a 6:7:8)
Depending on the starting interval all would be more or less
divergent, and some divergence actually introduces interesting
variations (the 16/13 is a product of such divergence in the 64 : 75
series).
Now, as it's been discussed presently in this list, some will argue
that difference tones in practice may not be heard in all conditions.
They will be heard very well with double flutes and bells, and less
with strings but then the strings can make profit of such scales for
an other aspect, the synchronicity of harmonic beatings they also have.
This "fractal isrep" minor third, as you very well noticed, is quite
close to the superparticiular 7/6. It means here the 7th harmonic of
"64" is close to the 6th harmonic of "75" and their "harmonic
beating" is 6*75 - 7*64 = 2 ;
the next interval (75:88) will beat at 6*88 - 7*75 = 3, and the next
one (11:13) at 8. Therefore we can speak here of "beating
synchronicity", that is similarly found in many historical western tunings.
Interestingly enough,
if 75/64 generates, octaves lower, 11/8,
7/6 generates 4/3, and that's precisely the fourth you mention in
"Sazkar Jadid, approx. 1/1 7/6 39/32 4/3",
and the whole scale Sazkar Jadid - Bayyati you mention :
96 : 112 : 117 : 128 : 144 : 156 : 168 : 192
is remarquably coherent.

> Buzurg is one of my favorites! I tend to use the term generally not
> only for the full pentachord 1/1-14/13-16/13-4/3-56/39-3/2, but for
> the lower tetrachord, a tuning I love for Dastgah-e Bayat-e Esfahan.
> Indeed this is a beautiful permutation on Ibn Sina's 14:13-13:12-8:7,
> and I wonder if Safi al-Din or Qutb al-Din conceived it in this way.
> Combining two just slendro scales to get this result is ingenious!
> While getting the Ethno2 zip, I found a copy of your 1/1 article on
> slendro which I must read! And I see you have some intervals at around
> 943 cents, which reminded me of this little improvisation in a JI
> slendro:
> <http://www.bestII.com/~mschulter/ForErin.mp3>

That's a lovely sound and mood ! And I like very much the small
commas "Gamelan-style" dissonances.
About Buzurg, I have no idea if apart from the main pentachord my
version is very traditional, since in the remnant tetrachord I simply
did a transposition by 3/2, which was in the structure of the
slendros - that's why I call it "S-N-Buzurg", for "Surak" and
"Nat" (slendros) interleaved to form this ten tones matrix that
contains many heptatonic scales, among which also some sorts of
Pelogs also. It was created for a suite of pieces entitled
"Estrangetés and Arabesques", (a name inspired by baroque
divertissment pieces playing on the forbidden side of the meantone),
and interpreted by my microtonal ensemble, in which we were
continuously juggling between the Persian and Javanese sides of the
tuning.

> In the second part of my article on your isrep_75 and my variation of
> 1/1-7/6-11/8-13/8, I plan to discuss your soria12, which as you
> intended is a fine tuning for Shur Dastgah in an Ibn Sina kind of
> interpretation. This will just be opening the subject, and I eagerly
> await your 17-tone Soria.
>
> One comment for now. In your s-n-buzurg.scl, you show how a Persian
> tuning such as Buzurg can be realized in a scale with both septimal
> intervals such as 8:7 and 7:4, and in certain positions hemi-fourths
> at around 240-260 cents, along with intervals around 940-960 cents.
> I'm wondering whether or how, in your Soria-17, you could combine the
> features of both soria.scl (with 951 cents above the 1/1) and
> soria12.scl (with 974 cents, close to Ibn Sina's 7/4).
>
> Amine Beyhom has measured steps of around 242 cents in a Turkish
> version of Hijaz, and the leading Persian performer and scholar
> Dariush Tala`i writes that steps of around 240 or 250 cents are usual
> for Chargah, the Persian equivalent of Hijaz. The 7:6 step of Qutb
> al-Din is also very popular in Persian and Turkish versions. So
> there's your musicological justification, if you're inclined to take
> Soria-17 in this direction of including some hemi-fourths as well as
> septimal intervals.

When I developped the first version (of the Ethno archive) I remember
I found that those strange hemi-fourths had some character, and being
in hurry I left the scale with that "very flat Bb" (of 951 c.) as it
was. Coming back to it I thought it was exagerated in a Persian
context, and my aim for those Ethno tunings being to find the most
"realistically Persian intervals", I found this second recurrent
series, ending more classically with this Bb more reasonably close to
7/4.

Normally, if we extend the series to 17 tones, we can't have both
near each other. The 951 c. was just a local divergence, and we can
have one in only one place, so it would be a choice between having
just one at some special place, or none.
But actually I just tried now the two series and it seems that the
second one would arrive to something close to 17-edo but with very
high numbers, while the first one would resume to lower numbers, and
there is this very strange thing as the series of fourths
degenerates : after the flat Eb (259 c., quite low also) the series
produces again a Bb, this time of 967 c. (16c. higher than the first
one) ! - Was your question inspired by some sort of vision ? I never
seen such a funny thing ! - like if the series turned backwards to
fix its transgressions !
So finally the answer is yes, in that precise series we could combine
the features of both versions, without leaving the series. The scale
would have 18 tones then but it's not a problem. Do you see an
interest to have both Bb ? And wouldn't Eb be a better place for that
double note, as you seem to have some good examples of that ?
With C in 5330, the end of the Airos series of fourfths would then be :
C = 5330
F = 7120
Bb = 9503
Eb (252 c.) = 12330
Ab = 16536
Eb (268 c.) = 24889
(the series goes more and more crazy after with 28002 then 15856 :
99541 : 237178 then stops).

One question I would like to ask you (and others), is how I could
write the names of the 17 notes of, lets say more generally, a 17-ET,
in Persian music (with sori ad koron symbols) and in (western)
microtonal music ?
- - - - - - - -
Jacques

🔗Margo Schulter <mschulter@...>

🔗Jacques Dudon <fotosonix@...>

🔗Margo Schulter <mschulter@...>

Dear Jacques,

Please let me explain that my purpose here is to thank you for
your very helpful explanation of differential coherence, and to
raise a question about a tetrachord of Ibn Sina that might have
rather similar properties.

> These frequencies 11:13:16:24:64 are indeed the 1st order
> difference tones of the low-minor third intervals of the
> scale

> 64 : 75 : 88 : 104 : 128 : 192

> And the fact that they belong to the scale (because it also
> uses the octave as period), is what I call a property of
> "differential coherence" - this concept has been exposed in
> detail in 1/1, vol.11, #2 (2003), and I can send a copy in the
> Tuning List archives anyway.

Of course, I would very much like to read this article. Your
article on just gamelan tunings is fascinating, and I will
comment on one of your observations which very much fits my own
experience below, where you raise the topic of the "far side" of
meantone.

> Then the "fractality" comes from the fact that the same
> algorithm of differential coherence is applied recurrently
> between the terms of the sequence :
> If I resume the terms 64, 75, 88, 104, 128, 192 to
> H(0), H(1), H(2), H(3), H(4), H(5),
> we can generalise this property by saying that
> 8H(n+1) - 8H(n) = H(n+2)
> (ex : 8*75 - 8*64 = 88, etc.).

This makes the concept very undestandable.

> In a even more resumed form (like in these Scala files), I
> write it simply : 8x - 8 = x^2 and the general solution of
> this algorithm, where x = the fractal ratio of the generator
> is

> 4 - 2*sqrt of 2 = 1.1715728752538 or 274.136 c.

> You might be interested in another way I have to see this
> interval, as a "C#* : E interval of a Hijaz (in C) whose
> difference tone would result in G"...

> ex. (C = 208)> : 225 : 264 : 312 (264 - 225 = 39 = G)

This is interesting! My first reaction was to think of the Hijaz
tetrachord of Qutb al-Din al-Shirazi at 33:36:42:44 -- or, as I
now realize, specifically of the lower trichord (151-267 cents),
here instead 136-277 cents, yielding a 33/26 rather than 14/11.
Although this may be beside the immediate point, I notice that
277/208 would yield a very nice fourth at around 495.963 cents
for a Hijaz tetrachord plus a tone at 208:225:264:277:312.

Another curious point is that the difference of 264:277 is 13,
which somehow seems in keeping with the "spirit" of the ratios of
13 present such as 33:26, and possibly also 208:225 taken as
having an affinity to 13:12 at only 676:675 larger.

> We can find many other series using this algorithm, such as
> 204 : 239 : 280 : 328 : 384 : 448 : 512 (here it ends with a 6:7:8)

> Depending on the starting interval all would be more or less
> divergent, and some divergence actually introduces interesting
> variations (the 16/13 is a product of such divergence in the
> 64 : 75 series).

> Now, as it's been discussed presently in this list, some will
> argue that difference tones in practice may not be heard in
> all conditions. They will be heard very well with double
> flutes and bells, and less with strings but then the strings
> can make profit of such scales for an other aspect, the
> synchronicity of harmonic beatings they also have. This
> "fractal isrep" minor third, as you very well noticed, is
> quite close to the superparticiular 7/6. It means here the 7th
> harmonic of "64" is close to the 6th harmonic of "75" and
> their "harmonic beating" is 6*75 - 7*64 = 2 ; the next
> interval (75:88) will beat at 6*88 - 7*75 = 3, and the next
> one (11:13) at 8. Therefore we can speak here of "beating
> synchronicity", that is similarly found in many historical
> western tunings.

This "beating synchronicity" is generally something I have not
focused on in the tunings I mostly use; but it would be
interesting if this phenomenon could arise without my being aware
of it!

> Interestingly enough,
> if 75/64 generates, octaves lower, 11/8,
> 7/6 generates 4/3, and that's precisely the fourth you mention in
> "Sazkar Jadid, approx. 1/1 7/6 39/32 4/3",
> and the whole scale Sazkar Jadid - Bayyati you mention :
> 96 : 112 : 117 : 128 : 144 : 156 : 168 : 192
> is remarquably coherent.

Your remarks caused me to consider Ibn Sina's Mustaqim
tetrachord, with two conjunct tetrachords plus a 9:8 tone forming
a mode very similar to that of the modern Dastgah-e Segah, as I
recall you have pointed out, with the final placed on the third
step:

8 13 11
96 104 117 128
1/1 9/8 39/32 4/3
0 204 342 498
9:8 13:12 128:117
204 139 155

A curious question is whether the last difference of 11 has any
connection to the proximity between 128:117 and 12:11 at 352:351
smaller? That is, is there any special significance if the
differences suggest, for example, the prime factors present or
approximated in a given tuning?

[on your s-n-buzurg.scl]

> About Buzurg, I have no idea if apart from the main pentachord
> my version is very traditional, since in the remnant
> tetrachord I simply did a transposition by 3/2, which was in
> the structure of the slendros - that's why I call it
> "S-N-Buzurg", for "Surak" and "Nat" (slendros) interleaved to
> form this ten tones matrix that contains many heptatonic
> scales, among which also some sorts of Pelogs also.

The question of a Buzurg pentachord or its lower tetrachord as
the basis for a maqam is very interesting, although I find myself
often also simply adding another Buzurg tetrachord from 3/2 to
2/1. An upper tetrachord of Bayyati or Rast is also possible, but
maybe that's best discussed in another thread.

(Using a variation of your -c series 208:225:264:312, I can get a
nice Buzurg tetrachord at 208:225:257:277, and a complete Buzurg
pentachord at 208:225:257:277:299:312. Might these be fine-tuned
for greater coherence?)

> It was created for a suite of pieces entitled "Estranget?s and
> Arabesques", (a name inspired by baroque divertissment pieces
> playing on the forbidden side of the meantone), and interpreted
> by my microtonal ensemble, in which we were continuously
> juggling between the Persian and Javanese sides of the tuning.

Curiously, a modern maqam interpretation which may much like a
Buzurg tetrachord occurs in what is called Hijaz Gharib or Sikah
Gharib, literally a "foreign" or "estranged" Hijaz or Sikah. The
idea seems to be that the usual central step of an Arab Hijaz at
7:6 or larger has been "compressed" to possibly around 8:7, thus
more resembling the second step of a Sikah trichord at around
9:8. In a Turkish context, however, Buzurg evidently serves as a
frequent variety or shading of Hijaz, with a performance by Kudsi
Erguner as measured by Amine Beyhom showing one sequence at
131-368-501 cents (131-237-133 cents).

Your mention of the far side of meantone reminds me of my
Zest-24, a tuning I noticed had lots of slendro and pelog
shadings. It consists of two 12-note circles, each with eight
fifths in Zarlino's 2/7-comma meantone and the other four tuned
equally wide, placed at the distance of Zarlino's 2/7-comma
diesis, about 50.28 cents. Here's a piece using lots of
slendro-type intervals:

<http://www.bestII.com/~mschulter/LaPacifica.mp3>
<http://www.bestII.com/~mschulter/LaPacifica_Score.txt>

One thing I found, much as you describe it for a just 147:128 in
your gamelan JI article, is that an interval in Zest-24 at around
242 cents, which would appear in a regular 2/7-comma as the
augmented second (e.g. C#-Eb), and here as a regular mean-tone
plus diesis (e.g. C-D*), indeed can serve as a "small minor
third." Likewise, in _La Pacifica_, I found myself using a
near-just 20:13, the "wolf fifth" of a regular tuning (set to
precisely 20:13 in Gene Ward Smith's Ratwolf variation), as a very
small "minor sixth"!

Your article raises for me another question: should we perhaps
recognize a "central hemifourth" as a distinct type, say around
15/13 or 22/19, by comparison to 147/128 at the lower end of this
region, or possibly something like 297/256 at the high end?
However, getting back to your Persian/Javanese connection, a
medieval tuning occurs to me.

If one derives a maqam like a Zalzalian Rast or Ibn Sina's
Mustaqim from an anhemitonal pentatonic with the two minor third
steps each divided into neutral seconds, then a septimal tuning
of Safi al-Din al-Urmawi might be of interest for the kind of
stylistic mixture you discuss:

|---------------------|-----------------------|
64 56 52 48 42 39 36 32
1/1 8/7 16/13 4/3 32/21 64/57 16/9 2/1
0 231 359 498 729 857 996 1200
8:7 14:13 13:12 8:7 14:13 13:12 9:8
231 128 139 231 128 139 204

I am very much in love with the variation on a Rast tetrachord,
although I am not sure if a genre with 8:7 should get some other
name, just as I would consider Buzurg as distinct from `Iraq with
a central step around 9:8. At any rate, the presence of 32/21 in
this example given by Dr. Fazli Arslan suggested to me a slendro
like this:

1/1 8/7 4/3 32/21 16/9 2/1
0 231 498 729 996 1200
8:7 7:6 8:7 7:6 9:8
231 267 231 267 204

This tuning is identical to that of the MILLS gamelan starting
from the 9/8 (1/1-9/8-9/7-3/2-12/7-2/1), see slendro_7_3.scl in
the Scala archives. In my regular 24-note tuning at 704.607
cents, we could also have a wide octave:

D* F G* Bb C* Eb
0 231 495 726 991 1222
231 264 231 264 231

Please forgive me if this reply has been too long or rambling,
but your gamelan article is something that sets off lots of
ideas!

Best,

Margo

🔗jacques.dudon <fotosonix@...>

--- In tuning@yahoogroups.com, Margo Schulter <mschulter@...> wrote:
>
> Dear Jacques,
>
> Please let me explain that my purpose here is to thank you for
> your very helpful explanation of differential coherence, and to
> raise a question about a tetrachord of Ibn Sina that might have
> rather similar properties.
.../...

I am very pleased by your interest and all your questions and historical examples in return are of a great interest to me.
Unfortunately I have to organize some concerts and I can only fly over the many subjects you raised, which confirm that we both have been interested in our respective ways, in many similar middle-east harmonies !

> .../...
> A curious question is whether the last difference of 11 has any
> connection to the proximity between 128:117 and 12:11 at 352:351
> smaller? That is, is there any special significance if the
> differences suggest, for example, the prime factors present or
> approximated in a given tuning?

What you point here is one of the mysterious and exciting relations between differential and spectral coherence, which definitively have more than significance. That a 13-limit interval generates a 11-limit interval in a context where both would be coherent, would have significance for me, just as much as 35/32, very close to 128/117 invites 35/32 to be viewed in proper contexts as being related to 13 th harmonic based intervals.

> .../...
> Your mention of the far side of meantone reminds me of my
> Zest-24, a tuning I noticed had lots of slendro and pelog
> shadings. It consists of two 12-note circles, each with eight
> fifths in Zarlino's 2/7-comma meantone and the other four tuned
> equally wide, placed at the distance of Zarlino's 2/7-comma
> diesis, about 50.28 cents. Here's a piece using lots of
> slendro-type intervals:
>
> <http://www.bestII.com/~mschulter/LaPacifica.mp3>
> <http://www.bestII.com/~mschulter/LaPacifica_Score.txt>

I am not surprised you got interested in such ideas !
And I will have to take the time to listen carefully to this example...
Wether in quasi-equal or unequal form, larger fifths to complete a meantone is something I tried to achieve in several of my Ethno tunings as well.
"slendro_m-mean.scl" (placed in North-America...) is a Wilson fractal meantone sequence (x^4 = 2x + 2) ending surprisingly well in a -c (diffentially-coherent) version of Mill's Gamelan tuning (slendro "M") on the black keys !
Other ones are 12 of 19-ht (Africa 6), Over-under ht (EastAsia 7), Siam97 (S-E Asia 9)
I am still wandering what would be a correct name for such "WT-like" complentary combinations of meantones and superpyths : double-side temperaments ?
hybrid temperaments ??

> .../...
> One thing I found, much as you describe it for a just 147:128 in
> your gamelan JI article, is that an interval in Zest-24 at around
> 242 cents, which would appear in a regular 2/7-comma as the
> augmented second (e.g. C#-Eb), and here as a regular mean-tone
> plus diesis (e.g. C-D*), indeed can serve as a "small minor
> third." Likewise, in _La Pacifica_, I found myself using a
> near-just 20:13, the "wolf fifth" of a regular tuning (set to
> precisely 20:13 in Gene Ward Smith's Ratwolf variation), as a very
> small "minor sixth"!
>
> Your article raises for me another question: should we perhaps
> recognize a "central hemifourth" as a distinct type, say around
> 15/13 or 22/19, by comparison to 147/128 at the lower end of this
> region, or possibly something like 297/256 at the high end?

Completely indeed ! My article at that time refered only to the Lou Harrison L-7 models, but I do think hemifourths are essential in gamelan slendro tunings, and even more to african pentatonic tunings, as many of my balafon or n'goni tunings tried to give justice.

> .../...
> Please forgive me if this reply has been too long or rambling,
> but your gamelan article is something that sets off lots of
> ideas!
>
> Best,
>
> Margo

Forgive me to not be in measure to reply to it immediately !

Harmonically,
- - - - - -
Jacques

🔗Jacques Dudon <fotosonix@...>

🔗Margo Schulter <mschulter@...>

🔗Ozan Yarman <ozanyarman@...>

Dear Margo, this is a late reply:

(use a fixed-width font, why won't you?)

✩ ✩ ✩
www.ozanyarman.com

On May 4, 2010, at 9:13 AM, Margo Schulter wrote:
> SNIP
>
> ----------------------------
> 1. Journey to "Sazkar Jadid"
> ----------------------------
>
> Now for the main question: how might the steps of this intriguing
> structure be used in maqam music? The solution that occurred to
> me is a variation on Maqam Sazkar. The ascending form of the basic
> maqam is as follows:
>
> Sazkar Jadid tone Bayyati
> |-------------------|......|-----------------|
> A B* C* D E F* F#* A
> cents 0 264 341 495 705 837 969 1200
> JI approx 1/1 7/6 39/32 4/3 3/2 13/8 7/4 2/1
> 264 77 154 209 132 132 231
> 7:6 117:112 128:117 9:8 13:12 14:13 8:7
>
> This form draws on two beautiful JI tunings of the renowned
> 11th-century philosopher and music theorist Ibn Sina. His noble
> tuning known as Mustaqim (which in Arabic, like Rast in Persian,
> means "right, correct, standard") features a tetrachord of
> 1/1-9/8-39/32-4/3 or 0-204-342-498 cents (204-139-155 cents).
> Here there is a tone or major second, followed by two Zalazalian
> or neutral second steps, with the first (13:12, 139 cents)
> smaller than the second (128:117, 155 cents). In the Arab world
> today, this pattern is sometimes as "Rast Jadid" or "New Rast,"
> in contrast to a more usual Rast where the larger Zalzalian
> second precedes the smaller.

Sazkar being a Turkish contrivance, the AEU rendition or its 53
Holderian commas approximation seems closer to practice with the scale
of this maqam:

Degrees:
0 9 17 22 31 39 40 48 53 66 70

Steps:
5 9 8 9 5 13 4
8 5 9 (so-called Ushshaq tetrachord)
9 8 5 9 9 8 5

First the maqam starts off with a Segah openining, proceeds to expose
it further, then, possibly skipping the Ushshaq tetrachord, concludes
fully in Rast.

I don't know how Arabs use it today. I know their habit of lowering
perde segah to the point of invalidating the leading tone below it and
skipping all the way down to perde dugah. But what does this matter?
The maqam has been developed in the Ottoman court during the 19th
Century. The authentic intonation is ought to be searched in
Istanbuline aires.

(So much for 24-tET as the ultimate simple-resolution basis for all
maqamat, eh Carl? You ought to get your hands on some masters of
Classical Turkish music.)

>
> In Sazkar, the first interval of a Rast tetrachord at a major
> second is replaced by the striking leap of a minor third -- here
> the 7:6. Thus we have 0-264-341-495 cents, or 264-77-154 cents.
> The small middle interval is here our regular minor second or
> limma at 77 cents -- but with the quite extraordinary effect this
> step has in the context of Sazkar, or Sazkar Jadid as I term this
> variation.
>

Yes, it could be an interesting trial for Sazkar-i Jadid!

> The upper tetrachord (E-A) features another of Ibn Sina's
> tunings, in a just form a tetrachord sometimes read as either
> 28:26;24:21 or 1/1-14/13-7/6-4/3 (0-128-267-498 cents), with 7:6
> divided arithmetically into 14:13:12; or 12:13:14:16,
> 1/1-13/12-7/6-4/3 (0-139-267-498 cents), with 7:6 divided
> harmonically into 12:13:14. Either form is represented by a
> tempered 0-132-264-495 cents (132-132-231 cents),
>
> While I find this approximation satisfactory, it illustrates a
> form of "intonational color-blindness" to which this temperament
> is subject, losing the fine distinction between 14:13 and 13:12.
>
> The descending form brings into play the 11/8, and also a
> cadential step a larger neutral second below the final:
>
> G* A B* C* D* E F* F#* A
> cents -154 0 264 341 551 705 837 969 1200
> JI approx 11/12 1/1 7/6 39/32 11/8 3/2 13/8 7/4 2/1
> 154 267 77 209 154 132 132 231
> 12:11 7:6 117:112 44:39 12:11 13:12 14:13 8:7
>
> The D* or virtually just 11/8 is to me a kind of "mirror
> reflection" of the koron or lowered version of the fifth
> often used in Shur Dastgah when one descends toward the final:
> here, instead, the fourth is raised, so that in a Persian
> manner we might term D* a sori, or D>.
>
> Somehow the contour of the ascending tetrachord A-B*-C*-D, or
> the descending pentachord leading to the final, E-D*-C*-B*-A,
> seems "jazzy" or "Bluesy" to me, possibly because of the
> junxtaposition of a septimal minor third and Zalzalian or neutral
> third above the final. How it would sound to a Near Eastern
> musician familiar with Sazkar, I am not sure.
>

The first pentachord G* onward is surely Hijaz-i Qadim, which I'm sure
you'll remember from our earlier discussions. Was it Qutb ad-din
Shirazi who first mentioned it? Nasir Dede makes allusions to it
without specifying the source or the mathematical formulation. The
trick is the elevation of perde hijaz to uzzal and keeping the
augmented second down to segah the same by raising segah.

The rest of the scale going up sounds Saba-ish, except for the
presence of a narrow fifth of 16:11 between D* and F#*.

> If one wishes to develop this maqam while keeping within its
> basic structure, one possibility would be to focus on a third
> tetrachord revealed if we move from a septimal minor seventh at
> 969 cents (F#*) to a regular minor seventh at 991 cents (G):
>
> Sazkar Jadid tone Bayyati
> |-------------------|......|-----------------|
> Mustaqim
> |------------------|
> A B* C* D E F* G A
> cents 0 264 341 495 705 837 991 1200
> 17-steps 0 4- 5s 7 10 12s 14 17
> JI approx 1/1 7/6 39/32 4/3 3/2 13/8 39:22 2/1
> 267 77 154 209 132 154 209
> 4- 1 2L 3 2s 2L 3
> 7:6 117:112 128:117 9:8 13:12 12:11 44:39
>
> Here we can follow our ascending Sazkar (or Sazkar Jadid) with a
> conjunct tetrachord of Ibn Sina's Mustaqim at a tempered
> 0-209-341-495 cents or 209-132-154 cents. Note that our upper
> Bayyati tetrachord, which might be close to some Arab
> (e.g. popular Lebanese) practice and also to a typical Persian
> intonation for a Shur tetrachord, 0-132-286-495 cents
> (132-154-209 cents), remains idiomatic while presenting a subtle
> contrast to Ibn Sina's septimal form approximated in our earlier
> ascending form.

By placing a Mustaqim there, you have perturbed the Segah character
that is so vital for the opening of this maqam. F* is not permissible
I think. It should be an F#. But then, no room for Mustaqim anymore.
But then again, you may try to insert such a modulation as part of the
New Sazkar somewhere along the line!

>
> From here, one could move the striking minor third B* of Sazkar
> to its usual location for Mustaqim or Rast Jadid at B, arriving
> at a tempering of Ibn Sina's original maqam, with many
> possibilities for further development:
>
> Mustaqim tone Bayyati
> |-------------------|......|------------------|
> Mustaqim
> |-------------------|
> A B C* D E F* G A
> cents 0 209 341 495 705 837 991 1200
> 17-steps 0 4- 5s 7 10 12s 14 17
> JI approx 1/1 9/8 39/32 4/3 3/2 13/8 16/9 2/1
> 267 77 154 209 132 154 209
> 4- 1 2L 3 2s 2L 3
> 7:6 9:8 128:117 9:8 13:12 128:117 9:8
>
>

That is the necessary cadence for Sazkar or Sazkar-i Jedid.

But what is that? At this very moment, a wily efreet knocked off the
lid of my metronome in the other room where it started to tick-tock
loudly. Maybe he is vexed about this New Sazkar? :)

> --------------------------------------------------------
> 2. Analysis and modulation: Enter Qutb al-Din al-Shirazi
> --------------------------------------------------------
>
> While Sazkar Jadid was taking shape for me in its ascending and
> descending forms, I realized that the Sazkar Jadid tetrachord
> could lead to an interesting analysis if viewed in JI terms as
> follows:
>
> A B* C* D
> tempered: 0 264 341 495
> 264 77 154
>
> JI: 1/1 7/6 11/9 4/3
> 0 267 347 498
> 7:6 22:21 12:11
> 267 81 151

Ah, this is the permutation of the Hijaz-i Qadim tetrachord in its
pure form I was talking about. Rotate the intervals thus for the
rendition:

12:11 x 7:6 x 22:21.

Voila!

>
> While a reader might rightly call attention to the rather
> inaccurate representation of 11:9 in this temperament, which
> indeed is much closer to 28:23 or 39:32, our main interest here
> is in the adjacent intervals of 7:6, 22:21, and 12:11 (at
> 267-81-151 cents).
>
> These are, of course, the steps of Ptolemy's Intense Chromatic
> (22:21-12:11-7:6), famously permuted around 1300 by Qutb al-Din
> al-Shirazi in a classic form of Hijaz, which John Chalmers has
> temred "neo-chromatic" because of the placement of the large step
> in the middle:
>
> 1/1 12/11 14/11 4/3
> 0 151 418 498
> 12:11 7:6 22:21
> 151 267 81
>
> G* A B* C*
> 0 154 418 495
> 154 264 77
>

I was hasty. You formulated it rightly here!

> Thus my discovery or rediscovery of "Sazkar Jadid" could be taken
> as a demonstrating a permutation of Qutb al-Din's Hijaz -- in
> turn, a permutation of Ptolemy's Intense Diatonic!
>

Once again, I was hasty to speak and you formulated it right!

> In fact, as shown by my tempered example for Qutb al-Din's
> tetrachord, this theoretical model leads to an interesting
> modulation, moving from my descending form of Sazkar Jadid to a
> usual Hijaz on G*:
>
> Hijaz
> |------------------|
> G* A B* C* D* E F* F#* A
> cents -154 0 264 341 551 705 837 969 1200
> JI approx 11/12 1/1 7/6 39/32 11/8 3/2 13/8 7/4 2/1
> 154 267 77 209 154 132 132 231
> 2L 4- 1 3 2L 2s 2s 3+
> 12:11 7:6 117:112 44:39 12:11 13:12 14:13 8:7
>
> Once we establish a focus on this Hijaz tetrachord (G*-C*), the
> maqam we have shifted into might take shape like this:
>
> Hijaz Rast tone
> |------------------|------------------|......|
> G* A B* C* D* E F* G*
> Huseyni
> |-------------------|
> cents 0 154 418 495 705 859 991 1200
> JI approx 1/1 12/11 14/11 4/3 3/2 64/39 39/22 2/1
> 154 264 77 209 154 132 209
> 12:11 7:6 22:21 9:8 128:117 13:12 44:39
>

Once again, you rightly delve into the topic I tried to mention above.

> In its ascending form, this usual version of Maqam Hijaz (usual
> to me in this temperament, that is) has conjunct Hijaz and Rast
> tetrachords, the latter in one shading of the usual Arab pattern
> with the larger neutral second preceding the smaller (here
> 0-209-363-495 cents or 209-154-132 cents). In descending, the
> larger Zalzalian sixth at 859 cents (near 23/14 or 64/39), found
> at E*, might be inflected to a minor sixth at Eb or 782 cents,
> very close to a just 11/7. Some styles might favor one version or
> the other of this sixth degree, with others fluidly alternating
> between them.

Nice alteration. This scale has turned into a delectable Zavil now:
Rast diatonic with Hijaz tetrachord finish.

>
> The version with the Zalzalian sixth also has an upper tetrachord
> D*-E-F*-G* at 0-154-286-495 cents or 154-132-209 cents which I
> here call Huseyni, since the order of the larger Zalzalian second
> followed by the smaller is more typical of Maqam Huseyni than of
> Maqam Bayyati, in this tuning often 132-154-209 cents. However,
> the term "Bayyati" is often applied in Arab theory to either
> arrangement, the general concept being simply two Zalzalian
> seconds followed by a tone (or 3-3-4 in a usual 24-step
> notation).
>

I fear, 154 cents still not large enough an interval for Turkish
tastes in Huseyni.

> From this Maqam Hijaz on G* we might easily proceed to related
> destinations such as, in my style, Rast and related forms on G*.
>
>
> -----------------------------------------------------------
> 3. The 1/1-7/6-11/8-13/8 chord: resolutions and modulations
> -----------------------------------------------------------
>
> While the Sazkar Jadid introduces the notes of the chord, how
> might it be resolved in the context of what I shall term
> Zalzalian polyphony, or the application of polyphonic techniques
> to music drawing on the maqam and dastgah traditions, however
> closely or loosely.
>

Ahha, now it's getting interesting!

> In such a polyphonic style, a given vertical progression may
> serve either to realize the qualities of a given maqam or gusheh
> (i.e. a melodic theme or mode within the larger modal family of a
> dastgah), or to move from one such maqam or gusheh to another,
> possibly as part of a more or less standard modulatory scheme.
> Two possible modulations using 1/1-7/6-11/8-13/8 occurred to me.
>
> The first is as follows, with the tempered chord at 0-264-551-705
> cents, and the expanding resolution arriving at a tempered 2:3:4.
>
> F* +154 G
> D* -55 D
> B* +231 D
> A -209 G
>
> Here the expansions of the lower ~7:6 minor third to a fifth, and
> of the outer ~13:8 Zalzalian sixth to an octave, are quite
> routine in this type of neomedieval style (the "neomedieval"
> referring both to the Near Eastern tunings and 13th-14th century
> European polyphonic techniques which here have a "fusion" in the
> setting of a 21st-century temperament). The ~33:28 minor third
> between the two middle voices likewise has a usual resolution
> contracting to a unison, with melodic steps of 231 and 55 cents
> that might represent the 8:7 and 28:27 steps of the Archytas
> Diatonic. Stated more generically as 3-1 or 3-5 and 6-8, these
> basic patterns for resolutions can apply to major, minor, or
> Zalzalian (neutral) intervals alike.
>

A touch of Marchetto perhaps?

> Other resolutions here are a bit less "classical," for example
> the stepwise expansion of the upper ~13:11 minor third to a
> fourth (D*-F* to D-G), but the total effect is a progression
> "taking us somewhere" in a maqam performance, here to G. One
> colorful possibility for a new maqam on G is a form of Najdi or
> `Ajam Murassa:
>
> Najdi Mustaqim
> |---------------------------|--------------------|
> G A B C* D E F* G
> Mustaqim
> |--------------------|
> cents 0 209 418 551 705 914 1046 1200
> JI approx 1/1 44/39 14/11 11/8 3/2 56/33 11/6 2/1
> 209 209 132 154 209 132 154
> 44:39 182:121 121:112 12:11 128:117 121:112 12:11
>

This Najdi is but a variant of Penchgah it appears.

> One way that has been suggested to view this fascinating maqam is
> as two conjunct tetrachords of Rast (or here Mustaqim or Rast
> Jadid) with a tone added below to fill out the octave, and with
> this added step now felt as the final. The affinity to the
> descending form of Sazkar Jadid, with its 11/8 step above the
> final, may have drawn me to this maqam as a companion for use in
> an improvisation.
>
> Of course, one could follow the vertical resolution of our
> 1/1-7/6-11/8-13/8 sonority to G with many maqamat, but this
> choice is to me engaging.
>
> Another resolution leads in another direction:
>
> F* -77 E*
> D* +209 E*
> B* -209 A*
> A +55 A*
>

mp3 examples should facilitate understanding at this stage. Who's up
for preparing them?

> This resolution treats the outer small Zalzalian sixth at 837
> cents as a diminished seventh (which it is, being formed from
> three minor thirds) contracting to a fifth: the lowest voice
> ascends A-A* by a diesis or minimal semitone of 55 cents, while
> the highest voice descends F*-E* by a regular 77-cent limma.
> The two lower voices have a classic 3-1 resolution, one moving by
> a regular 209-cent tone and the other by a 55-cent semitone,
> which here may be said to represent 28:27 (63 cents). The middle
> pair of voices expand from regular minor third to fifth (3-5),
> and the highest pair from a like minor third to a unison (3-1),
> these progressions involving steps of a regular tone or semitone
> (209 or 77 cents).[1]

A touch of Vicentino this time.

>
> While this journey up a diesis or small semitone to A* could lead
> into many maqamat, one choice I like is a usual Huseyni, as if to
> offset the more "exotic" qualities of Sazkar Jadid:
>
> Huseyni tone Huseyni
> |--------------------|.......|--------------------|
> A* B C* D* E* F# G* A*
> cents 0 154 286 495 705 859 991 1200
> JI approx 1/1 12/11 13/11 4/3 3/2 64/39 16/9 2/1
> 154 132 209 209 154 132 209
> 12:11 13:12 44:39 9:8 128:117 13:12 9:8
>
> In Part II, I will present another maqam that later occurred to
> me as including 1/1-7/6-11/8-13/8 in a structure I would freely
> use either ascending or descending, with another possible
> resolution of this sonority, this time suggesting a modulation
> which offers an opportunity to touch on a topic which I hope will
> receive much fuller discussion: Jacques Dudon's "Soria" algorithm
> for a 17-note rational tuning, and some versions of 12-note
> subsets he has posted.
>
> ----
> Note
> ----
>
> 1. From the viewpoint of polyphonic technique, these two
> resolutions of A-B*-D*-F*, showing how a Zalzalian sixth can
> either expand to an octave, or less "classically" contract to a
> fifth, might recall the discussion by Marchettus of Padua (1317)

Ahha, once more, my haste!

> about how a major sixth typically expands to an octave, but
> through a "feigned" inflection or cadence can also contract to a
> fifth! In a 17-note system, or a larger system like this
> featuring most similar types of intervals, a Zalzalian seventh
> similarly may contract "classically" to a fifth (7-5), or
> strikingly expand to an octave, with George Secor educating me on
> the latter choice in the setting of his 17-tone well-temperament
> (17-WT). To take simple two-voice example, the small Zalzalian
> seventh or augmented sixth Eb-C# at 1046 cents or ~11:6 might
> resolve either by contracting to E-B (7-5) or expanding to the
> octave D-D. In a Near Eastern context, the first resolution can
> come up routinely in a polyphonic setting of Maqam Sikah on Eb,
> for example, while the second seems more likely to signal a
> dramatic and not unlikely surprising shift of focus.
>

But really, some mp3 demonstrations would help a lot.

> Most appreciatively,
>
> Margo Schulter
> mschulter@...
>

Oz.

🔗Margo Schulter <mschulter@...>

> Dear Margo, this is a late reply:
> (use a fixed-width font, why won't you?)
> [222]www.ozanyarman.com

Dear Ozan,

Thank you for such a thoughtful and informative reply, and one
especially appreciated at a time when you have been seeing to the
publication of your new book, for example.

One of the things your response to my Sazkar Jadid illustrates is how
the same name for a maqam can come with quite different understandings
in different regions of the Near East. It is somewhat amusing how the
two of us, in response to the name Sazkar, set out on quite different
understandings of the _seyir_ -- that is, the "path" or procedure --
to be followed in travelling through this maqam.

However, this confusion has brought forth at least two happy results,
I hope you will agree. First, I now have some understanding of an
Osmanli Sazkar, if that is the right term, along with a possible
hypothesis as to how this classic Ottoman seyir could have led to the
current Arab maqam, thanks to your clear explanation!

To keep this response at a more reasonable length and to make it
easier to follow, I will here limit myself mainly to these points: the
Ottoman conception of Sazkar and its seyir as you have so lucidly
presented them; whether and how this seyir might be adapted to my
regular temperament with its different intonation of Rast; and how the
quite different Arab conception of Sazkar might have evolved.

For the benefit of others who may be reading this, I should quickly
explain two units for measuring steps and intervals which we often
use. The Holdrian comma is equal to one step of 53-EDO, about 22.64
cents; while the yarman is a step in your 79MOS-159 generally equal to
almost precisely 2/3 of a Holdrian comma or 2/159 octave, and is
conveniently equal to about 15-1/8 cents. Thus multiplying the number
of yarmans by 15, and adding a cent for each eight yarmans, gives a
close estimate of the size in cents.

>> Sazkar Jadid tone Bayyati
>> |-------------------|......|-----------------|
>> A B* C* D E F* F#* A
>> cents 0 264 341 495 705 837 969 1200
>> JI approx 1/1 7/6 39/32 4/3 3/2 13/8 7/4 2/1
>> 264 77 154 209 132 132 231
>> 7:6 117:112 128:117 9:8 13:12 14:13 8:7

> Sazkar being a Turkish contrivance, the AEU rendition or its 53
> Holderian commas approximation seems closer to practice with the
> scale of this maqam:

Here I will add some sizes in cents which may help readers new to the
comma system.

> Degrees:
> 0 9 17 22 31 39 40 48 53 66 70
0 204 385 498 702 883 906 1087 1200 1494 1585
~ 1/1 9/8 5/4 4/3 3/2 5/3 27/16 15/8 2/1 64/27 5/2

In this interpretation of Rast, there are no neutral intervals, but
rather 5-limit steps of 8 and 5 commas, or around 10:9 and 16:15,
where a different style of interpretation such as mine would have
neutral or Zalzalian seconds of around 7 and 6 commas. Both
interpretations can be found in 10th-13th century Islamic sources.
Also, as will become clear in your presentation of the seyir, the step
at 39 commas or 5/3 is used in the opening portion of the maqam, and
the 27/16 step in the closing portion.

Before addressing the question you ask below about the Arab
interpretation of Sazkar, I might present another version of your
listing of the steps and interval sizes for Rast using commas, and
also giving the tempered sizes in my 704.607-cent regular tuning:

Degrees:
0 9 16 22 31 38 40 48 53 66 69
0 204 362 498 702 860 906 1064 1200 1494 1562
1/1 9/8 21/17 4/3 3/2 23/14 27/16 24/13 2/1 64/27 42/17
0 209 363 495 705 859 914 1068 1200 1486 1562

In fact, from this "Zalzalian" interpretation of what in the Ottoman
tradition would typically be more of a 5-limit intonation, I can
deduce a possible hypothesis for how the current Arab understanding of
Sazkar could have developed from the classic Ottoman interpretation,
as mentioned above!

However, it may first be of interest to see how your explanation of
the classic seyir might translate to a Zalzalian tuning of Rast of a
kind which I understand is sometimes practiced in Turkey also. Here I
take it that the first portion of the seyir begins on perde segah; the
second portion with the so-called Ushshaq tetrachord on perde dugah;
and the final portion in Rast, of course, ending on perde rast. First,
let me quote your seyir and step sizes, adding to your notation of
the steps in commas the sizes of these steps in cents, plus a JI
notation for the degrees above the 1/1 (perde rast) in ratios and
commas:

> Steps:
> 5 9 8 9 5 13 4
113 204 181 204 113 294 91
5/4 4/3 3/2 5/3 15/8 2/1 64/27 5/2
17 22 31 39 48 53 66 70
|---------------| |--------------|
Segah tone Hijaz

> 8 5 9 (so-called Ushshaq tetrachord)
181 113 204
> 9/8 5/4 4/3 3/2
9 17 22 31
|---------------|
Huseyni with 10:9

> 9 8 5 9 9 8 5
204 181 113 204 204 181 113
1/1 9/8 5/4 4/3 3/2 27/16 15/8 2/1
0 9 17 22 31 40 48 53
|-------------| |------------------|
Rast tone Rast

> First the maqam starts off with a Segah openining, proceeds to
> expose it further, then, possibly skipping the Ushshaq tetrachord,
> concludes fully in Rast.

Indeed the first portion appears to match your explanation of Maqam
Segah in your thesis. The optional second portion with the 8-5-9
tetrachord, the so-called Ushshaq, might better be called a version of
Huseyni, which in the Ottoman tradition might take a lower step either
around 10:9 (as here) or 11:10 (as in the example in your thesis). The
last part, as advertised, "concludes fully in rast."

Here it may be interesting to see how this seyir might translate to my
keyboard and system of intonation, taking F# as perde rast.

Degrees:
0 9 16 22 31 38 40 48 53 66 69
F# G# Bb B C# Eb Eb* F F# A Bb
1/1 9/8 21/17 4/3 3/2 23/14 22/13 63/34 2/1 26/11 42/17
0 209 363 495 705 859 914 1068 1200 1486 1562

Seyir part 1: Maqam Segah (Zalzalian version)

Steps:
6 9 7 9 6 13 3
132 209 154 209 132 286 77
21/17 4/3 3/2 23/14 63/34 2/1 26/11 42/17
16 22 31 38 47 53 66 69
Bb B C# Eb F F# A Bb
|----------------| |-----------------|
Segah tone Hijaz

Note that in either your correct Ottoman version, or my Zalzalian
variation, the first step of the Segah tetrachord is smaller than the
last, at 5-9-8 or 6-9-7 commas; and that in the upper Hijaz
tetrachord, the large central step is notably wider than the 7:6 often
favored as espcially apt.

Seyir part 2: A Ushshaq tetrachord

7 6 9 (actual Ushshaq tetrachord!)
154 132 209
> 9/8 21/17 4/3 3/2
9 16 22 31
G# Bb B C#
|----------------|
Ushshaq with ~12:11

Here, as it happens, 154 cents at around 12:11 or 128:117 evidently
fits an Ottoman conception of Ushshaq, despite the unsuitability of
the tuning as a whole for a Turkish style -- perhaps an instance of
the proverb that even a broken clock is right at least once a day!

Seyir part 3: Concluding in Rast

9 7 6 9 9 7 6
209 154 132 209 209 154 132
1/1 9/8 21/17 4/3 3/2 22/13 63/34 2/1
0 9 16 22 31 40 47 53
F# G# Bb B C# Eb*/D# F F#
|---------------| |----------------- -|
Rast tone Rast

The definition of Rast as around 9-7-6 commas is stated by theorists
such as Tawfiq al-Sabbagh of Syria and Salah al-Din. A yet more
accurate measure of this 9-7-6 variety of Rast as realized in my
regular temperament would be 14-10-9 yarmans.

> I don't know how Arabs use it today. I know their habit of lowering
> perde segah to the point of invalidating the leading tone below it
> and skipping all the way down to perde dugah. But what does this
> matter? The maqam has been developed in the Ottoman court during
> the 19th Century. The authentic intonation is ought to be searched
> in Istanbuline aires.

These matters regarding Arab intonation might be interesting topic for
another thread, and you have stirred my curiosity! However, what I
would like to address here is the Arab understanding of Maqam Sazkar
and a possible connection to the Ottoman conception as you have
artifully explicated it here.

> (So much for 24-tET as the ultimate simple-resolution basis for all
> maqamat, eh Carl? You ought to get your hands on some masters of
> Classical Turkish music.)

In the Arab, Persian, and Kurdish traditions also, for example, the
distinction between larger and smaller neutral seconds is important to
interpreters steeped in classical styles. When a step of 130 cents is
wanted (as in one popular Lebanese interpretation of a maqam I play
with a tetrachord of 132-154-209 cents), or a step of 165 cents (as in
your tuning of Huseyni in the Turkish manner), 24-EDO is hardly an
adequate substitute.

Now for the current Arab interpretation of Maqam Sazkar, and how it
may have evolved from the classic Ottoman Sazkar! Let us begin with
the usual tuning of Maqam Rast at 9-7-6 commas, here giving the Arabic
forms of the perde names, and then showing the strikingly modified
nature of this tetrachord above the final, perde rast of course, in
what is called Sazkar:

Typical 9-7-6 Rast

rast dukah sikah jahargah
F# G# Bb B
commas 0 9 16 22 yarmans 0 14 24 33
cents 0 209 363 495

Arab Sazkar jins: 13-3-6 (or 19-5-9 yarmans)

rast kurdi sikah jahargah
F# A Bb B
commas 0 13 16 22 yarmans 0 19 24 33
cents 0 286 363 495

Apart from the substitution of perde kurdi for dukah in this
tetrachord, the rest of the seyir is pretty much like a usual Maqam
Rast, with the same options for inflections, like evdj/acem and
huseyni/hisar. After the initial ascent, one possible development is
to use the usual perde dukah rather than kurdi, thus returning to a
usual Maqam Rast of the 9-7-6 type.

In fact, the hypothesis that occurs to me after reading your
explanation of Ottoman Sazkar as still understood in Turkey is that,
performing the upper Hijaz tetrachord of the seyir in a Zalzalian
style of intonation, Arab interpreters may have transposed the notes
kirdan-sinbulah-buzruk down an octave to rast-kurdi-sikah, thus
arriving at the striking trichord above the final of Arab Sazkar,
which with the usual jaharkah added forms the first tetrachord!

Opening of seyir, Ottoman Sazkar based on 9-7-6 Rast

Segah tone Hijaz
|---------------------| |----------------------|
commas 6 9 7 9 6 13 3
yarmans 9 14 10 14 9 19 5 cents 132 209 154 209 132 286 77
Bb B C# Eb F F# A Bb
sikah jahargah nawa hisar awj kirdan sunbulah buzruk
|------------------|
|
|
v----------------- (transpose down an octave)
|
|
|
Arab Sazkar tone Rast
|---------------------| |----------------------|
commas 13 3 6 9 9 7 6
yarmans 19 5 9 14 14 10 9
cents 286 77 154 209 209 154 132
F# A Bb B C# Eb*/D# F F#
rast kurdi sikah jahargah nava huseyni awj kirdan

This seems to me a not-too-unlikely hypothesis for the present form of
Arab Sazkar, one starting point for my Sazkar Jadid, which differs in
part by being based on a tetrachord of 9-6-7 commas, which the
20th-century Arab theorist Salah al-Din calls Rast Jadid by contrast
with the usual 9-7-6 commas, but which might well take Ibn Sina's name
of Mustaqim for a maqam with conjunct tetrachords of 1/1-9/8-39/32-4/3
or 204-139-155 cents, not too far from 14-9-10 yarmans or 209-132-154
cents in my regular temperament. This I explain not to delve here into
some of your following comments which we should explore further when
you have had a chance to reply to this message, Inshallah, but to shed
some perspective on your concluding remark.

> That is the necessary cadence for Sazkar or Sazkar-i Jedid. But
> what is that? At this very moment, a wily efreet knocked off the
> lid of my metronome in the other room where it started to tick-tock
> loudly. Maybe he is vexed about this New Sazkar? :)

Since I have now inquired and learned the wise teaching that an efreet
is also a creature capable of choosing good or evil, let me offer what
I hope will be a due measure of propitiation, out of simple justice as
well as possibly in the interest of your peaceful music making.

And so I would beg the pardon of your visiting efreet for uttering the
auspicious Ottoman name of Sazkar and then setting out to present a
variation upon the curious Sazkar I knew in what might be to classical
ears a provincial version, as understood and further taken in strange
directions by an alien to the region attempting, among other things,
to find a seyir for the Maqam Mustaqim described by Ibn Sina about a
millennium ago.

Yet in this very strangeness there may be a certain virtue: for any
knowledgeable person would quickly realize what I gladly acknowledge,
that such a curious style is neither a standard nor a substitute for
the classic Ottoman tradition that has done so much to enrich the Near
East and the world. Rather I would entreat that it be taken as a
pleasant diversion of the reason and senses, one sign of the
exuberance of a Renaissance, and here a Zalzalian Renaissance seeking
to honor the Mutazilah way of logic and art.

And to your guest, I would make a humble offering of my music and
theory, however uninformed or inept, as a gift meant to impart some
small measure of _tarab_ or enchantment which the infinite variety of
neutral or Zalzalian steps can bring; and as a gentle signpost,
however wayward my seyir, toward the best seyir, which is toward
Allah, or ha-Shem as we often also say in the Jewish tradition, the
compassionate giver of all good things including the wonders of music.

With many thanks,

Margo Schulter
mschulter@...